Krabbe (2003, in F.H. van Eemeren, J.A. Blair, C.A. Willard and A.F. Snoeck Henkemans (eds.), Proceedings of the Fifth Conference of the International Society for the Study of Argumentation, Sic Sat, Amsterdam, pp. 641–644) defined a metadialogue as a dialogue about one or more dialogues, and a ground-level dialogue as a dialogue that is not a metadialogue. Similarly, I define a meta-argument as an argument about one or more arguments, and a ground-level argument as one which is not a meta-argument. (...) Krabbe (1995, in F.H van Eemeren, R. Grootendorst, J.A. Blair, C.A. Willard and A.F. Snoeck Henkemans (eds.), Proceedings of the Third ISSA Conference on Argumentation, Sic Sat, Amsterdam, pp. 333–344) showed that formal-fallacy criticism (and more generally, fallacy criticism) consists of metadialogues, and that such metadialogues can be profiled in ways that lead to their proper termination or resolution. I reconstruct Krabbe’s metadialogical account into monolectical, meta-argumentative terminology by describing three-types of meta-arguments corresponding to the three ways of proving formal invalidity he studied: the trivial logic-indifferent method; the method of counterexample situation; and the method of formal paraphrase. A fourth type of meta-argument corresponds to what Oliver (1967, Mind 76, 463–478), Govier (1985, Informal Logic 7, 27–33), and Copi (1986) call refutation by logical analogy. A fifth type of meta-argument represents my reconstruction of arguments by parity of reasoning studied by Woods and Hudak (1989, Informal Logic 11, 125–139). Other particular meta-arguments deserving future study are Hume’s critique of the argument from design in the Dialogues Concerning Natural Religion, and Mill’s initial argument in The Subjection of Women about the importance of established custom and general feeling vis-à-vis argumentation. (shrink)

Using a short excerpt from Anselm's Responsio as an example, this paper tries to present logical reconstruction as a special type of exegetical interpretation by paraphrase that is subject to (adapted) hermeneutic maxims and presumption rules that govern exegetical interpretation in general. As such, logical reconstruction will be distinguished from the non-interpretative enterprise of formalization and from the development of theories of logical form, which provide a framework in which formalization and reconstruction take place. Yet, even though logical reconstruction (...) is dependent on methods of formalization, it allows us to use formal methods for the analysis and assessment of natural language texts that are not readily formalizable and is thus an important tool when it comes to applying the concepts and methods of formal logic to such texts. (shrink)

Traditionally, logic has been the dominant formal method within philosophy. Are logical methods still dominant today, or have the types of formal methods used in philosophy changed in recent times? To address this question, we coded a sample of philosophy papers from the late 2000s and from the late 2010s for the formal methods they used. The results indicate that the proportion of papers using logical methods remained more or less constant over that time period but (...) the proportion of papers using probabilistic methods was approximately three times higher in the late 2010s than it was in the late 2000s. Further analyses explored this change by looking more closely at specific methods, specific levels of technical engagement, and specific subdisciplines within philosophy. These analyses indicate that the increasing proportion of papers using probabilistic methods was pervasive, not confined to particular probabilistic methods, levels of sophistication, or subdisciplines. (shrink)

We highlight the limitations of formal methods by exhibiting two results in recursive function theory: that there is no effective means of finding a program that satisfies a given formal specification; or checking that a program meets a specification. We also exhibit a ‘simple’ MAS which has all the power of a Turing machine. We then argue that any ‘pure design’ methodology will face insurmountable difficulties in today’s open and complex MAS. Rather we suggest a methodology based on (...) the classic experimental method – that is ‘scientific foundations’ for the construction and control of complex MAS. (shrink)

In this article I want to continue the characteristics of philosophical methods specific to analytical philosophy, which were and are important for Professor Jan Woleński. So I refer to his work on the methods of analytical philosophy, but I also point out a few new methods that have grown up in the climate of studies of philosophers, especially analytical ontologists. I will therefore describe the following methods: generalization, specialization, formalization, de-formalization and topological hermeneutics. Instead of the term “method” I (...) use interchangeably the terms “operation” or “procedure”. I will show that each of these operations makes an important contribution to ontological investigations, and, in particular, to formal ontology. (shrink)

Techne and Truth. The problem of techne in the dispute between Gorgias and Plato -/- The source of the problem matter of the book is the Plato’s dialogue „Gorgias”. One of the main subjects of the discussion carried out in this multi-aspect work is the issue of the art of rhetoric. In the dialogue the contemporary form of the art of rhetoric, represented by Gorgias, Polos and Callicles, is confronted with Plato’s proposal of rhetoric and concept of art (techne). The (...) ingenuous and dramatic structure of the dialogue composed of three acts, in each of which Socrates’ consecutive interlocutors emerge, is difficult to interpret. It seems, however, that even though the first conversation between Socrates and Gorgias constitutes a small part of the dialogue, it forms the foundations for the discussion. This part, dealing with such important issues as the subject of art, knowledge, power and relation between art and good, is the starting point for the conversations which follow. What do the differences between the Gorgias’ and Plato’s concepts of art consist in? Any attempt to answer the question requires presentation of the background for the discussion taking place in Plato’s work as well as the reconstruction of Gorgias’ vision of the art of rhetoric and art in general, defining the relation between art and knowledge. The latter may be undertaken on the basis of two paraphrases of the treatise “On Non-existence”, two epideictic speeches entitled “Helen” and “Palamedes” and some smaller fragments which have been preserved from Gorgias’ creative output. The treatise “On Non–existence”, very paradoxical in its philosophical meaning, testifies to new, sophistic thinking represented by Gorgias of Leontinoi. The treatise is the polemic and attack on Eleatism based on certain principles and methods elaborated by the Eleatics themselves. It also shows that Gorgias – using traditional Eleatic schemes – is opposed to this tradition. Even though the treatise does not discuss the problem of art directly, it anticipates the considerations from epideictic speeches. “Helen” and “Palamedes” constitute further stages in the development of Gorgias’ thought and concept of art combining typically epideictic elements with some philosophical convictions. Gorgias refers to the Eleatic theme considering the issues of truth, knowledge and belief, yet defining them in the empirical spirit. Solutions in the cognitive sphere determine the horizon of Gorgias’ rhetoric. The word is separated from the existence. Human cognition is limited and therefore the word and visual images affect the belief. This promotes the great importance of rhetoric, painting and sculpture, i.e. the areas which influence in a specific way – creating the “delusion” (ἀπάτη). Through idealization art provides pleasure, which is its objective. Therefore the task of art is to create delusion. The rhetor of Leontinoi discusses the issue of “how?” to use the word ‘rhetoric’. Gorgias is aware that rhetoric may be used to talk about what is unknown and that technical correctness of a rhetoric statement is not identical with the truthfulness of the proclaimed message. Mentioning it, Gorgias shows his respect to the truth as a value which should be respected in speech on the one hand, and on the other emphasizes that the truth in itself has no persuasive power. For this reason it is not enough to proclaim the truth, but, to convince the listeners, the orator should possess the skill of speaking. What is then the relation between truth and art emerging from epideictic speeches? Gorgias undoubtedly emphasizes the formal aspect of speech, as rhetoric is art, thus an ability based on certain principles. According to Gorgias, the truth is the value which should be respected in speeches. Rhetoric is able to create a fictive world, as a great range of reality remains outside direct human experience. Rhetoric does not oppose the truth but discussing not only what is directly given concerns the area outside the sphere of direct experience. This concept of rhetoric is the basis of the discussion about art carried out in the dialogue “Gorgias”. Even though the first of the discussions in the dialogue – the conversation between Socrates and Gorgias – is directly concerned with rhetoric itself, numerous remarks testify to its much wider character. This is best exemplified by the way of carrying out the conversation by Socrates, who, asking questions about rhetoric practised by Gorgias, throughout the whole conversation compares it with other skills. Additionally, the manner and the structure of the conversation prove that Plato considers the issue of rhetoric from a wider perspective determined by the issue of art. The specific feature of the conversation is ordering it around main issues – such notions as πρᾶγμα, ἐπιστήμη, δύναμις, each of which has its own meaning in Plato. In the first part of Gorgias Plato presents the principles previously occurring in other dialogues in a certain order, thus constructing the structure of the conversation with Gorgias. The notions are not novum in Plato but the fact that he clearly wants to systematise them and present a certain concept of art is a new and significant aspect. This tendency is of paramount importance for the discussion because Gorgias’ answers are evaluated by Plato from the perspective of this clearly set concept consisting of not only established notions but also certain principles. The discussion between Socrates and Gorgias introduces a theme which is crucial for the dialogue: the relation between art and good, i.e. the technical and ethical spheres. The issue is introduced by Gorgias, who mentions that rhetoric may be used for evil purposes. On this basis Socrates proves that if rhetoricians can use rhetoric for evil purposes, they have no knowledge concerning the subject of their art – justice, because one who knows what is just, always acts justly. Thus the relation between the technical and ethical spheres transpires to be the main point of contention. The question is whether a technician following the principles of the art he practices may act against good. This paradoxical statement based on the well-known Socrates’ principle "nemo sua sponte peccat" acquires philosophical foundations in the dialogue. In its remaining two parts Plato presents a justification, placing the principle within the framework of a certain concept of art, as a result of which not only rhetoric but also many other skills are criticised. The notions on which the conversation with Gorgias focuses are more precisely defined in the subsequent parts of the dialogue. Additionally, Plato presents twice the conditions which art should fulfill. They oblige the “technicians” to know the nature and purpose of the art and to know the causes of undertaken activities and to be able to justify them. These conditions determine the relation between the two spheres – technical and ethical. According to Plato, art may not act against good because it should be the objective of its activities. Certain concepts of good and knowledge outlined in the dialogue are the guarantees of “technicality”. Good, which should be respected by every art, is understood objectively and is contrasted with subjective pleasure. Knowledge, which should be the basis of art, opposes experience, which uses observation and recollection. Additionally, the definition of knowledge, significance of order in the world assuming the form of “geometrical equality”, significance of mathematics becoming the ideal of exactness indicate that Plato’s concept of knowledge is formed in Gorgias. These conclusions render it impossible that the results of any activity deserving the name of art should oppose good. And this is Plato’s main reproach of Gorgias’ concept, who wrote about false speeches possessing the power of conviction because they were written according to the principles proof of art or who defined tragedy as “a deceit, where he who cheats is more just than he who does not and the cheated is wiser than he who was not cheated”. Such determination of the relation between the technical and ethical sphere resulted from Gorgias’ concept of the world and fundamental philosophical principles. The whole concept of art described by Plato in the dialogue opposes the view presented by Gorgias. According to Plato, every technical activity has a defined object (ἔργον), is based on knowledge (ἐπιστήμη) and is always aimed at the good of human soul or body. The danger revealed and presented in the dialogue by Plato exists in the very concept of art presented by Gorgias, i.e. in its empirical foundations and the resulting understanding of the relation between art and good. Gorgias’ concept of art based on empirical cognition, which concerns the world of phenomena and rejects the possibility of perfect knowledge, leads, according to Plato, to a dangerous falsification of the relation between art and good. Plato proves that this weakness of Gorgias’ concept is revealed when confronted with these representatives of “the magnificent art” who are not protected against radicalism by the adherence to the moral tradition. The comparison of two, completely contrasting concepts of art based on different philosophical understanding of knowledge and good is decisive for the criticism of rhetoric in Gorgias. The concept presented by Plato criticises contemporary rhetoric and sophistry but determines the direction of research of the real art of rhetoric. (shrink)

