We give a new negative solution to Keisler's problem regarding Skolem functions and elementary extensions. In contrast to existing ad hoc solutions due to Payne, Knight, and Lachlan, our solution uses well-known models.

Words like well, oh, and you know have long been observed and studied in spontaneous speech. With the proliferation of on-line dialogues, such as instant messaging between friends or back-and-forth postings at websites, there are increasing opportunities to observe them in spontaneous writing. In Experiment 1, the interpretation of discourse markers in on-line debates was compared to proposed functions of those markers identified in other settings. In Experiment 2, the use of discourse markers in spontaneous speech was compared (...) to their uses in spontaneous writing. Results support the conclusion that although they vary in frequency in spoken versus written domains, discourse markers are used similarly across domains, but with particular communicative functions that make them non-interchangeable. (shrink)

Bilingualism has been identified as a potential cognitive factor linked to delayed onset of dementia as well as boosting executive functions in healthy individuals. However, more recently, this claim has been called into question following several failed replications. It remains unclear whether these contradictory findings reflect how bilingualism is defined between studies, or methodological limitations when measuring the bilingual effect. One key issue is that despite the claims that bilingualism yields general protection to cognitive processes, studies reporting putative bilingual (...) differences are often focused on domain specific experimental paradigms. This study chose a broader approach, by considering the consequences of bilingualism on a wide range of cognitive functions within individuals. We utilised 19 measures of different cognitive functions commonly associated with bilingual effects, to form a “cognitive profile” for 215 non-clinical participants. We recruited Welsh speakers, who as a group of bilinguals were highly homogeneous, as means of isolating the bilingualism criterion. We sought to determine if such analyses would independently classify bilingual/monolingual participant groups based on emergent patterns driven by collected cognitive profiles, such that population differences would emerge. Multiple predictive models were trained to independently recognise the cognitive profiles of bilinguals, older adults and higher education attainment. Despite managing to successfully classify cognitive profiles based on age and education, the model failed to differentiate between bilingual and monolingual cognitive ability at a rate greater than that of chance. Repeated modelling using alternative definitions of bilingualism, and just the older adults, yielded similar results. In all cases then, using our “bottom–up” analytical approach, there was no evidence that bilingualism as a variable indicated differential cognitive performance – as a consequence, we conclude that bilinguals are not cognitively different from their monolingual counterparts, even in older demographics. We suggest that studies that have reported a bilingual advantage could well have confounded other key variables that may be driving reported advantages. We recommend that future research refine the machine learning methods used in this study to further investigate the complex relationship between bilingualism and cognition. (shrink)

We provide a new and elementary proof of strong normalization for the lambda calculus of intersection types. It uses no strong method, like for instance Tait-Girard reducibility predicates, but just simple induction on type complexity and derivation length and thus it is obviously formalizable within first order arithmetic. To obtain this result, we introduce a new system for intersection types whose rules are directly inspired by the reduction relation. Finally, we show that not only the set of strongly normalizing (...) terms of pure lambda calculus can be characterized in this system, but also that a straightforward modification of its rules allows to characterize the set of weakly normalizing terms. (shrink)

As it was proved in [4, Sect. 3], the poset of extensions of the propositional logic defined by a class of logical matrices with equationally-definable set of distinguished values is a retract, under a Galois connection, of the poset of subprevarieties of the prevariety generated by the class of the underlying algebras of the defining matrices. In the present paper we apply this general result to the three-valued paraconsistent logic proposed by Hałkowska–Zajac [2]. Studying corresponding prevarieties, we prove that (...) extensions of the logic involved form a four-element chain, the only proper consistent extensions being the least non-paraconsistent extension of it and the classical logic. RID=""ID="" Mathematics Subject Classification (2000): 03B50, 03B53, 03G10 RID=""ID="" Key words or phrases: Many-valued logic – Paraconsistent logic – Extension – Prevariety – Distributive lattice. (shrink)

The research presented in this paper was motivated by our aim to study a problem due to J. Bourgain [3]. The problem in question concerns the uniform boundedness of the classical separation rank of the elements of a separable compact set of the first Baire class. In the sequel we shall refer to these sets (separable or non-separable) as Rosenthal compacta and we shall denote by ∝(f) the separation rank of a real-valued functionfinB1(X), withXa Polish space. Notice that in [3], (...) Bourgain has provided a positive answer to this problem in the case ofKsatisfyingwithXa compact metric space. The key ingredient in Bourgain's approach is that whenever a sequence of continuous functions pointwise converges to a functionf, then the possible discontinuities of the limit function reflect a local ℓ1-structure to the sequence (fn)n. More precisely the complexity of this ℓ1-structure increases as the complexity of the discontinuities offdoes. This fruitful idea was extensively studied by several authors (c.f. [5], [7], [8]) and for an exposition of the related results we refer to [1]. It is worth mentioning that A.S. Kechris and A. Louveau have invented the rank rND(f) which permits the link between thec0-structure of a sequence (fn)nof uniformly bounded continuous functions and the discontinuities of its pointwise limit. Rosenthal'sc0-theorem [11] and thec0-index theorem [2] are consequences of this interaction.Passing to the case where either (fn)nare not continuous orXis a non-compact Polish space, this nice interaction is completely lost. (shrink)

We investigate the issues of Diophantine definability over the non-finitely generated version of non-degenerate modules contained in the infinite algebraic extensions of the rational numbers. In particular, we show the following. Let k be a number field and let K inf be a normal algebraic, possibly infinite, extension of k such that k has a normal extension L linearly disjoint from K inf over k. Assume L is totally real and K inf is totally complex. Let M inf be (...) a non-degenerate O k -module, possibly non-finitely generated and contained in O Kinf . Then M inf contains a submodule M¯ inf such that M inf /M¯ inf is torsion and O k has a Diophantine definition over M¯ inf. (shrink)

continent. 1.1 (2011): 27-32. “My”—what does this word designate? Not what belongs to me, but what I belong to,what contains my whole being, which is mine insofar as I belong to it. Søren Kierkegaard. The Seducer’s Diary . I can’t sleep till I devour you / And I’ll love you, if you let me… Marilyn Manson “Devour” The role of poetry in the relationalities between people has a long history—from epic poetry recounting tales of yore; to emotive lyric poetry; to (...) rude, irreverent limericks; to Hallmark cards which have ditties that allow one to cringe, and somehow fall in love at the same moment. Without going into a notion of aesthetics, or attempting to choose which form of poetry is superior, we might want to consider why the form of poetry itself has long been a part of relationality. And whilst doing so, we might always keep in mind that poetry—especially poetry that moves, transports us—is the form that Plato has been warning us about, particularly if we want to become good citizens.As Avital Ronell teaches us in Stupidity : the poet, irremediably split between exaltation and vulgarity, between the autonomy that produces the concept within intuition and the foolish earthly being, functions as a contaminant for philosophy—a being who at least since Plato, has been trying to read and master an eviction notice served by philosophy. The poet as genius continues to threaten and fascinate, menacing the philosopher with the beyond of knowledge. Philosophy cringes (287). And considering that the philosopher is the lover of wisdom, we might begin to ask ourselves why one lover is warning against another—if the philosopher is in love with wisdom, then is the poet perhaps his rival, his challenger, for that very love? For, one must also remember that Plato—through Socrates—mentions constantly that Homer is his favourite. Moreover, by adopting both his own voice, whilst mixing it with Socrates’, Plato is adopting the form of poetry that he warns most about—the warning almost serves more as a homage to poetry than anything else. Here, we might open the register that one of the main reasons that he ejects a particular kind of poet is on the grounds of effecting effeminacy on the populace—good poetry moves you, affects you, transports you, shifts you beyond reason, puts you “out of your mind.” However, Plato also teaches us that rhetoric in its highest form requires divine inspiration by way of the daemon, or the muse. This moment of divine intervention is one that seizes—perhaps even ceases—you; putting you “beyond yourself.” In other words, a good rhetorician must always already be open to the possibility of otherness—the same otherness that possibly resides in the feminine. One could also trace this back to the poet that he both loved, and feared, most—Homer. Perhaps the effect of effeminacy that Homer's poetry opened is precisely the source of its power: through listening to Homer, one's body, one’s habitus is opened to the possibility of the feminine. And here, one must remember that the source of all learning—and all teaching—also lies in mimesis, in repetition, in habit. Once the habitus is opened to the possibility of invasion, of intervention, of otherness, there is quite possibly no possibility of distinguishing whether the mimesis is that of reproduction, or if there is always already a productive aspect to it. And by extension, if learning cannot be controlled, the very notion of teaching itself is shifted from a master-student relationality to one where the master is potentially changed as well—the relationality between the master and the student is not only inter-changing, but one cannot even know who is teaching, or learning, at any point. All that can be said is that they are in a relationality; which means that one is ultimately unable to locate the locus of knowledge, of wisdom—the site of which Plato is attempting to convince us is the sole domain of the philosopher. And it is this that philosophy is cringing from. To compound matters, philosophy is striving for wisdom; which can only come from the Gods. In other words, this is a gift that has to be bestowed on them—and more than that, wisdom is always already exterior to one’s control and knowledge. At best, it is the role of one to recognise the gift, to answer the call as it were. Here, if we listen carefully, we can hear the echo of Alexander Graham Bell, and the telephone. And as we are attempting to respond to the call of wisdom—the call that both poetry and philosophy are listening out for—it might be helpful to recall the agreement between Alexander Graham Bell and his brother Melville. In the biography, Alexander Graham Bell and the Conquest of Solitude , Robert V. Bruce notes that Aleck and Melly made a “solemn compact that whichever of us should die first would endeavour to communication with the other if it were possible to do so” (63). Since Melville was the one who passed on first, this pact put the onus on Aleck to receive the call of his brother. If you take into consideration the fact that until Melville’s death, both brothers had been working on an early prototype of the telephone, the instrument of distant sound can be read as an attempt by Aleck to maintain the possibility of keeping in touch with Melly, of hearing the voice from beyond. However, this was a connection that was not premised on any knowing, reason, or rationality; it was rather, one that was based on hope, and born out of love. And here, if we eves-drop on a cross-line with The Telephone Book , we can pick up the voice of Avital Ronell once again and hear, “the connection to the other is a reading—not an interpretation, assimilation, or even a hermeneutic understanding, but a reading” (380). In other words, the telephone can be read as the openness to the possibility of responding to the other; one that might always remain unknown. Even in this day of caller-identification, we can never know for sure who the other person on the line is until we pick up: hence, the only decision we can make—the effects of which we remain blind to until it affects us—is to either pick up or not, to either respond or not. And it is not as if the decision to pick up comes without risks: each time we answer a call, we run the risk of it ruining our day. Even when we don’t know who the caller is, perhaps especially when we don’t know who the person on the other end of the line is—and here one only has to think of prank calls—we are leaving ourselves completely open to being affected by another. Thus, philosophy finds itself in the position of Vladimir and Estragon. Since they have no idea who Godot is, they can never know if or when he shows up—thus, if he (and we are taking his gender on the word of the boy, some boy—we don’t even know if it is the same boy—who comes round in the evening) has already come, they would not be in the position to know it. And even if someone comes to them and announces that “I am Godot,” the wait would not be over—without referentiality to the name, they would have to take on faith that that person is indeed Godot. Hence, all they can know is that they are waiting for Godot; and Godot is the name of that waiting itself. All philosophy can know is that it is waiting; and wisdom is the name of that waiting itself. Which brings us to Tina Turner’s eternal question, “what’s love got to do, got to do with it?” In order to begin to consider that, we have to first attempt to examine the notion of love itself. Perhaps we might begin to consider what the difficulty of the statement “I love you.” For, if love is a relationality between two persons—both of whom remain singular, and are attempting to respond to each other—this suggests that neither of them subsume the other under themselves. In other words, the other remains wholly other. If this is so, then the “you” in the statement always remains shrouded in mystery. And even if the “you” was replaced with the name of the person, the veiling remains: for, names refer both to the singularity that is the person, and also every other person bearing that name, at exactly the same time. To compound matters, the only time one has to utter a persons name is in their absence—thus, the correspondence of a name to that particular person is at best an affect of memory. And if we consider the notion of memory, we have to also open the register of forgetting—bringing along with it the problem that there is no object to forgetting. For instance, when one utters “I forgot,” all one is uttering is the fact that one has forgotten, and nothing more—the moment there is an object to the statement, one has strictly speaking remembered what one has forgotten. Moreover, we have no control over when forgetting happens to us. And since it is always already exterior to us, affects us, and has no necessary object, there is no reason to believe that every moment of memory might not bring with it a moment of forgetting. Hence, whenever we utter a name—even if we accept the correspondence between the utterance and the person in front of us—all we are doing is uttering the fact that we are naming. Thus, it is not so much that ‘a rose by any other name would smell as sweet’ but more appropriately, ‘a rose is a rose is a rose’—the relationality between its name and the phenomenon of its sweet smell can only be established after that moment of naming, that instance of catachresis. So, whenever one utters “I love you,” not only is it a performative statement, it is the very naming of that love—all you are doing is establishing a relationality between you and the other. And since there is no necessary referent—one is naming that referentiality as one utters it—this suggests that it is always already a symbolic statement; without which the mystery of the other cannot me maintained. In other words, one cannot love the other without maintaining this symbolic distance—through a ritual; in this case the utterance “I love you.” This might be why Valentine’s Day seems to provoke such a massive reaction: the most common one from people (besides florists) being, Valentine’s Day is mere commercialism. Those among the nay-sayers who maintain a soft spot for Karl Marx would proceed to call it the commodification of relationships; those who prefer the Gods would claim that the sanctity of relationships has been profaned; the gender theorists would note how the fact that males buy the gifts only serves to highlight the unequal power-relation between the genders. Whichever side and variation of the arguments they choose boils down to this: the discomfort lies in the fact that they are confronted with the notion of relationships moving into a mediated sphere. The underlying logic is that love is between two persons only; it should not only remain between them, but more pertinently, be an unmediated experience between two persons. Which of course completely misses the point. For, if we reopen the register that relationships are the result of a negotiation between two persons, there must then be a space between them for this very negotiation to occur. Otherwise, all that is happening is, one person is subsuming the other within their own sphere of understanding; effectively effacing the other. If that were the case, there would no longer be any relationality; all negotiation is gone and the other person is a mere extension of the self—one is in a masturbatory relationality with one’s imaginary. Hence, any relationship must always already carry with it the unknown, and possibly always unknowable. The other person is an enigma, remains—must remain—enigmatic to you. This is the only way in which the proclamation “I love you” remains singular, remains a love that is about the person as a singular person—and not merely about the qualities of the person, what the person is. For, if the mystery of the other is unveiled, then the love for the other person is also a completely transparent love: one that you can know thoroughly, calculate; a check-list. And if they are knowable, this suggests that they can also be negated, and hence, the love can also go away. Only when the love for the other person is an enigmatic one, one that cannot be understood, can that love potentially be an event—and if it is an event, then strictly speaking, it cannot be known before it happens; at best, it can be glimpsed as it is happening, or perhaps even only realised retrospectively. At the point in which it happens, it is a love that comes from elsewhere: this strange phenomenon is best captured in the colloquial phrase, I was struck by love;” or even more so by, “I was blinded by love.” This is a blinding to not only the subject of the encounter—the self—but also of the very object of that encounter, the “you”—all that can be said is that there is an encounter. And it is for this reason Cupid is blind: not just because love is random (and can happen to anyone at any time), but more importantly because even after it happens, both the reason you are in love, and the person you are in love with, remain blind to you. Since there is an unknowable relationality with the other person, the only way you can approach it is through a ritual. This is the lesson that religions have taught us: since one is never able to phenomenally experience the God(s), one has no choice but to approach them symbolically. These rituals are strictly speaking meaningless—the actual content is interchangeable—as it is the form that is important. Rituals allow us momentary glimpses at secrets; and secrets are never about their content(s). Rather, secrets entail the recognition that they are secrets; the secret lies in their form as secret. This can be seen when we consider how group secrets work: since the entire group knows the secret, clearly the content of the secret is not as important as the fact that only members within the group are privy to this secret. Occasionally the actual content can be so trivial that even other people outside the group might know the information; they just do not realize its significance. For instance, if I used my date of birth as my bank-account password, merely knowing when I was born would not instantly give you the key to my life savings. In order for that to happen, you would have had to recognise the significance of the knowledge of my birthday. This means that you have to know that you know something. Since the God(s) are, strictly speaking, unknowable, this suggests that rituals put one in a position to potentially experience the God(s). The meaningless gestures on Valentine’s Day play precisely this ritualised role. It is not so much what you give the other person, but the fact that you give it to them. The gift in this sense is very much akin to an offering; the gift opens the possibility of an exchange. Gift-giving does not guarantee that you will like what is returned; there is always a reciprocation of the gift, but what is returned to you is never known in advance, until the moment it is received. This means that the worst thing that one can do is not give the gift: that would be akin to a cutting off of all possibilities, a complete closing of all communication with the other person. This at the same time also means that you cannot wait for the other person to give you something before you get them their gift: if that were the scenario, the reciprocal gift would be nothing more than a calculated return. The only manner in which both persons can give true gifts is to offer them independently of the other person, whilst keeping them in mind. In this way, the two gifts are always already both uncalculated (in the sense of not knowing what the return is) and also a reciprocation for the other (without knowing whether the other person actually has a gift in the first place). Naturally, this would seem like an irrational, even stupid, way of buying gifts. But it is precisely the stupidity involved that saves the relationship from being banal—more importantly, stupidity prevents it from entering the mere profane. This is not to say that an enigmatic love cannot end—of course it can. However, the difference lies in the fact that if the relationality is wholly transparent, it is subsumed under reason—completely predictable, within the self, and thus never open to the possibility of otherness, exteriority, musing. A love that is an event is one that is also open to the possibility of the divine, the sacred—always already closer to the possibility of wisdom. If we establish that both love and wisdom are exterior, to our knowledge, and the finitude to our selves, this suggests that both are names for the possibility of openness to otherness. In other words, and what choice do we have here but to use the words of the other, the philosopher—the lover of wisdom—is a name for one who is waiting, and nothing more. But that still leaves us with the question of this uncomfortable relationality between philosophy and poetry. But before we address that question, we have to take a momentary detour, and consider the whether it is possible to call one a poet. For, if we take the notion of a poet to be one who reaches the highest levels of rhetoric (beyond the lawyer, and the orator, who only aim to either please the crowds, or convince by way of sophistry), then we must also acknowledge that one can only become a poet at the moment of seizing, the point of inspiration, by the muses. Without this divine moment, all (s)he can do is practice her craft. As no one can control when the muses make their appearance, one could always be practising in vain—in some way, one is always already practising to be least in the way when the muse whispers into one’s ear; one is practising so as not to be vain. And since one cannot know when the muse will appear, there is no time frame to the practising—unlike the lawyer who speaks against a clock, poetry knows no time; the only time that matters is the time appropriate to poetry itself. Thus, all the poet (if one can use this term) is practising for the possibility of effacing her/him self—and waiting. Thus, in order for poetry to occur, in order to be seized, the poet—along with all her concerns—must cease. In other words, there is no poet; there is only the possibility of poetry. However, even as there is no time frame to this waiting, even as all we can say is that poetry is a name for waiting, the one who is practising is always already also in time. And since (s)he is in a symbolic relationality with the possibility of poetry, this suggests that the practising is her sacrifice, and time is precisely what she is sacrificing. Here, it might be helpful to turn to a strange source when it comes to poetry—Georges Bataille—and consider his teachings in the first volume of The Accursed Share where he reminds us that, the “essence [of sacrifice] is to consume profitlessly .” This is where each exchange is beyond rationality, beyond calculability, beyond reason itself, “unsubordinated to the ‘real’ order and occupied only with the present.” He continues: Sacrifice destroys that which it consecrates. It does not have to destroy as fire does; only the tie that connected the offering to the world of profitable activity is severed, but this separation has the sense of a definitive consumption; the consecrated offering cannot be restored to the real order.” (58) Since there is no need for a physical change in the object of sacrifice—“it does not have to destroy as fire does”—this suggests that the tie is severed symbolically. Hence, there is an aspect of trans-substantiation in this sacrifice: the form remains the same; in fact there is no perceivable change—this is the point at which all phenomenology fails—but there is always already a difference, an absolute separation from the “real order,” from logic, calculability, reason. The object of sacrifice, the victim [,] is a surplus taken from the mass of useful wealth…Once chosen, he is the accursed share , destined for violent consumption. But the curse tears him away from the order of things…” (59). And it is this tearing away from the order of things—the order of rationality—that “restores to the sacred world that which servile use has degraded, rendered profane” (55). For, only when it is no longer useful, when it is no longer abstracted—subjected, subsumed under—merely a use-value, can the object be an object as such, can a subject be a subject as such; be a singularity. Thus, it is never so much who or what is sacrificed, but the fact that there is a sacrifice. So even as (s)he is sacrificing her time to poetry, it is always already beyond her knowledge whether what (s)he is doing is actually preparing her for poetry or not—all (s)he can know is that she is sacrificing and nothing more. Hence, all (s)he can do is to open her self to the possibility of this relationality—all (s)he can do is be in love with poetry. At the moment the muse whispers into her ear, (s)he ceases to be, and becomes a medium for poetry—and since this possession is always already beyond our cognitive knowledge, this is also a moment of divine wisdom. In other words, there is no difference between poetry and wisdom—the moment of poetry is the moment of wisdom. And this might be the very reason for the philosopher’s aversion to poets. Not so much because they may corrupt the youth (this is after all the aim of all thinking, all philosophy), but precisely because in order to do so, the philosopher must wait for a moment of possession, for divine musing, for poetry. Hence, all thought, all thinking, all philosophy, is nothing but the waiting for the possibility of poetry itself. (shrink)

In this note we show that the so-called weakly extensional arithmetic in all finite types, which is based on a quantifier-free rule of extensionality due to C. Spector and which is of significance in the context of Gödel"s functional interpretation, does not satisfy the deduction theorem for additional axioms. This holds already for Π0 1-axioms. Previously, only the failure of the stronger deduction theorem for deductions from (possibly open) assumptions (with parameters kept fixed) was known.

................English....................... The purpose of this study is to reveal university students’ perceptions regarding Holy Qur’an through metaphors. The survey group of study consists of 194 participants who were studying in Theology Department and Social Service Department at Gümüşhane University in the 2014-2015 academic terms. Both quantitative and qualitative methods are used together. The study’s data was collected through a form with the phrase “The Holy Qur’an is similar/like…, because...” and some demographical variables. The Content Analysis Technique was used to interpret (...) data. Results of this study determined that 44 different metaphors regarding Holy Qur’an were given by participants. Theme of these metaphors were compiled as 9 categories consisting of directional, life source, explanatory, key, protective, curative, instructive, speech, and other categories. Top metaphors are in the directional, life source and explanatory categories. Key words are metaphor, perception, The Qur’an perception, religious concepts, and religious symbols. Getting data through comprehensive and in-dept analysis can help to have information about concepts of holy books in the human mind. The purpose of this study is to pick out perceptions of university students with regard to the Holy Qur’an through metaphors. For this reason, these questions are searched by researchers: 1) What are the metaphors which used by university students on description of perceptions regarding the Holy Qur’an? 2) How are the metaphors regarding the Holy Qur’an categorized in terms of common characteristics which produced by university students? 3) Are there any links between socio-demographic variables and composed metaphoric categories? One of the qualitative data collection technics, data collecting through metaphors method is used, and is asked open-ended question in the study. Picking up similarities and diversities under thematic topics is quite easy in the method. Therefore, this method has a functional feature in the sociology, psychology and anthropology, and it gives a wealthy and qualified image about matter, phenomenon, event and situation (Yıldırım & Şimşek 2005, 212). The target population of the study consists of students who were taking education at Gümüşhane University. Easily accessible and availability principles pursued in the sample choosing. In the distribution of participants according to the demographical features, females have 61.9 percent (n:120) and males have 38.1 percent (n:74) in terms of gender. Students who graduated from religious vocational high school is 61.3 percent (n:119), and others who from other high schools is 38.7 percent (n:75) in terms of graduated from different high schools. Students in theology department have 68.0 percent (n:132), and students who were educated in the social service department have 32.0 percent (n:62). Research data is gathered through survey form includes “The Holy Qur’an is like/similar to…, because…” sentence and demographical variabilities. Data, gathered from 194 survey forms, is transferred to the Excel and the SPSS program. In an attempt to reliability of study, gathered metaphors is examined by four area expert. Frequencies (f) and percentages (%) is taken into consideration in the process of replacing metaphors to the tables. Data analysis technique is used on the getting relationships and explaining gathered data, while content analysis technique is used on the interpreting of data. The SPSS program is used in the analysis of quantitative data. Obtained data from the surveys and composed categories is associated with descriptive statements in the verses of the Holy Qur’an. In the composed categories demonstrate distribution of produced 44 different metaphors with regard to the Holy Qur’an as 9 categories. According to this, the sample is represented in the categories as 64.4 % (f:125) is in the ‘directional’, 11.3 % (f:22) is in the ‘life source’, 7.7 % (f:15) is in the ‘explanatory’, 3.1 % (f:6) is in the ‘key’, 3.1 % (f:6) is in the ‘protective’, 2.1 % (f:4) is in the ‘curative’, 2.1 % (f:4) is in the ‘instructive’, 2.1 % (f:4) is in the ‘speech’ and 4.1 % (f:8) is in the ‘other’ categories. Distributions of composed categories are represented according to common characteristics as frequencies and percentages in the next tables. In the distribution of produced metaphors in the ‘directional’ category, university students produced 7 different metaphors (f:125). Frequencies of produced metaphors in the category are such that: guide (f:41), advisor (f:25), mentor (f:19), compass (f:16), road map (f:8), route (f:3) and other (f:13). According to the result, it is understood that aspects of guide, advisor, mentor and compass stood mostly out in the category. In the ‘life source’ category, 6 different metaphors (f:22) is developed by participants. Developed metaphors’ frequencies in the category are the following: life (f:4), lifeblood (f:4), weather (f:2), water (f:2), inheritance (f:2) and others (f:7). So, life and lifeblood aspects stood mostly out in the category. In the ‘explanatory’ category, 5 different metaphor (f:15) is developed by participants. Frequencies of produced metaphors in the category are such that: light (f:5), sun (f:3), flashlight (f:2), torch (f:2) and other (f:3). According to the result, it is understood that aspects of light and sun stood mostly out in the category In the ‘protective’ category, 5 different metaphors (f:6) is developed by participants. Frequencies of produced metaphors in the category are such that: saver (f:2), lifeguard (f:1), hereafter-saving (f:1), escapeway (f:1) and branch to catch (f:1). According to the result, it is understood that aspect of saver stood mostly out in the category. In the ‘instructive’ category, 4 different metaphors (f:6) is developed by participants. Frequencies of produced metaphors in the category are such that: reference book (f:1), dictionary (f:1), priceless book (f:1) and life encyclopedia (f:1). In the ‘speech’ category, it is seen that 4 different metaphors (f:6) is developed by participants. Frequencies of produced metaphors in the category are such that: divine message (f:1), speaking truth (f:1), Allah’s dialogue with us (f:1) and final word (f:1). In the ‘key’ category, 3 different metaphors (f:6) is developed by participants. Frequencies of produced metaphors in the category are such that: a key (f:4), the key of heaven (f:1) and the key of salvation (f:1). In the ‘curative’ category, 2 different metaphors (f:4) is developed by participants. Frequencies of produced metaphors in the category are such that: a pill (f:3) and doctor (f:1). In the ‘others’ category, 8 different metaphors (f:8) is developed by participants. Frequencies of produced metaphors in the category are such that: world (f:1), the friend of lonely passenger (f:1), the tree with fruit (f:1), hereafter (f:1), priceless treasure (f:1), miracle (f:1), philosophy (f:1) and mirror (f:1). Participants composed of 44 different metaphors regarding the Holy Qur’an. The metaphors were summed up in the 9 categories as ‘directional’, ‘life source’, ‘explanatory’, ‘key’, ‘protective’, ‘curative’, ‘instructive’, ‘speech’ and ‘other’ To results of the study; guide, advisor, mentor and compass aspects of the Qur’an came into prominence at most in the ‘directional’ category, when life and lifeblood aspects of the Qur’an came into prominence at most in the ‘life source’ category. Light and sunny aspects of the Qur’an came into prominence at most in the ‘explanatory’ category, while saver aspect of the Qur’an came into prominence at most in the ‘protective’ category. Instructive aspect of the Qur’an came into prominence at most in the ‘instructive’ category. Speech aspect of the Qur’an came into prominence at most in the ‘speech’ category, while key aspect of the Qur’an came into prominence at most in the ‘key’ category. Moreover, pill aspect of the Qur’an came into prominence at most in the ‘curative’ category. Whatsoever world, friend of single traveler, tree with fruit, hereafter, priceless treasure, miracle, philosophy and mirror aspects of the Qur’an came into prominence at most in the ‘other’ category. It is inferred that significant relationships between demographic variables and metaphor categories. In terms of major variable; theology students were composed of more metaphor in the ‘explanatory’ and ‘instructive’ categories, while social service students were composed of more metaphor in the ‘life source’ category. In terms of gender variable; females composed of more metaphor in the ‘curative’ and ‘other’ categories, while males composed of more metaphor in the ‘directional category. In terms of graduating high school variable, students who graduated from religious vocational high school composed of more metaphor in the ‘key’ and ‘speech’ categories, when students who graduated from other high school composed of more metaphor in the ‘directional’ category. Whatsoever, in terms of having the Qur’an education in their life status variable, had the Qur’an education in their life students composed of more metaphor in the ‘curative’ and ‘other’ categories, while other group composed of more metaphor in the ‘directional’. Moreover, in terms of perception of subjective religiousness, students who think themselves are ‘religious’ composed of more metaphor in the ‘key’ and ‘other’ categories, while students who think themselves are ‘less religious’ composed of more metaphor in the ‘explanatory’ category. In terms of perception of family religiousness, students who think own family ‘less religious’ composed of more metaphor in the ‘directional’ and ‘life source’ categories, when students who think own family ‘religious’ composed of more metaphor in the ‘key’ category. It can be suggested by the results of this study; perception of the Qur’an can be studied with the different study techniques, or it can be studied in the different research groups with the same technique. Muslims’ perceptions regarding the Holy Qur’an can be examined with intercultural comparative studies. Perceptions regarding the Holy Qur’an can be researched through interviews. Members’ perception regarding holy book that have different religious faith can be comparatively examined. Individuals’ perceptions regarding different religious concepts can be studied through metaphors. .................. Turkish...................Bu araştırmanın amacı üniversite öğrencilerinin Kur’an-ı Kerim’e ilişkin algılarını metaforlar aracılığıyla ortaya çıkarmaktır. Araştırmanın çalışma grubunu, 2014-2015 eğitim öğretim yılında Gümüşhane Üniversitesi İlahiyat Fakültesi ve Sosyal Hizmetler bölümünde öğrenim gören 194 katılımcı oluşturmaktadır. Araştırmada nitel ve nicel yöntemler birlikte kullanılmıştır. Araştırma verileri, “Kur’an-ı Kerim……gibidir, çünkü……” cümlesini ve demografik değişkenleri içeren bir form aracılığıyla toplanmıştır. Verilerin analizi ve yorumlanmasında içerik analizi tekniği kullanılmıştır. Araştırmada Kur’an’a ilişkin 44 farklı metafor geliştirildiği tespit edilmiştir. Bu metaforlardan ‘yönlendirici’, ‘yaşam kaynağı’, ‘açıklayıcı’, ‘anahtar’, ‘koruyucu’, ‘öğretici’, ‘derman’, ‘kelam’ ve ‘diğer’ olmak üzere 9 farklı kategori oluşturulmuştur. Üretilen metaforların ‘yönlendirici’, ‘yaşam kaynağı’ ve ‘açıklayıcı’ kategorilerinde yoğunlaştığı görülmüştür. Demografik değişkenler ile metafor kategorileri arasındaki ilişkiyi ortaya çıkarmak araştırmanın ikincil amaçlarındandır ve bu yönüyle sonuçlar değerlendirildiğinde değişkenler ile kategoriler arasında anlamlı ilişkiler olduğu tespit edilmiştir. Demografik değişkenler ile kategori ilişkisinde fakülte değişkeni açısından ilahiyat öğrencileri ‘açıklayıcı’ ve ‘öğretici’ kategorilerinde daha fazla metafor üretirken sosyal hizmet öğrencileri ‘yaşam kaynağı’ kategorisinde daha fazla metafor üretmiştir. Cinsiyet değişkeni açısından ise kız öğrenciler ‘derman’ ve ‘diğer’ kategorilerinde daha fazla metafor üretirken erkek öğrenciler ‘yönlendirici’ kategorisinde daha fazla metafor üretmiştir. Lise mezuniyeti açısından bakıldığında da İHL’den mezun olanlar ‘anahtar’ ve ‘kelam’ kategorilerinde daha fazla metafor üretirken diğer lise mezunları ‘yönlendirici’ kategorisinde daha fazla metafor üretmiştir. Kur’an Kursu eğitimi alma değişkeni açısından ise Kur’an kursu eğitimi alanlar ‘derman’ ve ‘diğer’ kategorilerinde daha fazla metafor üretirken Kur’an Kursu eğitimi almayanlar ‘yönlendirici’ kategorisinde daha fazla metafor üretmiştir. Ayrıca öznel dindarlık ve aile dindarlık algılarıyla metafor kategorileri arasında da anlamlı ilişkiler elde edilmiştir. (shrink)

