In this paper I am concerned with an analysis of negative existential sentences that contain proper names only by using negative or neutral free logic. I will compare different versions of neutral free logic with the standard system of negative free logic (Burge, Sainsbury) and aim to defend my version of neutral free logic that I have labeled non-standard neutral free logic.
There are statements of the form “There are no Fs” that we would like to count as true, yet it is hard to see how they could be true (at least, operating within the semantic framework of structured propositions). The relevant Fs are general terms that we take to be semantically fundamental or primitive, especially those native to metaphysical discourse. A case can be made the problem is no less difficult than the corresponding problem for singular terms.
Suppose there are possible worlds in which God exists but Anselm does not. Then (I argue) there are possible worlds in which Anselm does not exist, but God cannot even entertain the thought that he does not. In such worlds Anselm does not exist, but God does not know that. This, I argue, is incompatible with (a straightforward construal of) the doctrine of God's essential omniscience. Considerations involving negativeexistentials also call into question a certain picture of creation, (...) on which God chooses which particular (possible) individuals to create. They suggest that there is an element of brute contingency about which individuals exist. (shrink)
The problem of negativeexistentials arises because utterances of such sentences have the paradoxical feature of denying what they presuppose, thus undermining their own truth. There are only two general strategies for solving the problem within the constraints traditional static semantics, and both strategies attempt to explain away this paradoxical feature. I argue that both strategies are fundamentally flawed, and that an adequate account of negativeexistentials must countenance, and not explain away, this paradoxical feature. Moreover, (...) I argue that a framework of dynamic semantics can achieve this result. Thus negativeexistentials provide a case in support of dynamic semantics. (shrink)
In The Theory of Objects, Alexius Meinong used true negativeexistentials to argue in favour of non-existent objects: in order to assert veridically that an object O does not exist, one has to refer to O itself1. From Bertrand Russell's "On Denoting" onwards, it has become a commonplace to say that this argument does not work. For every sentence apparently concerning non-existents one can provide a paraphrase which eliminates the singular term contained in it and therefore dispels the (...) illusion of a reference to a non-existent item2. As is well known, this strategy implies that such a singular term is a camouflaged definite description. However, Saul Kripke and other supporters of the so-called new theory of reference have claimed that singular terms directly referring to their designation (ordinary proper names, indexicals, mass and substance terms: from now on, DR terms) are not at all synonymous with descriptions. In their opinion, true negativeexistentials represent no exception to this claim. In what follows I would like to stress that, though Kripke's critique of the Russellian treatment of negativeexistentials is convincing, his treatment of true negativeexistentials containing a DR term is flawed. Nor do other contemporary accounts that share Kripke's critique as far as these sentences are concerned fare any better. In fact, I think that Meinong's argument may be correct where true negativeexistentials containing DR terms are concerned. But I shall aim to demonstrate this elsewhere. (shrink)
(Schroeder 2007) presents a puzzle about negative reason existentials—claims like ‘There's no reason to cry over spilled milk’. Some of these claims are intuitively true, but we also seem to be committed to the existence of the very reasons that are said not to exist. I argue that Schroeder's own pragmatic solution to this puzzle is unsatisfactory, and propose my own based on a contrastive account of reasons, according to which reasons are fundamentally reasons for one thing rather (...) than another, instead of reasons for things simpliciter, as has been traditionally held. (shrink)
Recent discussion of the problem of negativeexistentials for truthmaker theory suggests a modest solution to the problem: fully general negative truths like do not require truthmakers, whereas partially general negative truths like do. This modest solution provides a third alternative to the two standard solutions to the problem of negativeexistentials: the endorsement of truthmaker gaps, and the appeal to contentious ontological posits. We argue that this modest, middle-ground position is inconsistent with certain (...) plausible general principles for truthmaking. The only stable positions are to treat all negative truths as requiring truthmakers, or admit that no negative truths require truthmakers. Along the way, we explore some previously unaddressed questions for nonmaximalist truthmaker theory. (shrink)