Different notions of analysis have been both theorized and put to use in early analytic philosophy. Two of them stand out: connective analysis and analysis as paraphrase. The latter played a central role in the development of analytic philosophy from Frege to Quine and beyond. With the advent of formal semantics of natural language in the 1970s, paraphrase came to be characterizable as translation into a formal “target language”. While I claim that the method cannot (...) achieve its original philosophical aims, I insist that, in spite of them, it is far from being a theoretically empty operation and that it lives on in some contemporary philosophical enterprises. (shrink)

This thesis is a collection of three self-contained papers on related themes in the area of formal and social epistemology. The first paper explores the possibility of measuring the coherence of a set with multiplicative averaging. It has been pointed out that all the existing probabilistic measures of coherence are flawed for taking the relevance between a set of propositions as the primary factor which determines the coherence of the set. What I show in this paper is that a (...) group of measures, namely the confirmation-based ones, can be saved from this problem if we adopt a nonlinear averaging function to measure the coherence of a set. The second paper discusses how people should conciliate in disagreements. Some epistemologists take linear averaging as the only way of conciliating and claim that conciliating leads to fallacious results. In the paper, I show that the problem is not conciliating, but taking linear averaging as the only way to conciliate. Since there is no reason for us to insist on conciliating with linear averaging, we can adopt nonlinear averaging functions for conciliating and thereby avoid the formal deficiencies. The third paper focuses on the pragmatic results of taking conciliating as a general strategy in disagreements. There is a potential dilemma about conciliating: if everyone always conciliates, it is likely for an epistemic bubble to arise. If everyone refuses to conciliate, an epistemic echo chamber may appear. A possible way of solving the dilemma is to develop a diachronic strategy which tells people how to both conciliate and update their estimate of their interlocutors’ reliability. Although the three papers differ in the subject, they jointly offer some unifying reflections on the way we approach philosophical problems with formal tools. From 5 the first two papers, we see that a formal analysis of a philosophical position is incomplete if philosophers fail to consider a sufficiently wide range of formal tools. The third paper, on the contrary, shows that we should change the ordinary way of modelling a notion if required. This thesis concludes by proposing a pluralistic view of formal methods in formal epistemology. (shrink)

The thesis aims at a methodological reflection of logical reconstruction and tries to develop this method in detail, especially with regard to the reconstruction of natural language arguments. First, the groundwork for the thesis is laid by presenting and, where necessary, adapting its foundations with regard to the philosophy of language and the theory of argument. Subsequently, logical reconstruction, especially the logical reconstruction of arguments, is presented as a hermeneutic method and as a tool for the application of (...) (formal) logic and argumentation theory to natural language arguments. Logical reconstruction is presented as a special type of exegetical interpretation by paraphrase that is subject to (adapted) hermeneutic maxims and presumption rules that govern exegetical interpretation in general. However, in contrast to the interpretation of texts by natural language paraphrases, logical reconstruction leads to interpretantia that are logically explicit formal language texts and can be analyzed using formal methods and meta-theoretical concepts that are not directly applicable to natural language texts. By providing explicit and precise records of different readings, logical reconstruction can thus help to clarify (and maybe even solve) persistent interpretation controversies. Through an adaptation and specification of hermeneutic maxims and presumption rules, the thesis aims at providing suitable means for the systematic guidance and evaluation of logical reconstructions of argumentative texts. As a genuinely interpretative undertaking, logical reconstruction will be distinguished from the non-interpretative enterprise of formalization and from the development of theories of logical form, which provide a framework in which formalization and reconstruction take place. As exegetical interpretations, logical reconstructions of texts that are not readily formalizable can still be assessed with respect to their hermeneutic quality. The hermeneutic method of logical reconstruction can thus widen the scope for the application of logic and argumentation theory, because it allows us to use formal methods for the analysis and assessment of "difficult" natural language texts in a non-arbitrary, albeit indirect way. The last part of the thesis presents a manual for the logical reconstruction of natural language arguments, whose application is illustrated step by step. (shrink)

Provides comprehensive coverage of logical structure as well as the techniques of formal reasoning.

Masses of Formal Philosophy is an outgrowth of Formal Philosophy. That book gathered the responses of some of the most prominent formal philosophers to five relatively open and broad questions initiating a discussion of metaphilosophical themes and problems surrounding the use of formal methods in philosophy. Including contributions from a wide range of philosophers, Masses of Formal Philosophy contains important new responses to the original five questions.