The discourse marker use of the word like is considered by many to be superfluously sprinkled into talk, a bad habit best avoided. But a comparison of the use of like in successive tellings of stories demonstrates that like can be anticipated in advance and planned into stories. In this way, like is similar to other words and phrases tellers recycle during story telling. The anticipation of like contrasted with the uses of other discourse markers such as oh, (...) you know, and well, which almost never re-occurred in similar locations across tellings. Um and uh did sometimes re-occur; these uses are contrasted with like. Although discourse markers are generally used on the fly to handle various issues that come up in coordinating talk as it unfolds, like can be used as an integral part of the story -a marked contrast to the prevalent idea that likes are speech tics. (shrink)

Observing others in conversation is a common format for comprehending language, yet little work has been done to understand dialog comprehension. We tested whether overhearers use addressee backchannels as predictive cues for how to integrate information across speaker turns during comprehension of spontaneously produced collaborative narration. In Experiment 1, words that followed specific backchannels were recognized more slowly than words that followed either generic backchannels or pauses. In Experiment 2, we found that when the turn after the backchannel (...) was a continuation of the narrative, specific backchannels prompted the fastest verification of prior information. When the turn after was an elaboration, they prompted the slowest, indicating that overhearers took specific backchannels as cues to integrate preceding talk with subsequent talk. These findings demonstrate that overhearers capitalize on the predictive relationship between backchannels and the development of speakers’ talk, coordinating information across conversational roles. (shrink)

Phenomenal consciousness or the subjective experience of feeling sensory stimuli is fundamental to human existence. Because of the ubiquity of their subjective experiences, humans seem to readily accept the anthropomorphic extension of these mental states to other animals. Humans will typically extrapolate feelings of pain to animals if they respond physiologically and behaviourally to noxious stimuli. The alternative view that fish instead respond to noxious stimuli reflexly and with a limited behavioural repertoire is defended within the context of our current (...) understanding of the neuroanatomy and neurophysiology of mental states. Consequently, a set of fundamental properties of neural tissue necessary for feeling pain or experiencing affective states in vertebrates is proposed. While mammals and birds possess the prerequisite neural architecture for phenomenal consciousness, it is concluded that fish lack these essential characteristics and hence do not feel pain. (shrink)

In arguing against the likelihood of consciousness in non-human animals, Descartes advances a slippery slope argument that if thought were attributed to any one animal, it would have to be attributed to all, which is absurd. This paper examines the foundations of Thomas Willis’ comparative neuroanatomy against the background of Descartes’ slippery slope argument against animal consciousness. Inspired by Gassendi’s ideas about the corporeal soul, Thomas Willis distinguished between neural circuitry responsible for reflex behaviour and that responsible for cognitively or (...) consciously mediated behaviour. This afforded Willis a non-arbitrary basis for distinguishing between animals with thought and consciousness and those without, a methodology which retains currency for neuroscience today. (shrink)

Chapter 1 First Person Access to Mental States. Mind Science and Subjective Qualities -/- Abstract. The philosophy of mind as we know it today starts with Ryle. What defines and at the same time differentiates it from the previous tradition of study on mind is the persuasion that any rigorous approach to mental phenomena must conform to the criteria of scientificity applied by the natural sciences, i.e. its investigations and results must be intersubjectively and publicly controllable. In Ryle’s view, philosophy (...) of mind needs to adopt an antimentalist stance to achieve this aim. Antimentalism not only definitively rejects the idea that mind is a substance separated from the body, it also denies that mental phenomena radically differ from physical phenomena by virtue of several unique features. Most problematically, mental phenomena have a conscious character (mental states are related to specific qualitative feelings) and are accessible only to the first-person (only the subject knows directly what s/he is experiencing inside his/her mind). Ryle takes a strong stance on antimentalism going so far as to maintain that an approach to mind which aims to meet the criteria of scientificity set by the natural sciences must avoid any reference to internal, unobservable mental states. In his view (which is considered a specifically philosophical version of psychological behaviorism and also addresses questions put forward in psychological research), mental states can be redescribed in terms of behavioral dispositions. In this chapter, we address the historical roots of the antimentalist view and analyze its relation to the later tradition of research on mind. We show that, compared to the antimentalist stance, functionalism and cognitivism take a step back when they maintain that direct reference to mental states is necessary since mental states cause and therefore explain human behavior. This step backwards is often interpreted as a return to mentalism. However, this is only partially true. Indeed, we suggest that these later traditions retain one important element of Ryle’s antimentalism, i.e. the idea that mental states must be uniquely identified using external and publicly observable criteria, while excluding any reference to introspection and those qualitative dimensions of a mental state, which are accessible only to the first-person. According to the perspective we put forward, this epistemological stance has continued to influence contemporary research on mind and current philosophical and psychological theories which both tend to exclude the subjective qualities of human experience from their accounts of how the mind works. The issue we raise here is whether this is legitimate or whether subjective qualities do play a role with respect to the way our mind works. The conclusion of this chapter anticipates the argument the book makes in in favor of this latter position, starting from a particular angle, i.e. the problem of how we categorize concepts related to our internal states. -/- Chapter 2 The Misleading Aspects of the Mind/Computer Analogy. The Grounding Problem and the Thorny Issue of Propriosensitive Information -/- Abstract. After the crisis of behaviorism, cognitivism and functionalism became the predominant models in the field of psychology and of philosophy, respectively. Their success is mainly due to the new key they use for interpreting mental processes: the mind/computer analogy. On the basis of this analogy, mental operations are seen as cognitive processes based on computations, i.e. on manipulations of abstract symbols which are in turn understood as informational unities (representations). This chapter identifies two main problems with this model. The first is how these symbols can relate to and communicate with perception and thus allow us to identify and classify what we perceive through the senses. Here we limit ourselves to presenting this issue in relation to the classical symbol grounding problem originally put forward by Harnad on the basis of Searle’s Chinese room argument. An attempt to address the problem raised here will be made in chap. 3. The second point we discuss in relation to the mind/computer analogy concerns the idea of information it fosters. Indeed, following this analogy, information is something available in the external world which can be captured by the senses and transmitted to the central system without being influenced or modified by the procedures of transmission. This perspective does not take into account that – unlike computers – in living beings information is acquired by means of the body. As Ulric Neisser has already pointed out, the body is itself an informational source that provides us with additional sensory experience that influences (modifies or complements) the information extracted from the external world by the senses. To develop this line of analysis and to determine exactly what information is provided by the body and how this might influence cognition, we examine Sherrington’s and Gibson’s positions. Moving on from their views, we qualify bodily information in terms of ‘proprioception’. We use ‘proprioception’ in a broad sense to describe any kind of experience we have of our internal states (including postural information as well as sensations related to the general state of the body and its parts). Following Damasio’s and Craig’s studies, we further elaborate this position, arguing that living beings are equipped with an internal propriosensitive monitoring system which maps all the changes that constantly occur in our body and that give us perceptual (‘proprioceptive’ or propriosensitive) information about what happens inside us. Moreover, relying on Goldie’s and Ratcliffe’s view, we show that emotional information can also be considered as a form of ‘proprioception’ which contributes to determining everything we perceive. This analysis leads us to the second main thesis of this book: ‘proprioception’ is a form of internal perception and it is an essential component of the sensory information we can access and use for all cognitive purposes. -/- Chapter 3 Semantic Competence from the Inside: Conceptual Architecture and Composition -/- Abstract. Concepts are essential constituents of thought: they are the instruments we use to categorize our experience, i.e. to classify things and group them together in homogeneous sets. Here we define concepts as the internal mental information (representations) that allows us, among other things, to master words in natural language. By analyzing the way in which individuals master word meanings we explore a number of hypotheses regarding the nature of concepts. Following Diego Marconi’s research, we differentiate between two kind of abilities that underpin lexical competence – so-called ‘referential’ and ‘inferential competence’ – and we suggest that, in order to support these abilities, concepts must also include two corresponding kinds of information, i.e. inferential and referential information. We point out that the most widely used and acknowledged theories of concepts do not make this distinction, instead broadly characterizing the information used for categorization in terms of propositionally described feature lists. However, we show that while feature lists can explain inferential competence, they do not account for referential competence. To address the issue of referential competence we examine Ray Jackendoff’s hypothesis that to account for the possibility of linking perceptual and conceptual information we need to assume the existence of a (visual) representation that encodes the geometric and topological properties of objects and bridges the gap between the percept and the concept. Furthermore, we analyze the extension of this work by Jesse Prinz who introduced the notion of a proxytype, a perceptual representation of a class of objects that incorporates structural and parametric information related to their appearance. However, as we point out, proxytypes can only explain the relationship between perception and concepts with respect to instances that can be perceived through the senses and that belong to the same class by virtue of their physical similarity. We suggest that this notion be extended to include larger conceptual classes. To accomplish this, we further develop Mark Johnson, George Lakoff and Jean Mandler’s idea of a schematic image and argue that conceptual representations include a perceptual schema. Perceptual schemata are non-linguistic, structured experiential gestalts (patterns or maps) that make use of information taken from all sensory modalities, including body perception. They accomplish a quasi-conceptual function: they allow us to recognize and to classify different instances. In this work, we hypothesize that perceptual schemata are an essential component of concepts, but not identical to them. Instead, we suggest that concepts include both perceptual and propositional information with perceptual schemata providing the ‘perceptual core concept’ that grounds related propositional information. -/- Chapter 4 In the Beginning There Were Categories. The Bodily Origin of Prelinguistic Categorical Organization: The Example of Folkbiological Taxonomies -/- Abstract. Studies of categorization in psychology and the cognitive sciences have made use of the notions of ‘category’ and ‘concept’ without precisely defining what is meant by either; in fact, often these terms have been used as synonyms, making it difficult to address specific issues related to conceptual development. This chapter begins by discussing the definitions of, as well as the distinctions between, ‘categories’ and ‘concepts’ in the classical philosophical tradition (Aristotle, Kant and Husserl). We introduce our view of categories with reference to Husserl. Categorization is defined as the way in which our experience is originally (pre-linguistically) organized in a passive and fully unconscious manner on the basis of universal structuring principles. Conceptualization is explained as a later process in which the earlier categorical macro-classes are further subdivided into more specific and detailed sets; this later process also relies on linguistic learning and exposure to culture. On the basis of Ray Jackendoff, Jean Mandler, George Lakoff and Mark Johnson’s work, we hypothesize that categorization is a two-step process that begins with the formation of homogeneous sets of entities partitioned into regions that describe the ontological boundaries of the objects that humans perceive (categories) and continues at a later stage with the development of more specific classifications (concepts). In this chapter, we mainly address three related issues: Why should we assume that there is categorical organization which precedes the development of a conceptual system? How do categories and concepts relate to each other? Shall we hypothesize that categories are innate or that they are formed before concepts on the basis of information and organizational structure available at a very early developmental stage? We show that categorical partitions are necessary for categorization and, following Mandler, that the general categories we form at an early age do not match our adult superordinate concepts. As for the third issue, we argue that there might be no need to assume that categories are innately present in the human mind, since their formation can be explained – at least in certain cases – by basic mechanisms that work on body (propriosensitive) information. This hypothesis will not be discussed in general, but in relation to a particularly relevant example of categorical partition, i.e. the folk-biological dichotomy between ANIMATE/INANIMATE. This is compared with other dichotomies that derive from it, but are not directly categorical such as LIVING/NON-LIVING and BIOLOGICAL/NON-BIOLOGICAL. -/- Chapter 5 Internal States: From Headache to Anger. Conceptualization and Semantic Mastery -/- Abstract. Here we ask if we can also apply the distinction between referential and inferential competence we introduced in Chapter 3 to words that do not refer to things that are perceived using the external senses, especially to words/concepts that denote bodily experiences (such as pain, thirst, hunger, etc.) or emotions. We introduce and discuss the hypothesis that – even though such words/concepts do not refer to intersubjectively identifiable entities in the external world – they do have a kind of referent that can be accessed via direct perception, more specifically ‘proprioception’, as we have defined it in terms of all propriosensitive information we can consciously access. In the first part of the chapter, we specifically consider terms denoting bodily experiences such as ‘pain’ or ‘hunger’ and argue that their referents are identified and classified from a first-personal point of view on the basis of four main characteristics: their specific intensity, their localization in the body, their co-occurrence with other signals and above all their specific qualitative sensations. Emotions are addressed in the second part of the chapter. We suggest that there is a continuity between bodily experiences and emotions. In particular, we argue for a perceptual theory of emotions in line with that proposed by James and Lange at the end of the 19th century and developed more recently by authors such as Damasio (see also chap. 2§5, §6). The hypothesis we put forward is that the referential information that supports the categorization of emotions and therefore also our mastery of terms referring to emotions consists in the perception (i.e. the ‘proprioception’) of those bodily states and changes in bodily states which constitute our emotional experience. In the context of this discussion we examine some objections to this line of reasoning that arise from a cognitivist perspective and following authors such as Oatley, Johnson-Laird and Frijda, we distinguish between basic emotions that can be identified and classified solely on the basis on how they feel and complex emotions whose identification and classification additionally depends on cognitive factors. To describe how emotions are identified and classified on the basis of how they feel, we rely on Marcel and Lambie’s distinction between an ‘emotion state’ and an ‘emotion experience’. Both notions indicate kinds of feelings that we consciously experience. However, they describe first-order and second order emotion awareness respectively. The emotion state is the feeling we have of the bodily states and changes that occur when we are experiencing an emotion, while the emotion experience is the fully developed and integrated emotion we both experience and are, with reflection, aware of experiencing. On the basis of this differentiation, we also show that the same characteristics that aid in the identification and classification of bodily experiences (specific qualitative sensations; somatic localization; specific intensity; presence/absence of specific concomitant sensations) can also be used for the identification and classification of emotions – at least basic emotions. In the last two sections of the chapter we present some clinical evidence on the semantic competence of people who suffer from Alexithymia and Autism Spectrum Disorder which supports the conclusions of our preceding analyses. -/- Chapter 6 The ‘Proprioceptive’ Component of Abstract Concepts -/- Abstract. In this chapter, we address the issue of whether the mastery of abstract words requires only inferential knowledge and thus, if the concepts that support the mastery of abstract words include only linguistic information. We start by differentiating the notions of ‘abstract’ and ‘general’ which are often erroneously confused. We then identify a strict definition of abstract, as contrasted with ‘concrete’, that applies to words or concepts whose referent cannot be experienced by the senses. We argue that abstract words/concepts would be better described as theoretical, because they are usually conceived as structured sets of inferential knowledge expressed linguistically; that is, as small theories. Pointing out parallels with Carnap’s analysis of this issue in philosophy of science, we hypothesize that words/concepts denoting non-observable entities are not all ‘equally theoretical’, because their link to sensory experience can be stronger or weaker. We revive the distinction, inspired by Quine, between theoretical and intertheoretical concepts/words. This distinction relies on the fact that the former – unlike the latter – retains a strong, although indirect, connection with perception. In Quine’s discussion, perception is understood uniquely in terms of observability, i.e. of external sensory experience. Here we argue, however, that bodily, ‘proprioceptive’ (i.e. propriosensitive) experience can also serve to referentially ground theoretical (i.e. abstract) concepts/words. We frame this issue using the example of the theoretical concept ‘freedom’ and Lakoff’s hypothesis that this concept is developed on the basis of bodily information. We contrast this with the example of ‘democracy’ which more closely resembles an intertheoretical concept/word. Furthermore, we show that one of the classical views put forward in psycholinguistic research to explain how abstract concepts are mentally represented – i.e. Paivio’s Dual Coding Theory – points in the same direction as our analysis. The same is true of Barsalou’s work suggesting that we use internal information to understand at least some abstract words. To sustain this position, we put forward two lines of evidence: the first comes from psycholinguistic studies while the second examines deficits of semantic competence exhibited by people with Autism Spectrum Disorder. On the basis of our analysis, we put forward a classification that distinguishes between different kinds of concreteness and different degrees of abstraction: concepts/words referring to body experiences and basic emotions are described as analogous to concrete concepts/words because they are grounded in perceptual (i.e. propriosensitive) experience, while abstract concepts/words are considered more or less abstract depending on whether they are intratheoretical (and rely entirely on inferential information) or theoretical (and are partially grounded in perceptual – or more often in propriosensitive perceptual – information). In the last section of the chapter we consider two scales that have been used in psycholinguistic research to measure the degree of concreteness vs. abstractness of words and we show that – used conjointly – they can provide a measure of the internal vs. external grounding of specific words. (shrink)

Humans are equipped with the remarkable ability to comprehend an infinite number of utterances. Relations between grammatical categories restrict the way words combine into phrases and sentences. How the brain recognizes different word combinations remains largely unknown, although this is a necessary condition for combinatorial unboundedness in language. Here, we used functional magnetic resonance imaging and multivariate pattern analysis to explore whether distinct neural populations of a known language network hub—Broca’s area—are specialized for recognizing distinct simple word combinations. (...) The phrases consisted of a noun (flag) occurring either with a content word, an adjective (green flag), or with a function word, a determiner (that flag). The key result is that the distribution of neural populations classifying word combination in Broca’s area seems sensitive to neuroanatomical subdivisions within this area, irrespective of task. The information patterns for adjective + noun were localized in its anterior part (BA45) whereas those for determiner + noun were localized in its posterior part (BA44). Our findings provide preliminary answers to the fundamental question of how lexical and grammatical category information interact during simple word combination, with the observation that Broca’s area is sensitive to the recognition of categorical relationships during combinatory processing, based on different demands placed on syntactic and semantic information. This supports the hypothesis that the combinatorial power of language consists of some neural computation capturing phrasal differences when processing linguistic input. (shrink)

Jaina Studies is a relatively new and rapidly expanding field of inquiry for scholars of Indian religion and philosophy. In Jainism, "yoga" carries many meanings, and this book explores the definitions, nuances, and applications of the term in relation to Jainism from early times to the present. Yoga in Jainism begins by discussing how the use of the term yoga in the earliest Jaina texts described the mechanics ofmundane action or karma. From the time of the later Upanisads, the word (...) Yoga became associated in all Indian religions with spiritual practices of ethical restraint, prayer, and meditation. In the medieval period, Jaina authors such as Haribhadra, Subhacandra, and Hemacandra used the term Yoga in reference to Jaina spiritual practice. In the modern period, a Jaina form of Yoga emerged, known as Preksa Dhyana. This practice includes the physical postures and breathing exercises well known through the globalization of Yoga. By exploring how Yoga is understood and practiced within Jainism, this book makes an important contribution to the fields of Yoga Studies, Religious Studies, Philosophy, and South Asian Studies. (shrink)

In this paper we study iterated circular multisets in a coalgebraic framework. We will produce two essentially different universes of such sets. The unisets of the first universe will be shown to be precisely the sets of the Scott universe. The unisets of the second universe will be precisely the sets of the AFA-universe. We will have a closer look into the connection of the iterated circular multisets and arbitrary trees. RID=""ID="" Mathematics Subject Classification (2000): 03B45, 03E65, 03E70, 18A15, (...) 18A22, 18B05, 68Q85 RID=""ID="" Key words or phrases: Multiset – Non-wellfounded set – Scott-universe – AFA – Coalgebra – Modal logic – Graded modalities. (shrink)

Let $ be the restriction of usual order relation to integers which are primes or squares of primes, and let ⊥ denote the coprimeness predicate. The elementary theory of $\langle\mathbb{N};\bot, , is undecidable. Now denote by $ the restriction of order to primary numbers. All arithmetical relations restricted to primary numbers are definable in the structure $\langle\mathbb{N};\bot, . Furthermore, the structures $\langle\mathbb{N};\mid, and $\langle\mathbb{N};=,+,x\rangle$ are interdefinable.

It Is My Pleasure To Introduce this discussion of Naoko Saito's American Philosophy in Translation. We have contributions from three experts in American philosophy, all of whom have been in conversation with the author for many years: Jim Garrison, Vincent Colapietro, and Steven Fesmire. Prior to their contributions, I would like to set the scene with some brief remarks to introduce the book and to explain something of its background.Over the past two decades, I have worked closely with Saito on (...) a number of projects, and I have been familiar with her ideas for this book since its inception. In some respects, the book is the product of studies in American philosophy that go back to her time as an undergraduate in Tokyo in the 1980s, ideas that were advanced considerably when she did an MA at Harvard, taking classes with Stanley Cavell and Hilary Putnam, and subsequently when she completed her PhD at Teachers College, with René Arcilla as her advisor and Cavell as a member of her committee. It was against this background that, in 2006, Saito published her first singly authored book, The Gleam of Light: Moral Perfectionism and Education in Dewey and Emerson. As that title indicates, she was already exploring the relation between Dewey and pragmatism, on the one hand, and American transcendentalism, on the other. Her sense back then of some separation between these traditions of thought, and of the nature of the tensions between them, has been refined and, for the most part, strengthened in the years since that earlier publication. No doubt she has been influenced in this by Cavell, who, in one essay, for example, asks: “What's the use of calling Emerson a pragmatist?” In any case, her account of this relationship is extended and altered significantly in American Philosophy in Translation.Through the course of her research, Saito has been conscious of the fact that she is studying American philosophy from a distance—a distance that is geographical, cultural, and linguistic—and she retains a thoughtful humility in relation to this. But she also sees here a possible opening to the perception and release of untapped aspects of these traditions of thought, in ways that might fertilize and extend the ground in which the inheritance of American philosophy has flourished. This is very much the line that she pursues in this book. In the light of this, and as the book's title indicates, there is a particular focus on language and translation. It is important that the latter term is understood not merely as an attractive metaphor for change and transformation: crucial to her developing argument is the experience of translating between languages and the reality of the experience in the lives of so many today, within the academy and without. In the course of this experience, one is sometimes confronted, quite self-consciously, with a word or phrase that resists translation. But sometimes—more often in the life of the accomplished or habituated speaker of the foreign language in question—the experience persists as an undercurrent, subtly opening a world that is other in some respects from the one that comes to light in the mother tongue.By contrast, to the many (especially Anglophone) monolingually minded, the need for translation can appear as an unwanted barrier, something of a nuisance, a problem to be solved. This is by no means a response confined, however, to the uneducated (or the Anglophone or the monolingual). There is also a sophisticated variant of this narrowness of outlook where faith is placed in an artificial or technical language with the power, the fantasy runs, to overcome the vagaries of natural language. Hilary Putnam recalls how Rudolf Carnap, whose stature as a thinker and as a human being he does not doubt, felt strongly that “for all x, planned x is better than unplanned x” and was drawn to the idea of a common world language: Thus the idea of a socialist world in which everyone spoke Esperanto (except scientists, who, for their technical work, would employ notations from symbolic logic) was one which would have delighted him. And I recently had a conversation with a student who remarked quite casually that it would not be a bad idea if there were only one language and one literature: “We would get used to it, and it might help to prevent war.” (Putnam 185)Putnam does not deign to respond to the latter assertion. What is foregrounded in his discussion is that monolingualism is likely to hide the plurality of goods that is realized in different cultures. The importance of that plurality is surely something that the luminaries of American philosophy bring to light. Indeed, Putnam's key point of reference in making these remarks is William James.The undercurrent of translation in the experience of the more accomplished speaker of a foreign language can act then as a sensitization to cultural difference, to different possibilities of thought and being. But in fact, this shifting of thought can apply within any language itself, not just inter- but intra-lingually, opening an insight that is close to the heart of American philosophy. If one can hear the cry of the rooster, then one may be wakened also by Thoreau's turn of expression in the idea of the “father tongue”: through a maturing experience of the language we are brought up with, we come to “a reserved and select expression, too significant to be heard by the ear, which we must be born again in order to speak” (Thoreau 69). This renewed investment in language, this continual return to our words, is what opens them to new thought and gives them interest. It is first an inheritance from the culture we are brought up in, but it dies in our speech and thinking if we do not turn it to something new. To build, we must begin by borrowing an axe, but we can return it sharper than when we borrowed it.If translation is operative in our language as a whole, as Saito's argument shows, this points to the many little rebirths within ourselves and in our interactions with one another. In fact, the point becomes political in that democracy depends upon this renewal of our words. This renewal resists not only the allure of ideology but also the now familiar etiolated rhetoric of “political realism.” Moreover, it points beyond the reliance, within the politics of recognition, on the defining of groups and categories toward a politics of acknowledgment.In this vein, Saito's outsider perspective is in tune with what Richard Bernstein has called the “global resurgence of American pragmatism.” The borderline or outsider perspective can have a powerful effect on thought, in relation to which Saito invites the reader to recall that America's past was itself an outsider-past: it was outside Europe, a relation with which it was bound to struggle, but it was also ready, as Emerson and Thoreau demonstrate, to draw from greater cultural distances, where it found congenial aspects in East Asian thought.Saito stresses the anti-foundationalist character of American philosophy as of critical importance for both philosophy and politics, and again her discussion of language is crucial to this. Dewey's emphasis on communication, with his relatively flat style of prose, is contrasted with the stylistic experiment and invention that she finds in Emerson, Thoreau, and Cavell. She sees the style of these writers, in some contrast to that of Dewey, as having a salutary, destabilizing effect. She wants to destabilize Dewey. It is entirely consonant with her position, furthermore, that she raises doubts about the bland acceptance of a politics of inclusion. Not only can this become a surreptitious form of discipline and control: it can engender the conformism that Emerson worked so hard to prevent.The book finishes on a more aesthetic note, taking up lines of thought in Dewey's aesthetics but turning this toward the more extravagant elision, in Thoreau, of the functional and the beautiful. The thematization of the aesthetic in this way is, she tries to show, crucial to our (political) world. (shrink)