This paper defends the Meinongian thesis that “there are objects of which it is true that there are no such objects,” re: fictitious and illusory objects. I first formulate the problem of negativeexistentials in a novel way, and discuss why this new version is more forceful against anti-Meinongians. Additional data is then raised to vex anti-Meinongians—e.g., the truth of ‘Pegasus is imaginary’, and a reading of ‘There actually are illusory objects’ where it comes out true. The Meinongian, (...) in contrast, easily and uniformly explains the same data, by allowing the existence Pegasus, pink elephants, and the like. But contra Meinong, these cases suggest that the nonexistent objects are mind-dependent objects, and I clarify and defend this suggestion from several objections. The resulting Meinongianism is thus “conservative” in that it merely acknowledges the sense in which there are mind-dependent objects, imaginary and illusory objects being prime examples. Of special note, the “ideology” is conservative as well in that the typical Meinongian jargon of “nuclear” or “encoded” properties is paraphrased away. I end by arguing that it is presumptive to use Occham’s razor against Meinongian objects, since this would assume we can achieve empirical adequacy without them. Yet this assumption is now seen as contentious, in light of the data provided. (shrink)
Some hold that proper names and indexicals are “Kaplan rigid”: they designate their designata even in worlds where the designata don’t exist. An argument they give for this is based on the analogy between time and modality. It is shown how this argument gains forcefulness at the expense of carefulness. Then the argument is criticized as forming a part of an inconsistent philosophical framework, the one with which David Kaplan and others operate. An alternative account of a certain class of (...)negativeexistentials is developed, one which eliminates both the inconsistency and the need for Kaplan rigidity. After all, mustn’t whatever is referred to exist? (shrink)
Joseph Almog says concerning “a certain locus where Quine doesn’t exist…qua evaluation locus, we take to it [singular] propositions involving Quine [as a constituent] which we have generated in our generation locus.” This seems to be either murder, or worse, self-contradiction. It presumes that certain designators designate their designata even at loci where the designata do not exist, i.e., the designators have “Kaplan rigidity.” Against this view, this paper argues that negativeexistentials such as “Quine does not exist” (...) are true only at ordered couples of loci (times or possible worlds) < l, l’ > such that the constituents of the truthmaker are the designatum itself from l and whatever corresponds to “does not exist” from l’. (shrink)
Peter Geach's puzzle of intentional identity is to explain how the claim 'Hob thinks a witch has blighted Bob's mare, and Nob wonders whether she (the same witch) killed Cob's sow' is compatible with there being no such witch. I clarify the puzzle and reduce it to the familiar problem of negativeexistentials. That problem is a paradox, of representations that seem to include denials of commitment (implicitly, here), to carry commitment to what they deny commitment to, and (...) to be true. The best proposed solutions can be understood through this paradox; I evaluate them, and defend a new solution. (shrink)
It is widely held that there is a problem of talking about or otherwise representing things that not exist. But what exactly is this problem? This paper presents a formulation of the problem in terms of the conflict between the fact that there are truths about non-existent things and the fact that truths must be answerable to reality, how things are. Given this, the problem of singular negative existential statements is no longer the central or most difficult aspect of (...) the problem of non-existence, despite what some philosophers say. (shrink)
In this paper, we set out what we see as a novel, and very promising, approach to resolving a number of the familiar linguistic puzzles that provide philosophy of language with much of its subject matter. The approach we promote postulates semantic pretense at work where these puzzles arise. We begin by briefly cataloging the relevant dilemmas. Then, after introducing the pretense approach, we indicate how it promises to handle these putatively intractable problems. We then consider a number of objections (...) to pretense views, taking this as an opportunity to provide more detailed explanation of what a pretense account amounts to, what the pretense approach commits us to, and why it is a promising approach in philosophy of language. (shrink)