Mainstream economics has been accused of excessive mathematization, whereas the rejection of mathematical and other formal methods is often cited as a crucial trait of Austrian economics. Based on a systematic discussion of potential benefits and drawbacks of formalization, this paper corroborates legitimate concerns that predominant types of mathematization induce a shift of attention away from the key concepts of Austrian economics. Taking this shift to the extreme, predominant modes of mathematization tend to accompany a detachment from ‘reality’ incompatible (...) with Austrian pleas for realisticness. Contrary to popular prejudice however, the most prominent representatives of the Austrian School including Carl Menger, Ludwig Mises, Friedrich Hayek, Israel Kirzner, and Peter Boettke neither provide a justification for a wholesale rejection of formalization nor actually reject it. Adequate formalization can serve as a remedy for lacking logical and semantic rigor in standard mathematical economics as well as in murky verbal chains of reasoning. (shrink)

Warren Goldfarb, Deductive Logic, Hackett Publishing Company, 2003.    : 0872206602. Deductive Logic is an introductory textbook in formal logic. The book is divided into four parts covering truth-functional logic, monadic quantifi- cation, polyadic quantification and names and identity, and there are exercises for all these topics at the end of the book. In the truth-functional logic part, the reader learns to produce paraphrases of English statements and arguments in logical notation, then about the semantic properties of (...) such paraphrased statements and arguments, such as satisfiability, implication and equivalence and finally there is an axiomatic proof method and some important extras such as disjunctive normal form and expressive adequacy. Parts two and three mirror this analysis/assessment/reflection structure for monadic and polyadic quantification, though this time the proof system is a natural deduction one, and part three contains a completeness proof for that system. The fourth part of the book introduces names, the identity predicate and descriptions and examines the additional expressive power which these provide. I do not think there should be any doubt that this is an excellent book; it presents the essential topics of a first logic course with accuracy, clarity and attention to detail, and it makes material that can be confusing the first time round—say, the translation of conditionals—transparent and easy to understand. But there are a lot of good introductory logic textbooks out there, so I will say something about how it resembles and differs from some other books, and then discuss one minor irritation with this one. (shrink)

Provides comprehensive coverage of logical structure as well as the techniques of formal reasoning.

This paper investigates how participants in cross-functional project groups use a formal work method in their sense making when dealing with the complexity of innovative work, especially in its inventive phase. The empirical basis of the paper is a prospective case study in which three project groups in three different companies are followed as they try to frame and solve their innovation tasks consisting in problems of a relatively general and vague character. The data are analyzed by means (...) of a modified version of the principles of grounded theory. This means that the lessons drawn from the empirical data are guided by a relational sense making perspective in which the formal method used by the participants is seen as a technological artifact. Among the lessons learned by using this frame of reference are that a formal method may be seen as an entity with a meaning depending on the relations it is embedded in; as an enacted cue for interpretation and action; and as a non-human actor. Compared to the tradition of organizational development, these lessons represent an alternative conception of the implementation of a work method and illuminate prevailing notions about the importance of improvisation in innovation. (shrink)

ion is arguably one of the most important methods in modern science in analysing and understanding complex phenomena. In his book The Philosophy of Information, Floridi (The philosophy of information. Oxford University Press, Oxford, 2011) presents the method of levels of abstraction as the main method of the Philosophy of Information. His discussion of abstraction as a method seems inspired by the formal methods and frameworks of computer science, in which abstraction is operationalised extensively in programming (...) languages and design methodologies. Is it really clear what we should understand by levels of abstraction? How should they be specified? We will argue that levels of abstraction should be augmented with annotations, in order to express semantic information for them and reconcile the method of level of abstraction (LoA’s) with other approaches. We discuss the extended method when applied e.g. to the analysis of abstract machines. This will lead to an example in which the number of LoA’s is unbounded. (shrink)