Recent arguments in plant biology that claim to be uncovering the scientific basis for sentience in plants are grounded on assumptions that have not been sufficiently scrutinized. This paper focuses on two assumptions in particular – the semantic assumption that psychological predicates are non-rigid and hence can be extended to plants, and the assumption that Darwinian gradualism is inconsistent with consciousness emerging at a specific place on the phylogenetic tree. We interrogate both assumptions, advocating that a careful semantic analysis of (...) psychological predicates does not warrant their extension to plants on the available evidence, and that gradualism and emergentism, properly construed, are not inconsistent. (shrink)

continent. 1.4 (2011): 230—233. A word about the quotation marks. People ask about them, in the beginning; in the process of giving themselves up to reading the poem, they become comfortable with them, without necessarily thinking precisely about why they’re there. But they’re there, mostly to measure the poem. The phrases they enclose are poetic feet. If I had simply left white spaces between the phrases, the phrases would be read too fast for my musical intention. The (...) quotation marks make the reader slow down and silently articulate—not slur over mentally—the phrases at the pace, and with the stresses, I intend. They also distance the narrative form myself. I am not Alette. Finally they may remind the reader that each phrase is a thing said by a voice: this is not a thought, or a record of thought process, this is a story, told.(1) We read (reread) the poems that keep the discourse with ourselves going. —Wallace Stevens We have to break open words or sentences, too, and find what’s uttered in them. —Gilles Deleuze “The Descent of Alette” “is an allegorical poem” “in four books” “first published” “in 1992” “by Alice Notley.” “In the Descent of Alette,” “the double quotation mark” “is wrapped around” “words, phrases, sometimes whole sentences, and utilized as bones for structure and tonality.” “The winged” “dbl quotation” “like angels or devils” “descending from elsewhere” “function as” “poetic feet.” “Distance” “in the text through the use of dbl quotes,” “according to Notley,” “was a way to distance” “her self” “from the narrative.” I know someone who tattooed double quotes on her shoulder blades. In other words, the body is quotable. To be able to say that one is quotable. A body filled with other’s sayings. I never asked her what for, what is the double quote tattoo for and why on the shoulder blades? I prefer my own interpretation that keeps shifting every time I see her. First words of every poem in every book: Book One One ... On ... A ... There ... I ... We ... An ... A ... A ... I ... At ... A ... When ... When ... There ... I ... In ... At ... I ... Once ... A ... A ... In ... A ... A ... Two ... I ... I ... Eyeball ... In ... I... A ... I ... I ... On ... I ... There ... What ... As ... As Book Two I ... When ... I ... I ... As ... I ... I ... There ... I ... There ... I ... A ... I ... I ... I ... I ... I ... I ... I ... I ... I ... I ... I ... I ... I ... I ... I ... I ... I ... I ... I ... I ... I ... I Book Three The ... Presently ... I ... I’m ... I ... We ... What ... My ... I ... Who ... But ... Lay ... My ... I ... The ... Your ... The ... I ... It’s ... As ... The ... Talon’s ... When ... We ... I ... Slowly ... I ... I ... The ... How ... The Book Four I ... I ... You ... The ... Now ... She ... The ... There ... As ... Then ... The ... All ... Let’s I ... You ... The ... Thus ... The ... I ... The ... I ... There ... Have ... The ... As ... The Defamiliar Object “Poetry is a defamiliarized language, whose formations, so far from being simply formations of meaning, are aesthetic structures...”(2) “The same can be” “irresponsibly associated” “with the use of punctuation.” “The dbl quotation as a measure” “of poetic feet” “is treated as such” “because the author” “injects artfulness into it.” “The dbl quote is an object—” “a joystick” “to control breadth” “(of breath.)” “To de-familiarize” “said sign” “is also to” “impart the sensation of [it] as [it is] perceived and not as they are known.”(3) “The dbl quote” “nests previous words, phrasings and sayings.” “How many have come and gone” “through the doorway of this punctuation sign.” “There are also air quotes and virtual quotes.” “There is emphasis and there’s irony.” “It would be aggravating” “or interesting” “to watch a reading of” “The Descent of Alette” “with someone” “raising and curling” “fingers” “bent out of shape” “in what could be used as” “peace signs.” “I am trying to avoid” “scare quotes.” “I looked up” “what they are” “and supposedly they arose” “in the early 20th century.” “The scare quote” “is a mark around a word or phrase to indicate that it doesn’t signify conventional or literal meaning.” “This isn’t how Notley” “intended to use them” “in The Descent of Alette.” “The characters, places, and things” “signify nothing” “beyond” “their literal meaning” “ within the allegory .” “I’d like to stress” “within the allegory;” “that’s why its” “italicized.” “It is told through” “the main character/voice of” “Alette.” “The author reminds us she is not Alette.” “The author marvelously found a way” “to distance” “her self” “from the narrative.” “This was attempted” “by tonal and intimate” “affect of the dbl quote” “used as poetic feet.” “Its as though” “punctuation in this regard” “becomes a magical toy.” “Arguably, punctuation” “(as perceived)” “undergoes a kind of” “ defamiliar ” “make-over.” “The text” gently forces the reader” “to slow down,” “read slowly.” “At some point” “one begins to sense” “lines of text” “moving on its own.” “Broken words, phrases, and sentences” “shuttling left to right” “like a subway” “that stops” “from station to station;” “open quote to end quote.” Double Quote Occupied “There are two worlds; one above ground” “and one underground.” “The world above ground is where,” “the tyrant” “with a capital t” “lives.” “(The “T” gets tangled in the claws of the dbl quote.)” “Alette becomes an owl and kills him.” “In the last book the tyrant dies.” “ “...the tyrant” “a man in charge of” “the fact” “that we were” “below the ground” “endlessly riding” “our trains, never surfacing” “A man who” “would make you pay” “so much” “to leave the subway” “that you don’t” “ever ask” “how much it is” “It is, in effect,” “all of you & more” “Most of which you already” “pay to live below” “But he would literally” “take your soul” “Which is what you are” “below the ground” “Your soul” “your soul rides” “this subway” “I saw” “on the subway a” “world of souls” ”(4) “New York;” “the city of cities” “and its subways—” “worlds underground,” “above ground,” “& above the above ground.” “Skyscrapers,” “Wall Street,” “old money,” “new money,” “and falling further down a cleavage;” “the middle class” “slipping away.” “Contemporary artist ” “Ligorano Reece” “recently made” “a sculpture of ice ” “a block of ice” “carved to read” “middle class” “(in all upper case letters)” “and let it melt” “naturally” “for however long—” “hours,” “days.” “It didn’t take very long to melt.” A global uprise of mass demonstrations; a cacophony of bodies on the street, in parks and universities, on City Hall lawns, coastal ports, neighborhoods, etc., and for what? The reasons are endless and finite. Not a single body is unaffected by the movement even when not “occupying.” “Occupiers” “stormed into a Sotheby’s auction” “protesting” “via human microphone” “that the CEO takes home” “about” “six thousand dollars” “a day.” “(The a/Art market” “is not a reflection” “of a desire” “for a/Art” “but a reflection” “of a desire” “for money” “confused with a/Art.)” What could it mean to occupy that which has been written or said? Someone with double quotes tattooed on both shoulders attempts to reclaim the sign; re-invent it privately-publicly since the body is always split between both spheres. A genre of hide-and-seek; the speaking and silent body which can never mean what it says even while it so desires to mean something. To nest (and hold hostage) someone in double quotes is an act of violence; a gesture of displacement where one is arrested, dislocated, and scrutinized under a distant gaze. “The air quote” “also known as” “finger quote or ersatz quote” “supposedly” “harks back to” “1927.” “The brevity of this gesture” “ as something invisible” “like virtual money or credit” “doesn’t really exist” “though it take up space;” “its the ghostliest of all punctuation signs” “and one that requires the presence and appearance of a body.” “ “she made a form” “in her mind” “an imaginary” “form” “to settle” “in her arms where” “the baby” “had been” “We saw her fiery arms” “cradle air” “She cradled air...” ”(5) “The air” “gets occupied” “by one or two hands” “with thumb, forefinger, and middle finger” “which alternately could be used” “to shoot rubber bullets,” “pepper spray,” “tear gas.” “How three fingers” “could be responsible for so much:” “satire, sarcasm, irony” “and ultimately” “bruises, blood, death.” (“The violence of the dbl quote is to eagerly to place oneself inside a tornado.)” “The violence of this” “embodied punctuation mark” “stems from a discordance with others.” “Is the name, word, or phrase” “placed in dbl quotes” “heroic” “ or brave?” “An act of displacement;” “must there always be” “bright or negative lights—” “a leaderless act” “to inhabit, to occupy” “space removed” “from normative use.” “Of course” “I’m also wondering” “what it means to re-occupy” “public/private space—the street, neighborhood or page” “policed” “by laws, limits, and” “to some extent” “punctuation.” Echo, Mirror “There are first, second, and third voices interwoven.” “ “Braid of voices,”(6) ” “Some lines read as internal thoughts,” “dialogues,” “and scene descriptions,” “all of which make up the allegory.” “It seems appropriate” “for the word” “allegory” “to nest in dbl quotes” “for perhaps it might be” “a gesture to echo on and on” “eternally referencing” “whatever came before.” I notice the first tooth of the double quote, when paying too close attention, gets caught in the hook of the “f”. I space bar to untangle them; the f does not resist the closed bite of “deaf” and I resist to know what it could mean, because it could doubly mean nothing. “ “He looked” “so familiar” “to me...”(7) ” “The second-person” “echoes in one of two directions:” “further into” “or farther from” “me.” “Its as though” “the second-person amplifies” “or else the opposite” “in which he,” “who looks so familiar,” “retreats further” “like stars in a telescope.” “The dbl quote” “has this kind of affect” “concerning distance and dimension” “as also illusory” “as something twice removed” “and unreal” “in a similar way” “movie stars are unreal and far away.” “ “I entered” “a car” “in which I seemed” “to see double” “Each person I” “looked at seemed” “spread out” “as if doubled” “Gradually” “I perceived that” “each person” “was surrounded by a ghostly” “second image” “was encased in it” “& each” / “of those images,” “those encasings,” “was exactly the same” “each was in fact” “the tyrant...” ”(8) A daydream of a mirror-less world while staring through window blinds; a palm tree behind. It was dark with nothing there. A world with no mirrors “in my mind,” though my mind could only reflect what it knew: a palm tree. Naturally then, palm trees multiplied; a world of palm trees reflected the daydream with no mirror in sight. “The mirror” “(prior to obsidian manufacturing ca. 6000 B.C)” “was wherever water” “could be found.” “Its interesting” “mirrors have been around” “before humans—its funny” “animals and humans” “get born into” “a world of mirrors,” “therefore, simulation” “is always already” “a given—” “a sparkly consequence to be born with a dbl.” NOTES 1. Notley, Alice. “Author’s Note” in The Descent of Alette (New York, 1996) 2. Bruns, Gerald L. “ From Intransitive Speech to the Universe of Discourse” in Modern Poetry And The Idea of Language (New Haven & London, 1974), p.75 3. Ibid. p.77 4. Notley, Alice. The Descent of Alette (New York, 1996). p.3 5. Ibid. p.10 6. Ibid i. p.9 7. Ibid ii. p.16 8. Ibid iii. p.12. (shrink)

PREFACEProf. Göran Sundholm of Leiden University inspired the group of Logic at Lille and Valparaíso to start a fundamental review of the dialogical conception of logic by linking it to constructive type logic. One of Sundholm's insights was that inference can be seen as involving an implicit interlocutor. This led to several investigations aimed at exploring the consequences of joining winning strategies to the proof-theoretical conception of meaning. The leading idea is, roughly, that while introduction rules lay down the conditions (...) under which a winning strategy for the Proponent may be built, the elimination rules lay down those elements of the Opponent's assertions that the Proponent has the right to use for building winning strategy. It is the pragmatic and ethical features of obligations and rights that naturally lead to the dialogical interpretation of natural deduction.During the Visiting Professorship of Prof. Sundholm at Lille in (2012) the group of Lille started delving into the ways of implementing Per Martin-Löf's Constructive Type Theory with the dialogical perspective. In particular, Aarne Ranta's (1988) paper, the first publication on the subject, was read and discussed during Sundholm’s seminar. The discussions strongly suggested that the game-theoretical conception of quantifiers as deploying interdependent moves provide a natural link between CTT and dialogical logic. This idea triggered several publications by the group of Lille in collaboration with Nicolas Clerbout and Juan Redmond at the University of Valparaíso, including the publication of the book (2015) by Clerbout / Rahman that provides a systematic development of this way of linking CTT and the dialogical conception of logic. However the Clerbout / Rahman book was written from the CTT perspective on dialogical logic, rather than the other way round. The present book should provide the perspective from the other side of the dialogue between the Dialogical Framework and Constructive Type Theory. The main idea of our present study is that Sundholm's (1997) notion of epistemic assumption is closely linked to the Copy-Cat Rule or Socratic Rule that distinguishes the dialogical framework from other game-theoretical approaches. One way to read the present book is as a further development of Sundholm’s extension of Austin's (1946, p. 171) remark on acts of assertion to inference. Indeed, Sundholm (2013, p. 17) gave the following forceful formulation: When I say therefore, I give others my authority for asserting the conclusion, given theirs for asserting the premisses.Per Martin-Löf, in recent lectures, have utilized the dialogical perspective on epistemic assumptions to get out of a certain circle that threatens the explanation of the notions of inference and demonstration. A demonstration may be explained as a chain of (immediate) inferences starting from no premisses. That an inference J1... Jn—————Jis valid means that the conclusion J can be made evident on the assumption that J1, …, Jn are known. The notion of epistemic assumption thus enters in the explanation of valid inference. We cannot, however, in this explanation understand 'known' in the sense of demonstrated, for then we are explaining the notion of inference in terms of demonstration, whereas demonstration has been explained in terms of inference. Martin-Löf suggests that we here understand 'known' in the sense of asserted, so that epistemic assumptions are judgements others have made, judgements for which others have taken the responsibility; that the inference is valid then means that, given that others have taken responsbility for the premisses, I can take responsibility for the conclusion:The circularity problem is this: if you define a demonstration to be a chain of immediate inferences, then you are defining demonstration in terms of inference. Now we are considering an immediate inference and we are trying to give a proper explanation of that; but, if that begins by saying: Assume that J1, …, Jn have been demonstrated – then you are clearly in trouble, because you are about to explain demonstration in terms of the notion of immediate inference, hence when you are giving an account of the notion of immediate inference, the notion of demonstration is not yet at your disposal. So, to say: Assume that J1, …, Jn have already been demonstrated, makes you accusable of trying to explain things in a circle. The solution to this circularity problem, it seems to me now, comes naturally out of this dialogical analysis. […]The solution is that the premisses here should not be assumed to be known in the qualified sense, that is, to be demonstrated, but we should simply assume that they have been asserted, which is to say that others have taken responsibility for them, and then the question for me is whether I can take responsibility for the conclusion. So, the assumption is merely that they have been asserted, not that they have been demonstrated. That seems to me to be the appropriate definition of epistemic assumption in Sundholm's sense. One of the main tenets of the present study is that the further move of relating the Socratic Rule rule with judgemental equality provides both a simpler and more direct way to implement the constructive type theoretical approach within the dialogical framework. Such a reconsideration of the Socratic Rule, roughly speaking, amounts to the following. 1.A move from P that brings-forward a play-object in order to defend an elementary proposition A can be challenged by O. 2.The answer to such a challenge, involves P bringing forward a definitional equality that expresses the fact that the play-object chosen by P copies the one O has chosen while positing A. For short, the equality expresses at the object-languaje level that the defence of P relies on the authority given to O to be able to produce the play-objects she brings forward. More generally, according to this view, a definitional equality established by P and brought forward while defending the proposition A, expresses the equality between a play-object (introduced by O) and the instruction for building a play-object deployed by O while affirming A. So it can be read as a computation rule that indicates how to compute O's instructions. Let us recall that from the strategic point of view, O's moves correspond to elimination rules of demonstrations. Thus, the dialogical rules that prescribe how to introduce a definitional equality – correspond – at the strategic level – to the definitional equality rules for CTT as applied to the selector-functions involved in the elimination rules. So, what we are doing here is extending the dialogical interpretation of Sundholm's epistemic assumption to the rules that set up the definitional equality of a type.The present work is structured in the following way:•In the Introduction we state the main tenets that guide our book•Chapter II contains a brief overview of Constructive Type Theory penned by Ansten Klev with exercises and their solutions. •Chapter III offers a novel presentation of the dialogical conception of logic. In fact, the first two sections of the chapter provide an overview of standard dialogical logic – including solved exercises, slightly adapted to the content of the present volume. The rest of the sections develop a new dialogical approach to Constructive Type Theory. •Chapters IV and V contain the main body of our study, namely the relation between the Socratic Rule, epistemic assumptions, and equality. The chapter provides the reader with thoroughly worked out examples with comments. •After the Final Remarks the book containsa.An appendix containing a an overview of all the rules for the new formulation of dialogical approach to constructive type theory developed in the book; b.a brief outline of Per Martin-Löf's informal presentation of the demonstration of the axiom of choice.c.two examples of a tree-shaped graph of an extensive strategy. Acknowledgments: Many thanks to Mark van Atten (Paris1), Giuliano Bacigalupo (Zürich), Charles Zacharie Bowao (Univ. Ma Ngouabi de Brazzaville, Congo), Christian Berner (Lille3), Michel Crubellier (Lille3), Pierre Cardascia (Lille3), Oumar Dia (Dakar), Marcel Nguimbi ((Univ. Marien Ngouabi de Brazzaville, Congo), Adjoua Bernadette Dango (Lille3 / Alassane Ouattara de Bouaké, Côte d'Ivoire), Steephen Rossy Eckoubili (Lille3), Johan Georg Granström (Zürich), Gerhard Heinzmann (Nancy2), Muhammad Iqbal (Lille3), Matthieu Fontaine (Lille3), Radmila Jovanovic (Belgrad), Hanna Karpenko (Lille3), Laurent Keiff (Lille3), Sébastien Magnier (Saint Dennis, Réunion), Clément Lion (Lille3), Gildas Nzokou (Libreville), Fachrur Rozie (Lille3), Helge Rückert (Mannheim), Mohammad Shafiei (Paris1), and Hassan Tahiri (Lisbon), for rich interchanges, suggestions on the main claims of the present study and proof-reading of specific sections of the text. Special thanks to Gildas Nzokou (Libreville), Steephen Rossy Eckoubili (Lille3) and Clément Lion (Lille3), with whom a Pre-Graduate Textbook in French on dialogical logic and CTT is in the process of being worked out – during the visiting-professorship in 2016 of the former. Eckoubili is the author of the sections on exercises for dialogical logic, Nzokou cared of those involving the development of CTT-demonstrations out of winning-strategies. Special thanks also to Ansten Klev (Prague) for helping with technical details and conceptual issues on CTT, particularly so as author of the chapter introducing CTT. (shrink)

Stewart Shapiro's ambition in Vagueness in Context is to develop a comprehensive account of the meaning, function, and logic of vague terms in an idealized version of a natural language like English. It is a commonplace that the extensions of vague terms vary according to their context: a person can be tall with respect to male accountants and not tall (even short) with respect to professional basketball players. The key feature of Shapiro's account is that the extensions of (...) vague terms also vary in the course of conversations and that, in some cases, a competent speaker can go either way without sinning against the meaning of the words or the non-linguistic facts. As Shapiro sees it, vagueness is a linguistic phenomenon, due to the kinds of languages that humans speak; but vagueness is also due to the world we find ourselves in, as we try to communicate features of it to each other. (shrink)

The basic motivation behind this work is to tie together various computational complexity classes, whether over different domains such as the naturals or the reals, or whether defined in different manners, via function algebras (Real Recursive Functions) or via Turing Machines (Computable Analysis). We provide general tools for investigating these issues, using two techniques we call approximation and lifting. We use these methods to obtain two main theorems. First, we provide an alternative proof of the result from Campagnolo et (...) al. (J Complex 18:977–1000, 2002), which precisely relates the Kalmar elementary computable functions to a function algebra over the reals. Second, we build on that result to extend a result of Bournez and Hainry (Theor Comput Sci 348(2–3):130–147, 2005), which provided a function algebra for the ${\mathcal{C}}^2$ real elementary computable functions; our result does not require the restriction to ${\mathcal{C}}^2$ functions. In addition to the extension, we provide an alternative approach to the proof. Their proof involves simulating the operation of a Turing Machine using a function algebra. We avoid this simulation, using a technique we call lifting, which allows us to lift the classic result regarding the elementary computable functions to a result on the reals. The two new techniques bring a different perspective to these problems, and furthermore appear more easily applicable to other problems of this sort. (shrink)