Dummett defines a ‘predicate’ as that which combines with one or more singular terms to form a sentence. His account of ‘singular term’ is syntactical, involving three necessary conditions. He discusses a fourth, ‘Aristotelian’, criterion before propounding a criterion of predicate quantification which he claims to be superior to it. He tentatively proposes that the three necessary conditions plus the criterion of predicate quantification yield sufficient conditions for being a singular term. I show that Dummett’s necessary conditions fail with regard (...) to referentially opaque contexts, negativeexistentials and wide-scope negations, and that he overlooks an important class of predicative expressions that satisfy his three supposedly necessary conditions for singular terms, namely, those that may appear either as adjectives or as nouns. I argue that Dummett cannot use the ‘Aristotelian’ criterion without circularity; and that, in any case, the ‘Aristotelian’ criterion fails dramatically. I also show that his criterion of predicate quantification fails with regard to expressions for colours. I end by casting doubts on the adequacy of any purely syntactical approach. (shrink)
Guerzoni and Sharvit (Linguistics and Philosophy 30:361–391, 2007) provide an argument that plural, but not singular, wh-phrases may contain a negative polarity item in their restriction, and connect this with the semantic property of exhaustivity. I will show that this claim is factually incorrect, and that the theory of negative polarity licensing does not need to be complicated by taking number distinctions into account. In addition, I will argue that number distinctions do not appear to be relevant for (...) polarity items in the restriction of definite noun phrases either. (shrink)
Fauconnier (1975a) noticed that existential quantification, if it is related to a scale endpoint, can force entailment along the scale and as such have the effect of universal quantification: assume a partially ordered set (X, ⪰) and a predicate Ø such that for all x, y ∈ X, x ⪰ y, if Ø is true of x, it is also true of y; then if there exists an element z that is ordered before all other elements and Ø(z) is true, (...) then Ø is true for all elements in X. This paper claims that the clausal Comparative licences context sensitive Negative Polarity Items (NPIs) like English any and ever, and German jemals (‘ever’), due to its property of enabling entailment along a scale. I argue that the licensing condition of any and ever/jemals is not itself the ‘semantic scope of a downward entailing function’ (Ladusaw 1979), but rather that a downward entailing function provides one appropriate kind of context that satisfies the actual condition which is part of the NPI's meaning (following Kadmon & Landman 1993; Krifka 1994, 1995; Jackson 1995): any and ever/jemals are indefinites that are licensed in particularly strong statements. The new idea is to define an assertion containing an indefinite NPI as strong if the existentially quantified formula entails a particular wide scope universal statement: assume that ‘Babajaga doesn't see any tree’ means that it is not true that there exists some tree that Babajaga sees. This entails that for all trees, Babajaga does not see them. In general, entailment will be granted if existential quantification is either in the scope of a downward entailing function or occurs in the context of a scale, the latter enabling entailment along the scale: if ‘Babajaga is smarter than any witch’ actually means that Babajaga is smarter than one of the smartest witches, then this entails that for all witches, Babajaga is smarter. (shrink)
Reference and Existence, Saul Kripke's John Locke Lectures for 1973, can be read as a sequel to his classic Naming and Necessity. It confronts important issues left open in that work -- among them, the semantics of proper names and natural kind terms as they occur in fiction and in myth; negative existential statements; the ontology of fiction and myth (whether it is true that fictional characters like Hamlet, or mythical kinds like bandersnatches, might have existed). In treating these (...) questions, he makes a number of methodological observations that go beyond the framework of his earlier book -- including the striking claim that fiction cannot provide a test for theories of reference and naming. In addition, these lectures provide a glimpse into the transition to the pragmatics of singular reference that dominated his influential paper, "Speaker's Reference and Semantic Reference" -- a paper that helped reorient linguistic and philosophical semantics. Some of the themes have been worked out in later writings by other philosophers -- many influenced by typescripts of the lectures in circulation -- but none have approached the careful, systematic treatment provided here. The virtuosity of Naming and Necessity -- the colloquial ease of the tone, the dazzling, on-the-spot formulations, the logical structure of the overall view gradually emerging over the course of the lectures -- is on display here as well. (shrink)
Negative facts get a bad press. One reason for this is that it is not clear what negative facts are. We provide a theory of negative facts on which they are no stranger than positive atomic facts. We show that none of the usual arguments hold water against this account. Negative facts exist in the usual sense of existence and conform to an acceptable Eleatic principle. Furthermore, there are good reasons to want them around, including their (...) roles in causation, chance-making and truth-making, and in constituting holes and edges. (shrink)