Reproduced with the kind permission of the author. Currently available in the collection I Looked Alive . © 2010 The Brooklyn Rail/Black Square Editions | ISBN 978-1934029-07-7 Originally published 2003 Four Walls Eight Windows. continent. 1.1 (2011): 43-51. Introduction Ben Segal What interests me is instigated language, language dishabituated from its ordinary doings, language startled by itself. I don't know where that sort of interest locates me, or leaves me, but a lot of the books I see in the stores (...) seem to lack language entirely. Gary Lutz (2006). This issue of continent.'s fiction section features a reprint of “This Is Nice of You” from the first edition of Gary Lutz's collection I Looked Alive . That book was originally released by Four Walls Eight Windows in 2003 and has since been reissued in 2010 by The Brooklyn Rail/Black Square Editions. Calamari Press has also reissued Lutz's Stories in the Worst Way (originally published by Knopf, largely forgotten and dismissed, and then re-issued by the too-short-lived 3rd Bed). “This Is Nice of You” was edited for the re-issue of I Looked Alive and, as the original book is out of print, the earlier version of the story has been hard to come by for some time. This initial version is a bit longer than the new version—Lutz is a master of tightening down his texts to their most linguistically intensified cores—but it is in no way sloppy. It is a great privilege for continent. to be able to make available rare texts of (first) aesthetic and (second) scholarly value. For those readers unfamiliar with Gary Lutz, I believe this story will serve as a worthy introduction. Like Raymond Carver, Diane Williams, Christine Schutt, and so many other important twentieth century and contemporary short story writers, Lutz studied with and was edited by Gordon Lish. This connection is apparent in his attention to sound and the sentence as compositional unit, but Lutz's is a unique voice. “This Is Nice of You” bears Lutz's trademark torqued and turning syntax, his sexed-but-nameless characters, his rendering of the human body and its emissions as utterly discomfiting. Lutz's preoccupations with the mundane raise ordinariness, via startling language and observation, to grandiosity and grotesquery. In the fall of 2008, Lutz delivered a lecture entitled “The Sentence is a Lonely Place” to writing students at Columbia University. The lecture was later printed in The Believer (and is linked below). In it, he spoke about the importance of the sentence as a compositional unit, as even the distinguishing formal characteristic of prose. Specifically, Lutz explained that, from Lish, he had developed a "poetics of the sentence." Accordingly, Lutz constructs his stories at the level of the sentence, paying extreme attention to the material of words- their letters and their sounds- and the way they abut one another and interact on this material level even before they are employed in the service of traditional aims of fiction like meaning or story. Lutz often uses a(n almost constraint-related) technique called consecution. Letters or sounds from one word are carried forward into the following, producing drama and movement in the language itself at a level entirely apart from that of plot. For example, you can see how the 't's in the first sentence of “This Is Nice of You” repeat fast and hard through met and then soften into the 'th's of brothers and they. This close attention to the specific material and characteristic conditions of prose means that Gary Lutz's work always involves both a happening in language and of language. “This Is Nice of You” has a richness and depth that is hidden not in symbolism or obscure reference but on the surface of the page, in the language of every sentence. FURTHER READING Lutz, Gary. “ The Sentence Is a Lonely Place. ” The Believer January, 2009. Web. Short stories and excerpts at Web del Sol . Web. Taylor, Justin. “ An Interview with Gary Lutz .” Bookslut. July, 2006. Web. THIS IS NICE OF YOU [156] [1] I was a man dropping already well through my forties, filthy with myself, when, taking a turn at the toilets one afternoon, I met two brothers-they said they were brothers-who swore they had a sister, a schoolteacher, an officer of instruction at the county college, a whirlwind midlife turmoil of everything already put to ruin, who had gone off from a new marriage in an old car, an upkept and ennobling sedan, but had returned now to the apartment and [157] was living there alone with the little runoff there was from the marriage-some outcurved appliances, apparently, and low-posted furniture promoting its own mystery but becoming figurable in certain concentrations of TV light-and, above all, a telephone (on a pedestal, they insisted), the handpiece of which she gripped in lieu of exercise, or in fury, and I thus let out my little, reliable cry that I was in fact a student of the telephone, that it was a debasing apparatus in the main, with its meager economy of bells and tones, and the intimacy of the mouthpiece that sent your breath, tiny aftervapors of it, back toward your lips, so that regardless of the party accepting the outgoing products of your voice, you were, at most, in a further, rivaling exchange with yourself alone, and this is what must have brought the two of them around, the men who proclaimed brotherhood with the woman, because they offered me her phone number, put it at my disposal on a piece of paper one of them had already committed it to, a tearing from a menu, and the looks the men were now giving me had deletions in them, already, of my exact, beanpole shape and size. So off I went to a pay phone, the nearest canopied one I could find. The woman answered after the second ring and said she needed a lift right that very moment into the little, unlevel city close by. She was idling in the doorway of the building when I pulled up in front, and I helped her into the car, then got back in myself. I had always had a way of not having to look at people that nonetheless brought them to me in full, and so I still am certain of the susceptive and impressible comp-[158]lexion, the shimmer on the mouth, a lipstick of low brilliance, a difficulty around the eyes, the hair short and rayed out exclamation ally, skin bagged up over the elbow bone, conflict even in how her arms stayed at her sides—in sum, a spinal loveliness for me, an off-blonde quantity with shadowed, thumbworn hollows that put me out of as much as I might have ever known of women before. I set the two of us into the narrow traffic, and I remember telling her, by way of explaining the little burden which I had shifted, by now, from the shelf of the dashboard and onto my lap, that when you lived in filth, as I then did, a daily newspaper came to count for a lot, although instead of the thick-supplemented local paper I bought a trimmer one from a backlying town—not, of course, for any affluences of native data it carried, but as an article of house ware: a rough immaculacy in four lank sections, a set of fresh, hygienic surfaces to come between the table, say, and whatever I had going for me at the table, if the table was where I was going forward—because what else so cheap comes so clean and far-spreading? The woman told me that her own trouble with paper was that through a modest hole, no larger than a quarter, that had been drilled a foot or so above the floor (the standard height, she had reasoned, of legitimate electrical outlets), and by means of which her faculty office had at last gained communication with the roomier but unoccupied office next door, more and more often shot a single sheet of paper, plain copier paper she had rolled just barely into a tube, [159] so that after landing on the floor of the neighboring office the paper would preserve little if any of the curl, and there would be nothing written or typed on it, of course, and it was always a blank sheet that had been ageing on her desk for some time and had already been moved around, or advanced, from station to station on the desktop, coming into further creaselets and crimps and other infirmities—paper, in short, still too bare and unfraught to be thrown responsibly and forgettably away, and yet too seasoned and beset with irritations of the surface (a molelike blemish, say, or what looked like a tiny hair, an eyelash, sunk into it, or frecklings, or notational pressings of a fingernail), too wrought, in sum, for the paper to be appointed to any secure curricular purpose. Her office, she claimed, was in fact full of such paper, much-handled and singularized sheets of it by the loose, functionless hundred. I had to get it across to the woman that I myself no longer had an office, or any other place to divide me reliably from everybody else, and that for much of the daylight I thus appeared to be among people because I kept putting myself where people came together into even closer-fitting assortments, the viewing areas and showrooms and rotundas and such: I took in the lean-to look of the women, the tongues coming and going in what the men kept thinking of to say—whole families of low knees for me to bark my shins against during the crowded and involving way out. At home afterward, in the one room where my life was packed down, I would keep my nose stuck in the safehold of the phone [160] book, where the names of people suffered reduction to mere episodes of the alphabet and underwent humbling declensions down every column (Lail, Lain, Laine, Lainerd), and he names of streets, of the towns and townships, got docked in crude, heedless abbreviations (the vowels almost always the first to get poked out), and I would run my eyes over the telephone numbers themselves, each sequence of digits another fallible run of the infinite. I thus corrected my feelings for people and assembled myself emotionally into whatever else I had at hand—the obligating arms of the clothes hangers, usually, or the keen-angled understructure, the guardian legginess, of the ironing board. The woman said that in her case, though, it was more a matter of making slow circuits of the classroom where she had to put across the Emporial Sciences, retail theory and methods, to heat-giving and suggestive young women, some of them world cruelties already. There was the cooing of empty stomachs in the hour just before lunch, and the braying and fizzle of loaded stomachs in the low hours of the afternoon. She would recite her notes in a voice barely loyal to anyone octave, a tiny alluvium of slaver hardening at the corners of her mouth on the days she gave the glassy lozenges a slow, warming suck, and she would take lowering notice of how whatever she said succumbed at once to freak spellings and razzing paraphrase in the big, dividered notebooks; and because in midafternoon light the world looked as thorough, as filled in, as it was ever going to get, a better way to set about ruining her eyes was to review how hair had [161] established itself on the arms of the young women, because almost every arm had brought across itself a welcome and diversifying shadow. On one girl it would be a fine, driftless haze afloat above the white of the arm, never seeming to touch down on the skin itself. (An atmosphere, at most, of chestnut brown.) On another, it was as if copper wire, the narrowmost lengthlets of it, had been stuck into the fleshy batter of the thick, freckled forearms. On a third: a field of it–wheat-colored, thin-spun. On a fourth; a differencing, darkish updrift that shaded off as it approached the inner bend of the elbow, then re-emerged at the base of the upper arm as whiskery fringe. On others it was a brassy or rust-colored frizz, or it was as coarse as cornsilk, or it looked fussed on, as if the arm had been slowly stroked with charcoal. But here the woman broke off, or I may well have made an interruption of my own—I think I must have asked whether she was hungry, and she said if I was, and so on one of the lesser streets I parked the car and led her down into a belowstairs eating house I still remembered. Sandwiches were presently lowered in front of us. I watched her remove the festooned toothpick from hers and then play her fingers over the toasted planes before she took a fond first bite. "This is nice of you," she said. I must have looked at her in the way I then had of getting people to speak so they would not seem to be dwelling any longer on my features, because if on the well-set face the mouth and eyes are said to seem frozen in elegant orbit about the til) of the nose, then mine was a face that behold-[162]ers, regarders, could not help trying to round off with greater success, to goad the particulars of it back into the arcs they had wandered away from—the mouth, for instance, having been pursed and pinched suchwise that it seemed resident more on one side of the face than the other—and there were other signs of original strife to be busied with (slapdash eyebrows unbunched, it appeared, from reserves of hair elsewhere on my person; a showing of adult acne, a shrivelly little relevance of it, confined to the declivity of my nose); and so to be polite, the woman thus sank her gaze into her sandwich, and told me, in a voice lowered accordingly, that, one late-childhood summer, she had devoted herself to collecting postage stamps: it was a tongue-involving sideline to early-arriving puberty, and she liked having to lick the pale, gummed hinges instead of the sticky backs of the stamps themselves before entering everything into the hosting album; and once, during some foul weather between her and a brother (the older, thrown-over one, who had already made a habit of fooling the underside of his arm across the top of hers and calling her "pussified"), she reached for the shoe box in which she had let duplicate stamps accumulate—Spanish ones, mostly, of a fading orange—and sent the box slooshing through the lower air so that the stamps showered onto the brother's bare legs with a full, delicate harm. The woman was now touching up the surface of her iced tea with tiny activities, initiatives, of the longspun spoon. I myself was good at getting my touch onto things, although in a way that seemed to mix up the motive atoms inside [163] them, but I was satisfied that for the moment my sandwich, the unbitten-at half of it, was displayable and fit and local to my plate. The woman went on to say that, as a child, she had been bundled off, many an afternoon, to the slope-ceilinged quarters of a bachelor uncle who, when speaking of anybody not immediately present, could not bring himself to use the person's name but instead would say "an acquaintance of mine in ..." and then mention the name of some lapsed homeland, or little-loved rural orchestra, or backset building about to come down; and it was never a riddle, this device of his (not once could the girl have been expected to identify any of the subjects), and no matter how often and aloud he insisted that particularizing persons any further—bringing even a first name down upon anyone of them—would have been indecent, he claimed, much like doing things to people while they slept, the girl accepted all of the uncle's prim and extravagant evasion for what he surely must have intended it to be: a neat, protective trick to space the world out a little further in her favor, to scatter the population so that