continent. 2.2 (2012): 66–75 ~*~ We’re Doomed. Pessimism is the night-side of thought, a melodrama of the futility of the brain, a poetry written in the graveyard of philosophy. Pessimism is a lyrical failure of philosophical thinking, each attempt at clear and coherent thought, sullen and submerged in the hidden joy of its own futility. The closest pessimism comes to philosophical argument is the droll and laconic “We’ll never make it,” or simply: “We’re doomed.” Every effort doomed to failure, every (...) project doomed to incompletion, every life doomed to be unlived, every thought doomed to be unthought. Pessimism is the lowest form of philosophy, frequently disparaged and dismissed, merely the symptom of a bad attitude. No one ever needs pessimism, in the way that one needs optimism to inspire one to great heights and to pick oneself up, in the way one needs constructive criticism, advice and feedback, inspirational books or a pat on the back. No one needs pessimism, though I like to imagine the idea of a pessimist activism. No one needs pessimism, and yet everyone—without exception—has, at some point in their lives, had to confront pessimism, if not as a philosophy then as a grievance—against one’s self or others, against one’s surroundings or one’s life, against the state of things or the world in general. There is little redemption for pessimism, and no consolation prize. Ultimately, pessimism is weary of everything and of itself. Pessimism is the philosophical form of disenchantment—disenchantment as chanting, a chant, a mantra, a solitary, monophonic voice rendered insignificant by the intimate immensity surrounding it. In pessimism, the first axiom is a long, low, funereal sigh. ~*~ We’re Still Doomed. No one has time for pessimism. After all, there are only so many hours in a day. Whatever our temperament, happy or sad, engaged or disengaged, we know pessimism when we hear it. The pessimist is usually understood as the complainer, forever pointing out what is wrong with the world without ever once offering a solution. But more often than not pessimists are the quietest of philosophers, submerging their own sighs within the lethargy of discontent. What little sound it makes is of interest to no one—“I’ve heard it all before,” “tell me something I don’t know,” sound and fury, signifying nothing. In raising problems without solutions, in posing questions without answers, in retreating to the hermetic, cavernous abode of complaint, pessimism is guilty of that most inexcusable of Occidental crimes—the crime of not pretending it’s for real. Pessimism fails to live up to the most basic tenet of philosophy—the “as if.” Think as if it will be helpful, act as if it will make a difference, speak as if there is something to say, live as if you are not, in fact, being lived by some murmuring non-entity both shadowy and muddied. Had it more self-assurance and better social skills, pessimism would turn its disenchantment into a religion, possibly calling itself The Great Refusal. But there is a negation in pessimism that refuses even such a Refusal, an awareness that, from the start, it has already failed, and that the culmination of all that is, is that all is for naught. Pessimism tries very hard to present itself in the low, sustained tones of a Requiem Mass, or the tectonic rumbling of Tibetan chant. But it frequently lets loose dissonant notes at once plaintive and pathetic. Often, its voice cracks, its weighty words abruptly reduced to mere shards of guttural sound. ~*~ Maybe It’s Not So Bad, After All. If we know pessimism when we hear it, this is because we’ve heard it all before—and we didn’t need to hear it in the first place. Life is hard enough. What you need is a change of attitude, a new outlook, a shift in perspective... a cup of coffee. If we have no ears for pessimism, this is because it is always reducible to something as reliably mutable as a voice. If pessimism is so frequently disparaged, it is because it brings everyone down, determined as it is to view each day as a bad day, if only by virtue of the fact that it is not yet a bad day. For pessimism the world is brimming with negative possibility, the collision of a bad mood with an impassive world. In fact, pessimism is the result of a confusion between the world and a statement about the world, a confusion that also prevents it from fully entering the hallowed halls of philosophy. If pessimism is so often dismissed, this is because it is often impossible to separate a “bad mood” from a philosophical proposition (and do not all philosophies stem from a bad mood?) The very term “pessimism” suggests a school of thought, a movement, even a community. But pessimism always has a membership of one—maybe two. Ideally, of course, it would have a membership of none, with only a scribbled, illegible note left behind by someone long forgotten. But this seems unrealistic, though one can always hope. ~*~ Anatomy of Pessimism. Though it may locate itself at the margins of philosophy, pessimism is as much subject to philosophical analysis as any other form of thought. Pessimism’s lyricism of failure gives it the structure of music. What time is to the music of sorrow, reason is to a philosophy of the worst. Pessimism’s two major keys are moral and metaphysical pessimism, its subjective and objective poles, an attitude towards the world and a claim about the world. For moral pessimism, it is better not to have been born at all; for metaphysical pessimism, this is the worst of all possible worlds. For moral pessimism the problem is the solipsism of human beings, the world made in our own image, a world-for-us. For metaphysical pessimism, the problem is the solipsism of the world, objected and projected as a world-in-itself. Both moral and metaphysical pessimism are compromised philosophically; moral pessimism by its failure to locate the human within a larger context, and metaphysical pessimism by its failure to recognize the complicity in the very claim of realism. This is how pessimism makes its music of the worst, a generalized misanthropy without the anthropos . Pessimism crystallizes around this futility—it is its amor fati , rendered as musical form. ~*~ Melancholy of Anatomy. There is a logic of pessimism that is fundamental to its suspicion of philosophical system. Pessimism involves a statement about a condition . In pessimism each statement boils down to an affirmation or a negation, just as any condition boils down to the best or the worst. With Schopenhauer, that arch-pessimist, the thinker for whom the philosopher and the curmudgeon perfectly overlap, we see a no-saying to the worst, a no-saying that secretly covets a yes-saying (through asceticism, mysticism, quietism), even if this hidden yes-saying is a horizon at the limits of comprehension. With Nietzsche comes the pronouncement of a Dionysian pessimism, a pessimism of strength or joy, a yes-saying to the worst, a yes-saying to this world as it is. And with Cioran yet another variation, futile yet lyrical, a no-saying to the worst, and a further no-saying to the possibility of any other world, in here or out there. With Cioran one approaches, but never reaches, an absolute no-saying, a studied abandonment of pessimism itself. The logic of pessimism moves through three refusals: a no-saying to the worst (refusal of the world-for-us, or Schopenhauer’s tears); a yes-saying to the worst (refusal of the world-in-itself, or Nietzsche’s laughter); and a no-saying to the for-us and the in-itself (a double refusal, or Cioran’s sleep). Crying, laughing, sleeping—what other responses are adequate to a life that is so indifferent? ~*~ Cosmic Pessimism. Both moral and metaphysical pessimism point to another kind, a pessimism that is neither subjective nor objective, neither for-us nor in-itself, and instead a pessimism of the world-without-us. We could call this a cosmic pessimism ... but this sounds too majestic, too full of wonder, too much the bitter aftertaste of the Great Beyond. Words falter. And so do ideas. And so we have a cosmic pessimism, a pessimism that is first and last a pessimism about cosmos , about the necessity and possibility of order. The contours of cosmic pessimism are a drastic scaling-up or scaling-down of the human point of view, the unhuman orientation of deep space and deep time, and all of this shadowed by an impasse, a primordial insignificance, the impossibility of ever adequately accounting for one’s relationship to thought—all that remains of pessimism is the desiderata of affects—agonistic, impassive, defiant, reclusive, filled with sorrow and flailing at that architectonic chess match called philosophy, a flailing that pessimism tries to raise to the level of an art form (though what usually results is slapstick). ~*~ Song of Futility. An ethics of futility pervades pessimism. Futility, however, is different from fatality, and different again from simple failure (though failure is never simple). Failure is a breakage within the heart of relations, a fissure between cause and effect, a fissure hastily covered over by trying and trying again. With failure, there is always plenty of blame to go around; it’s not my fault, it’s a technical difficulty, it’s a miscommunication. For the pessimist, failure is a question of “when,” not “if”—failure as a metaphysical principle. Everything withers and passes into an obscurity blacker than night, everything from the melodramatic decline of a person’s life to the banal flickering moments that constitute each day. Everything that is done undone, everything said or known destined for a kind of stellar oblivion. When scaled up in this way, failure becomes fatality. Fatality is the hermeticism of cause and effect. In fatality, everything you do, whatever you do, always leads to a certain end, and ultimately to the end—though that end, or the means to that end, remain shrouded in obscurity. Nothing you do makes a difference because everything you do makes a difference. Hence the effects of your actions are hidden from you, even as you deceive yourself into thinking that, at last, this time you will outwit the order of things. By having a goal, planning ahead, and thinking things through carefully, we attempt, in a daily Prometheanism, to turn fatality to our advantage, to gain a glimpse of an order that seems buried deeper and deeper in the fabric of the universe. But even fatality has its comforts. The chain of cause and effect may be hidden from us, but that’s just because disorder is the order we don’t yet see; it’s just complex, distributed, and requires advanced mathematics. Fatality still clings to the sufficiency of everything that exists... When fatality relinquishes even this idea, it becomes futility. Futility arises out of the grim suspicion that, behind the shroud of causality we drape over the world, there is only the indifference of what exists or doesn’t exist; whatever you do ultimately leads to no end, an irrevocable chasm between thought and world. Futility transforms the act of thinking into a zero-sum game. ~*~ Song of the Worst. At the center of pessimism lies the term pessimus , “the worst,” a term as relative as it is absolute. The worst is about as bad as it gets, “the worst” as “the best” in disguise, shrouded by the passage of time or the twists and turns of fortune. For the pessimist, “the worst” is the propensity for suffering that gradually occludes each living moment, until it eclipses it entirely, overlapping perfectly in death... which, for the pessimist, is no longer “the worst.” Pessimism is marked by an unwillingness to move beyond “the worst,” something only partially attributable to a lack in motivation. In pessimism “the worst” is the ground that gives way beneath every existent—things could be worse, and , things could be better. “The worst” invariably implies a value judgment, one made based on scant evidence and little experience; in this way, pessimism’s greatest nemesis is its moral orientation. Pessimism’s propositions have all the gravitas of a bad joke. Perhaps this is why the true optimists are the most severe pessimists—they are optimists that have run out of options. They are almost ecstatically inundated by the worst. Such an optimism is the only possible outcome of a prolonged period of suffering, physical or metaphysical, intellectual or spiritual. But does this not also describe all the trials and tribulations of each day—in short, of “life?” It seems that sooner or later we are all doomed to become optimists of this sort (the most depressing of thoughts...) ~*~ Song of Doom. Rather than serving as a cause for despair, gloom and doom are the forms of consolation for any pessimist philosophy. Neither quite affects nor quite concepts, gloom and doom transform pessimism into a mortification of philosophy. Doom is not just the sense that all things will turn out badly, but that all things inevitably come to an end, irrespective of whether or not they really do come to an end. What emerges from doom is a sense of the unhuman as an attractor, a horizon towards which the human is fatally drawn. Doom is humanity given over to unhumanity in an act of crystalline self-abnegation. Gloom is not simply the anxiety that precedes doom. Gloom is literally atmospheric, climate as much as impression, and if people are also gloomy, this is simply the by-product of an anodyne atmosphere that only incidentally involves human beings. Gloom is more climatological than psychological, the stuff of dim, hazy, overcast skies, of ruins and overgrown tombs, of a misty, lethargic fog that moves with the same languorousness as our own crouched and sullen listening to a disinterested world. In a sense, gloom is the counterpoint to doom—what futility is to the former, fatality is to the latter. Doom is marked by temporality—all things precariously drawn to their end—whereas gloom is the austerity of stillness, all things sad, static, and suspended, a meandering smoke hovering over cold lichen stones and damp fir trees. If doom is the terror of temporality and death, then gloom is the horror of a hovering stasis that is life. At times I like to imagine that this realization alone is the thread that connects the charnel ground Aghori and the graveyard poets. ~*~ Song of Spite. There is an intolerance in pessimism that knows no bounds. In pessimism spite begins by fixing on a particular object of spite—someone one hardly knows, or someone one knows too well; a spite for this person or a spite for all of humanity; a spectacular or a banal spite; a spite for a noisy neighbor, a yapping dog, a battalion of strollers, the meandering idiot walking in front of you on their smart phone, large loud celebrations, traumatic injustices anywhere in the world regurgitated as media blitz, spite for the self-absorbed and overly performative people talking way too loud at the table next to you, technical difficulties and troubleshooting, the reduction of everything to branding, spite of the refusal to admit one’s own errors, of self-help books, of people who know absolutely everything and make sure to tell you, of all people, all living beings, all things, the world, the spiteful planet, the inanity of existence... Spite is the motor of pessimism because it is so egalitarian, so expansive, it runs amok, stumbling across intuitions that can only half-heartedly be called philosophical. Spite lacks the confidence and the clarity of hatred, but it also lacks the almost cordial judgment of dislike. For the pessimist, the smallest detail can be an indication of a metaphysical futility so vast and funereal that it eclipses pessimism itself—a spite that pessimism carefully places beyond the horizon of intelligibility, like the experience of dusk, or like the phrase, “it is raining jewels and daggers.” ~*~ Song of Sleep. A paraphrase of Schopenhauer: what death is for the organism, sleep is for the individual. Pessimists sleep not because they are depressed, but because for them sleep is a form of ascetic practice. Sleep is the askesis of pessimism. If, while sleeping, we have a bad dream, we abruptly wake up, and suddenly the horrors of the night vanish. There is no reason to think that the same does not happen with the bad dream we call “life.” ~*~ Song of Sorrow. Nietzsche, commenting on pessimism, once castigated Schopenhauer for taking things too lightly. He writes: ...Schopenhauer, though a pessimist, really —played the flute. Every day, after dinner: one should read his biography on that. And incidentally: a pessimist, one who denies God and the world but comes to a stop before morality—who affirms morality and plays the flute... what? Is that really—a pessimist? We know that Schopenhauer did possess a collection of instruments, and we also know that Nietzsche himself composed music. There is no reason to think that either of them would ever banish music from the Republic of philosophy. But Nietzsche’s jibes at Schopenhauer are as much about music as they are about pessimism. For the pessimist who says no to everything and yet finds comfort in music, the no-saying of pessimism can only be a weak way of saying yes—the weightiest statement undercut by the flightiest of replies. The least that Schopenhauer could’ve done is to play the bass. I’m not a big fan of the flute, or, for that matter, wind instruments generally. But what Nietzsche forgets is the role that the flute has historically played in Greek tragedy. In tragedy, the flute ( aulos ) is not an instrument of levity and joy, but of solitude and sorrow. The Greek aulos not only expresses the grief of tragic loss, but it does so in a way that renders weeping and singing inseparable from each other. The classicist Nicole Loraux calls this the mourning voice . Set apart from the more official civic rituals of funerary mourning, the mourning voice of Greek tragedy constantly threatens to dissolve song into wailing, music into moaning, and the voice into a primordial, disarticulate anti-music. The mourning voice delineates all the forms of suffering—tears, weeping, sobbing, wailing, moaning, and the convulsions of thought reduced to an elemental unintelligibility. In the collapsed space between the voice that speaks and the voice that sings, pessimism discovers its mourning voice. Pessimism: the failure of sound and sense, the disarticulation of phone and logos . Have we rescued Schopenhauer from Nietzsche? Probably not. Perhaps Schopenhauer played the flute to remind himself of the real function of the mourning voice—sorrow, sighs, and moaning rendered indistinguishable from music, the crumbling of the human into the unhuman. Failure par excellence of pessimism. ~*~ Song of Nothing. In Buddhist thought, the First Noble Truth of existence is encapsulated in the Pali term dukkha , conventionally translated as “suffering,” “sorrow,” or “misery.” The Buddhist teachings are clear, however, that this is an objective claim, and not simply one point of view among others. Existence is suffering and sorrow—and yet this is not, the teachings tell us, a pessimistic attitude. It is likely that Schopenhauer, reading the Buddhist texts available to him, recognized some filiation with the concept of dukkha . But dukkha is a multi-faceted term. There is, certainly, dukkha in the usual sense of the suffering, strife, and loss associated with living a life. But this is, in turn, dependent on the finitude and temporality of dukkha , existence as determined by impermanence and imperfection. And this ultimately points to the way in which both suffering and finitude are grounded by the paradoxical groundlessness of dukkha as a metaphysical principle—the insubstantiality and the emptiness of all that is. Beyond what is worse to me, beyond a world ordered for the worst, there is the emptiness of dukkha as an impersonal suffering... the tears of the cosmos. In this context, it is easy to see how Schopenhauer’s pessimism attempts to compress all the aspects of dukkha into a nothingness at the core of existence, a Willlessness coursing through the Will. Though one thing for certain is that with Schopenhauer we do not find the “ever-smiling” countenance of Buddhism—or do we? The texts of the Pali Canon also contain lists of the different types of happiness—including the happiness of renunciation and the strange happiness of detachment. But Buddhism considers even the different types of happiness as part of dukkha , in this final sense of nothingness or emptiness. Perhaps Schopenhauer understood Buddhism better than he is usually given credit for. Thus the experiment of Schopenhauer’s philosophy—the point at which a Western pessimus and an Eastern dukkha overlap or exchange glances. Empty sorrow, a lyricism of indifference. The result is a strange, and ultimately untenable, nocturnal form of Buddhism. ~*~ Cioran once called music a “physics of tears.” If this is true, then perhaps metaphysics is its commentary. Or its apology. ~*~ Pessimism would be more mystical were it not for its defeatism. Mysticism is much too proactive for the pessimist, and pessimism too impassive even for the mystic. At the same time, there is something enviable about mysticism—despite its sufferings. There is a sense in which pessimists are really failed mystics. ~*~ You, the Night, and the Music. In a suggestive passage, Schopenhauer once noted that, “music is the melody to which the world is the text." Given Schopenhauer’s view on life—that life is suffering, that human life is absurd, that the nothingness before my birth is equal to the nothingness after my death—given all this, one wonders what kind of music Schopenhauer had in mind when he described music as the melody to which the world is text—was it opera, a Requiem Mass, a madrigal, or perhaps a drinking song? Or something like Eine kleine Nachtmusik , a little night music for the twilight of thought, a sullen nocturne for the night-side of logic, an era of sad wings sung by a solitary banshee. Perhaps the music Schopenhauer had in mind is music eliminated to non-music. A whisper would suffice. Perhaps a sigh of fatigue or resignation, perhaps a moan of despair or sorrow. Perhaps a sound just articulate enough that it could be heard to dissipate. ~*~ Teach me to laugh through tears. ~*~ Pessimism always falls short of being philosophical. My back aches, my knees hurt, I couldn’t sleep last night, I’m stressed-out, and I think I’m finally coming down with something. Pessimism abjures all pretenses towards system—towards the purity of analysis and the dignity of critique. We didn’t really think we could figure it out, did we? It was just passing time, taking a piss, something to do, a bold gesture put forth in all its fragility, according to rules that we have agreed to forget that we made up in the first place. Every thought marked by a shadowy incomprehension that precedes it, and a futility that undermines it. That pessimism speaks, in whatever voice, is the singing testimony to this futility and this incomprehension—take a chance and step outside, lose some sleep and say you tried... ~*~ Is there a music of pessimism? And would such a music be audible? ~*~ The impact of music on a person compels them to put their experience into words. When this fails, the result is a faltering of thought and language that is itself a kind of music. Cioran writes: “Music is everything. God himself is nothing more than an acoustic hallucination.” ~*~ If a thinker like Schopenhauer has any redeeming qualities, it is that he identified the great lie of Western culture—the preference for existence over non-existence. As he notes: “If we knocked on the graves and asked the dead whether they would like to rise again, they would shake their heads.” In Western cultures it is commonly accepted that one celebrates birth and mourns death. But there must be a mistake here. Wouldn’t it make more sense to mourn birth and celebrate death? Strange though, because the mourning of birth would, presumably, last the entirety of that person’s life, so that mourning and living would the be same thing. ~*~ To the musical idea of the harmony of the universe corresponds the philosophical principle of sufficient reason. Like the music of mourning, pessimism gives voice to the inevitable breakdown of word and song. In this way, music is the overtone of thought. ~*~ The Patron Saints of Pessimism. The patron saints of pessimism watch over suffering. Laconic and sullen, the patron saints of pessimism never seem to do a good job at protecting, interceding, or advocating for those who suffer. Perhaps they need us more than we need them. Lest we forget, there do exist patron saints of philosophy, but their stories are not happy ones. There is, for instance, the fourth century Saint Catherine of Alexandria, or Catherine of the Wheel, named after the torture device used on her. A precocious fourteen year old scholar, Catherine was subject to continual persecution. After all forms of torture failed—including the “breaking wheel”—the emperor finally settled for her decapitation, a violent yet appropriate reminder of the protector of philosophers. There are also patron saints of music and musicians, but theirs too are sad stories. In the second century, Saint Cecilia was also subject to persecution and torture. As she knelt to receive the blade that would separate her head from her body, she ardently sang a song to God. It took three attempts before she was fully decapitated, all the while she continued, perhaps miraculously, to sing. Does pessimism not deserve its own patron saints, even if they are unworthy of martyrdom? But in our search, even the most ardent nay-sayers frequently lapse into brief moments of enthusiasm—Pascal’s love of solitude, Leopardi’s love of poetry, Schopenhauer’s love of music, Nietzsche’s love of Schopenhauer, and so on. Should one then focus on individual works of pessimism? We could include Kierkegaard’s trilogy of horror— Sickness Unto Death , The Concept of Dread , and Fear and Trembling —but all these are undermined by their fabricated and unreliable authors. Besides, how can one separate the pessimist from the optimist in works like Unamuno’s The Tragic Sense of Life , Shestov’s Postetas Clavium , or Edgar Saltus’ under-read The Philosophy of Disenchantment ? Even in cases where the entire corpus of an author is pessimistic, the project always seems incomplete—witness Cioran’s trajectory, from his first book, On the Heights of Despair , to the last unpublished notebooks of acrid and taut aphorisms. And this is to say nothing of literary pessimism, from Goethe’s sorrowful Werther, to Dostoevsky’s underground man, to Pessoa’s disquiet scribbler; Baudelaire’s spleen and ennui, the mystical Satanism of Huysmans and Strindberg, the hauntologies of Mário de Sá-Carniero, Izumi Kyoka, H.P. Lovecraft, grumpy old Beckett... even the great pessimist comedians. All that remains are singular, perhaps anomalous statements of pessimism, a litany of quotes and citations crammed into fortune cookies. Patron saints are traditionally named after a locale, either a place of birth or of a mystical experience. Perhaps the better approach is to focus on the places where pessimists were forced to live out their pessimism—Schopenhauer facing an empty Berlin lecture hall, Nietzsche mute and convalescent at the home of his sister, Wittgenstein the relinquished professor and solitary gardener, Cioran grappling with Alzheimer’s in his tiny writing alcove in the Latin Quarter. ~*~ There’s a ghost that grows inside of me, damaged in the making, and there’s a hunt sprung from necessity, elliptical and drowned. Where the moving quiet of our insomnia offers up each thought, there’s a luminous field of grey inertia, and obsidian dreams burnt all the way down. ~*~ If pessimism has any pedagogical value, it is that the failure of pessimism as a philosophy is inextricably tied to the failure of pessimism as voice. I read the following, from Shestov’s The Apotheosis of Groundlessness : When a person is young he writes because it seems to him he has discovered a new almighty truth which he must make haste to impart to forlorn humankind. Later, becoming more modest, he begins to doubt his truths: and then he tries to convince himself. A few more years go by, and he knows he was mistaken all round, so there is no need to convince himself. Nevertheless he continues to write, because he is not fit for any other work, and to be accounted a superfluous person is so horrible. (shrink)

En este estudio se analiza el cambio de clase de palabras en el mapudungun a través del procedimiento de derivación, desde la perspectiva tipológica de la formación de palabra (Aikhenvald, 2007). Las palabras, en la lengua mapuche, usan ciertos procesos morfológicos y sintácticos que posibilitan el cambio de clase de palabra, ya sea por la intervención de algún sufijo derivacional, por la propiedad polisémica de los mismos, o por el cambio de posición de la palabra respecto a una palabra principal. (...) Los procesos más productivos de formación de palabras suelen ser la composición y la derivación, no obstante, por razones de extensión, este artículo solo se concentra en la derivación y en el análisis de los sufijos -tu, -küle/-le, -meke, y -nge. This study analyzes word classes changes process in Mapudungun through derivation, from the typological perspective of word class formation (Aikhenvald, 2007). Words, in the Mapuche language, use certain morphological and syntactic processes that make possible word class changes, in either of three ways: the intervention of a derivational suffix, by the polysemic property of derivational suffixes, or by changing the position of the word with respect to a principal word. While the most productive processes of word formation often are composition and derivation, due to length reasons this article will focus on the derivation process and analysis of only the suffixes -tu, -küle/-le,-meke, and -nge. (shrink)

For his contribution to the general series of Harper Essays in Philosophy, Hilary Putnam selects only one of several philosophical problems in the interrelated fields of logic and/or mathematics that have interested him, viz. the nominalism-realism issue: Are the "abstract entities" spoken of in these sciences, such as classes, number, functions from various kinds of things to real numbers, things that "really exist" or not? He is concerned to present a detailed argument for his own "qualified realism" rather than (...) a survey of current opinions. He argues persuasively that while a nominalist would like to eliminate all talk of logical classes such as S, M and P in favor of such circumlocutions as "The following schema turns out to be true no matter what words or phrases of the appropriate kind one may substitute for the letters S, M and P," etc., such descriptions avoid references to classes only by replacing them with equally nonphysical entities such as "all possible words, strings of letters, formalized languages," etc., and that the notion of truth or validity itself cannot be applied to physical objects or material inscriptions, but to what sentences mean or say, and the things they say are not physical. He rejects Quine's distinction that first order statements or arguments such as "All crows are black; all back things absorb light, therefore," etc., are logical truths, whereas "For all classes S, M and P, if all S is M and all M is P, then all S is P," are mathematical. This runs counter, he says, to the whole logical tradition. The natural intention of the logician in setting down first-order schemata is to assert implicitly their validity and that itself is a second-order assertion. All logic, therefore, including quantification theory, involves references to classes. This also highlights the difficulty of distinguishing between logic and mathematics in terms of first and second order logic, for if only the former is stipulated to be the proper domain of logic, then we must accept the awkward consequence that validity and implication turn out to be notions that belong to mathematics rather than logic. Since the nominalistic position presents the same problems for mathematics as for logic, Putnam sees no point in trying to draw any sharp distinction between the two, which explains his initial broad interpretation of logic as including all of pure mathematics and also the title of the book. To avoid some of the classical objections to a realistic interpretation of sets, he points up the distinction between a predicative and impredicative conception of set. Whereas the latter speaks of all sets of individuals as a well-defined totality, the former defines "set" only for a particular language N or a hierarchic series of languages, N, N', N", etc. in which it is still nonsensical to speak of "all sets" without qualification, though one can speak of "all" up to any given level in the series. While some form of set theory is necessary for all the sciences, both formal and physical, one can get along with predicative set theory. Putnam's basic argument for realism then comes down to this. Quantification over mathematical entities such as things, real numbers and functions is indispensable for logic, mathematics and the physical sciences and this commits one to accept the existence of such entities. In the final stages of the argument he examines and rejects the alternative options to realism, namely that realistic locutions about such entities represent logically deviant forms of speech, or that mathematical truths are "true by pure convention" or that such "entities" are useful fictions. In the closing paragraphs he indicates two other philosophical problems in logic that merit extensive discussion, namely the problem of equivalent constructions which is relevant to the question of whether mathematics needs "foundations" and the problem of whether we may not have to revise logical principles as we have geometrical ones on the grounds that in some sense logic may have empirical foundations.--A. B. W. (shrink)