In World Poverty and Human Rights, Thomas Pogge argues that the global rich have a duty to eradicate severe poverty in the world. The novelty of Pogges approach is to present this demand as stemming from basic commands which are negative rather than positive in nature: the global rich have an obligation to eradicate the radical poverty of the global poor not because of a norm of beneficence asking them to help those in need when they can at little (...) cost to themselves, but because of their having violated a principle of justice not to unduly harm others by imposing on them a coercive global order that makes their access to the objects of their human right to subsistence insecure. In this paper, I claim that although Pogge is right in arguing that negative duties are crucial in an account of global justice, he is wrong in saying that they are the only ones that are crucial. Harming the global poor by causing their poverty provides a sufficient but not a necessary condition for the global rich to have a duty of justice to assist them. After engaging in a critical analysis of Pogges argument, I conclude by suggesting the need for a robust conception of cosmopolitan solidarity that includes positive duties of assistance which are not mere duties of charity, but enforceable ones of justice. (shrink)
In contemporary literature, the fact that there is negative causation is the primary motivation for rejecting the physical connection view, and arguing for alternative accounts of causation. In this paper we insist that such a conclusion is too fast. We present two frameworks, which help the proponent of the physical connection view to resist the anti-connectionist conclusion. According to the first framework, there are positive causal claims, which co-refer with at least some negative causal claims. According to the (...) second framework, negative causal claims are generated from mapping and comparing different scenarios, which can fully be accounted for in purely positive terms. Since the positive causal claims evoked by both frameworks pose no obvious difficulties for the physical connection view, these frameworks make it possible for the connectionists to accommodate negative causal claims into their theory. Once these strategies are available, the connectionists become able to render all the arguments starting from the observation that there are negative causal claims in our causal discourse inconclusive with regard to the viability of the physical connection view. (shrink)
Substantial metaphysical theory has long struggled with the question of negative facts, facts capable of making it true that Valerie isn’t vigorous. This paper argues that there is an elegant solution to these problems available to anyone who thinks that there are positive facts. Bradley’s regress and considerations of ontological parsimony show that an object’s having a property is an affair internal to the object and the property, just as numerical identity and distinctness are internal to the entities that (...) are numerically identical or distinct. For the same reasons, an object’s lacking a property must be an affair internal to the object and the property. Negative facts will thus be part of any ontology of positive facts. (shrink)
This paper provides a critical interpretation of the theme, point, and methodological status of Adorno’s so-called negative dialectic. The theme at issue, ‘non-identity’, comes in several varieties; and the point of Adorno’s dialectic, namely reconciliation, is multifaceted. Exploration of those topics shows that negative dialectic seques into substantive doctrines, including a version of transcendentalism and a claim about deformation. The peculiar methodological status of negative dialectic explains that adumbration. In the appraisive register, my principal contentions include these: (...) Adorno’s transcendentalism makes some sense of the aforementioned deformation claim; and negative dialectic qua method avoids mystery and metaphysical excess. (shrink)
This style of argument comes up everywhere in the philosophy of practical reason, leveled against theories of the norm of means-end coherence on intention, against Humean theories of reasons, and many other places. It comes up in normative moral theory – for example, in arguments against buck-passing. It comes up in epistemology, in discussions of how to account for the rational connection between believing the premises of a valid argument and believing its conclusion. And it comes up in political philosophy, (...) where one of its most salient occurrences is in the so-called ‘leveling down’ objection to egalitarianism. (shrink)