wherever her hand might at last come down, it would have to be on herself alone. And here I could sense that the woman wanted from my mouth an account of as much as I myself might have ever managed of attachment, so I told her I had once owned a house (a rising, really, of much-fingered, handwrought architecture that amounted to a little family of rooms above garages: a boxlike building with a rattly thorax of downspouts [164] and drainpipes and an unfolded but full-toned fire escape), and I had had for a time a boarder, a student, a high-colored, loose-packed representative of declining girlhood, hung with necklaces and barrettes, a girl of precise but shifting leanings and inclinations; and the afternoon she had come round to ask after the room, I stood in the entranceway, handshaken and asweat, and from what would later be my memory of the girl, I made off with, first, how every pore of her nose seemed to be sheltering within itself a tiny dark seedlet, a grain of something immediately, enormously valuable. And an almost lipless mouth (just a slit, practically), the teeth inside looking wet, watered-it was my life's chore, at that instant, to keep from sending the back of my thumb blotterlike across the line of them (I was later to learn she drank everything cold and through the narrowest of straws). And her hair: it was tea-colored hair she had, long and reachful, an unstopped downcome of it. Tall for a girl, but she managed to stay out of much of her height and put herself across as somebody backward, or behind. I must have told the girl, as best I could, that I of course had a wife, a full-faced, imperishable partner, though for the moment she was gone otherwhere in the marriage, and here the woman, my present companion, my tablemate, whose feet were now parked, in parallel, on the grade of my upper leg, interrupted to say that her husband, too, had been such a liar, and what could I bring up by way of reply other than that a lie is a truth struck through with other, further truth, or that a lie is the present multiplied by the past or that a lie [165] is an outcry of borrowed hope? The woman gave me an allowed look of disgust, her eyes lowered but still popular with me, and on I went with what had now become the girl of my story. For there had been a great, gainful carpet in the room I put the girl into, a matty expanse of coarse, grabby piles, an engrossing affair that took things into itself and held them tight, misered them, and I of course insisted that the girl not bother herself with its upkeep, that I enjoyed weekly access to a prestigious, upstanding vacuum cleaner; but no sooner was the girl out of the house each morning than I would withdraw from my room, where time was unportionable, and loose myself into the ticktock impertinence of the girl's room and get down on my knees, and, going after the carpet first with my fingers, then with a forceps, and finally by unspooling lengths of clear package-sealing tape and pressing them against the tufts in neat rectangles to catch what I might have missed, I brought vast tracts of the carpet to depletion, recovering not simply the girlinesses, the girleries, one would expect (buttons, straight pins, downed jewelry), but flirtier personalia in the form, say, of a stray confetto brought into the world when a page had been wrung with out caution from a spiral-bound notebook, or some pleated paper shells of the chocolates she required, or one of the bargain antihistamines she took to get her naps going, or a trash-bag tie ragged enough to show the kinked line of the wire within (this I would get wound around my finger), or a cough drop enwrapped like a bonbon (I would undo the [166] wings of the wrapper and have to decide whether to suck the drop all down or begin chewing it midway)—I became the following, the public, that these things, these off-faIlings, had come to have; but mostly there was hair, afloat above the uppermost pushings of the fabric of the carpet an almost continuous haziness of loose hairs of all lengths and sources, and I would have to set them out on a fresh sheet of paper and assort them according to the regions of the body they had taken their departure from, and in no time I had nest-like filiations of broken filaments and smaller involvements of the hairs that made me think of hooks, of barbs, of treble clefs, and each pile required a separate envelope, to be filed in a separate shoe box for every sector of the body until, I hoped, the boxes themselves would no longer be enough and I would have raised something semblable, brought up something equal in volume to the comprehensive girl herself. And her wastebasket! For every bit of rubbish, every dreariment she tossed into the thing, I would, in secret, deposit a reciprocal discard of my own, matching a spotted, confessory tissue of hers with a lurid throwaway after my own heart–the cardboard substructions of a fresh parcel of underwear, maybe, or tearings from pantyhose I now and again pressed against a span of my forearm to work onto it the complications of female shading I otherwise made do, choosily, without. I thus built the two of us up together in her trash! One afternoon-it was another of those lifeful, unsam-[167]pled days on which the world humors us each a little differently to keep us nicely on our last legs—I discovered in the wastebasket an inch-deep textbook of hers, a paperback with a celery-colored cover that had come partly unglued, and this dilapidation I paired off, naturally, with a name-your baby guide to whose pages, during my recurrent turnings of them, in bed or at table, I had contributed dried produces of my person, a chemical splendor entirely mine. This coupling sent a sudden spigoty thrill from me that forced an unbuckling and an unzipping and a cleanup with a handkerchief I then ventured responsively into the wastebasket as well. It was in the bathroom afterward that I found a suds-clouded puddle on the unlevel floor of the tub, a little undrained remainder, rimmed with offscum, of the girl's prolonged early-morning soak, and this was as much as I needed to get on my hands; I pressed them flat against the wet porcelain, then flapped them around in the air, and that was when I noticed it—in the amphitheater of the toilet bowl, an orange-yellow tint, or value, to the waters. When the girl arrived home that evening, I told her, of course, that I had discovered fresh, unforeseen trouble within the tank of thelet (a misalignment of the trip lever, a waywardness of the float ball, a ulation of the lift wires, kinks and defects, really, throughout the entire system) and that in fine it was an apparatus now operable only by means of advanced and strenuous equilibrial manipulations that it would be unseemly, inhospitable, of me to pre-[168]sume to burd to burden her with–so that from here on out, following any leak or evacuation she need merely lower the lid and then, before quitting the room, ring the handbell that had been placed on the would seeeverythinghing else. But the bell never rang, not even once, and from my window the next morning I watched the girl carry from the house a little plastic bag distended balloonishly, much like those bags you will remember having seen in the hands of children bearing homeward their solitary carnival-prize goldfish. In fact, I never ran across the likes of the girl again. The man who came to collect her things-not the father, apparently, but an advocate, an upholder-l found to be dull-eared and lax in his speech, and the better part of his face seemed to have already begun making tiny, rotational departures from whatever it was that the eyes, themselves impressively mobile, were just that moment having to take in. (Was there a lamp in the house that was not that night slopping its wattage over everything?) I guess I was waiting for the man to take a laggard, last-minute interest in me, and by now I was pushing everything out into the paired first person–it was, I said, “Our night shot,” and I began including the two of us in whatever it might be doing out, the expected sprinkles and such—but he was no friendship buff, and he paid no heed to my telling him that the only dress of hers I'd ever twidged myself into even part of the way had been the simplest of them all, a large-buttoned wonder of depthless blue, and then only on the principle that one naturally fits whatever one has into whatever somebody else [169] had first, or how else would the world keep getting any taller with people? The man just went about the removal of the girl's things without having to be reminded too noticeably, I guess, of how every dick hangs by a thread. My listener, though, had by this time brought about some becoming slowings of her arm—it was an arm inclinable to langorous diagonals and magicianly swoops through the air above the tabletop—but it no longer was involving itself with her plate, so I suggested we shove off, I made payment for the food, and on our way to the car, and then in the car as I took to following her pointings, the directional tilts of her head, she said that you naturally kept putting more and more of yourself into another person, at first wondering how much she can take, how much of you is accumulable and how much she can hold, and you're letting things out, disbursing yourself, and you've soon got things set up in her, and room is being made for even more of you, and if you bring this off with enough people, even two or three, what you've got is at first a comfort, because you can pass yourself along and move a little more widely through the world and leave it to these others to man your grievances, your disappointments; and what brought this to mind, the woman said, was a term of financial hardship she had contrived for herself a few years back, an unpaid leave of absence from scrupling letter grades onto quiz papers (propped-up As, and upended Bs made to look, rather, like fannies; all As and Bs, no Cs or anything lower, the difference between an A and a B having less to do with the accuracy of whatever facts might [170] have been impounded in provided for an answer than with anything recallable about the way the enrollee ad conformed her body to the confining perpendiculars of her chair and the navel-level writing surface that projected from it, or the way there might one day have been an unignorable blush on the instep of a once-moseying foot, disburdened of its shoe, that had got itself trapped in the grillwork of that cagelike involvement, intended for books, that was welded to, or otherwise schemed into, the underworks of the chair)—this had been a duration, in short, of controlled difficulty when the misexpenditure of even a twenty-dollar bill had set her thrilling, gloating, over everything she would miss out on, and one afternoon she had made an engagement for a haircut, just a trim, and very early in the session the haircutter, a woman ill-defined in the face but otherwise full of conspicuities of emotion, set down the prevailing scissors and pressed the flat of a lukewarm hand against the woman's cheek, held it there for a good minute or longer, while the other hand eventually found its way into a drawer, a shallow treasury of slender specialty scissors, one pair of which the cutter withdrew and began routing deductively through the woman's hair, the other hand staying put on the cheek, longer and longer, and the woman went home and for afterward the bathtub was now a more likely destination than any of the upright furniture, and it got easier to fill the tub with further clarifying volumes than to clear space on the difficult heights of the sofa, and she was hardly claiming to have become a cleaner [171] person in result—she in fact would often discover, voyaging about her body, a browned, fractionary detail of a larger crepe of toilet tissue that must have got itself stuck in some assy crevice and was impossible to get plucked out of the revolving suds—she was saying only that she spent more and more of her time thus immersed, ill off in water, and the haircutter had surely had a hand in it, the woman was doing some of the cutter's life now, coming into some of its wrong, because you sometimes have to look to somebody else's life to get dimensions set back even part of the way around your own, and it should not have to be any less your own life when it comes from somebody else, and you could surely fudge a society out of anyone available person and get this person doubling for the many, so that in the little run of things perpetuable from one person to the next, every loose moment stood to become a complete, active finality. But by now this was a new day, with only an hour or so off it already, and the place the woman had made me bring us to, the man's place, with a promise that the man was elsewhere—this was on a little offshoot of a street, a stewy efficiency apartment the color had long ago gone out of; and when, once in bed, still clothed, I found among the sheets and blankets a spoiling pair of the man's underpants, one of the leg openings of which was puckered into an avid, sloppy mouth, I held myself accountable for redisposing the fabric until I got a befitting featurelessness back onto it; but all the while, I am sure I had to make myself go over again in my mind that if the body is the porter of as many organs of affec-[172]tion as there might one day turn out to be, then the idea was to let the thing carry you to where you would otherwise never have any reason to arrive, because I listened for the unmelodiof the the thede ofthe woman's zipper, and then the woman made me put myself out of my own clothes, the attritional corduroys and overshirt, and got herself up at last onto the topic not of the man whose apartment it was (because his story was scarcely the story of how the boy who decides he is half a girl no sooner starts to worry about where the other half might than he gets careless with where he rests his eyes, or what he gives even the feeblest of fingerholds to, and anything, even a crumbly triangle of pie offered on a saucer instead of on a pie plate proper, comes in easy, ready, wronging answer), but of her husband, and how, no more than a couple of months into the marriage, he had begun snugging away in his undershorts a little source of chanc, reliable frictions to nudge him onward through the workday—anything company-keeping that could be counted on not to slide out of the elasticky leg holes: a half-dollar packet of chocolate tittles, maybe, that was barely noticeable in the baggy surround of the widecut trousers so popular at the time. For by now the woman had at last brought what is usually called the other mouth to within only inches of my lips, but it is not a mouth, obviously, although I let myself go along with the goodwill behind the comparison, the way I will remain loyal to anything deliberately and faithfully misunderstood, and I fussed my tongue against the vital trifles hung inside of her, as much of the curtailed finery as I could find, [173] and gave the whole insimplicity of it a slow-circling, examinational lick, until I was taking a sudden tepid downwash on the tongue. It was a familiar, latrine in dribble that must have tasted, no doubt, like trouble just starting out.p [1] Editor's Note: Original pagination from first edition print denoted with bracketed page numbers. (shrink)