This paper aims to suggest a new approach to Plato’s theory of being in Republic V and Sophist based on the notion of difference and the being of a copy. To understand Plato’s ontology in these two dialogues we are going to suggest a theory we call Pollachos Esti; a name we took from Aristotle’s pollachos legetai both to remind the similarities of the two structures and to reach a consistent view of Plato’s ontology. Based on this theory, when Plato (...) says that something both is and is not, he is applying difference on being which is interpreted here as saying, borrowing Aristotle’s terminology, 'is is (esti) in different senses'. I hope this paper can show how Pollachos Esti can bring forth not only a new approach to Plato’s ontology in Sophist and Republic but also a different approach to being in general. -/- Keywords Plato; being; difference; image; pollachos esti; pollachos legetai 1. Being, Not-Being and Difference The three dialogues where the notion of "difference" attaches to the notion of being, namely Parmenides II, Sophist and Timaeus,and specifically the first two we try to discuss here. In these dialogues, Plato is going to achieve a new and revolutionary understanding of being which is not anymore based on the notion of "same" as it was before in Greek ontology. It was his discovery, I think, that the notion of being in the Greek ontology is attached to the notion of the "same" and it is because of this attachment that there have always been many problems understanding being especially after Parmenides. That being has always been relying on the "same" can be found out from the way most of the Presocratics understood it. It was based on such a relationship between being and "same" that a later Ionian, Heraclitus of Ephesus, rejected Being by rejecting its sameness: unable to be the same, being cannot be being anymore but becoming. Heraclitus’ criticism of his predecessors’ understanding of being was due to his discovery that what they call being is not the same but different in every moment. The relation of being and sameness reaches to its highest point in Parmenides. What Plato does in using the "difference" is nothing but the establishment of a creative relation between being and "difference". In this new relation, although he is in agreement with Heraclitus that being is not the same but different, he does not do it by use of becoming. He disagrees, on the other hand, with Parmenides that such a relation between being and difference leads to not being. At Parmenides 142b5-6 it is said that if One is, it is not possible for it to be without partaking (μετέχειν) of being (οὐσίας), which leads to the distinction of being and one: -/- So there would be also the being of the one (ἡ οὐσία του̑ ἑνὸς) which is not the same (ταὐτὸν) as the one. Otherwise, it wouldn’t be its being, nor the one would partake of it. (142b7-c1) -/- The fact that what is (ἔστι) signifies (σημαῖνον) is other (ἀλλο) than what One signifies (c4-5), is being taken as a reason for their distinction. The conclusion is that when we say 'one is', we speak of two different things, one partaking of the other (c5-7). Having repeated these arguments of the otherness of being and one at 143a-b, Parmenides says that the cause of this otherness can be neither Being nor One but "difference": -/- So if being is something different (ἕτερον) and one something different (ἕτερον), it is not by being one that the one is different from being nor by its being being that being is other than one, but they are different from each other (ἕτερα ἀλλήλων) by difference (τῷ ἑτερῳ) and otherness (ἄλλῳ). (143b3-6) -/- The fifth hypothesis, 'one is not' (160b5ff.) is also linked with the notion of difference. When we say about two things, largeness and smallness, that they are not, it is clear that we are talking about not being of different (ἕτερον) things (160c2-4). When it is said that something is not, besides the fact that there must be knowledge of that thing, we can say that it entails also its difference: 'difference in kind pertains to it in addition to knowledge' (160d8). Parmenides explains the reason as such: -/- For someone doesn’t speak of the difference in kind of the others when he says that the one is different from the others, but of that thing’s own difference in kind. (160e1-2) -/- Although the theory of being as "difference" is not fulfilled yet, an exact look at what occurs in Sophist can make us sure that this was the launching step for "difference" to get its deserved role in Plato’s ontology. The notion of the "difference" is not yet well-functioned in Parmenides because we can see that being is still attached to the same: -/- For that which is the same is being (ὄν γὰρ ἐστι τὸ ταὐτόν) (162d2-3). -/- The notion of difference in Sophist is the key element based on which a new understanding of being is presented and the problem of not being is somehow resolved. The friends of Forms, the Stranger says, are those who distinguish between being and becoming (248a7-8) and believe that we deal with the latter with our body and through perception while with the former, the real being (ὄντως οὐσίαν) with our soul and through reasoning (a10-11). Being is then bound with the "same" by adding: -/- You say that being always stays the same and in the same state (ἣν ἀεὶ κατὰ ταὐτὰ ὡσαύτως ἔχειν) but becoming varies from one time to another (δὲ ἄλλοτε ἄλλως). (248a12-13) -/- That the theory of the relation of being and capacity (247d8f., 248c4-5) matches more with becoming than with being (248c7-9) must be rejected because being is also the subject of knowledge which is kind of doing something (248d-e). It does, however, confirm that 'both that which changes and also change have to be admitted as existing things (ὄντα) (249b2-3). I believe that this is what Socrates would incline to do at Theaetetus 180e-181a, that is, putting a fight between two parties of Parmenidean being and Heraclitean becoming and then escaping. The solution is that becoming is itself a kind of being and we ought to accept what changes as being. This is what must be done by a philosopher, namely, to refuse both the claim that 'everything is at rest' and that 'being changes in every way' and beg, like a child, for both and say being (τὸὄν) is both the unchanging and that which changes (249c10-d4). This kind of begging for both is obviously under the attack of contradiction (249e-250b). For both and each of rest and change similarly are (250a11-12) but it cannot be said either that both of them change or both of them rest, being must be considered as a third thing both of the rest and change associate with (250b7-10). The conclusion is that 'being is not both change and rest but different (ἕτερον) from them instead' (c3-4). The notion of difference helps Plato to take being departed from both rest and change because it was their sophisticated relation with being that made the opposition of being and becoming. Plato is now trying to separate being from rest and, thus, from "same" by "difference". Such a crucial change is great enough to need a 'fearless' decision (256d5-6). The possibility of being of not being is resulted (d11-12) comes as the answer to the question 'so it’s clear that change is not being and also is being (ἡ κίνησις ὄντως οὐκ ὄν ἐστι καὶ ὄν) since it partakes in being?' (d8-9). It is then by the notion of difference that becoming is considered as that which both is and is not. This coincidence of being and not being about change is apparently similar to Socrates’ paradoxical statement at Republic 477a about what both is and is not. -/- Introduction The Republic 476-477 has always been a matter of controversy mainly about two interwoven points. The first problem is the meaning of being here; that whether what he has in mind is a veridical, existential or propositional sense of being. The second problem is his distinction between the objects of knowledge and opinion which seems to lead, some believe, to the Two Worlds (TW) theory. The crucial point in Republic is that what is considered between knowledge (ἐπιστήμης) and ignorance (α͗γνοιας), namely opinion, must have a different object that leads Socrates to draw the distinction of knowledge and opinion between their objects. The problem of understanding being in the fifth book of the Republic is that when it is said that the Form of F is F but a particular participating in F, both is and is not F, it sounds too bizarre and unacceptable. It cannot be imaginable how a thing can be existent and non-existent at the same time. At the first sight, the only solution seems to be the degrees of existence which is called by Annas (1981, 197) a 'childish fallacy' and a 'silly argument'. Kirwan (1974, 118) thinks that Republic V does not attribute 'any doctrine about existence' to Plato and Kahn (1966, 250) claims that the most fundamental value of einai when used alone (without predicate) is not "to exist" but "to be so", "to be the case" or "to be true". The problems of understanding being in Republic and Sophist besides the difficulties of the existential reading led scholars to the other senses of being, mostly related to the well-known Aristotelian distinctions between different senses of being. In the predicative reading, Annas, for example, refers this difference to the qualified and unqualified application. Whereas the Form of F is unqualifiedly F, a particular instance of F can be F only qualifiedly (1981, 221). Vlastos’ well-known substitution of 'degrees of reality' for 'degrees of being/existence' must be categorized as a predicative reading. Kahn thinks that the basic sense of being for Plato is 'something like propositional structure, involving both predication and truth claims, together with existence for the subject of predication' (2013, 96). Believing that the complete-incomplete distinction terminology is misleading about Plato, he thinks that semantic functions are only second-order uses of the verb and it is the predicative or incomplete function which is fundamental. Suggesting a veridical reading, Fine (2003, 70 ff) thinks that while both existential and predicative readings separate the objects of knowledge and belief, it is only her reading which does not force such separation of the objects and thus does not imply TW. Stokes (1998, 266) thinks that though Fine is right saying that Plato does not endorse TW in book V, she is wrong in rejecting existential in favor of the veridical reading. The reception of existential reading can be seen more obviously in Calvert who thinks, in agreement with Runciman, that 'it would be safer to say that Plato’s gradational ontology is probably not entirely free from degrees of existence' (1970, 46). At Sophist 254d-e Plato singles out five most important kinds (or Forms!?) in which the same (ταὐτὸν) and difference (θάτερον) are regarded besides being, rest and change. They are, therefore, neither the same nor the difference but share in both (b3). Being (τὸ ὄν) cannot be the same also because if they 'do not signify distinct things' both change and rest will have the same label when we say they are (255b11-c1). We have then four distinct kinds, being, change, rest and same, none of them is the other. The case of difference is more complicated. When the stranger wants to assess the relation of being and difference, he can say simply neither that they are distinct nor that they are not. He has to make an important distinction inside being to get able to draw the relation of being and difference: -/- But I think you'll admit that some of the things that are (τῶν ὄντων) are said (λέγεσθαι) by themselves (αὐτὰ καθ’ αὑτά) but some [are said] always referring to (πρὸς) other things (ἄλλα) (255b12-13) -/- The difference is always said referring to other things (τὸδέγ’ ἕτερον ἀεὶ πρὸς ἕτερον) (255d1). It pervades all kinds because each of them should be different from the others and is so due to the difference and not its own nature (253e3f.) After asserting that change is different from being and therefore both is and is not (256d), the difference is described as what makes all the other kinds not be, by making each different from being. Given that all of them are by being, this association of being and difference is the cause of their being and not-being at the same time, the issue that its version at RepublicV made all those controversies we discussed above: -/- So in the case of change and all the kinds, not being necessarily is (Ἔστιν ἄρα ἐξ ἀναγκης τὸ μὴ ὄν). Τhat’s because as applied to all of them, the nature of the difference (ἡ θατέρον φύσις) makes each of them not be by making it different from being. And we’re going to be right if we say that all of them are not in the same way. And conversely [we’re also going to be right if we say] that they are because they partake in being. (Sophist 256d11-e3) -/- Plato’s new construction of five distinct kinds and the role he gives to thedifference among them is aimed to resolve the old problem of understanding being which has always been annoying from the time of Heraclitus and Parmenides. Both the ontological status of becoming and that of not being were, in Plato’s mind, based on the absolute domination of the notion of the Same over being. Now, not only becoming is understandable as being but also not being which is not the contrary of being anymore but only different (ἕτερον) (257b3-4). Though I agree partly with Frede that the account of not being which is needed for false statements is more complicated than just saying, as Cropsey (1995, 101) says, that Plato is substituting 'X is not Y' with 'X is different from Y', I totally disagree with him that when we say X is not beautiful, Plato could not have thought that it is not a matter of its being different from beautiful because 'it would be different from beauty even if it were beautiful by participation in beauty' (1992, 411). Conversely, as we will discuss, it is exactly the relation of the beautiful thing, X, and the beautiful itself, in which X shares that is to be solved by the notion of not being as difference. Though it is beautiful because of sharing in beauty, X is not beautiful because it is different from beautiful itself. What the difference is to do is to show how something can both be and not be the same thing. The difference is what makes one thing both be and not be a certain other thing. This equips the difference with the ability to explain a certain thing’s not-being when it is. Thanks to the notion of difference, it is now possible to explain not only not being but also the simultaneous being and not being of a thing: 'What we call "not-beautiful" is the thing that ἕτερόν ἐστιν from nothing other than του̑ καλου̑ φύσεως' (257d10-11). The result is that not beautiful happens to be (συμβέβηκεν εἶναι) one single thing among kinds of beings (τι τῶν ὄντων τινὸς ἑνὸς γένους) and at the same time set over against one of the beings (πρός τι τῶν ὄντων αὖ πάλιν ἀντιτεθὲν) (257e2-4) and thus be something that happens to be not beautiful (εἶναί τις συμβαίνει τὸ μὴ καλόν); a being set over against being (ὄντος δὴ πρὸς ὄν ἀντίθεσις) (e6-7). Neither the beautiful is more a being (μα̑λλον ... ἐστι τῶν ὄντων) nor not beautiful less (e9-10) and thus both the contraries similarly are (ὁμοίως εἶναι) (258a1). This conclusion, it is emphasized again (a7-9), owes to θατέρου φύσις now turned out as being. Therefore, each of the many things that are of the nature of the difference and set over each other in being (τῆς τοῦ ὄντος πρὸς ἄλληλα ἀντικειμένων ἀντίθεσις) is being as being itself is being (αὐτοῦ τοῦὄν τοςοὐσία ἐστιν) and not less. They are different from, and not the contrary of, each other (a11-b3). This is exactly τὸμὴὄν, the subject of the inquiry (b6-7). Hence, not being has its own nature (b10) and is one εἶδοςamong the many things that are (b9-c3). Such far departing from Parmenides’ ontological principle is done on the basis of the nature of the difference. It was the discovery of such a notion that made the stranger brave enough to say that not being is each part of the nature of the difference that is set over against being (258d7-e3, cf. 260b7-8). That the relation of being and difference is difference is the key element of the new ontology. The difference is, only because of its sharing in being, but it is not that which it shares in but different from it (259a6-8). Not being is exactly based on this difference: ἕτερον δὲ τοῦ ὄντος ὄν ἔστι σαφέστατα ἐξ ἀνάγκης εἶναι μὴ ὄν (a8-b1). 2. Difference and the Being of a Copy We discussed above that the sense of being of particulars in Republic V made so many debates that whether being is there used in an existential sense or not. Particulars in Republic are regarded as images in the allegories of Line and Cave. The being of an image/copy makes, thus, the same problem. Plato’s analogy of original -copy for the relation of Forms and their particulars in Republic has obviously a different attitude to being. The main question is that what is the ontological status of a copy in respect of its original? Are there two kinds of being, 'real being' versus 'being' as Ketchum says (1980, 140) or only one kind? What is the difference of being in an original and its copy? Is it a matter of degrees of being or reality as some commentators have suggested? Is it a matter of being relational? By reducing the ontological issue to an epistemological one, Vlastos’ suggestion of degrees of reality in an article with the same name does neither, I think, pay attention to the problem nor resolve it. He agrees that Plato never speaks of "degrees" or "grades" of reality (1998, 219). What allows him to entitle it as such are some of Plato’s words in Republic as well as Plato’s words in some other dialogues (1998, 219). When Plato states that the Forms only can completely, purely or perfectly be real he means, Vlastos says, they are cognitively reliable (1998, 229); an obvious reduction of the issue to an epistemological one. He thinks that when in Republic we are being said that a particular’s being F is less pure than its Form, it is because it is not exclusively F, but it is and is not F and this being adulterated by contrary characters is the reason of our confused and uncertain understanding of it (1998, 222). Ketchum rightly criticizes Vlastos’ doctrine in its disparting from ontology thinking that 'to understand Plato’s talk of being as talk of reality is to obscure the close relation that exists between "being" and the verb "to be"' (1980, 213). He thinks, therefore, that οὐσία must be understοοd as being rather than reality, τὸὄν as "that which is" and not "that which is real" and … (ibid). His conclusion is that degrees of reality cannot interpret Plato correctly and we must accept degrees of being. Allen believes that a 'purely epistemic' reading of the passage in Republic is patently at odds with Plato’s text (1961, 325). He thinks that not only degrees of reality but also degrees of reality must be maintained (1998, 67). What Cooper suggests gets close to this paper’s solution: -/- Plato does not I think wish to suggest that existence is a matter of degree in the way in which being pleasant or painful is a matter of degree. Rather there are different grades of ontological status. (1986, 241) -/- A more ontological solution for the problem of understanding the being of a copy and its relation with the being of its original is suggested by the theory of copy as a relational entity. Based on this interpretation, 'the very being of a reflection is relational, wholly dependent upon what is other than itself: the original…' (Allen, 1998, 62). As relational entities, particulars have no independent ontological status; they are purely relational entities which derive their whole character and existence from Forms (ibid, 67). Although these relational entities are and have a kind of existence, we must also say that 'they do not have existence in the way that Forms, things which are fully real, do' (ibid). Allen (1961, 331) extends his theory to Phaedo where it is said that particulars are deficient (74d5-7, 75a2-3, 75b4-8), 'wish' to be like (74d10) or desire to be of its nature (75a2); an extension that, like F.C. white (1977, 200), I cannot admit. He correctly states that Plato did not start out with a doctrine of particulars as images and semblances but come to such a view after Phaedo, or perhaps after Republic V (1977, 202). Though we may not agree with him about Republic V, if we have to consider its last pages also, we must agree with him that not only the ontology of Phaedo but also that of Republic II-V (except the last pages of the latter book) are somehow different from (but at the same time appealing to) the ontology of original-copy which should exclusively assign to Sophist, Timaeus and RepublicVI-VII besides the last pages of book V. The answer to the problem of Plato’s sense of being in RepublicV can be reached only if we read Republic V based on and as following Sophist. We can find out his meaning of that which both is and is not only by the ontological status he assigns to a copy in Sophist. The kind of being of a copy in Sophist reveals as Plato’s key for the lock of the problem of not being. Let’s see how the ontological status of a copy is the critical point of Plato’s ontology. In the earlier pages of Sophist, we are still in the same situation about not being. To think that that which is not is is called a rash assumption (237a3-4) and Parmenides’ principle of the impossibility of being of not being is still at work (a8-9). At 237c1-4, the problem of "not being" is noticed in a new way which shows some kinds of a more realistic position to the problem of not being. Nevertheless, not being is still unthinkable, unsayable, unutterable and unformulable in speech (238c10). Soon after mentioning that it is difficult even to refuse not being (238d), the solution to the problem appears: the being of a copy (εἴδωλον) (239d). A copy is, says Theaetetus, something that is made referring to a true thing (πρὸς τἀληθινὸν) but still is 'another such thing (ἕτεροντοιου̑τον)' (240a8). Nevertheless, this 'another such thing' cannot be another such real or true thing. In answer to the question of the Stranger that if this 'another such thing' is the true thing (240a9), Theaetetus answers: οὐδαμῶς ἀληθινόν γε, ἀλλ’ ἐοικὸςμὲν (240b2). A copy’s being 'another such thing' does not mean another true thing but only a resemblance of it. Not only is not a copy another true thing besides the original, but it is the opposite of the true thing (b5) because only its original is the thing genuinely and being a copy is being the thing only untruly. The word ἐοικὸς is opposed to ὄντως ὄν in the next line (240b7): 'So you are saying that that which is like (ἐοικὸς) is not really that which is (οὐκ ὄντως [οὐκ] ὄν)'. But still a copy 'is in a way (ἔστι γε μήν πως)' (b9). While it is not really what it is its resemblance, it has its own being and reality because it really is a likeness (εἰκων ὄντως) (b11). The Stranger asks: -/- So it is not really what is (οὐκ ὄν ἄρα [οὐκ] ὄντως ἐστὶν) but it really is what we call a likeness (ὄντως ἣν λέγομεν εἰκόνα)? (b12-13) -/- This is Plato’s innovative ontological solution to the problem of not being. Theaetetus’ answer confirms this: 'Maybe that which is not is woven together with that which is' (c1-2). Therefore, a copy neither is what really is nor is not-being but only is what in a way is. Thanks to the ontological status of a copy, the third status intermediate between being and not being is brought forth. The essence of an image, in Kohnke’s words, does not consist 'solely in the negation of what is genuine and has real being' because otherwise 'it would be an ὄντως οὐκ ὄν,essentially and really a not being' (1957, 37). The characteristics of a copy can be summed up as folows: i) A copy is a copy by referring to a true thing (πρὸς τἀληθινὸν). ii) A copy is different from that of which it is a copy (ἕτερον). iii) A copy is not itself a true thing (ἀληθινόν) as that of which it is a copy but only that which is like it (ἐοικὸς). iv) It is not really that which really is (ὄντως ὄν) but only really a likeness (εἰκων ὄντως). The conclusion is that: v) A copy in a way (πως) is that means it both is and in not, the product of interweaving being with not being. This leads to the refutation of father Parmenides’ principle, accepting that 'that which is not somehow is (τό τε μὴ ὄν ὡς ἔστι)' and 'that which is, somehow is not (τό ὄν ὡς οὐκ ἔστι) (241d5-7). Besides copies and likenesses (εἰκόνων), we have also imitations (μιμημάτων) and appearances (φαντασμάτων) as the subjects of this new kind of being and thus false belief (241e3). In Timaeus, the world of becoming which cannot correctly be called and thus we have to call it "what is such" (τὸ τοιου̑τον) (49e5) or "what is altogether such" (τὸ διἀ παντὸς τοιου̑τον) (e6-7), consists solely of imitations (μιμημάτα) (50c5) which are identifiable only by the things that they are their imitations. The word τοιου̑τον which had been used to determine the situation of a copy in respect of its original, now becomes the definition of the world of becoming in which everything is an image of another thing, a Being, that stays always the same and is different and separated from its image. Cherniss, in my view rightly, draws attention to the very important point about the ontological status of an image that can at the same time be considered a criticism of the relational theory. What we are being said in Timaeus, he thinks,cannot be explained by saying that an image is not self-related and making its being relational. What is crucial about an image is that it 'stands for something, refers to something, means something and this meaning the image has not independently as its own but only in reference to something else apart from it' (1998, 296). This function finds its best explanation in the theory we are to suggest in the following. 3. πολλαχῶς ἔστι The best way to understand the ontological status of an image in Plato is to see first how his most clever pupil, Aristotle, resolved the same problem that Plato brought his theory of image for its sake. Aristotle’s theory of pollachos legetai is a brilliant and, at the same time, deviated version of Plato’s theory that is able, however, to help us read Plato in a better way. We discuss Aristotle’s theory to reach to a full understanding of Plato’s theory because it is, firstly, constructed in Aristotle in a more clear way and, secondly, it can also be taken as an evidence that our reading of Plato is legitimate. The phrase τὸ ὄν πολλαχῶς λέγεται, a so much repeated phrase in Aristotle’s works, is his resolution for some of the ontological problems of his predecessors all treating being as if it has only one sense. Aristotle is right in his criticism of the philosophical tradition specially Heraclitus, Parmenides and Plato since all did presuppose only one sense for being and his theory is, thus, a creative and revolutionary solution for many problems that all the past philosophers were stuck in. But it is at the same time somehow a borrowed theory. As we will discuss, both the structure of the doctrine and the problems it tries to resolve are the same as Plato’s doctrine (and even is comparable in its phraseology) though it is in Aristotle, as can be expected, a more clear and better structured doctrine. 1) Associated with the theory of pros hen and the theory of substance, the theory of several senses of being provides a structure which, I insist, is the best guide to understand Plato’s theory of Being in Sophist, Timeaus and Republic. a) Although the theory of pollachos legetai is not necessarily based on the theory of pros hen, they become tightly interdependent about being: -/- Being is said in many ways/senses (τὸ δὲ ὄν λέγεται μὲν πολλαχῶς) but by reference to one (πρὸς ἕν) [way/sense] and one kind of nature (μίαν τινὰ φύσιν). (Metaphysics 1003a33-34) -/- The doctrine of pros hen which is Aristotle’s initiative third alternative besides the homonymous and synonymous application of words, is primarily a linguistic theory that tries to provide a new theory to explain the different implementations of the same word. The pros hen implementation of being is to provide an alternative for the theory of the synonymous (in Plato: homonymous) implementation of being which says being is said in one sense (kath hen) (1060b 32-33). That both the pros hen and the kath hen implementation of a word has one thing (hen) as what is common, makes them in opposition to the homonymous implementation which does not consider anything in common. Whereas both pros hen and kath hen assume a common nature, with which all the implementations of the word have some kind of relation, their difference is that while kath hen takes all the implementations of the word as the same with the common nature, pros hen makes them different. Substance is called πρῶτον ὄν because it is said to be primarily: -/- For as is (τὸ ἔστιν) is predicated of all things, not however in the same way (οὐχ ὁμοίως) but of one sort of thing primarily and of others in a secondary way. So too τὸτί ἐστιν belongs simply (ἁπλῶς) to substance but in a limited sense (πῶς) to the others [other categories] (1030a21-23). -/- The word ἁπλῶς standing against κατὰ συμβεβηκός tries to make substance different from the accidents. When we are being said that τὸ ὄν πολλαχῶς λέγεται, it means that only the substance that is simply (ἁπλῶς) the ἕν, the common nature, τὸὄν. When we use the word 'being' about a substance, the being is said differently from when we use 'being' about an accident. The distinction between the substance and the other categories is a distinction between what simply is said to be and what only with reference to (pros) the substance is said to be. The doctrine of pros hen, changing kath hen to pros hen in respect of to on, makes a distinction that wants to show that while there is a kind of implementing the word being that is simply being, there is another kind which is called being only by reference to that which is simply being. In the doctrine of pros hen it is not so that all the things that are said to be are only by reference to a common one thing, but that while one thing is called being because it is that thing itself, the other things are called so without being that thing itself but only by referring to it. At the very beginning of book Γ, it is said that: -/- Being is said in many senses but all refer to one arche. Some things are said to be because they are substances, others because they are affections of substances, others because they are a process towards substances or destructions or privations or qualities of substances … (1003b5-9, cf. 1028a18-20) -/- Substance is what really is said to be and all other things that are said to be are said only in favor of it. This difference of substance from all other senses of being is what is, I believe, primarily aimed in Aristotle’s interrelated theories of pollachos legetai,pros hen and the theory of substance. b) The difference of the implementation of being in the case of substance and the accidents goes so deep that while substance is considered as the real being, the accidents are almost not being. An accident is a mere name (Metaphysics 1026b13-14) and is obviously akin to not being (b21). Aristotle adds that Plato was 'in a sense not wrong' saying that sophists deal with not being (τὸ μὴ ὄν) because the arguments of sophists are, above all, about the accidental (1026b13-16). At the beginning of book , he says about quality and quantity (which look to be more of a being than other accidents) that they are not existent (οὐδ̕ ὄντα ὡς εἰπεῖν) in an unqualified sense (ἁπλῶς) (1069a21-22). The two above-mentioned points, Aristotle’s (a) interwoven theories of pollachos legetai, pros hen and the theory of substance and (b) taking accidents almost as not being, comparedwith substance, brings forth a structure that I shall call Pollachos Legetai (with capital first letters). What is of the highest importance in this structure for me is the difference of substance from accidents and the kind of relation which is settled between them. There is a substance that without any qualification is said to be and the accidents that are said to be only by reference (pros) to it. Adding Aristotle’s point about accidents that they are nearly not being to this relation and difference, we can obviously see how much this structure is close to Plato’s original-copy ontology. We spoke of the relation of being and difference in Plato’s model and the way Plato construes the being of a copy. A copy is a copy only by referring to (pros) a model; it is different from (ἕτερον) that of which it is a copy; it is not itself a true thing as its model and not really that which is (ὄντως ὄν) but only is in a way (πῶς). If we behold the difference of substance and accident in the context of the theory of pollachos legetai and pros hen, we can observe its fundamental similarity with Plato’s original-copy theory in its structure. Allen draws attention to the fact that the relation between Forms and particulars in Plato’s original-copy model is 'something intermediate between univocity and full equivocity' (1998, 70, n. 24) and the same as what Aristotle calls it pros hen (ibid). What made us compare the two structures was not, of course, the complete similarity of two structures (we have to agree with many possible differences of the two theories) but exactly the specific relation between an original and its copy on the one hand, and a substance and its accident on the other hand. As substance and accident do not share a common character and the substance -accident model hints that they stand in a certain relation, there is no common character between the original and copy in Plato’s model as well. Furthermore, their similarity is not confined to their structure only; they are also aimed to solve the same problem. The central point of the theory is that all the predecessors took being in one sense and this was their weakness point. Besides the mentioned above passages about the relation of pollachos legetai and presocratics’, as well as Plato’s, ontology, the relation of the theory with the problem of not being is clear in several passages. In Metaphysics, it is said: 'Being is then said in many senses… It is for this reason that we say even of not being that it is not being' (1003b5-10). Discussing the accidental sense of being, Aristotle points that it is in the accidental way that we say, for example, that not-white is because that of which it is an accident is (1017a18-19, cf. 1069a22-24). We mentioned that he thought Plato was right saying that sophistic deals with not being because sophistic deals with accidental, which is somehow not being (1026b14-16). Plato turned sophistic not-being to what both is and is not and Aristotle to what accidentally is said to be. What helps Aristotle to resolve the problem of not being is his distinction between ἁπλῶς and κατὰ σθμβεβηκός. Aristotle’s "qua" (ᾕ) which is directly linked with his distinction between καθ’ αὑτο λέγεται and κατὰ συμβεβηκός λέγεται, is used to resolve the old problem of coming to be out of not being (Physics 191b4-10). He strictly asserts that his predecessors could not solve the problem because they failed to observe the distinction of "qua itself" from "qua another thing" (b10-13). He then continues: -/- We ourselves are in agreement with them in holding that nothing can be said simply (ἁπλως) to come from not being (μὴὄντος). But nevertheless we maintain that a thing may come to be from not being in an accidental way (κατὰ συμβεβηκός). For from privation which ὅ ἐστι καθ’ αὑτο μὴ ὄν, nothing can become. (Phy. 191b13-16, cf. b19-25) . (shrink)