This essay represents part of an effort to rewrite the history metaphysics in terms of what philosophy never said, nor could say. It works from the Neoplatonic commentary tradition on Plato's Parmenides as the matrix for a distinctively apophatic thinking that takes the truth of metaphysical doctrines as something other than anything that can be logically articulated. It focuses on Damascius in the 5—6th century AD as the culmination of this tradition in the ancient world and emphasizes that Neoplatonism represents (...) the crisis of Greek metaphysics on account of the inability to give a rational account of foundations for knowing and of the ultimate principle of beings. Neoplatonism discovered how all such ultimate principles were necessarily beyond the reach of reason and speech. This apophatic insight is drawn out with the help of contemporary criticism of Neoplatonic philosophy, defining also some points of divergence. The essay then discusses the motives for thinking the unsayable in postmodern times on the basis of this parallel with Neoplatonic thought. Discourse's becoming critical of itself to the point of self-subversion animates them both. However, the tendency in postmodern thought to totally reject theology, including negative theology, is a betrayal of its own deepest motivations. This tendency is debated through an examination of the thought of Jean-Luc Nancy. While any traditional discourse can be negated, the negating and self-negating capacity of discourse itself is infinite, and this is where a perennial negative theological philosophy of the unsayable is to be located. Language, eminently the language of philosophy, as infinitely open, points in a direction which becomes equally and ineluctably theological. (shrink)
A layered approach to the evaluation of action alternatives with continuous time for decision making under the moral doctrine of Negative Utilitarianism is presented and briefly discussed from a philosophical perspective.
Corporate crises call for effective communication to shelter or restore a company's reputation. The use of corporate social responsibility (CSR) claims may provide an effective tool to counter the negative impact of a crisis, but knowledge about its effectiveness is scarce and lacking in studies that consider CSR communication during crises. To help fill this gap, this study investigates whether the length of company's involvement in CSR matters when it uses CSR claims in its crisis communication as a means (...) to counter negative publicity. The use of CSR claims in crisis communication is more effective for companies with a long CSR history than for those with a short CSR history, and consumer skepticism about claims lies at the heart of this phenomenon. (shrink)
Truthmaker maximalism is the claim that every truth has a truthmaker. The case of negative truths leads some philosophers to postulate negative states of affairs or to give up on truthmaker maximalism. This paper defends a version of the incompatibility view of negative truths. Negative truths can be made true by positive facts, and thus, truthmaker maximalism can be maintained without postulating negative states of affairs.
Thomas Pogge has argued that typical citizens of affluent nations participate in an unjust global order that harms the global poor. This supports his conclusion that there are widespread negative institutional duties to reform the global order. I defend Pogge’s negative duty approach, but argue that his formulation of these duties is ambiguous between two possible readings, only one of which is properly confined to genuinely negative duties. I argue that this ambiguity leads him to shift illicitly (...) between negative and positive duties, and ultimately to overstate the extent of the negative ones. I also argue that recognition of this ambiguity makes it possible to draw a meaningful distinction between the relevant positive and negative duties, and that Pogge’s analysis can therefore be revised in a way that reveals substantial negative institutional duties to the global poor, albeit less extensive ones than Pogge asserts. In order to demonstrate this, I discuss two aspects of the global order that Pogge has criticized: the system of intellectual property rights in pharmaceuticals and the rights of de facto rulers to dispose of a nation’s natural resources. In each case, although I do not specify the relevant negative institutional duties precisely, I try to identify intelligible questions whose answers would reveal genuinely negative duties and show that their likely answers are distinct from the conclusions asserted by Pogge and suggested by his analysis. (shrink)