In order to show how formal analogies between different physical systems play an important conceptual work in physics, this paper analyzes the evolution of Einstein’s thoughts on the structure of radiation from the point of view of the formal analogies he used as “lenses” to “see” through the “black box” of Planck’s blackbody radiation law. A comparison is also made with his 1925 paper on the quantum gas where he used the same formal methods. Changes of (...) class='Hi'>formal points of view are most of the time taken for granted or passed over in silence in studies on the mathematization of physics as if they had no special significance. Revisiting Einstein’s classic papers on the nature of light and matter from the angle of the various theoretical tools he used, namely entropy and energy fluctuation calculations, helps explain why he was in a unique position to make visible the particle structure of radiation and the dual nature of light and matter. Finally, this case study calls attention to the more general question of the surprising creative power of formal analogies and their frequent use in theoretical physics. This aspect of intellectual creation can be useful in the teaching of physics. (shrink)

This book features mathematical and formal philosophers’ efforts to understand philosophical questions using mathematical techniques. It offers a collection of works from leading researchers in the area, who discuss some of the most fascinating ways formal methods are now being applied. It covers topics such as: the uses of probable and statistical reasoning, rational choice theory, reasoning in the environmental sciences, reasoning about laws and changes of rules, and reasoning about collective decision procedures as well as about action. (...) Utilizing mathematical techniques has been very fruitful in the traditional domains of formal philosophy – logic, philosophy of mathematics and metaphysics – while formal philosophy is simultaneously branching out into other areas in philosophy and the social sciences. These areas particularly include ethics, political science, and the methodology of the natural and social sciences. Reasoning about legal rules, collective decision-making procedures, and rational choices are of interest to all those engaged in legal theory, political science and economics. Statistical reasoning is also of interest to political scientists and economists. (shrink)

The method of reflective equilibrium (MRE) is a method of justification popularized by John Rawls and further developed by Norman Daniels, Michael DePaul, Folke Tersman, and Catherine Z. Elgin, among others. The basic idea is that epistemic agents have justified beliefs if they have succeeded in forming their beliefs into a harmonious system of beliefs which they reflectively judge to be the most plausible. Despite the common reference to MRE as a method, its mechanisms or rules are (...) typically expressed in a metaphorical or simplified manner and are therefore criticized as too vague. Recent efforts to counter this criticism have been directed towards the attempt to provide formal explications of MRE. This paper aims to supplement these efforts by providing an informal working definition of MRE. This approach challenges the view that MRE can adequately be characterized only in the negative as a set of anti-essentialisms. I argue that epistemic agents follow MRE iff they follow four interconnected rules, which are concerned with a minimalistic form of foundationalism, a minimalistic form of fallibilism, a moderate form of holism, and a minimalistic form of rationality. In the critical spirit of MRE, the corresponding working definition is, of course, provisional and revisable. In general, the aim is to contribute to a reflective equilibrium (RE) concerning MRE. If it is successful, this working definition provides a better grasp of the most basic elements of the method and thereby enhances our understanding of it. (shrink)

The paper presents a new method for generating typologies of formal-ontological relations. The guiding idea is that formal relations are those sorts of relations which hold between entities which are constituents of distinct ontologies. We provide examples of ontologies (in the spirit of Zemach’s classic “Four Ontologies” of 1970), and show how these can be used to give a rich typology of formal relations in a way which also throws light on the opposition between threeand four-dimensionalism.

In this article, we reflect on the use of formal methods in the philosophy of science. These are taken to comprise not just methods from logic broadly conceived, but also from other formal disciplines such as probability theory, game theory, and graph theory. We explain how formal modelling in the philosophy of science can shed light on difficult problems in this domain.

I came to philosophy as a refugee from mathematics and statistics. I was impressed by their power at codifying and precisifying antecedently understood but rather nebulous concepts, and at clarifying and exploring their interrelations. I enjoyed learning many of the great theorems of probability theory—equations rich in ‘P’s of this and of that. But I wondered what is this ‘P’? What do statements of probability mean? When I asked one of my professors, he looked at me like I needed medication. (...) That medication was provided by philosophy, and I found it first during my Masters at the University of Western Ontario, working with Bill Harper, and then during my Ph.D. at Princeton, working with Bas van Fraassen, David Lewis, and Richard Jeffrey—all deft practitioners of formal methods. I found that philosophers had been asking my question about ‘P’ since about 1650, but they were still struggling to find definitive answers. I was also introduced to a host of other philosophical problems, and it became clear to me within nanoseconds of arriving at U.W.O. that I wanted to spend my life pursuing some of them. But I kept being drawn back to the formal methods of mathematics, and in particular of probability theory. It may be worthwhile to pause for a moment and to ask “What are formal methods?” Of course, it’s easy to come up with examples: the use of various logical systems, computational algorithms, causal graphs, information theory, probability theory and mathematics more generally. What do they have in common? They are all abstract representational systems. Sometimes the systems are studied in their own.. (shrink)

This essay concerns itself with the methodology of practical ethics. There are a variety of methods employed in ethics. Although none have been firmly established as dominant, it is generally agreed that casuistry, or the case-based method, is one important strategy commonly used for resolving ethical issues. Casuists compare the case under consideration to a relevantly similar precedent case in which judgements have already been made, and they use these earlier judgements to determine the proper resolution of the present (...) case. In this article, I try to provide a better understanding of the nature of contemporary casuistry. To accomplish this, I explain the basic features of casuistic reasoning. The second section focuses on the logic of casuistry. By assessing casuistic reasoning from the logical viewpoint, casuistry can be reconstructed as a logically correct method of reasoning. The third section looks at casuistry from the epistemic point of view and investigates the justificatory force of casuistic reasoning. Finally, in the fourth section, I show the usefulness of formal casuistry. (shrink)