Regarding the relation of Plato’s early and middle period dialogues, scholars have been divided to two opposing groups: unitarists and developmentalists. While developmentalists try to prove that there are some noticeable and even fundamental differences between Plato’s early and middle period dialogues, the unitarists assert that there is no essential difference in there. The main goal of this article is to suggest that some of Plato’s ontological as well as epistemological principles change, both radically and fundamentally, between the early and (...) middle period dialogues. Though this is a kind of strengthening the developmentalistic approach corresponding the relation of the early and middle period dialogues, based on the fact that what is to be proved here is a essential development in Plato’ ontology and his epistemology, by expanding the grounds of development to the ontological and epistemological principles, it hints to a more profound development. The fact that the bipolar and split knowledge and being of the early period dialogues give way to the tripartite and bound knowledge and benig of the middle period dialogues indicates the development of the notions of being and knowledge in Plato’s philosophy before the dialogues of the middle period. -/- Keywords Plato; early dialogues; middle dialogues; being; knowledge; development -/- Introduction The differences between two groups of the early and middle period dialogues have always been a matter of dispute. Whereas the developmentalists like Vlastos, Silverman (2002), Teloh (1981), Dancy (2004) and Rickless (2007) think that from the early to the middle dialogues Plato’s philosophy changes, at least in some essential points, the unitarists like Kahn, Cherniss and Shorey believe that there happens no development and the differences must be taken as natural, ignorable and even pedagogic. In his well-known article, Socrates contra Socrates in PLATO, Vlastos lists ten theses of difference between two groups of dialogues. The first group which includes Plato’s early dialogues he divides to 'elenctic' (Apology, Charmides, Crito, Euthyphro, Gorgias, Hippias Minor, Ion, Laches, Protagoras and Republic I) and 'transitional' (Euthydemus, Hippias Major, Lysis, Menexenus and Meno) dialogues. These transitional come after all the elenctic dialogues and before all the dialogues of the second group which compose Plato’s middle period dialogues, including (with Vlastos' chronological order) Cratylus, Phaedo, Symposium, Republic II-X, Phaedrus, Parmenides and Theaetetus (1991, 46-49). Vlastos asserts strictly that his list of differences are 'so diverse in content and method that they contrast as sharply with one another as with any third philosophy you care to mention, beginning with Aristotole’s' (ibid, 46). Vlastos’ list of differences between two Socrateses is considered a view breaking sharply between the early and the middle dialogues. Besides all ten differences between the two Socrateses in Vlastos’ list that can be supportive for our doctrine here, we intend to focus on some ontological as well as epistemological distinctions that have not completely been discussed hitherto. Contrary to the developmentalist theory of Vlastos, unitarian theory of Charles Kahn wishes to eliminate any substantial difference between the early and the middle dialogues. He distinguishes seven 'pre-middle' or 'threshold' dialogues including Laches, Charmides, Euthyphro, Protagoras, Meno, Lysis and Euthydemus from the other Socratic dialogues which he calls 'earliest group' (1996, 41). The threshold dialogues, Kahn thinks, 'embarke upon a sustained project' that is to reach to its climax in the middle period dialogues, namely Phaedo, Symposium and Republic. Believing in that there is no 'fundamental shift'between the early and middle dialogues (ibid, 40), Kahn thinks the Socratic dialogues are just the 'first stage' with a 'deliberate silence' towards the theories of later periods (ibid, 339). One of the reasons of the surprising fact that Plato gives no hint of the metaphysics and epistemology of the Forms in the early dialogues, he thinks, is the pedagogical advantages of aporia. He thinks that Plato 'obscurely', and mostly because of education, hinted to some doctrines and conceptions in his early dialogues and with the aim of clarifying them only in the later ones (ibid, 66). The seven threshold dialogues, Kahn asserts, 'had been designed from the first' to prepare the pupils and readers for the views expounded in the middle period dialogues (ibid, 59-60). To show that the differences of the two Socrateses of the early and middle period dialogue are in their onto-epistemological grounds and thence cannot be explained by a unitaristic view, we try to draw the ontological and epistemological principles of the early dialogues in the first part below in order to show, in the second part, that those principles have been developed in the middle period dialogues. -/- A. The Onto-Epistemologic Principles of the Early Dialogues Socratic dialogues are paradoxical about knowledge because while being knowledge-oriented always searching for knowledge, they deny it and even never discuss it directly. Three elements of Socrates’ way of searching Knowledge throughout the early dialogues, i.e. Socratic 'what is X?' question, his disavowal of knowledge and his elenctic method combined together produce something like a circle which works, more or less, in the same way in these dialogues. Though this circle is an embaressing inquiry always resulting in ignorance instead of knowledge, its motivation is surprisingly Socrates’ passionate enthusiasm for knowledge, an intensive love of wisdom. The starting point of this circle is Socrates’ confession of having no knowledge which might be explicitly asserted or presupposed, maybe because it was one of the famous characteristics of Socrates; a confession always paradoxically accompanied with his intense longing for knowledge (e.g., Gorgias 505e4-5). Every time Socrates encounters with someone who thinks he knows something (οἴεταί τι εἰδέναι) (Apology 21d5) and tries to examine him. This examination seems to be the simplest one asking just what it is that he knows. Socrates’ elenchus, therefore, is always connected with 'what is X?' (τίς ποτέ ἐστιν) question, a question that most of the early dialogues of Plato are concerned with; 'what is courage?' in the Laches, 'what is piety?' in Euthydemus, 'what is temperance?' in Charmides and 'what is beauty?' in Hippias Major. This question we call here 'Socratic question' and probably is the very question the historical Socrates used to employ, is tightly interrelated with both his disavowal and his elenchus. He disclaims knowledge because he cannot find the answer to the question himself and he rejects others’ since they cannot offer the correct answer too. Every interlocutor can claim he knows X, if and only if he can answer the Socratic question. Otherwise, he is more of an ignorant than of a knower of τί ποτέ ἐστι X. Knowing the answer to this question is, thus, knowledge’s criterion for Socrates. Having found out that he cannot answer what it is which he would claim to know, the interlocutor comes to the point Socrates was there at the beginning. The least advantage of this circle is that he becomes as wise as Socrates does about the subject, becoming aware that he does not know it. At the end of the circle they are both still at the beginning, not knowing what X is. So let us first take a glance at these three elements. Socratic disavowal of knowledge is strictly asserted in some passages. At Apology 21b4-5, Socrates says: -/- I do not know of myself being wise at all (οὔτε μέγα οὔτε σμικρὸν σύνοιδα ἐμαυτῷ σοφὸς ὤν) -/- Moreover, at 21d4-6: -/- None of us knows anything worthwhile (καλὸν κἀγαθὸν εἰδέναι) …. I do not know (οἶδα) neither do I think I know. -/- In Charmides Socrates speaks about a fear about his probable mistake of thinking that he knows (εἰδέναι) something when he does not (166d1-2). The somehow generalization of this disavowal can be seen in Gorgias. After calling his disavowal 'an account that is always the same' (509a4-5), Socrates continues (a5-7): -/- I say that I do not know (οἶδα) how these things are, but no one I have ever met, like now, who can say anything else without being absurd. -/- At the end of Hippias Major (304d7-8), Socrates affirms his disavowal of knowledge of 'what is X?' this time about the fine: -/- I do not know (οἶδα) what that is itself (αὐτὸ τοῦτο ὅτι ποτέ ἐστιν). Some other passages, however, made a number of scholars dubious about Socrates’ disavowal. Vlastos mentions Apology 29b6-7 as an evidence : 'that to do wrong and to disobey one’s master, both god and men, I know (οἶδα) to be evil and shameful'. He thinks that if we give this single text 'its full weight' it can suffice to show that Socrates does claim knowledge of a moral truth (1985, 7). Vlastos’ claim is not admittable since it would be too strange, I think, for a man like Socrates to violate his disavowal claim just after emphasizing it. We can see his claim just before the already mentioned passage: -/- And surely it is the most blameworthy ignorance to believe that one knows what one does not know. It is perhaps on this point and in this respect, gentlemen, that I differ from the majority of men and if I were to claim that I am wiser than anyone in anything it world be in this, that, as I have no adequate knowledge (οὐκ εἰδὼς ἱκανῶς) of things in the underworld, so I do not think I have (οὐκ εἰδέναι) (Apology 29b1-6) Vlastos tries to solve what he calls the 'paradox' of Socrates’ disavowal of knowledge distinguishing the 'certain' knowledge from 'elenctic' knowledge (1985, 11) and thinking that when Socrates avows knowledge, we must perceive it as an elenctic knowledge, a knowledge its content 'must be propositions he thinks elenctically justifiable' (ibid, 18). Irwin’s solution is the distinction of knowledge and belief. He approves that Socrates does not 'explicitly' make such a distinction, but still thinks that Socrates’ 'test for knowledge would make it reasonable for him to recognize true belief without knowledge, and his own claims are easily understood if they are claims to true belief alone' (1977, 40). While I agree with Vlastos up to a point, I strongly disagree with Irwin about the early dialogues. As I will try to show below, we are not permitted to consider any kind of distinction within knowledge in Socratic dialogues because only one category of knowledge is alluded to there and the distinction of knowledge and belief thoroughly belongs to the second Sorcates. Although no kind of distinction can be admittable here, I think Vlastos’ distinction can be accepted only if we regard it as a distinction between knowledge, which is unique and without any, even incomparable, rival, and a semi-idiomatic and ordinary one that is a necessary requirement for any argument, and thus, unavoidable even for someone who does not claim any kind of knowledge. An apparent evidence of this is Gorgias 505e6-506a4: -/- I go through the discussion as I think it is (ὡς ἄν μοι δοκῇ ἔχειν), if any of you do not agree with admissions I am making to myself, you must object and refute me. For I do not say what I say as I know (οὐδὲ γάρ τοι ἔγωγε εἰδὼς λέγω ἃ λέγω) but as searching jointly with you (ζητῶ κοινῇ μεθ᾽ ὑμῶν). -/- The minimal degree of knowledge everyone must have to take part in an argument, conduct it and use the phrase "I know" when it is necessary is what Socrates cannot deny. We can call it elenctic knowledge only if we agree that it is not the kind of knowledge that Socrates has always been searching, the one that can be accepted as the answer of Socratic 'what is X?' question. His disavowal of knowledge is applied only to the knowledge which can truly be the answer of Socratic question and pass the elenctic exam; a knowledge that, I believe, is never claimed by first Socrates. Socrates conducts his method of examining his interlocutors’ knowledge, our second element here, by almost the same method repeated in Socratic dialogues. That whether we are allowed to regard all the examinations of Socrates in the early dialogues as based on the same or not has been a matter of dispute. Vlastos himself (1994, 31) distinguished Euthydemas, Lysis, Menexenns and Hippias Major from the other Socratic dialogues because he thinks Socrates has lost his faith to elenchus in there. Irwin (1977, 38) distinguishes Apology and Crito where Socrates’ own convictions is present. Contrary to some scholars like Benson (2002, 107) who take elenchus in all the Socratic dialogues as a unique method, Michelle Carpenter and Ronald M. Polansky (2002, 89-100) argue pro the variety of methods of elenchus. Thomas C. Brickhouse and Nicholas D. Smith (2002, 145-160) even reject such a thing as Socratic elenchus which can gather all of the Socrates’ various arguments under such a heading. There can be no solution for the problem of elenchus, they think, is due to 'the simple reason that there is no such thing as 'the Socratic elenchos"'(p.147). Though we consider elenchus a somehow determined process and a part of Socratic circle in the early dialogues, all we assume is that whatever differences it might have in different dialogues, it has the same onto-epistemological principles and, thus, we are not going to take it necessarily as a unique method. This method sets out to prove that the interlocutors are as ignorant as Socrates himself is. That whether elenchus is constructive, capable of establishing doctrines as Vlastos (1994) or Brickhouse and Smith (1994, 20-21) believe or not is another issue to which this paper is not to claim anything. What is crucial for our discussion here is that elenchus does not reach to the very knowledge Socrates is looking for. This is strictly against Irwin who thinks that not only elenchus leads to positive results, 'it should even yield knowledge to match Socrates’ conditions'(1977, 68, cf. 48). He does not explain where and how they really yield to that kind of knowledge. He explains his elenctic method in his apology in the court (Apology 21-22), that how he used to examine wise men, politicians, poets and all those who had the highest reputation for their knowledge and every time found that they have no knowledge. If we accept, as I strongly do, that Socrates’ disavowal of his knowledge is not irony, it might seem more reasonable to agree that the process that has that disavowal as its first step cannot be irony as well. The key of the circle which can explain why Socrates disclaims knowledge and how he can reject others’ claim of having any kind of knowledge lies in the third element, Socratic question. In Hippias Major (287c1-2), Socrates asks: 'Is it not by Justice that just people are Just? (ἆρ᾽ οὐ δικαιοσύνῃ δίκαιοί εἰσιν οἱ δίκαιοι). He insists at 294b1 that they were searching for that by which (ᾧ) all beautiful things are beautiful (cf. b4-5, 8). At Euthyphro 6d10-11 it is said that the Socratic question is waiting for 'the form itself (αὐτὸ τὸ εἶδος) by which (ᾧ) all the pious actions are pious; and at 6d11-e1: -/- Through one form (που μιᾷ ἰδέᾳ) impious actions are impious and pious actions pious. -/- Since the X itself is that by which X is X, knowing 'X itself' is the only way of knowing X. It is probably because of this that Socrates makes the distinction between the ousia as a right answer to the question and effect as a wrong one: -/- I am afraid, Euthyphro, that when you were asked what piety is (τὸ ὅσιον ὅτι ποτ᾽ ἐστίν) you did not wish to make clear its nature itself (οὐσίαν … αὐτοῦ) to me, but you said some effect (πάθος) about it. (Euthp. 11a6-9) -/- 1. Knowledge of what X is Now it is time to look for the onto-epistemological principles of Socratic circle and its three elements. It cannot reasonably be expected from the first Socrates to present us explicitly and clearly formulated principles of his onto-epistemology when such explications cannot be found even in the second Socrates who has some obviously positive theoris. Since there must be some principles underlying this first systematic inqury of knowledge, we must seek to them and be satisfied with elicitation of the first Socratas’ principle. What will be drawn out as his principles cannot and must not, thus, be taken as very fix and dogmatic principles. Some very slightest principles and grounds suffice for our purposes here. The first principle that is the prima facie significance of the Socratic question and his implementation of all those elenctic arguments I call the principle of 'Knowledge of What X is' (KWX): -/- KWX To know X, it is required to know what X is. -/- Aristotle (Metaphysics 1078b23-25, 27-29, 987b4-8) takes Plato’s τί ἐστι question as seeking the definition of a thing that is the same as historical Socrates’ search but applying to a different field. That Plato’s 'what is X?' question was a search for definition became the prevailed understanding of this question up to now. I am going neither to discuss the answer of Socratic question nor to challenge taking it as definition. What I am to insist is that knowledge is attached firmly to the answer of the question: Knowledge of X is not anything but the knowledge of what X is. It entails, certainly, the priority of this knowledge to any other kind of knowledge about X but it also has something more fundamental about the relation of knowledge and Socratic question. Socrates’ exclusive focus on the answer of his question can authorize the consideration of such an essential role for KWX in his epistemolgoy. The total rejection of his interlocutors’ knowledge when they are unable to answer the question can be regarded as a strong evidence for it. Socrates’ elenctic method and his rejection of others’ knowledge in the early dialogues, which all end aporetically with no one accepted as knower and nothing as knowledge, prevent us from finding any positive evidence for this. We have to be content, therefore, of negative evidences which, I think, can be found wherever Socrates rejects his interlocutors’ knowledge when they are not able to give an acceptable answer to his 'what is X?' question. 2. Bipolar Epistemology Socrates’ rejection of his interlocutors’ knowledge has another epistemological principle as its basis. Let me call this principle Bipolar Epistemology' (BE): BE There is no third way besides knowledge and Ignorance. -/- BE says that about every object of knowledge there are only two subjective statuses: knowledge and Ignorance. Socrates’ disavowal, however, says nothing but that he is ignorant of knowledge of X because he does not know what X is. This means that BE is presupposed here. Socrates’ elenchus and his rejection of interlocutors’ having any kind of knowledge are the necessary results of the fact that he does not let any third way besides knowledge and ignorance. The first Socrates never let anyone partly know X or have a true opinion about it, as he would not let anyone know anything about X when he did not know what X is. -/- 3. Bipolar Ontology The principle of BE in first Socrates’ epistemology is parallel to another principle in his ontology. Plato’s bipolar distinction between being and not being is as strict and perfect as his distinction between knowledge and ignorance. This principle I shall call the principle of 'Bipolar Ontology' (BO): BO Being is and not being is not. BO is apparently the same with the well-known Parmenidean Principle of being and not being (cf. Diels-Kranz (DK) Fr. 2.2-5). Euthydemus’ statement against the possibility of false knowledge can be good evidence for this principle: -/- The things which are not surely do not exist (τὰ δὲ μὴ ὄντα … ἄλλο τι ἢ οὐκ ἔστιν). (Euthydemus 284b3-4) -/- He continues (b4-5): -/- There is nowhere for not being to be there (οὖν οὐδαμοῦ τά γε μὴ ὄντα ὄντα ἐστίν). -/- That BE does not let true opinion as a third option besides knowledge and ignorance seems to be related to BO’s rejecting a third option besides being and not being, which is itself the basis of the impossibility of false belief. Socrates’ elaborate discussion of the problem of false belief in Theatetus that leads to a more decisive discussion and finally to some solutions in Sophist can make our consideration of BO for the first group of dialogues authentive. -/- 4. &5. Split Knowledge and Split Being The fourth principle I shall call the principle of 'Split Knowledge' (SK): -/- SK Knowledge of X is separated from any other knowledge (of anything else) as if the whole knowledge is split to various parts. -/- This Principle is hinted and criticized as Socrates’ way of treating with knowledge in Hippias Major: -/- But Socrates, you do not contemplate the entireties of things, nor do people you have used to talk with (τὰ μὲν ὅλα τῶν πραγμάτων οὐ σκοπεῖς, οὐδ᾽ ἐκεῖνοι οἷς σὺ εἴωθας διαλέγεσθαι). (301b2-4) -/- Contrary to Rankin who regards the passage as 'antilogical, almost eristic in tone rather than presenting a serious philosophy of being' (1983, 54), I think it can be taken as serious. Hippias criticizes Sorcates that he does not contemplate (σκοπεῖς) the entireties of things (ὅλα τῶν πραγμάτων), a critique which Socrates is not its only subject but all those whom Socrates accustomed to talk with (ἐκεῖνοι οἷς σὺ εἴωθας διαλέγεσθαι). This last phrase, I think, extends this critic beyond this dialogue to other Socratic dialogues. Hippias’ use of the perfect tense of the verb ἔθω (to be accustomed) is a good evidence of this extension. We can get, thus, these ἐκεῖνοι as Socrates’ interlocutors in his other dialogues that hints that this criticism has the epistemological groundings of the previous dialogues as its subject. What ἐκεῖνοι οἷς σὺ εἴωθας διαλέγεσθαι points to is that Hippias does not have in mind Socrates’ way of treating things only in this dialogue, but he is also criticizing Socrates’ way throughout his dialogues. At 301b4-5, Socrates and his interlocutors’ way of beholding things is described as such: -/- You people knock (κρούετε) at the fine and each of the beings (ἕκαστον τῶν ὄντων) by taking each being cut up in pieces (κατατέμνοντες) in words (ἐν τοῖς λόγοις). This leads us to our next principle that is parallel to, and the ontological side of, SK, the principle of 'Split Being'(SB): -/- SB Everything (being) is separated from any other thing as if the whole being is split to many beings. -/- Socrates and his interlocutors and thus, as we saw, the Socratic dialogues are accused to regard everything as it is separated from all other things. This separation is en tois logois that, I think, can reasonably be taken as saying that Socratic dialogues (it refers of course to the dialogues before Hippias Major) cut up all things which have the same name/definition from all other things and try to understand them separately, without considering other things that are not in their logos. They, for example in Hippias Major, are cutting up to kalon and try to understand what it and all others inside this logos are by separating it from all other things. This is directed straightly against Socratic question and the way Socratic dialogues follow to find its answer, every time separating one logos. As Meyer (1995, 85) points out, every question 'presupposes that the X in question in a logos is something' and 'every answer to every question aims at unity' (84). The critique of Hippias Major is, therefore, at the same time a critique of SK and SB. It is also a critique of KWX because it is only based on KWX that Socratic dialogues could search for the answer of 'what is X' question supposing that knowing what X is is enough for the knowledge of X. SK and KWX are absolutely interdependent. What Socrates and all his previous interlocutors have neglected in Socratic dialogues, Hippias says, was 'continuous bodies of being' (διανεκῆ σώματα τῆς οὐσίας) (301b6). Either this theory actually belongs to the historical Hippias as it is being said or not, it is strictly criticizing SB. We have the same phrase with changing sūma to logos some lines later at 301e3-4: διανεκεῖ λόγῳ τῆς οὐσίας. Although this theory that can be observed as both an ontological and an epistemological theory is rejected by Socrates (301cff.), it is still against first Socrates’ onto-epistemological principles and might let us look at what is rejected as Socratic prineple. -/- 6. Knowledge is of Being The sixth principle that I think is presupposed by the first Socrates, is the 'Knowledge of Being' Principle (KB): -/- KB Knowledge is of Being. -/- This principle is obviously the source of the problem of false knowledge, a very important problem throughout Plato’s philosophy. We face this problem maybe for the first time in Euthydemus. In less than 20 Stephanus’ pages, 276-295, we are encountered with different interwoven problems about knowledge , all grounded in the problem of false opinion. Having challenged the obvious possibility of telling lies at 283e, at 284 Euthydemus discusses it saying that the man who speaks is speaking about 'one of those things that are (ἓν μὴν κἀκεῖνό γ᾽ ἐστὶν τῶν ὄντων)' (284a3) and thus speaks what is (λέγων τὸ ὄν) (a5). He must necessarily be saying truth when he is speaking what is because he who speaks what is (τὸ ὄν) and the things that are (τὰ ὄντα) speaks truth (τἀληθῆ λέγει) (a5-6). This is based on Parmenidean principle of the impossibility of being of not being which Euthydemus restates (284b3-4) and we mentioned discussing BO principle above. The things that are not are nowhere (οὐδαμοῦ) and there is no possibility for anyone to do (πράξειεν) anything with them because they must be made as being before anything else can be done, which is impossible (b5-7). The words, then, are of things that exist (εἰσὶν ἑκάστῳ τῶν ὄντων λόγοι) (285e9) and as they are (ὡς ἔστιν) (e10). The result is that no one can speak of things as they are not. It is this impossibility of false speach that is extended to thinking (δοξάζειν) at 286d1 and leads to the impossibility of false opinion (ψευδής … δόξα) (286d4). The general conclusion is asserted at 287a extending this impossibility to actions and making any kind of mistake. Not only knowledge is of being but speech, thought and action are of being simply because of the fact that nothing can be of not being. -/- B. First Socrates’ Principles in the Middle Period Dialogues Out of what were presupposed or criticized mostly in five dialogues, Euthyphro, Euthydemus, Hippias Major, Laches and Charmides, we tried to draw the first Socrates’ principles. Our inquiry here is directed to find out the fate of these principles in the three dialogues of the middle period, Meno, Phaedo and Republic. To do this, first we ought to check the situation of Socratic circle in these dialogues. The Socratic circle that was predominant in the early dialogues, does not look like a circle here anymore though they certainly have some features in common. Meno, Phaedo and Republic II-X are not committed to the principles of the circle and the whole circle in disrupted in them. The difference of the two Socrateses towards acquiring knowledge is obvious. The Socrates of Meno, Phaedo and Republic is evidently more self-confident that he can get to some truths during his arguments as he does. They are in their first appearance, as almost all other dialogues, committed to Socrates’ disavowal. All of them try to keep the shape of the Socratikoi Logoi genre, which is committed to the historical Socrates’ way of discussion; a dramatic personage who is to challenge his interlocutors, ask them and refuse the answers. Nevertheless, the fact is that what we have in common between two groups of dialogues is mostly a dramatic structure. Whereas the first group’s arguments are based on Socrates’ disavowal and lead to no positive results, the second group is decisively going to achieve some positive results. The aim of the first Socrates was to show others that they are ignorant of what they thought they knew. The new Socrates of Meno, on the opposite, makes so much efforts to show that the slave boy has within himself true opinions (ἀληθεῖς δόξαι) about the things that he does not know (οἶδε) (85c6-7). Despite his lack of knowledge, he has true opinions nevertheless. The way from these true opinions to knowledge, as Socrates states, is not so long. These true opinions are now like a dream but 'can become knowledge of the same things not less accurate than anyone’s' (οὐδενὸς ἧττον ἀκριβῶς ἐπιστήσεται περὶ τούτων) (c11-d1), if they be repeated by asking the same questions. The most outstanding text regarding Socrates’ disavowal is Meno 98b where he explicitly claims knowledge: -/- And indeed I also speak as (ὡς) one who does not know (εἰδὼς) but is guessing (εἰκάζων). However, [about the fact] that true opinion and knowledge are different, I do not altogether expect (δοκῶ) myself to be guessing (εἰκάζειν), but if I say about anything that I know (εἰδέναι) -which about few things I say- this is one of the things that I know (οἶδα). (98b1-5) This passage is very significant about Plato’s disavowal of knowledge. There can hardly be found, I think, anywhere else in Plato’s corpus where Socrates speaks about his knowledge of something as such. He says first that he speaks as someone who does not know. This ὡς οὐκ εἰδὼς λέγω comparing with what he used to say in the first group, οὐκ οἶδα, has this added ὡς. Socrates does not claim strongly anymore that he does not know anything but speaks only as someone who does not know. He needs this ὡς not only because he is going to accept that he does know some, though few, things immediately after this sentence, but also because he needs his previous disavowal to be loosened from Meno on. He does not merely say here that he knows something. It is then different from the examples mentioned before which could be taken as idiomatic or at least not emphatic. Socrates’ remarkable emphasis on distinguishing εἰδέναι from εἰκάζειν departs it from all other passages where he says only he knows something. Moreover, he claims definitely that he has knowledge about few (ὀλίγα) things. From the early to the middle dialogues, Socrates’ attitude to knowledge has totally renewed its face. He brings forth a new concept, true opinion, and he does not speak of knowledge as he used to before; the rough, perfect and unachievable knowledge of the first group has turned to something more smooth, realistic and achievable. Comparing with the early dialogues that did not set out from the first to reach positive results, the middle ones are extraordinarily and surprisingly positive and hence destroy the basis of the Socratic circle. The questions and answers are purposely directed to some specific new theories; most of them are not directly related to the topics or the main questions of the dialogues. They are suggested when Socrates draws the attention of the interlocutor away from the main question because of the necessity of another discussion. Even if the main question remains unanswered, we have still many positive theories, prominently of metaphysical type. These theories are so abundant and dominant in these dialogues, especially Phaedo and Republic, that one might think that they may appear to be arbitrarily sandwiched in there. This helps dialogues to keep their original Socratic structure while they are suggesting new theories. Hence, the Socratic question of 'what is X?', though is still used to launch the discussion, is loosened and is forgotten for most part of the dialogues. Meno that has first a differently formulated question, 'can virtue be taught?', leads finally to the Socratic question of 'What is virtue?'. Phaedo is dedicated to the demonstration of the immortality of soul and the life after death without having a central Socratic question. The case of Republic is more complicated. The first book, on the one hand, has all the criteria of a Socratic circle: its 'what is justice?' question, Socrates’ strong disavowal (e.g. 337d-e), his rejection of all answers and coming back to the first point without finding out any answer. This Book, considered alone, is a perfect Socratic dialogue, as many scholars regard it as early and separated from other books. The books II-X are, on the other hand, far from implementing a Socratic circle. They have still the 'what is justice?' question as their incentive leading question, but they are, in most of the positive doctrines and methods that encompass the main parts, ignoring the question. Even these books that, I believe, are the farthest discussions from the Socratic circle are so cautious not to break the Socratic structure of the dialogue as long as it is possible. What is changed is not the structure of the dialogue but the ontological and epistemological grounds based on which new theories are suggested. -/- 1. Knowledge of the Good We can clearly see in the second group of dialogues that the KWX principle loses the place it had before in our first group. It is not, of course, rejected, but still we cannot say that it has the same situation. KWX that was based on Socratic question, as we discussed before, was the leading principle of the first Socrates’ epistemology and of the highest position. Other epistemological principles, SK directly and BE indirectly, were relying on Socratic question and therefore on KWX. Such a position does not belong to KWX from Meno on. What makes it different in the second Socrates is another principle that is needed it not only as its complementary principle but also as what is more fundamental. Plato, then, does not reject KWX in this period, but, it seems, he transcends to another more basic principle; a principle we shall call the principle of 'Knowledge of the Good' (KG): -/- KG Knowledge of X requires knowledge of the Good. -/- Whereas all the dialogues of our first group are free from any discuscon about KG, it bears a very important role in the second group so as becomes the superior principle of knowledge in Republic. Trying to solve the problem of teachability of virtue, Socrates says that it can be teachable only if it is a kind of knowledge because nothing can be taught to human beings but knowledge (ἐπιστήμην) (Meno 87c2). The dilemma will be, then, whether virtue is knowledge or not (c11-12) and since virtue is good, we can change the question to: whether is there anything good separate from knowledge (εἰ μέν τί ἐστιν ἀγαθὸν καὶ ἄλλο χωριζόμενον ἐπιστήμης) (d4-5). Therefore, the conclusion will be that if there is nothing good which knowledge does not encompass, virtue can be nothing but knowledge (d6-8). What let us discuss KG as an epistemological principle for the second Secrates is the relation he tries to establish between knowledge and the Good which, though is alongside with the mentioned thesis and the idea of virtue as knowledge, goes much deeper inside epistemology asking to regard the Good as the basis of knowledge. The effort of Phaedo cannot succeed in establishing the Good as the criterion of explanation and knowledge since, I think, it needs a far more complicated ontology of Republic where Socrates can finally announce KG. What is said in Republic is totally compatible with Phaedo 99d–e and the metaphor of watching an eclipse of the sun. In spite of the fact that we do not have adequate knowledge of the Idea of the Good, it is necessary for every kind of knowledge: 'If we do not know it, even if we know all other things, it is of no benefit to us without it' (505a6-7). The problem of our not having sufficient knowledge of the Idea of Good is tried to be solved by the same method of Phaedo 99d-e, that is to say, by looking at what is like instead of looking at thing itself (506d8-e4). It is this solution that leads to the comparison of the Good with sun in the allegory of Sun (508b12-13). What the Good is in the intelligible realm corresponds to what the sun is in the visible realm; as sun is not sight, but is its cause and is seen by it (b9-10), the Good is so regarding knowledge. It has, then, the same role for knowledge that the sun has for sight. Socrates draws our attention to the function of sun in our seeing. The eyes can see everything only in the light of the day being unable to see the same things in the gloom of night (508c4-6). Without the sun, our eyes are dimmed and blind as if they do not have clear vision any longer (c6-7). That the Good must have the same role about knowledge based on the analogy means that it must be considered as a required condition of any kind of knowledge: -/- The soul, then, thinks (νόει) in the same way: whenever it focuses on what is shined upon by truth and being, understands (ἐνόησέν), knows (ἔγνω) and apparently possesses understanding (νοῦν ἔχειν). (508d4-6) -/- Socrates does not use agathon in this paragraph and substitutes it with both aletheia and to on. He links them with the Idea of the Good when he is to assert the conclusion of the analogy: -/- That which gives truth to the objects of knowledge and the power of knowing to the knower, you must say, is the Idea of the Good: being the cause of knowledge and truth (αἰτίαν δ᾽ ἐπιστήμης οὖσαν καὶ ἀληθείας) so far as it is known (ὡς γιγνωσκομένης μὲν διανοοῦ). (508e1-4) Knowledge and truth are called goodlike (ἀγαθοειδῆ) since they are not the same as the Good but more honoured (508e6-509a5). KG, which had been implicitly contemplated and searched in Phaedo, is now explicitly being asserted in Republic. As what was quoted clearly proves, this principle is the very one which we can observe as the most fundamental principle of the second Socrates in Republic, corresponding to the role KWX had in the first Socrates. The Form of the Good in Republic, of which Santas speaks as 'the centerpiece of the canonical Platonism of the middle dialogues, the centerpiece of Plato’s metaphysics, epistemology, ethics and …' (1983, 256) much more can be said. Plato’s Cave allegory in Book VIII dedicates a similar role to the Idea of the Good. The Idea of the Good is there as the last thing to be seen in the knowable realm, something so important that its seeing equals to understanding the fact that it is the cause of all that is correct and beautiful (517b). Producing both light and its source in visible realm, it controls and provides truth and understanding in the intelligible realm (517c). -/- 2. Tripartite Epistemology BE is thoroughy rejected in the second Socrates and substituted by its opposite, the principle of 'Tripartite Epistemolgy' (TE): -/- TE Opinion is an epistemological status between knowledge and ignorance. BE of the first Socrates was denying any third way besides knowledge and ignorance which was the foundation of Socratic circle without which Socrates could not reject his interlocutors’ possessing any kind of knowledge. We cannot say, however, that the first Socrates had a third epistemological status in mind but rejected it. Such a status was unacceptable for him so that one can say that he would reject any kind of such status if suggested. There were only two possibilities about knowledge: either one knows something or he does not know it. TE, thus, was not the first Socrates’ discovery and, I think it is not the second Socrates’discovery. All we can see in our second group of dialouges is that he uses this principle as an already demonstrated one. Having examined the slave boy in Meno for the prupose of showing the working of recollection, it truns out that he has some opinions in him while he still does not know. Without trying to prove it, Socrates takes this as the distinction between knowledge and opinion: -/- So, he who does not know (οὐκ εἰδότι) about what he does not know (περὶ ὧν ἂν μὴ εἰδῇ) has within himself true opinions (ἀληθεῖς δόξαι) about the same things he did not know (περὶ τούτων ὧν οὐκ οἶδε) (85c6-7). -/- The same distinction is set between ὀρθὴν δόξαν and ἐπιστήμην at 97b5-6 ff. (also cf. 97b1-2: ὀρθῶς μὲν δοξάζων … ἐπιστάμενος). He connects then their difference to the myth of Daedalus, the statue that would run away and escape. So are true opinions, not willing to remain long in mind and thus not worthy until one ties them down by αἰτίας λογισμῷ (98a3-4). Socrates says that this tying down is anamnesis. We face, in Phaedo, the same relation is settled between knowledge as the process of being tied down and getting the capability to give an account, on the one hand, and anamnesis, on the other hand. When a man knows, he must be able to give an account of what he knows (Phaedo 76b5-6) and since not all people are able to give such an account, those who recollect, recollect what once they learned (76c4). Although the distinction between knowledge and opinion is not explicitly used in Phaedo, referring to the parallel link between knowledge plus account and anamnesis in Phaedo and Meno, one can say that those who cannot recollect are not able to give account and, thus, are in a state of opinion. What is said at Phaedo 84a, though not yet a definite distinction between knowledge and opinion, makes a distinction between their objects so as we can agree that it is presupposed. The soul of the philosopher, Socrates says, follows reason, stays with it forever and contemplates the divine, which is not the object of opinoin (ἀδόξαστον) (84a8, cf. Meno 98b2-5). The distinction of knowledge and belief in Republic has a significant difference with what we discussed in Meno and Phaedo since the distinction of Meno was based on anamnesis and thus more an epistemological distinction. Even in Phaedo that we do not have any elaborate discussion about the distinction, the only hint to the matter at 76 is bound to the theory of anamnesis. In addition to the relation of the distinction with this theory, there is another evidence that does not permit us to consider the distinction as an ontological distinction. Let’s see Meno 85c6-7: -/- So, he who does not know about what he does not know has within himself true opinions about the same things he did not know (τῷ οὐκ εἰδότι ἄρα περὶ ὧν ἂν μὴ εἰδῇ ἔνεισιν ἀληθεῖς δόξαι περὶ τούτων ὧν οὐκ οἶδε). (85c6-7) -/- This last sentence persists that the objects of knowledge and true opinion are the same. What Socrates is to say here is that whereas he does not know X he has true opinion about the same X. I think Socrates’ sentence that the slave boy οὐκ εἰδότι ἄρα περὶ ὧν ἂν μὴ εἰδῇ and his restatement of it by saying περὶ τούτων ὧν οὐκ οἶδε is because he wants to emphasize that the slave boy who does not know, has true opinion about the same thing. Socrates could say this just with using τούτων and there would be no necessity to bring περὶ ὧν ἂν μὴ εἰδῇ for οὐκ εἰδότι if he did not want to emphasize. -/- 3. Tripartite Ontology The distinction between knowledge and true opinion in Republic, on other side, has nothing to do with recollection, but is based on an ontological principle, 'Tripartite Ontology' (TO): -/- TO There are things that both are and are not. -/- This principle I confine, among our three dialogues of the second group, to Republic not extended to Meno and Phaedo, is obviously the opposite of BO. Speaking about the lovers of sights and sounds in the fifth book, Socrates distinguishes them from philosophers because their thought is unable to understand the nature of beautiful itself besides beautiful things (476a6-8) and hence they can only have opinions. The philosopher who, on the contrary, believes in beautiful itself and can distinguish it from beautiful things (476c9-d3), has knowledge because he knows, contrasting others who have opinion because they only opine (d5-6). Since those whose knowledge were degraded as opinion will complain about Socrates’ such calling their thought, he provides them the following argument (476e7-477b1): -/- - Does the person who knows, knows (γιγνώσκει) something (τὶ) or nothing (οὐδέν)? - He knows something (τί). - Something that is (ὂν) or is not (οὐκ ὄν)? - Something that is (ὂν) for how could something that is not be known (πῶς γὰρ ἂν μὴ ὄν γέ τι γνωσθείη)? - Then we have an adequate grasp of this: No matter how many ways we examine it, what completely is (παντελῶς ὂν) is completely knowable (παντελῶς γνωστόν) and what is in no way (μὴ ὂν δὲ μηδαμῇ) is in every way unknowable (πάντῃ ἄγνωστον). - A most adequate one. - Good. Now, if anything is such as to be and also not to be (ὡς εἶναί τε καὶ μὴ εἶναι), won’t it be intermediate (μεταξὺ) between what purely is (εἰλικρινῶς ὄντος) and what in no way is (μηδαμῇ ὄντος)? - Yes, it’s intermediate. - Then as knowledge (γνῶσις) is set over what is (τῷ ὄντι), while ignorance (ἀγνωσία) is of necessity set over what is not (μὴ ὄντι) mustn’t we find an intermediate between ignorance (ἀγνοίας) and knowledge (ἐπιστήμης) to be set over the intermediate, if there is such a thing? -/- From the third status of being we must reach to the third status of knowledge. The simple reading of this text can be an existential reading, taking the "is" of the mentioned sentences as existence. The problem is that when it is said that there is something that both is and is not reading "is" existentially, it sounds too bizarre to be acceptable. It cannot easily be understandable to have something as both existent and non-existent at the same time. This problem arose so many debates and led many scholars to reject the existential reading of "is" and suggest some other readings like predicative or veridical readings. I think though Plato’s complicated ontology of Republic cannot be correctly understood by a simple existential reading, this "is" cannot be free from existential sense of being and, thus, cannot be reduced to just a predicative or veridical sense of being. -/- 4. Bound Knowledges In addition to KG, the Good is also the basis of another principle in the second Socrates, namely the principle of 'Bound Knowledge' (BK): -/- BK Knowledge of everything is bound to the knowledge of the Good. -/- We distinguished BK from KG because we want to insist, in BK, on what had not been insisted upon in KG, that is, the binding role that the Good plays in the second Socrates, contrasting the absence of such a role in the first Socrates. Socrates remembers, in Phaedo, his wonderful keen on natural philosophers' wisdom when he was young. The origin of this enthusiasm was Socrates’ hope to know the cause of everything as they used to claim. When he was searching the matters of his interest on their basis, Socrates says, he became convinced he can get no acceptable answer from them and found himself blind even to the things he thought he knew before. One day he hears Anaxagoras’ theory that 'it is Mind that arranges and is the cause of everything (ὡς ἄρα νοῦς ἐστιν ὁ διακοσμῶν τε καὶ πάντων αἴτιος)' (Phd. 97c1-2 cf. DK, Fr.15.8-9, 11-12, 12-14) and thinks that he can finally find what he has always expected, i.e. something which can explain all things. What I intend to show here is that what makes Socrates hopeful is that Anaxagoras’ theory tries 1) to explain all things by one thing and 2) this explanation is understood by Socrates as if it is based on the concept of the Good. That Socrates was searching for one explanation for all things can be proved even from what he has been expecting from natural philosophers. The case is, nonetheless, more clearly asserted when he speaks about Anaxagoras’ theory. In addition to διακοσμῶν τε καὶ πάντων αἴτιος of 97c2 mentioned above, we have τὸ τὸν νοῦν εἶναι πάντων αἴτιον (c3-4) and τόν γε νοῦν κοσμοῦντα πάντα κοσμεῖν (c4-5) all emphasizing on the cause of all things (πάντα) which can clearly prove that one of the reasons which caused Socrates to embrace it delightfully was its claim to provide the cause of all things by one thing. Another reason was that Anaxagoras’ Mind, at least in Socrates’ view, was attempting to explain everything by the concept of the Good. This connection between Mind and Good belongs more to the essential relation they have in Socrates’ thinking than Anaxagoras’ theory because there are almost nothing about such a relation in Anaxagoras. The reason for Socrates’ reading can be that Mind is substantially compatible with Socrates’ idea of the relation between good and knowledge. Both the thesis 'no one does wrong willingly' and the theory of virtue as knowledge we pointed to above are evidences of this essential relation. Nobody who knows that something is bad can choose or do it as bad. The reason, when it is reason, that means when it is as it should be, when it is wise or when it knows, works only based on good-choosing. In this context, when Socrates hears that Mind is considered as the cause of everything, it sounds to him like this: good should be regarded as the basis of the explanation of all things. We see him, thus, passing from the former to the latter without any proof. This is done in the second sentence after introducing Mind: -/- I thought that if this were so, the arranging Mind would arrange all things and put each thing in the way that was Best (ὅπῃ ἂν βέλτιστα ἔχῃ). If one then wished to find the cause of each thing by which it either perishes or exists, one needs to find what is the best way (βέλτιστον αὐτῷ ἐστιν) for it to be, or to be acted upon, or to act. On these premises then it befitted a man to investigate only, about this and other things, what is the most excellent (ἄριστον) and best (βέλτιστον). The same man must inevitably also know what is worse (χεῖρον), for that is part of the same knowledge. (97c4-d5) This passage is a good evidence of Socrates’ leap from Anaxagoras’ Mind to his own concept of the Good that can explain why Socrates found Anaxagoras theory after his own heart (97d7). Mind is welcomed because of its capability for explanation on the basis of good to 'explain why it is so of necessity, saying which is better (ἄμεινον), and that it was better (ἄμεινον) to be so' (97e1-3). What Socrates thought he had found in Anaxagoras can indicate what he had been expecting from natural scientists before. Socrates could not be satisfied with their explanations because they were unable to explain how it is the best for everything to be as it is. It can probably be said, then, that it was the lack of the unifying Good in their explanation that had disappointed him. We must insist that we are discussing what Socrates thought that Anaxagoras’ theory of Mind should have been, not about Anaxagoras’ actual way of using Mind. Phaedo 97c-98b, is not about what Socrates found in Anaxagoras but what he thought he could find in it. On the contrary, it should also be noted that it was not this that was dashed at 98b, but Anaxagoras’ actual way of using Mind. It was Anaxagoras’ fault not to find out how to use such an excellent thesis (98b8-c2, cf. 98e-99b). Socrates gives an example to show how not believing in 'good' as the basis of explanation makes people be wanderers between different unreal explanations of a thing. His words δέον συνδεῖν (binding that binds together) as a description for the Good we chose as the name of BK principle: They do not believe that the truly good and binding binds and holds them together (ὡς ἀληθῶς τὸ ἀγαθὸν καὶ δέον συνδεῖν καὶ συνέχειν οὐδὲν οἴονται). (99c5-6) -/- Having in mind Plato’s well-known analogy of the sun and the Good at Republic 508-509, we can dare to say that his warning of the danger of seeing the truth directly like one watching an eclipse of the sun in Phaedo (99d-e) is more about the difficulty of so-called good-based explanation than its insufficiency, a difficulty which is precisely confirmed in Republic (504e-505a, 506d-e). Moreover, BK is asserted in a more explicit way in the Republic, where the Good is considered not only as a condition for the knowledge of X, as was noted above discussing KG, but also as what binds all the objects of knowledge and also the soul in its knowing them. At Republic VI, 508e1-3, when Socrates says that the Form of the Good 'gives truth to the things known and the power to know to the knower (τοῦτο τοίνυν τὸ τὴν ἀλήθειαν παρέχον τοῖς γιγνωσκομένοις καὶ τῷ γιγνώσκοντι τὴν δύναμιν ἀποδιδὸν)', he wants to set the Good at the highest point of his epistemological structure by which all the elements of this structure are bound. This binding aspect of the Good is by no means a simple binding of all knowledges or all the objects of knowledge, but the most complicated kind of binding as it is expected from the author of the Republic. The kind of unity the Good gives to the different knowledges of different things is comparable with the unity which each Form gives to its participants in Republic: as all the participants of a Form are united by referring to the ideas, all different kinds of knowledge are united by referring to the Good. If we observe Aristotle's assertion that for Plato and the believers of Forms, the causative relation of the One with the Forms is the same as that of the Forms with particulars (e.g. Metaphysics 988a10-11, 988b4), that is to say the One is the essence (e.g., ibid, 988a10-11: τοῦ τί ἐστὶν, 988b4-6: τὸ τί ἢν εἶναί) of the Forms besides his statement that for them One is the Good (e.g., ibid, 988b11-13) the relation between the Good and unity may become more understandable. Since the quiddity of the Good (τί ποτ᾽ ἐστὶ τἀγαθὸν) is more than discussion (506d8-e2), we cannot await Socrates to tell us how this binding role is played. All we can expect is to hear from him an analogy by which this unifying role is envisaged, the sun. The kind of unity that the Good gives to the knowledge and its objects in the intelligible realm is comparable to the unity that the sun gives to the sight and its objects in the visible realm (508b-c). The allegory of Line (Republic VI, 509d-511), like that of the Sun, tries to bind all various kinds of knowledges. The hierarchical model of the Line which encompasses all kinds of knowledge from imagination to understanding can clearly be considered as Plato’s effort to bind all kinds of knowledges by a certain unhypothetical principle. The method of hypothesis starts, in the first subsection of the intelligible realm, with a hypothesis that is not directed firstly to a principle but a conclusion (510b4-6). It proceeds, in the other subsection, to a 'principle which is not a hypothesis' (b7) and is called the 'unhypothetical principle of all things' (ἀνυποθέτου ἐπὶ τὴν τοῦ παντὸς ἀρχὴν) (511b6-7). This παντὸς must refer not only to the objects of the intelligible realm but to the sensible objects as well. Plato does posit, therefore, an epistemological principle for all things, a principle that all things are, epistemologically, bound and, thus, unified by. -/- 5. Bound Beings The ontological aspect of BK we shall call the principle of 'Bound Beings' (BB): -/- BB Being of all things are bound by the Good. -/- We saw in our principle of Split Being (SB) how the first Socrates was criticized because of his approach to split being and separate each thing from other things. The principle of Bound Beings intends to make the things more related, a duty which is done again by the Good. In the allegory of Sun, there are two paragraphs that evidently and deliberately extend the binding role of the Good to the ontological scene: -/- You will say that the sun not only makes the visible things have the ability of being seen but also coming to be, growth and nourishment. (509b2-4) -/- This clearly intends to remind the ontological role the sun plays in bringing to being all the sensible things in order to display how its counterpart has the same role in the intelligible realm (b6-10): -/- Not only the objects of knowledge (γιγνωσκομένοις) owe their being known (γιγνώσκεσθαι) to the Good, but also their existence (τὸ εἶναί) and their being (οὐσίαν) are due to it, though the Good is not being but superior to it in rank and power. That the Good is here represented as responsible for being of things in addition to their being known means, in my opinion, that Plato wants to posit BB in addition to BK. The allegory of Cave at the very beginning of the seventh Book (514aff.) can be taken as another evidence. The role of the Good, one might say, is confined to the intelligible realm because it is asserted that the role the Good plays in this realm is corresponding to that of the sun in the visible realm. The fact that Plato wants to observe the Good also as the ontological cause of the sensible things is obvious from his saying, in the allegory of Cave, that the Form of the Good 'produces light and its source (τὸν τούτου κύριον) [i.e. the sun] in the visible realm' (517c3). We can conclude, then, that the ontological function of the Good is not confined to the intelligible realm in which it is the lord and provides truth and understanding (c3-4) because it is also responsible to produce τὸν κύριον of light. 6. Proportionality of Being and Knowledge Insofaras BE and BO principles of the first Socrates gave way to TE and TO principles of the second Socrates, we cannot expect him to preserve KB in the same way as it was in the first Socrates. The new tripartite ontology and epistemology necessitates some modifications in KB which results in the principle of 'Proportionality of Being and Knowledge' (PBK): -/- PBK To every class of being there is a proportionate category of knowledge. -/- This principle, of course, does not entail the refutation of KB and thus is not kind of rejecting PBK but only a more complicated version of it. Based on PBK, we can still agree that knowledge is of being (KB) but the issue is that since none of the concepts of knowledge and being in the second Socrates are as simple as they were for the first Socrates, we need a more complicated principle for their relation here. Although from Meno 97a where the distinction of knowledge and true opinion is drawn out in the second group of the dialogues, we can expect a new relation, it is articulated in its most complete way in Republic and specifically in the allegory of Line. All the beings are divided there hierarchically to four classes, to each of them belongs a class of knowledge: imagination to images, belief to the sensible things (more correctly: the things of which they[in previous class] were images (ᾧ τοῦτο ἔοικεν)), thought to mathematical objects (?) and understanding to the Forms and the first principle. The degree of clarity that each of the classes of knowledge shares in (σαφηνείας ἡγησάμενος μετέχειν) is proportionate to the degree that its object shares in truth (ἀληθείας μετέχει). (511e2-4) -/- Conclusion From the six onto-epistemilogical principles of the first Socrates, four principles turn to their opposite in the middle period dialogues. While bipolar epistemology and ontology of the early dialogues give place to tripartite epistemology in the middle period dialogues and tripartite ontology in Republic, the split knowledge and being of the first Socrates are inclined to be substituted by bound knowledges and bound beings in the second Socrates and specifically in Republic. Not all our system of principles in this article is necessarily determinative. Either they are rightly formulated or not, our result would not be vulnerable if we accept that 1) making the distinction of knowledge and belief, 2) accepting the being of not being and 3) trying to bind both being and knowledge by the concept of the Good happens only in middle period dialogues, having been absent in the early ones. These are the favourite results all those somehow arbitrary and even oversimplified principles were to illustrate; that there is kind of a development in the epistemological as well as the ontological grounds of Plato’s philosophy. -/- Notes . (shrink)