The so called Ramsey test is a semantic recipe for determining whether a conditional proposition is acceptable in a given state of belief. Informally, it can be formulated as follows: (RT) Accept a proposition of the form "if A, then C" in a state of belief K, if and only if the minimal change of K needed to accept A also requires accepting C. In Gärdenfors (1986) it was shown that the Ramsey test is, in the context of some other (...) weak conditions, on pain of triviality incompatible with the following principle, which was there called the preservation criterion: (P) If a proposition B is accepted in a given state of belief K and the proposition A is consistent with the beliefs in K, then B is still accepted in the minimal change of K needed to accept A. (RT) provides a necessary and sufficient criterion for when a 'positive' conditional should be included in a belief state, but it does not say anything about when the negation of a conditional sentence should be accepted. A very natural candidate for this purpose is the following negative Ramsey test: (NRT) Accept the negation of a proposition of the form "if A, then C" in a consistent state of belief K, if and only if the minimal change of K needed to accept A does not require accepting C. This note shows that (NRT) leads to triviality results even in the absence of additional conditions like (P). (shrink)
This paper discusses the semantics of bare existentials , i.e. existentials in which nothing follows the post copular NP (e.g. There are four sections ). While it has sometimes been recognized that the interpretation of such sentences depends in some way on context, the exact nature of the context dependence involved has not been properly understood. It is shown that the meaning of bare existentials involves a set-denoting implicit argument, and that the range of interpretations found with (...) bare existentials is predictable from the general properties of implicit arguments. An explicit analysis within a dynamic setting is presented. (shrink)
Kumārila’s commitment to the explanation of cognitive experiences not confined to valid cognition alone, allows a detailed discussion of border-line cases (such as doubt and error) and the admittance of absent entities as separate instances of cognitive objects. Are such absent entities only the negative side of positive entities? Are they, hence, fully relative (since a cow could be said to be the absent side of a horse and vice versa)? Through the analysis of a debated passage of the (...) Ślokavārttika , the present article proposes a reconstruction of Kumārila’s view of the relation between erroneous cognitions and cognitions of absence ( abhāva ), and considers the philosophical problem of the ontological status of absence. (shrink)
DH Mellor has argued that there can be no negative, disjunctive, or conjunctive properties. This argument has been criticized by Alex Oliver on the grounds that it rests on a contentious identity criterion for facts, but it seems to me that a simpler criticism is available. According to this criticism, the problem with Mellor's argument is that it trades on an ambiguity in the semantics of the phrase "the fact that", according to which "the fact that" can be understood (...) as creating either an intensional or an extensional context. (shrink)
This paper seeks to differentiate negative properties from positive properties, with the aim of providing the groundwork for further discussion about whether there is anything that corresponds to either of these notions. We differentiate negative and positive properties in terms of their functional role, before drawing out the metaphysical implications of proceeding in this fashion. We show that if the difference between negative and positive properties tabled here is correct, then negative properties are metaphysically contentious entities, (...) entities that many philosophers will be unwilling to countenance. (shrink)
The purpose of socially responsible investing (SRI) is to: (1) allow investors to reflect their personal values and ethics in their choices, and (2) encourage companies to improve their ethical, social, and environmental performance. In order to achieve these ends, the means SRI fund managers employ include the use of negative screening, or the exclusion of companies involved in “sinful” industries. We argue that there are problems with this methodology, both at a theoretical and at a practical level. As (...) a consequence, current SRI offerings cannot accurately reflect the values and ethical beliefs they propose to represent. Moreover, the use of a␣priori criteria is potentially misleading, as we show by discussing examples of glue and wine making. Applying this flawed approach SRI funds fail to influence the direction of the firms they deem most in need of re-directing. Rather than engaging in the simple a␣priori assumption that some industries are “saints” while others are “sinners” (Freeman, 2007) we suggest a new framework upon which the SRI screening methodology could be grounded. Embracing the philosophical tradition of American pragmatism, we suggest that SRI methodology could be improved by engaging in an analysis based on (1) the actual impacts of the company’s products and services, (2) the company’s relationships with its specific, real stakeholders, and (3) the contingent environment (social, economic, political, legal, and cultural) in which the business operates. (shrink)
We refute the conjecture that all negative translations are intuitionistically equivalent by giving two counterexamples. Then we characterise the negative translations intuitionistically equivalent to the usual ones.