Deductive Logic is an introductory textbook in formal logic. The book is divided into four parts covering (i) truth-functional logic, (ii) monadic quantifi- cation, (iii) polyadic quantification and (iv) names and identity, and there are exercises for all these topics at the end of the book. In the truth-functional logic part, the reader learns to produce paraphrases of English statements and arguments in logical notation (this subsection is called “analysis”), then about the semantic properties of such paraphrased statements and (...) arguments, such as satisfiability, implication and equivalence (“logical assessment”) and finally (“reflection”) there is an axiomatic proof method and some important extras such as disjunctive normal form and expressive adequacy. Parts two and three mirror this analysis/assessment/reflection structure for monadic and polyadic quantification, though this time the proof system is a natural deduction one, and part three contains a completeness proof for that system. The fourth part of the book introduces names, the identity predicate and descriptions and examines the additional expressive power which these provide. (shrink)

This paper investigates the formal relationship between two prominent approaches to the logic of belief change. The first one uses the idea of "relational partial meet contractions" as developed by Alchourrón, Gärdenfors and Makinson (Journal of Symbolic Logic 1985), the second one uses the concept of "epistemic entrenchment" as elaborated by Gärdenfors and Makinson (in Theoretical Aspects of Reasoning about Knowledge, M. Y. Vardi, Los Altos 1988). The two approaches are shown to be strictly equivalent via direct links between (...) the underlying formal relations. The paper closes with observations about the application of epistemic entrenchment to simple and iterated revisions. (shrink)

The papers collected in this volume exemplify some of the trends in current approaches to logic, language and computation. Written by authors with varied academic backgrounds, the contributions are intended for an interdisciplinary audience. The first part of this volume addresses issues relevant for multi-agent systems: reasoning with incomplete information, reasoning about knowledge and beliefs, and reasoning about games. Proofs as formal objects form the subject of Part II. Topics covered include: contributions on logical frameworks, linear logic, and different (...) approaches to formalized reasoning. Part III focuses on representations and formal methods in linguistic theory, addressing the areas of comparative and temporal expressions, modal subordination, and compositionality. (shrink)

Although not entirely mainstream, uses of formal methods for the study of the history of philosophy, the history of logic in particular, represent an important trend in recent philosophical historiography. In this chapter, I discuss what can be achieved by the application of formal methods to the history of philosophy, addressing both motivations and potential pitfalls. The first section focuses on methodological aspects, and the second section presents three case studies of historical theories which have been investigated with (...) formal tools: Aristotle’s syllogistic, Anselm’s ontological argument, and medieval theories of supposition. (shrink)