A new view of the functional role of the left anterior cortex in language use is proposed. The experimental record indicates that most human linguistic abilities are not localized in this region. In particular, most of syntax (long thought to be there) is not located in Broca's area and its vicinity (operculum, insula, and subjacent white matter). This cerebral region, implicated in Broca's aphasia, does have a role in syntactic processing, but a highly specific one: It is the neural home (...) to receptive mechanisms involved in the computation of the relation between transformationally moved phrasal constituents and their extraction sites (in line with the Trace-Deletion Hypothesis). It is also involved in the construction of higher parts of the syntactic tree in speech production. By contrast, basic combinatorial capacities necessary for language processing – for example, structure-building operations, lexical insertion – are not supported by the neural tissue of this cerebral region, nor is lexical or combinatorial semantics. The dense body of empirical evidence supporting this restrictive view comes mainly from several angles on lesion studies of syntax in agrammatic Broca's aphasia. Five empirical arguments are presented: experiments in sentence comprehension, cross-linguistic considerations (where aphasia findings from several language types are pooled and scrutinized comparatively), grammaticality and plausibility judgments, real-time processing of complex sentences, and rehabilitation. Also discussed are recent results from functional neuroimaging and from structured observations on speech production of Broca's aphasics. Syntactic abilities are nonetheless distinct from other cognitive skills and are represented entirely and exclusively in the left cerebral hemisphere. Although more widespread in the left hemisphere than previously thought, they are clearly distinct from other human combinatorial and intellectual abilities. The neurological record (based on functional imaging, split-brain and right-hemisphere-damaged patients, as well as patients suffering from a breakdown of mathematical skills) indicates that language is a distinct, modularly organized neurological entity. Combinatorial aspects of the language faculty reside in the human left cerebral hemisphere, but only the transformational component (or algorithms that implement it in use) is located in and around Broca's area. Key Words: agrammatism; aphasia; Broca's area; cerebral localization; dyscalculia; functional neuroanatomy; grammatical transformation; modularity; neuroimaging; syntax; trace deletion. (shrink)

This paper shows how to conservatively extend theories formulated in non-classical logics such as the Logic of Paradox, the Strong Kleene Logic and relevant logics with Skolem functions. Translations to and from the language extended by Skolem functions into the original one are presented and shown to preserve derivability. It is also shown that one may not always substitute s=f(t) and A(t, s) even though A determines the extension of a function and f is a (...) class='Hi'>Skolem function for A. (shrink)

The monadic second-order theory of trees allows quantification over elements and over arbitrary subsets. We classify the class of trees with respect to the question: does a tree T have definable Skolem functions? This continues [6] where the question was asked only with respect to choice functions. A natural subclass is defined and proved to be the class of trees with definable Skolem functions. Along the way we investigate the spectrum of definable (...) well orderings of well ordered chains. (shrink)

If the cortex is an associative memory, strongly connected cell assemblies will form when neurons in different cortical areas are frequently active at the same time. The cortical distributions of these assemblies must be a consequence of where in the cortex correlated neuronal activity occurred during learning. An assembly can be considered a functional unit exhibiting activity states such as full activation (“ignition”) after appropriate sensory stimulation (possibly related to perception) and continuous reverberation of excitation within the assembly (a putative (...) memory process). This has implications for cortical topographies and activity dynamics of cell assemblies forming during language acquisition, in particular for those representing words. Cortical topographies of assemblies should be related to aspects of the meaning of the words they represent, and physiological signs of cell assembly ignition should be followed by possible indicators of reverberation. The following postulates are discussed in detail: (1) assemblies representing phonological word forms are strongly lateralized and distributed over perisylvian cortices; (2) assemblies representing highly abstract words such as grammatical function words are also strongly lateralized and restricted to these perisylvian regions; (3) assemblies representing concrete content words include additional neurons in both hemispheres; (4) assemblies representing words referring to visual stimuli include neurons in visual cortices; and (5) assemblies representing words referring to actions include neurons in motor cortices. Two main sources of evidence are used to evaluate these proposals: (a) imaging studies focusing on localizing word processing in the brain, based on stimulus-triggered event-related potentials (ERPs), positron emission tomography (PET), and functional magnetic resonance imaging (fMRI), and (b) studies of the temporal dynamics of fast activity changes in the brain, as revealed by high-frequency responses recorded in the electroencephalogram (EEG) and magnetoencephalogram (MEG). These data provide evidence for processing differences between words and matched meaningless pseudowords, and between word classes, such as concrete content and abstract function words, and words evoking visual or motor associations. There is evidence for early word class-specific spreading of neuronal activity and for equally specific high-frequency responses occurring later. These results support a neurobiological model of language in the Hebbian tradition. Competing large-scale neuronal theories of language are discussed in light of the data summarized. Neurobiological perspectives on the problem of serial order of words in syntactic strings are considered in closing. Key Words: associative learning; cell assembly; cognition; cortex; ERP; EEG; fMRI; language; lexicon; MEG; PET; word category. (shrink)

We examine the conditions under which we can keep simplicity or categoricity after adding a Skolem function to the theory.

In lieu of an abstract, here is a brief excerpt of the content:On John Hollander’s “Owl”Eleanor CookSuppose we start with grammar, assuming we’ve glanced at the look of “Owl” on the page, as if through the eyes of May Swenson. Here is the way she began to read a poem: “I like to see the poem first as a shut box or package to be opened, within which is an invention whose particular working I hope to discover. Something can be (...) felt about it even before beginning to read: its profile on the page, its regular or irregular pattern of stanzas, length of lines, their symmetry, its wide or thin shape, its look of bulk or lightness.” 1 So here, we observe a one-word title: a noun, no article, and so more like Bishop’s “Sandpiper” than Frost’s “The Oven Bird.” Then quatrains, twenty-four of them, each shorter in its third and more in its fourth line; the pulse iambic and 5 5 4 3 (pentameter twice, tetrameter, trimeter), the rhyme a b a b. Each stanza, in little, looks and listens like an owl, narrowing down to its fourth line, listening to the sounds and silences both—the sounds of the full end-rhymes, assonance, midline rhyming, schematic echoes, and so on; and the silences resonating in the vacant space left by one fewer foot in the third line, then two in the fourth, an effect especially noticeable in the end-stopped lines. This stanza form is (I believe) John Hollander’s own, 2 and it teaches us how to listen better. Owls hunt with their ears as well as their eyes, and with only their ears if necessary.In starting with grammar, I am simply choosing one partner in the dance of grammar, rhetoric, and dialectic that constitutes all writing. I shall touch on lexical questions and two senses of voice, before turning to the heart of the matter, the poem’s figuration and fable, then end [End Page 167] with some remarks on “Owl” as part of all Hollander’s work and also as a poem of our moment.The grammar, then, and first the syntactic variety of the sentences. T. S. Eliot wrote in 1918 that technique is not simply “what may be learned from a manual of prosody. This is making technique easy.... Technique is more volatile; it can only be learned, the more difficult part of it, by absorption. Try to put into a sequence of simple quatrains the continuous syntactic variety of Gautier or Blake....” 3 Something of Hollander’s distinctive voice in both poetry and prose lies in his great command of grammatical structures, including his syntactic variety. “Owl” is strongly predicative in style (note the complex syntax, and the remarkably high use of participles, past and present). The sentences give the effect of generating themselves, especially through their parallel grammatical constructions, where the last term in a double or triple set is likely to be modified by a clause or phrase—the whole sentence ramifying and exfoliating, as if we were watching a zoological or genealogical tree grow under our eyes. [See, for example, the parallel participles in the last line of stanza 4 and stanza 5: “Taking heed... you more than see.” Or consider how one participle leads to another in stanzas 15 through 17, beginning with “Trembling....”]Such syntactic energy gives a quick, vital rhythm to the sentence—a fast pace, given the richness of thought, hints, implications. A pace sometimes slightly nervous, curbing and steadying its own energies, partly through the regular beat of the simple rhyme scheme and quatrain. It seems to me that the forward propulsion of both the grammar and dialectic is steadied, directed, by the rhetorical schemes—that rhetoric here offers what I want to call something like a discipline of simplicity. This is a function we may not associate with rhetorical schemes, those “surface patterns of words” that “carry no meanings per se.” 4 In Roman Jakobson’s terms—and his discussion of parallelism was really the only thing that helped with what I was hearing—what I am hearing is the pull between a regular, simple parallelism of stanza form and a much-varied, complex parallelism of... (shrink)

We prove the following extension of a result of Keisler and Morley. Suppose U is a countable model of ZFC and c is an uncountable regular cardinal in U. Then there exists an elementary extension of U which fixes all ordinals below c, enlarges c, and either (i) contains or (ii) does not contain a least new ordinal. Related results are discussed.

In lieu of an abstract, here is a brief excerpt of the content:On John Hollander’s “Owl”Eleanor CookSuppose we start with grammar, assuming we’ve glanced at the look of “Owl” on the page, as if through the eyes of May Swenson. Here is the way she began to read a poem: “I like to see the poem first as a shut box or package to be opened, within which is an invention whose particular working I hope to discover. Something can be (...) felt about it even before beginning to read: its profile on the page, its regular or irregular pattern of stanzas, length of lines, their symmetry, its wide or thin shape, its look of bulk or lightness.” 1 So here, we observe a one-word title: a noun, no article, and so more like Bishop’s “Sandpiper” than Frost’s “The Oven Bird.” Then quatrains, twenty-four of them, each shorter in its third and more in its fourth line; the pulse iambic and 5 5 4 3 (pentameter twice, tetrameter, trimeter), the rhyme a b a b. Each stanza, in little, looks and listens like an owl, narrowing down to its fourth line, listening to the sounds and silences both—the sounds of the full end-rhymes, assonance, midline rhyming, schematic echoes, and so on; and the silences resonating in the vacant space left by one fewer foot in the third line, then two in the fourth, an effect especially noticeable in the end-stopped lines. This stanza form is (I believe) John Hollander’s own, 2 and it teaches us how to listen better. Owls hunt with their ears as well as their eyes, and with only their ears if necessary.In starting with grammar, I am simply choosing one partner in the dance of grammar, rhetoric, and dialectic that constitutes all writing. I shall touch on lexical questions and two senses of voice, before turning to the heart of the matter, the poem’s figuration and fable, then end [End Page 167] with some remarks on “Owl” as part of all Hollander’s work and also as a poem of our moment.The grammar, then, and first the syntactic variety of the sentences. T. S. Eliot wrote in 1918 that technique is not simply “what may be learned from a manual of prosody. This is making technique easy.... Technique is more volatile; it can only be learned, the more difficult part of it, by absorption. Try to put into a sequence of simple quatrains the continuous syntactic variety of Gautier or Blake....” 3 Something of Hollander’s distinctive voice in both poetry and prose lies in his great command of grammatical structures, including his syntactic variety. “Owl” is strongly predicative in style (note the complex syntax, and the remarkably high use of participles, past and present). The sentences give the effect of generating themselves, especially through their parallel grammatical constructions, where the last term in a double or triple set is likely to be modified by a clause or phrase—the whole sentence ramifying and exfoliating, as if we were watching a zoological or genealogical tree grow under our eyes. [See, for example, the parallel participles in the last line of stanza 4 and stanza 5: “Taking heed... you more than see.” Or consider how one participle leads to another in stanzas 15 through 17, beginning with “Trembling....”]Such syntactic energy gives a quick, vital rhythm to the sentence—a fast pace, given the richness of thought, hints, implications. A pace sometimes slightly nervous, curbing and steadying its own energies, partly through the regular beat of the simple rhyme scheme and quatrain. It seems to me that the forward propulsion of both the grammar and dialectic is steadied, directed, by the rhetorical schemes—that rhetoric here offers what I want to call something like a discipline of simplicity. This is a function we may not associate with rhetorical schemes, those “surface patterns of words” that “carry no meanings per se.” 4 In Roman Jakobson’s terms—and his discussion of parallelism was really the only thing that helped with what I was hearing—what I am hearing is the pull between a regular, simple parallelism of stanza form and a much-varied, complex parallelism of... (shrink)

We give an axiomatic characterization for complete elementary extensions, that is, elementary extensions of the first-order structure consisting of all finitary relations and functions on the underlying set. Such axiom systems have been studied using various types of primitive notions . Our system uses the notion of partial functions as primitive. Properties of nonstandard extensions are derived from five axioms in a rather algebraic way, without the use of metamathematical notions such as formulas (...) or satisfaction. For example, when applied to the real number system, it provides a complete framework for developing nonstandard analysis based on hyperreals without having to construct them and without any use of logic. This has possible pedagogical and expository applications as presented in, e.g., [5], [6]. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:On John Hollander’s “Owl”Eleanor CookSuppose we start with grammar, assuming we’ve glanced at the look of “Owl” on the page, as if through the eyes of May Swenson. Here is the way she began to read a poem: “I like to see the poem first as a shut box or package to be opened, within which is an invention whose particular working I hope to discover. Something can be (...) felt about it even before beginning to read: its profile on the page, its regular or irregular pattern of stanzas, length of lines, their symmetry, its wide or thin shape, its look of bulk or lightness.” 1 So here, we observe a one-word title: a noun, no article, and so more like Bishop’s “Sandpiper” than Frost’s “The Oven Bird.” Then quatrains, twenty-four of them, each shorter in its third and more in its fourth line; the pulse iambic and 5 5 4 3 (pentameter twice, tetrameter, trimeter), the rhyme a b a b. Each stanza, in little, looks and listens like an owl, narrowing down to its fourth line, listening to the sounds and silences both—the sounds of the full end-rhymes, assonance, midline rhyming, schematic echoes, and so on; and the silences resonating in the vacant space left by one fewer foot in the third line, then two in the fourth, an effect especially noticeable in the end-stopped lines. This stanza form is (I believe) John Hollander’s own, 2 and it teaches us how to listen better. Owls hunt with their ears as well as their eyes, and with only their ears if necessary.In starting with grammar, I am simply choosing one partner in the dance of grammar, rhetoric, and dialectic that constitutes all writing. I shall touch on lexical questions and two senses of voice, before turning to the heart of the matter, the poem’s figuration and fable, then end [End Page 167] with some remarks on “Owl” as part of all Hollander’s work and also as a poem of our moment.The grammar, then, and first the syntactic variety of the sentences. T. S. Eliot wrote in 1918 that technique is not simply “what may be learned from a manual of prosody. This is making technique easy.... Technique is more volatile; it can only be learned, the more difficult part of it, by absorption. Try to put into a sequence of simple quatrains the continuous syntactic variety of Gautier or Blake....” 3 Something of Hollander’s distinctive voice in both poetry and prose lies in his great command of grammatical structures, including his syntactic variety. “Owl” is strongly predicative in style (note the complex syntax, and the remarkably high use of participles, past and present). The sentences give the effect of generating themselves, especially through their parallel grammatical constructions, where the last term in a double or triple set is likely to be modified by a clause or phrase—the whole sentence ramifying and exfoliating, as if we were watching a zoological or genealogical tree grow under our eyes. [See, for example, the parallel participles in the last line of stanza 4 and stanza 5: “Taking heed... you more than see.” Or consider how one participle leads to another in stanzas 15 through 17, beginning with “Trembling....”]Such syntactic energy gives a quick, vital rhythm to the sentence—a fast pace, given the richness of thought, hints, implications. A pace sometimes slightly nervous, curbing and steadying its own energies, partly through the regular beat of the simple rhyme scheme and quatrain. It seems to me that the forward propulsion of both the grammar and dialectic is steadied, directed, by the rhetorical schemes—that rhetoric here offers what I want to call something like a discipline of simplicity. This is a function we may not associate with rhetorical schemes, those “surface patterns of words” that “carry no meanings per se.” 4 In Roman Jakobson’s terms—and his discussion of parallelism was really the only thing that helped with what I was hearing—what I am hearing is the pull between a regular, simple parallelism of stanza form and a much-varied, complex parallelism of... (shrink)