Negative attitudes toward robots are considered as one of the psychological factors preventing humans from interacting with robots in the daily life. To verify their influence on humans‘ behaviors toward robots, we designed and executed experiments where subjects interacted with Robovie, which is being developed as a platform for research on the possibility of communication robots. This paper reports and discusses the results of these experiments on correlation between subjects’ negative attitudes and their behaviors toward robots. Moreover, it (...) discusses influences of gender and experience of real robots on their negative attitudes and behaviors toward robots. (shrink)
This paper proposes a new explanation for the oddness of presuppositional and negative islands, as well as the puzzling observation that these islands can be obviated by certain quantificational elements. The proposal rests on two independently motivated assumptions: (i) the idea that the domain of manners contains contraries and (ii) the notion that degree expressions range over intervals. It is argued that, given these natural assumptions, presuppositional and negative islands are predicted to lead to a presupposition failure in (...) any context. (shrink)
Unlike natural numbers, negative numbers do not have natural physical referents. How does the brain represent such abstract mathematical concepts? Two competing hypotheses regarding representational systems for negative numbers are a rule-based model, in which symbolic rules are applied to negative numbers to translate them into positive numbers when assessing magnitudes, and an expanded magnitude model, in which negative numbers have a distinct magnitude representation. Using an event-related fMRI design, we examined brain responses in 22 adults (...) while they performed magnitude comparisons of negative and positive numbers that were quantitatively near (difference 6). Reaction times for negative numbers were slower than positive numbers, and both showed a distance effect whereby near pairs took longer to compare. A network of parietal, frontal, and occipital regions were differentially engaged by negative numbers. Specifically, compared to positive numbers, negative number processing resulted in greater activation bilaterally in intraparietal sulcus (IPS), middle frontal gyrus, and inferior lateral occipital cortex. Representational similarity analysis revealed that neural responses in the IPS were more differentiated among positive numbers than among negative numbers, and greater differentiation among negative numbers was associated with faster reaction times. Our findings indicate that despite negative numbers engaging the IPS more strongly, the underlying neural representation are less distinct than that of positive numbers. We discuss our findings in the context of the two theoretical models of negative number processing and demonstrate how multivariate approaches can provide novel insights into abstract number representation. (shrink)
Along the same line as that in Ono (Ann Pure Appl Logic 161:246–250, 2009), a proof-theoretic approach to Glivenko theorems is developed here for substructural predicate logics relative not only to classical predicate logic but also to arbitrary involutive substructural predicate logics over intuitionistic linear predicate logic without exponentials QFL e . It is shown that there exists the weakest logic over QFL e among substructural predicate logics for which the Glivenko theorem holds. Negative translations of substructural predicate logics (...) are studied by using the same approach. First, a negative translation, called extended Kuroda translation is introduced. Then a translation result of an arbitrary involutive substructural predicate logics over QFL e is shown, and the existence of the weakest logic is proved among such logics for which the extended Kuroda translation works. They are obtained by a slight modification of the proof of the Glivenko theorem. Relations of our extended Kuroda translation with other standard negative translations will be discussed. Lastly, algebraic aspects of these results will be mentioned briefly. In this way, a clear and comprehensive understanding of Glivenko theorems and negative translations will be obtained from a substructural viewpoint. (shrink)
For the one who studies the socio-anthropology of religions, the book itself is the main character of the fascinating journey that Moshe Idel proposes in Perfections that absorb. Cabala and interpretation Starting from the imaginary of the book in the Judaic mystical literature, as presented by Moshe Idel, we have found four main hypostases of the book: the book as a pre-existent paradigm, the book as creation, the book as a paradox, and the book as a knowledge tool. We have (...) noticed that these hypostases are to be found also in the folk products from the traditional Romanian settings this showing the presence of similar aspects regarding the representations of the book on a social imaginary level in various cultural areas. Thus, we have tried to present the hermeneutics of the negative and its applicability for the socio-anthropological study of some divinatory phenomena that make reference to the book or whose central point is the book. Moreover, the conclusions of this analysis have demonstrated the large applicability of the hermeneutics of the negative so well described by professor Moshe Idel. This can also be extended to other socio-humanistic sciences. (shrink)