continent. 1.1 (2011): 60-67. At the beginning of Martin Heidegger’s lecture “Time and Being,” presented to the University of Freiburg in 1962, he cautions against, it would seem, the requirement that philosophy make sense, or be necessarily responsible (Stambaugh, 1972). At that time Heidegger's project focused on thinking as thinking and in order to elucidate his ideas he drew comparisons between his project and two paintings by Paul Klee as well with a poem by Georg Trakl. In front of Klee's (...) Saints from the Window and Death of Fire —though we wouldn’t absolutely understand what we were seeing—he writes, “we should want to stand…a long while.” In a similar manner, of Trakl’s poem “Septet of Death”—although it is likely we are unsure in what we hear—Heidegger states that, “we should want to hear…[it] often.” Heidegger further states that in appreciating these, “we “should abandon any claim that [they] be immediately intelligible” (1). So also we must we approach, Heidegger continues, the realm of theoretical physics, in which the difficult work of Werner Heisenberg, be listened to “without protest” and without “any claim that he be immediately understood.” These works, like his own project, merit the time they take to be originally (mis)understood. But this is not necessarily true for philosophy, Heidegger advises, because, “That thinking is supposed to offer ‘worldly wisdom’ and perhaps even a ‘way to a blessed life’” (1). Philosophy is in the unique position of being both abstract (what do we talk about when we talk?) and at the same moment, useful. There are demands that it make sense, that it be, grounded, immediate, and most importantly, rational. Heidegger draws these comparisons between the works of Klee and Trakl and Heisenberg not to claim that philosophy is totally irresponsible. He does not claim that the poet, the painter, nor the physicist have acted irresponsibly. Rather, he would say, they are rising to the highest levels of intelligibility, though it is perhaps an intelligibility that is commonly unavailable to us. In Trakl’s case, as we shall see, mastery is the end result of difficult words. Instead, Heidegger seems be making pleas: for a period of uninterrupted unintelligibility (pure unintelligibility); and that there is a time (that time is now) when, “thinking is…placed in a position which demands of it reflections that are far removed from any useful, practical wisdom” (1-2). Heidegger argues that philosophy requires a period of time in which, instead of focusing on the practical—or even on the worldly—the discipline draw its “determination” instead from the place of painting and poetry and physics. In doing so, “we should have to abandon any claims to immediate intelligibility” (2). But Heidegger doesn’t offer this as a way out. We still have to turn up, we “still have to listen, because we must think what is inevitable, but preliminary” (2). The point for Heidegger, is not to listen to a series of propositions, but instead to “follow the movement of showing” (2). I. … Maybe we're here only to say: house, bridge, well, gate, jug, olive tree, window— at most: pillar, tower … but to say them, remember, oh, to say them in a way that the things themselves never dreamed of existing so intensely.… Rainer Maria Rilke, “The Ninth Elegy” There is little more fundamental, preliminary, in the world than language. We use language, in the form of speech, constantly, whether we are saying anything or not. “Man speaks,” Heidegger writes, and goes on to describe in his essay “Language” (2001) the constant speaking that we do. “We are always speaking, even when we do not utter a single word aloud, but merely listen or read, and even when we are not particularly speaking or listening but are attending to some work or taking a rest” (187). Speaking is expression, an utterance of something internal. It is a recognition of a world. It is a way of communicating thought and it is an activity that we all do, inevitably. Speaking separates the human from the animal world, and despite advances in primatology that seek to give ‘voice’ to primates and other non-human animals, it can safely be said that our form of communication—what we call speech and know as language—is the most advanced, the most complicated. We use it to present and represent the world around us; through actual utterances (vocalization) or through the written word or through ‘unvoiced thoughts’ and dreams. We use language, but more specifically speech—naming—to transmit moods, thoughts, desires, aversions, and feelings. These expressions, mere utterances, nearly always find a source in words, whether spoken or not. Heidegger writes that this common view of language means “that only speech enables man to be the living being he is as man. It is as the one who speaks that man is—man” (187). Speaking then—utterance—surrounds us constantly, whether in the form of careful thought—in the form of an academic paper, say—or in the half mutterings and forgotten thoughts of a nearly remembered dream. Like scaffolding, the apparatus of speech sustains and explains the world, making, in a sense, the world rational, making it apparent. When we speak, we describe, and in doing so, name the world. We use words, through this process of naming, to interpret and sustain the world we see, and the world we imagine. Like Rilke’s naming of jug, and bridge, and window, and stream, we describe—and inscribe upon—the world through an activity of naming. Are we here, perhaps, to name? Is it possible not to name? Is it possible to regard and to view and to look around without naming what we see? Is it possible to feel—to experience—world without giving utterance to that feeling, that process? Sadness, grief, joy, ecstasy, hunger, thirst. Desk, light, room, pen, book, world. White, black, tomorrow, today. Each of these words is a name given to a thing I see in front of me, or a concept that I imagine (in the case of tomorrow or world). What arises in my mind has already existed. If I imagine it, it is named. The word for ‘tomorrow’ and ‘desk’ and ‘light’ precedes me, and precedes my concept of it. The idea of it is already pre-informed, and I must, in a certain sense, bend my ideas to it. When I imagine a table, I imagine my own table (or I imagine an idea of table) but that imagining must follow certain general rules; while, perhaps, it might not always require four legs and a horizontal surface, it must, at least not be, say, a pool of water, or a pile of excrement. It must have some tableness to it to be a table. It must, with Heidegger, table. Otherwise, speech is reduced to gibberish. For Heidegger however, the discussion of language points to something deeper than its “scientific and analytic” study as a communicative device. Indeed, Heidegger seeks to understand language not in reference to man or woman, not as an utterance of humanity, but in reference to itself. In doing so he abandons the conversation—that is, he casts away the traditional arguments surrounding philosophy of language; that it is a means of expression; that it is a human activity; and that it is somehow a representation of something that is—in order to seek to understand language as language, on its own terms. Heidegger is not a philosopher of language, but a philosopher of world, of being. Despite these “correct ideas” holding sway “over the whole field of the varied scientific perspectives on language…they ignore completely the oldest natural cast of language” (191). What is this “oldest natural cast of language? It is the act of language itself. Language is language and language speaks. “Most often,” Heidegger writes, “and too often, we encounter what is spoken only as the residue of a speaking long past” (195). Speech, as we normally encounter it, is like Echo herself calling out to Narcissus, doomed to repeat what has already been said, a mere remnant of what was once language, a trace left behind in the gathering silence of becoming. In both the essay “Language” and in his three lecture course “The Nature of Language” (1982), Heidegger attempts to unpack the seeming tautology of language as language. In each, he focuses on poetry as a way out, or into, a true discussion of the oldest natural cast of language. Poetry is pure speech. In poetry, language is brought to language and language speaks ( Die Sprach spricht ). In the act of poetry, the act of pure speech, the poet names (on the surface not different from how I name this table, this computer) but in the poet naming, the naming does not “hand out titles,” “apply terms,” but rather the naming is a call, a calling forth of entities that bring them into their own, allow them to take their place purely, without compromise. This calling, Heidegger (2001) states, “here calls into a nearness. But even so the call does not wrest what it calls away from the remoteness, in which it is kept by the calling there. The calling calls into itself and therefor always here and there—here into presence, there into absence” (196). II. Window with falling snow is arrayed, Long tolls the vesper bell, The house is provided well, The table is for many laid. Wandering ones, more than a few, Come to the door on darksome courses. Golden blooms the tree of graces Drawing up the earth’s cool dew. Wanderer quietly steps within; Pain has turned the threshold to stone. There lie, in limpid brightness shown, Upon the table bread and wine. Georg Trakl “A Winter Evening” Heidegger is often given short shrift as an abysmally difficult writer, as one that makes no sense and is needlessly difficult. In doing this though, we forget sometimes his eloquence, his simple beauty in writing. Of the above opening stanza, “Window with falling snow is arrayed/ Long tolls the vesper bell.” he writes (2001), This speaking names the snow that soundlessly strikes the window late in the waning day, while the vesper bell rings. In such a snowfall, everything lasts longer. Therefore the vesper bell, which daily rings for a strictly fixed time, tolls long. The speaking names the winter evening time (197). The speaking names the winter evening time. It is almost impossible to comment on that one line by Heidegger. It is as though it must exist on its own completely, without elucidation—as though in front of it we must stand as we do in front of a painting by Klee, that is, we must abandon any claim . Silent and devoted. The speaking of the poem here is not clearly different from common speech ( rede ) yet there is, via Heidegger, an invitation to experience that auracular quality of light and stillness that a gentle, dusk tinged snowfall gives; words evoking a quality so clear, so poignant that, in a sense, Heidegger’s work, at this moment, has been done. But what does this naming accomplish? What does the call call? Remember, it is not the poet that calls, but the naming which calls. The poet has only brought the words forward; it is now the words— snow, vesper bell, window— that take new life in the pure language of the poem. Entities are called forth into presence, like the speaking that names the winter evening time. Not to be present amongst us now, however; naming ‘table’ in the poem does not place it in front of us in this room. Rather, the naming places entities into a gathering which is also a sheltering. The naming brings them to be. In an act of appropriation, things come to be purely as their own, unimpeded by a predetermined expectation. They are called to themselves into an arrival. In Being and Time (1962), Heidegger famously describes the movement between present-at-hand and ready-to-hand in his analysis of the hammer, and of equipment in general. This analysis is already known, if not always clear, to most readers of Heidegger. Briefly, a hammer is ordinarily zuhanden or ready-to-hand; it is part of the background of the world, equipment used and never thought about, like this desk, this sheet of paper, this room. Our interaction with it is temporary and it is historically different for each entity and each relation. We need a hammer, we use a hammer. If all goes according to plan, the hammer remains ready-to-hand; it remains, in a sense, undisclosed and certainly unobtrusive. Our world is undisturbed by the hammer. Only when the hammer or the car or the computer is broken (or sometimes unused or unrecognized or missing) does it intrude into our world, become conspicuous as an object present-at-hand, or vorhanden . In this case, we reach for the hammer, it is broken and we suddenly notice it’s being, broken though it is. The thing which was always ready to hand—handy—is suddenly abstract, something to be examined, if only in its absence or disfunction. This can be exhibited for all entities, and it is important to note that in this analysis the zuhanden / vorhanden split is not restricted to a specific form of constructed material; zuhanden does not refer to the car, and vorhanden the sunset. No entity is ever exclusively ready-to-hand or present-at-hand; they are instead, interpenetrated with each others mode of being, one informing the other in a way that both brings things forth into the world—discloses is the word Heidegger chooses—and at the same time conceals them. As one mode is coming to be so another mode is withdrawing. This flux and movement between modes is precisely what brings the world forward, and what makes it manifest. It exists beyond where we tread and before man took dubious control of the world. We go to find a book or turn on the computer and it is missing or broken and we become aware of the object, as though for the first time. We walk to the water to glimpse the sunset and miss it, or it is less than stellar; in the sunset’s grayness, we become aware of it’s being sunset. The thing is disclosed in its withdrawal. Echoing Heraclitus, we can say that as something is coming to be, it is already becoming something other. Of similar importance to the fact that things are never all of one, or all of the other, they are also never alone. The hammer is never a single object, but is in relation always to the whole. Heidegger (1962) states, Equipment—in accordance with its equipmentality—always is in terms of its belonging to other equipment: ink-stand, pen, ink, paper, blotting pad, table, lamp, furniture, windows, doors, room. These ‘Things’ never show themselves proximally as they are for themselves…What we encounter as closest to us…is the room; and we encounter it not as something ‘between four walls’ in a geometrical, spatial sense, but as equipment for residing…it is in this that any ‘individual’ item of equipment shows itself. Before its does so, a totality of equipment has already been discovered (97). Equipment resides—dwells—in its relations, in its proximal being to other beings. Within the structure of totality, a series of relations is always occurring. The hammer is on the workbench in the carpenter’s hand in the workshop in the village under the sky and under the sun. It doesn’t stop there. Equipment surrounds us and the focus is not on what it does, or what one does with it—the carpenter with the hammer, the writer with laptop—but with the fact that it is. Equipment occurs in relation and is always occurring around us overhead, underfoot, by the stream and in the city. There is a constant exchange of relations happening, and as this occurs, so the world occurs, so the world both discloses and withdraws, into and out of itself. In a very real sense, language is also equipment. It is the thing that we use most often without thought, it is ready-to-hand (except when it’s not.) As we re- cognize the world around us, as we offer names for things and make lists, we are using language much like we might use a hammer, that is, bluntly. Most of the time it is invisible and we draw on it without wondering how we are going to say something. When language does intrude, it does so in an awkward moment, that moment when we can’t remember the right word, when we forget a phrase. At that second, it “speaks itself as language,” it reveals itself as malfunctioning equipment, and we “undergo” an experience with language, in Heidegger’s famous formulation. Language is not a tool anymore that we use to bludgeon an object, but something instead that we submit to, that we experience. In “The Nature of Language,” Heidegger (1982) writes, But when does language speak to us as language? Curiously enough, when we cannot find the right word for something that concerns us, carries us away, oppresses or encourages us. Then we leave unspoken what we have in mind and, without rightly giving it a thought, undergo moments in which language itself has distantly and fleetingly touched us with its essential being (59). The poet’s words become themselves, become appropriate, only when they no longer function in the prosaic world; they instead intrude as they come to be. Language itself brings itself to language. Names, like the entities they indicate, are always becoming something else. As noted above, language, through the poet, has brought forth entities from words previously “known.” I thought that I knew snow, but through Trakl’s re- presentation of the word, language calls forth a new image of snow, indeed calls forth snow itself. The vesper bell tolls longer, the table is for many laid. In bringing forth things , language has brought the world to presence. In everyday naming, word occludes world, preventing, in its everydayness, its coming forth, its disclosing. But what is this world that word has been brought forth into? In the same way that language speaks, world worlds. World, left alone, un-interfered with, comes into itself. It worlds. Again, this sounds like a tautology, but it is essential to Heidegger’s thought (and in my mind is more of a “god killer” than Nietzsche.) One of the most overlooked (and under-appreciated) aspects of Heidegger is his later examination and enthusiasm for the “fourfold,” or the system through which things come to be, through which things thing in a world worlding. The fourfold is the interaction of earth and sky, mortals and gods. Things come to be in the interstices and gathering of the fourfold. The fourfold provides both a place of being, and a sheltering, a place to dwell. Heidegger writes that “the things that were named, thus called, gather to themselves sky and earth, mortals and divinities. The four are united primally in being toward one another, a fourfold.” The poet has called, through the act of pure naming, things to come forth. In the purity of the fourfold—that is, when that is all that there is, when there are no other distractions, definitions, things—entities themselves can come to be. It is important to note that Heidegger is not saying that there are four formal things in the world, autonomous entities unto themselves. He is not evoking a pre-Socratic formula as to what makes up the world; instead, the four mirror each other constantly. (Heidegger calls this the ‘mirror-play.’) They interpenetrate in the same way that the modes of being of things interpenetrate themselves. There is no discrete exclusivity in being or the fourfold. What makes up things is not a precise recipe of the four main components; what makes up things is the action of the fourfold coming together, the movement of the fourfold which is a becoming. Heidegger (2001) writes that “this gathering, assembling, letting stay is the thinging of things.” And he later adds that “thinging, things are things. Thinging, they gesture—gestate—world” (197). Language brings the world to be. It works not again as a recipe added to things, but instead it is a bridge, or more precisely, a relation. Language relates world to thing, brings world to thing. In a sense, it does not say anything; rather it allows, or calls in its movement. Heidegger (2001) writes that, The intimacy of world and thing is not a fusion. Intimacy obtains only where the intimate—world and thing—divides itself cleanly and remains separated. In the midst of the two, in the between of world and thing, in their inter, division prevails: a dif-ference (199). It is in this inter that language prevails. Language is difference, it is the differential aspect between world and thing that brings world to thing. In the final stanza of Trakl’s poem “The Winter Evening,” Trakl evokes this difference in the second line when he writes, “Pain has turned the threshold to stone.” Christopher Fynsk, in his essay “Noise at the Threshold,” draws attention to this point when he writes “it is the figure of the threshold that is language itself, inasmuch as language is defined as the articulation of difference by which difference comes about” (25). Language, as used in the pure language of the poem, draws together world and thing, bridging relation between entity and world. The calling of language calls world to thing, world to being. Heidegger (2001) describes this difference as unique; “of itself, it holds apart the middle in and through which world and things are at one with each other” (200). III. Neither reading nor writing, nor speaking—and yet it is by those paths that we escape what has been said already, and knowledge, and reciprocity, and enter the unknown space, the space of distress where what is given is perhaps not received by anyone (99). Maurice Blanchot The Writing of Disaster So far, we have allowed Heidegger to put forward what language does, how it functions as a relation and how it operates as a threshold, as a bridge. What interests me is what happens beyond language, beyond the relation. What happens to the thing without the naming, without the poet, or even without the everyday chatter—Fynsk calls this ‘noise’—intruding on being? If language allows things to become by bringing thing to world, what happens when we remove this bringing, this threshold turned to pain? In “The Nature of Language,” Heidegger examines the work of the poet Stefan George, specifically “The Word”: Wonder or dream from distant land I carried to my county’s strand And waited till the twilight norn Had found the name within her bourn— Then I could grasp it close and strong It blooms and shines now the front along… Once I returned from happy sail, I had a prize so rich and frail, She sought for long and tidings told: “No like of these depths unfold.” And straight it vanished from my hand, The treasure never graced my land… So I renounced and sadly see: Where word breaks off no thing may be. That final line, “Where word breaks off no thing may be” is evoked on nearly every page of Heidegger’s essay. It is the line to which he returns over and over and bears repeating. Where word breaks off no thing may be. Where naming ends, no thing. We can interpret this in two ways (at least.) Where word—naming—breaks off, then there is nothing . Or, as I choose to read it, where word breaks off no thing may be. In this I see a hint forward, a marker left behind by Heidegger. What could this look like? What does no thing look like? Like a zen koan ( there is no mirror ) it is as thrilling and horrifying as contemplating what preceded the Big Bang. Because language as naming wasn’t always here; we weren’t always here. One or maybe two aspects of the fourfold (depending on your view of gods) were not always here, and there is no guarantee that we will always be around. What then? Heidegger (1982) describes the landscape that the poet finds, “It names the realm into which the renunciation must enter: it names the call to enter into that relation between thing and word which has now been experienced” (65). The poet, in renouncing, allows for the “may be” of “where word breaks off no thing may be.” This “may be” becomes “a kind of imperative, a command which the poet follows, to keep it from then on.” No thing is lacking. Where word breaks off, there may be, a totality, a completion. If we place the emphasis on may be , we make it affirmative, make it positive. One allows it. No thing is where the word, that is the name, is lacking. If we remove then (if we can remove) the word, the name, than that is where no thing is, that is where no thing may blossom, enrich, belong, become. What is no thing? Heidegger writes that “thing is anything that in any way is.” And just after this he writes that the “world alone gives being to the thing.” But what happens if there is no word? Word, in this formulation can be seen as an enframing, a challenging of language. By naming, by drawing a perimeter around an object, we hold it, by its definition (that is a brick) to an ordered future. If we borrow from Heidegger’s essay “The Question Concerning Technology” (1993) the idea of this standing-reserve of an ordered future, we see that “everywhere everything is ordered to stand by, to be immediately on hand, indeed to stand there just so that it may be on call for a further ordering” (322). What happens if there is no naming of the thing? Silence perhaps. Stillness. We can name—and do name—that which we know. We equate knowledge with knowing the name of something. A brick is a brick, a hammer is a hammer, the universe is the universe. By naming a thing, we create, and draw its parameters, the parameters of the thing, not as thing thinging in the fourfold, but as blunt object apparent. In the four dimensions relatively available to us, we observe (and name) that the brick takes up possibly six by four by two inches and is, in the sense that it currently occupies this time slot. It fulfills its destiny, its being, its brickness, it bricks . But what happens when we remove the name for this brick. We no longer know what to call this no-thing (if indeed we can even arrive at the point of uncalled calling.) In fact the it (this brick) is no longer a thing in the sense that by not naming—by removing the name—it still occupies the same dimension but is indiscernible from the world. It simply is , un-reliant, un- needed by me. By removing the subject (me) from it (the brick) do I not then also remove the object—or at least the duality objectifying it? Why is this important? Why does this matter? I have not really removed anything. I have not changed any thing , per se . The brick still occupies the same space in geographic and temporal dimensions. I have literally not even touched the brick sitting on my desk. But what I have done is removed the name, removed the word (the bridge, according to Heidegger) and in this (again, if this is even possible) there is something vertiginously liberating, not only for me (and my way of thinking) but also for the brick itself. Like the poet who calls the thing forward, by refusing to name, by avoiding any thing that demands me to name it, I release the thing into the fourfold. I am no longer challenging the thing to be there for me ; I do not en frame it through language. Rather I, in an act of extreme responsibility, am refusing the challenge. By refusing the name (refusing to name) one allows, (or no one allows no thing) the brick to be all things , to manifest its manifold being, to incorporate all things into its thinging . It becomes, quite literally, every thing . Because, in its infinite manifestness, it incorporates everything; the mud that gave it its current being, the water that formed the mud, the sun, the stars, the universe and it also allows it to become mud again, to become landfill, to become again, water and sun and stars and universe in an endless, infinite cycle of coming to be some thing (else). Perhaps this is what Heidegger is suggesting when he talks about the stillness at the end of his essay, “Language” (2001): The dif-ference stills particularly in two ways: it stills the things in thinging and the world in worlding. Thus stilled, thing and world never escape from the dif-ference. Rather, they rescue it in the stilling, where the dif-ference is itself the stillness (206). It is in this stillness that I can imagine a gellasenheit (here I mean both “releasement in the Heideggarean sense, as well as Meister Eckhart’s use of the term meaning “letting the world go and giving oneself to God”) of thing and world, a releasing into the stillness and silence of no thing beyond where word breaks off. It is here where I may no longer be, and yet no thing is, but may be. (shrink)

This paper studies systems of explicit mathematics as introduced by Feferman [9, 11]. In particular, we propose weak explicit type systems with a restricted form of elementary comprehension whose provably terminating operations coincide with the functions on binary words that are computable in polynomial time. The systems considered are natural extensions of the first-order applicative theories introduced in Strahm [19, 20].

A filter of a sentential logic ? is Leibniz when it is the smallest one among all the ?-filters on the same algebra having the same Leibniz congruence. This paper studies these filters and the sentential logic ?+ defined by the class of all ?-matrices whose filter is Leibniz, which is called the strong version of ?, in the context of protoalgebraic logics with theorems. Topics studied include an enhanced Correspondence Theorem, characterizations of the weak algebraizability of ?+ and of (...) the explicit definability of Leibniz filters, and several theorems of transfer of metalogical properties from ? to ?+. For finitely equivalential logics stronger results are obtained. Besides the general theory, the paper examines the examples of modal logics, quantum logics and Łukasiewicz's finitely-valued logics. One finds that in some cases the existence of a weak and a strong version of a logic corresponds to well-known situations in the literature, such as the local and the global consequences for normal modal logics; while in others these constructions give an independent interest to the study of other lesser-known logics, such as the lattice-based many-valued logics. (shrink)

Everyone, even when asserting unchallengeable authority from God or Science, thinks in language, in words and phrases, in expressions of moral, social and political impact, fighting words and words with and over which we fight. However, debates among the educated can be irrelevant elsewhere, ineffective against the highly motivated whose dogma instructs and guides them, their voting and their arming. The degeneration of “democracy” to “tyranny” such as Plato’s Republic postulated threatens in some lands “of the (...) free,” while in others it seems inexorably in progress. Today “democracy,” republic,” “liberty/freedom,” “justice,” “law and order” are adduced by their actual enemies to complement “nationalism,” “patriotism,” and frightening “empire.” Extremists on both sides decry “Tyranny!” each in fact seeking authoritarian power. All of which have instructive ancient precedents: in the History of the Peloponnesian War Thucydides offers horrific accounts of ancient nation-states “long ago and far away,” more or less democratic, that abandoned common sense, moral sense, and with them regard for value words and truth itself. In the early 2020s CE many persons and governments have done little better during the still lingering pandemic. A second horror is prompted by Thucydides’ report of civil war on Corcyra, telling how faction spawned riots, coups d’état, and outright civil war. The twenty-first-century media are uniquely potent, yet mechanics of seduction are timeless. Likewise techniques for winning true believers and votes, as illustrated by passages in Mein Kampf on the language of propaganda, its production and reception. Our hope is therefore Education for a New Era to help students to discover pitfalls of media(ted) “information,” to achieve independent critical thinking at levels of basic language use and foundations of argument. Besides recognizing mis- and disinformation as harmful, they must learn themselves to judge thoughtless use, cynical abuse, or, worse yet, brazen disdain of vocabulary indicating moral/ethical value. Scientists have key roles in this drama; humanists larger ones yet. (shrink)

A Kripke model ? is a submodel of another Kripke model ℳ if ? is obtained by restricting the set of nodes of ℳ. In this paper we show that the class of formulas of Intuitionistic Predicate Logic that is preserved under taking submodels of Kripke models is precisely the class of semipositive formulas. This result is an analogue of the Łoś-Tarski theorem for the Classical Predicate Calculus.In Appendix A we prove that for theories with decidable identity we can take (...) as the embeddings between domains in Kripke models of the theory, the identical embeddings. This is a well known fact, but we know of no correct proof in the literature. In Appendix B we answer, negatively, a question posed by Sam Buss: whether there is a classical theory T, such that ℋT is HA. Here ℋT is the theory of all Kripke models ℳ such that the structures assigned to the nodes of ℳ all satisfy T in the sense of classical model theory. (shrink)

In the article, the phenomenon of deviation, which is one of the important subjects of stylistics and rhetoric is discussed. The deviation is divided into three categories in terms of phonetic, word and grammar. The study was limited to morphological deviation defined as a transition from form to another. The morphological deviations and their relation with meaning reveal the importance of changes in word level. The linguistic and contextual elements are considered as two complementary parties in contextual linguistics. From phonetic (...) level to text consitency many linguistic elements play an important role in expression. Apart from the linguistic phenomenons that affect the meaning, non-linguistic elements should also be considered. In the research also word selection, meaning transfer and context are indicated. The deviation has expanded the use of Arabic words as well as the rich word derivation potential. In terms of Qur'ānic verses, it is an important criterion relationship of the word formula in the meaning for the Arabic language. The subtleties of this language phenomenon which is detected in Qur'ānic verses and fascinates the reader are explained by examples. Summary: Semantics, that is one of the most important areas of linguistics, initially focused on identifying the meanings of words; however, today it goes beyond that and tries to clarify the other elements of the language field. Linguists emphasize that the main goal of language studies is theme and the efforts made in this context are aimed at capturing the meaning. Metaphor and the ways of other extension of meaning should be considered in this context. As Ibn Jinnī (d. 392/1002) stated, language is generally composed of metaphor. This situation points to the necessity of examining the language with a wider perspective than the formal understanding in the field of linguistics research.In the writings of linguists such as Sībawayhi (d.180/796), Ibn Jinnī and al-Suyūṭī (d. 911/1505) and the works that focus on the superiority of wording of Qur'ān, it is seen that there is no distinction between the structure and function of language. Each sentence style is shaped for a purpose. What directs them to such a method is the thinking of first person, interlocutor and context together. It is possible to find this understanding in linguistic and religious sources such as qirā’āt, rhetoric and exegesis. Today, this relationship between grammar and meaning is one of the basic subjects of linguistics.Besides the grammatical structure, word selection is also significant. It is easy to determine a sentence with a grammatical error. While the use of a word is correct in a sentence, it may not be appropriate elsewhere. The degree of accuracy of the sentence is affected by the word selection, which is also a matter of grammatical tasks. This is the expression of the meaning in the appropriate language structure. Depending on the context of the statement, the appropriate word and phrase style should be chosen. The word choice has a great influence on the superiority of the style of the Qur'ān. When the Qur'ānicverses are examined, it is seen how well the chosen words are used.One of the main factors determining the accuracy of the word is context. The same word can be assumed to be true or false due to the context. In addition to linguistic elements, non-linguistic factors such as psychological status, socio-cultural factors and educational background are a measure of value in language.The factor that determines the function of word is the position of word in the phrase. Missing sentence structures gain new meanings as a result of a number of transformations. In Arabic sentence structures it is possible to see how the language structures affect the meaning. The expression tools should be enriched through sorting, increasing, decreasing and changing which are the factors contributing to the understanding of the superficial and deep structure of the language. In this context, the flexibility in the grammatical rules and the issue of deviation, which provides richness to phrases, are important in terms of revealing the place and value of meaning in the language.The deviation phenomenon is called as language deviation in Turkish sources. Due to a semantic and communicative concern deviation is a new way of expressing by leaving the built-in style in the language in order to strengthen the language, draw attention to the text, give a holistic effect, remove the word out of the ordinary and make the indicators more effective in terms of sound and meaning. The deviation is an important part of the stylistics, which goes beyond the path expressions and increases effect of the word. The development of the stylistics, which was accepted as an extension of the rhetoric in the modern period, raised interest rates for deviation. The deviation is divided into three categories in terms of voice, word and grammar.Morphological deviation, which is defined as the transition from one mold to another, is a phenomenon that gives the power of persuasion, influence and subtlety to the word that is appears in the mold and context of phrase. The context is the most important determinant of the deviationthrough which the literary meanings are gained that is the aim of the rhetoric. The effect of morphological deviationon meaning changes is an important subject of language researches. From this point the meanings which were added to the Qur'ānicwords by morphological deviationwas analyzed in detail in this article. Besides this, numerous verses have been handled with the idea that such a method will contribute to understanding of the subtlety meanings of the verses and transferring of their meanings to non-Arabic languages in the best way.Linguists have pointed to the meaning differences between Arabic patterns by taking into consideration the meaning potential of word molds. The language researches, which reveal the role of the word molds in determining the meanings, reflect that there are no two patterns of which meanings are exactly overlapping in Arabic language that is the views of the linguists. It is seen that the patterns such as active and passive participle, resembling participle, hyperbolic participle and gerund are used interchangeably because of their meaning relationship between each other. Similar uses of the verb should be added to this since time change in verbs is one of the linguistic phenomena in which deviationhas occurred. Types of deviationare the significant stylistic features of theQur'ānand have effects on meaning and expression. The fact that the Qur'ānpossesses an unusual style, but such a quality prevents its addressing from becoming ordinary. It is important to determine these kinds of uses, which are called as morphological deviation, to grasp the meaning of the word. When the language structures related to deviationare examined, it is understood that there is a deeply relationship between deviationand meaning. It is important to solve deviationthat enriches the meaning in the word, as well as other linguistic structures to comprehend the gnomic structure of the style of the Qur'ān. (shrink)

BL-algebras rise as Lindenbaum algebras from many valued logic introduced by Hájek [2]. In this paper Boolean ds and implicative ds of BL-algebras are defined and studied. The following is proved to be equivalent: (i) a ds D is implicative, (ii) D is Boolean, (iii) L/D is a Boolean algebra. Moreover, a BL-algebra L contains a proper Boolean ds iff L is bipartite. Local BL-algebras, too, are characterized. These results generalize some theorems presented in [4], [5], [6] for MV-algebras which (...) are BL-algebras fulfiling an additional double negation law x = x **. (shrink)