“Artworks are not being but a process of becoming” —Theodor W. Adorno, Aesthetic Theory In the everyday use of the concept, saying that something is grotesque rarely implies anything other than saying that something is a bit outside of the normal structure of language or meaning – that something is a peculiarity. But in its historical use the concept has often had more far reaching connotations. In different phases of history the grotesque has manifested its forms as a means of (...) subversive resistance against society’s prevailing notions of form and power. What aids this impact and distinguishes two of its basic stylistic features is the grotesque’s dissolution of form and its hyperbole. Such grotesqueries, however, soon solidify into new forms, new structures of meaning, hierarchy and practice, and in this sense the history of the grotesque is, on one hand, a continual opposition and transgression of the prevailing notions of art as well as of God and humanity, while on the other hand it offers continual resistance to its own solidifying process. As such the grotesque will not and cannot be contained in form without it losing the very thing that makes it grotesque. Even though it is somewhat easy to point out certain stylistic features of the grotesque, the sum of those features tell us very little about what is at play within it. Definitions concerned with the grotesque’s content rather than its form faces similar difficulties. Throughout history, expressions relating to the grotesque have been used in defense of a whole host of different social and cultural discourse including, for instance, Catholicism (See Erhard Schön’s Der Teufel mit der Sackpfeife , 1536), Protestantism (See Lucas Cranach’s Der Papstesel , 1523), a material folk culture (see Mikhail Bakhtin’s Rabelais and his World , 1984) and an idealistic romantic structure of meaning (see Wolfgang Kayser’s The Grotesque in Art and Literature , 1957). Thus though the grotesque cannot be reduced to the expression of certain forms or meanings, in order to examine what the grotesque is about one has to try to see how it’s relationship to flow and process and how, by maintaining this relationship, it attempts to avoid solidifying into form and meaning. The process of the grotesque alluded to here revolves around a play between periphery and center, the marginalized and the dominant. Most often this is expressed as a direct negation of the center of power. In the medieval grotesque tradition of the carnival, for example, it is expressed by its emphasis on the nether regions of the body as the center of creation of meaning. Spirit does not come from above, but from the belly, buttocks and genitals, and there is, expressed in this manner, a mockery of the predominant Christian notion of truth and meaning. Such inversions of the sites of meaning most often explicitly express an increased interest in materiality instead of ideal content which comes to the fore through the play between periphery and center. Even in early grotesque Renaissance art (for example in the works of Raphael) the depiction of the mythological or ideal reveals an exploration of the possibilities of the material. The works of art thus explore their own boundaries rather than act as vessels of the divine and in this way the grotesque explores the limits of form and materiality. This in turn brings to the fore a metaphysical dimension in the workings of the grotesque: It is an immanent exploration of its own boundaries. Materiality and metaphysics are joined together, because it is through the awareness of itself as a structuring (dis)order that it places itself in opposition to the prevailing notions of form and power. This way the grotesque expresses an awareness of the division of sign and reality and a search for this reality. It implicitly expresses the awareness that meaning is not something God-given and static, but fluctuating and man-made. In modern explorations of the history of the grotesque it is commonly seen as a form of realism that manifests a shift from the ideal towards the material, freeing art from representing some hidden higher order and instead making the work of art the very site of creation and meaning. Going even further, the grotesque actively opposes the notions of the ideal by marking a shift from an ahistorical view of the world towards the historical. However, this also makes clear why the grotesque has a tendency to solidify into new static forms of meaning, for by establishing itself as a subversive counterforce there is an idea of transgression and emancipation. That is why the grotesque often historicizes and relativizes only to repeat the mistakes of that which it negates: putting itself in the king’s chair. The exploration of the material seems to create new forms and notions of the ideal. The representation of an otherness outside the prevailing notions of meaning and truth becomes a positive manifestation of this otherness as truth itself. Thus the historical “truths” of the grotesque are superseded by history itself. When the expressions of the grotesque solidify into static form and meaning, they become mere objects like anything else in the world. Instead of being this elusive thing of process and flow, it becomes tangible to the existing hierarchy of power as well as history itself. In this way the grotesque can be expunged, included or simply revealed as yet another false notion of truth, which is precisely what has happened with the grotesque throughout the course of history. If from the beginning the expression of the grotesque has not already been in the service of some structure of meaning and truth, it has quickly been included or has quickly included itself in such a structure. But by doing so it rejects its own basis: the tension between periphery and center is replaced by the attempt to create a new center, a new structure of meaning and truth. The doubleness, ambiguity and flow of the grotesque are then rejected by the grotesque itself. THE NON-FORM OF FORM In the critical thinking of Theodor W. Adorno (1903-69) the problem of art, caught between a reductive and prevalent notion of truth and meaning and a peripheral and alienated otherness, is reexamined and reformulated. For Adorno, the instrumental rationality of Enlightenment itself reverts into a new form of mythology which is every bit as static and exclusive as the hierarchies of religion it supersedes. All is excluded that is non-identical to the instrumental mastery of the objects of the world, "For the Enlightenment, anything which cannot be resolved into numbers, and ultimately into one, is illusion; modern positivism consigns it to poetry." 1 As such the non-identical has been banished from the realm of thought and action, and banished specifically to the realm of art. But the realm of art is not able to provide a decent home for it because even modern art is not something entirely autonomous. While it is excluded from the notions of truth and meaning provided by instrumental rationality, it still originates from society. Just like instrumental rationality art is about mastery, structuring and exclusion. Therefore, the problem for art is that it cannot directly provide a space for the non-identical because its mode of operation is similar to that of instrumental rationality. Even worse, art has very few possibilities to free itself from this. If it becomes l’art pour l’art it is at the same time reduced to the very thing instrumental rationality claims it to be: a subjective judgment of taste.expressionism also stands as an example of this. Conversely, art cannot work within the framework of the identity-thinking of society, because any notion of freedom or emancipation would reproduce the exclusive practices of instrumental rationality. For example: Explicit socialist literature may establish itself in opposition to instrumental rationality while at the same time reproducing it. Its language may seem different, but in reality it merely provides a different set of reductive schematics for human life and experience. The problem for the art of the grotesque was, as I mentioned earlier, that far too often it was merely a symbolic manifestation of a notion of otherness—not otherness itself. Because of this the subversive character of the grotesque ends up shaping and containing otherness instead of providing a space for it. According to Adorno the only way to avoid this is to radicalize the grotesque. In order to avoid solidifying into form the work of art has to be an object which cannot be contained in thought or form—a non-form of form. The work of art has to work in a way that it strives for autonomy but without entirely leaving a discernible reality. In other words, it has to pull in two directions at once. Thus the work of art is a paradox. It is autonomous in the sense that it closes itself off from everything outside of the work of art, trying to shy away from the contaminating influence of the identity thinking of instrumental rationality. At the same time though the work of art is heteronomous in the sense that it originates from a specific historical context and is bound to be what society is not. Autonomy and heteronomy are inseparably intertwined. Unable to display otherness itself, but still trying to be a refuge for it, there is only one option for art: It has to turn against itself and destroy its own logic of form, thereby demonstrating how any representation of otherness is impossible. Art becomes a lamentation of the victims of the identity thinking of instrumental rationality and shows the traces of the otherness that is unable to appear. Adorno’s pessimistic theory of art and history stages art as a negative dialectical process where the work of art closes itself off and rejects everything outside, while the individual elements in the work of art destroys its very own logic of form from within: Artworks synthetize ununifiable, nonidentical elements that grind away at each other; they truly seek the identity of the identical and nonidentical processually because even their unity is only an element and not the magical formula of the whole […]. The resistance to them of otherness, on which they are nevertheless dependent compels them to articulate their own formal language, to leave not the smallest unformed particle as remnant. This reciprocity constitutes art’s dynamic; it is an irresolvable antithesis that is never brought to rest in the state of being. 2 Relative to a traditional understanding of the grotesque, Adorno radicalizes the tension between center and periphery, autonomy and heteronomy. In the traditional understanding of the grotesque, as we find it for example in the writings of Mikhail Bakhtin, the grotesque establishes the display of otherness as a new center of meaning and truth. However Adorno rejects such notions and argues instead for a modernism of the grotesque in which both center and periphery are included in a negative dialectical process and continually synthesizing and destabilizing each other’s positions. A modernism of the grotesque works on the inside of the sign or the artwork, continually outlining and questioning the boundaries between materiality and form. This moves the focus away from the relation between the sign or work of art as a conceptual manifestation on one side and the object it refers to on the other side. Instead it implicitly points to the amorphous mass from which the signs and thereby meaning have been carved, the remnants that have been left behind. Modernism of the grotesque does not imply that it is emancipatory or that it reconciles man with nature, and does not represent a new position or a new ideology. It merely remembers and insists on the double nature of man and art: to write or paint yourself or an artwork whole by inscribing meaning in life or by applying form on a canvas is at the same time both creation and destruction. The very signs we use to center meaning in our lives carry its own alienation in them. Meaning surfaces only when process and flow comes to a halt—solidifying, but at the same time excluding parts that do not fit into that particular structure of meaning. NOTHING DONE AND NOTHING UNDONE It has always been difficult for art historians to find a suitable category for the works of the Danish artist Leif Lage (b. 1933). In his paintings the sensitive figuration seems so fragile that it is on the verge of turning into abstraction. Or conversely: the figurative emerges cautiously and hesitantly out of abstraction. As an art critic once wrote, he can almost paint things away. 3 Working in some undefinable space between abstraction and figuration, the Lage’s works shy away from the realm of words, and as a result few critics have been able to write anything meaningful about his works. In fact even fewer have been able to write more than one or two pages. The Danish author and art critic Leif Hjernøe is one of those few, but even he starts off by saying how impossible it is to write about Lage, confessing that his works exist both as process and in a field of in-between which words cannot reach. He writes: Always you find yourself in a place where nothing is done and nothing left undone, and where the elements of the work of art rest in a continuous motion. Always there is the open wound, where infection rather than surgical intervention is considered as an opportunity. And the conflict between matter and antimatter makes all diagnoses uncertain and allows conditions of uncertainty to spread in a place of raw presence. 4 The art works against the diagnosis and the certainty. Words are being eaten up by what is outside the realm of words: tension, process and doubleness. An approach to an understanding of the work of Lage could be to follow his connection to Samuel Beckett (1906-89). One can note, therefore, that Lage has illustrated several of the Danish translations of Beckett’s works. Though one is an author and the other a painter both seek a place where figuration, where the word, erodes. For both this entails an attempt to question and examine and so move in behind the façade of the surface in an exploration of that something or nothing that may be behind representation. At the same time even in the vanishing point of figuration or words, the meaningless words or the disjointed lines still stand as signs of human activity—signs of movement in emptiness. With very few exceptions Lage’s artworks revolve around one motif: Man—most often “en face.” But unlike traditional portraitures Lage’s people are found within. The artworks do not sense the reality of appearances, but rather the existential dimensions within man. As a seismograph they are sensitive to the utmost subjectivity in order to display an objective, sensuous depiction of the very problem of subjectivity. Instead of a static façade of a man, Lage’s “en face” shows the process-character of man. The people in Lage’s paintings are always in process—in the midst of becoming or dissolving. I will take a closer look in the following at the ways in which Lage establishes this sense of being in constant process, of being in-between modes or categories. THE DOUBLENESS OF THE STROKE Lage’s etchings attract attention in particular for the tension conveyed there between the material and the form. The material physically opposes the violence of the needle. But instead of embracing the violence of the needle and the victory over matter—instead of making the artistic creation and figuration express a heroic mastery of the background it is made out of—Lage uses the stroke to express the very tension between stroke and material, figuration and background. In the drypoint etching Untitled from 1983, which illustrated the Danish translation of Beckett’s Ill Seen, Ill Said , the needle tears up the material in long rough lines: Together, the primarily horizontal and vertical lines form a face. Thus the force needed to etch a line in the metal-plate draws attention to itself: It is there in the absence of curves and nuances. Man emerges on the metal-plate after great exertion and in a very simplistic form. This way Lage enhances the nature of the material, as the material’s resistance is not something to overcome. On the contrary the figuration is smitten by its very resistance and as such expresses the violence of its own becoming. Even more pronounced is the fact that the lines do not just show the violence of creation—it actively erases figuration in the same process that creates it. For example the mouth consists of 8-10 horizontal strokes, of which some seem to be connected to each other as if the mouth has been quickly scratched out. The mouth speaks of the inability to speak. In the same way, the eyes are black holes due to a large amount of criss-cross cuts, which together form a dark middle. Those lines, at the same time, form the eyes of the figuration and scratch out the eyes of the figuration. The extroverted aspects of the face—connected to speech and sight—are portrayed as introverted as well. Just as the etchings down into the metal-plate makes something appear. Leif Lage, Untitled , 1983 (etching) The figuration of the etching is connected to creation. It expresses that something is wrought into existence out of nothing by sheer artistic force. However, this force is at the same time presented as a violence of creation, which makes it impossible for form to truly emerge. Herein lies one of the basic principles of Lage’s art, namely that art cannot be that nothing or something behind the realm of words or signs. Without form, art would lose its ability to express anything at all. Form is a necessity if art is to avoid becoming as devoid of expression as the reality is that we cannot reach behind the appearance of things. On the other hand, art cannot raise itself above its own material in joyous celebration of the beauty of form. This would use the material in the manner of an instrument and thus would suppress the otherness it attempts to rescue. When art becomes mere form, any traces of otherness will have dissolved. Then art would be a question of technique, in no way different from the instrumental rationality of society. Therefore art works in a particular space between form and non-form. As Hjernøe says of the works of Lage, it is in the center of the event, in the in-between where things neither are nor are not, "And everything takes place just before it changes character. As the blood just before it coagulates, as the milk just before it separates, as fried egg just before it turns white […]." 5 The precise emphasis on the in-between of Lage’s art points in particular to the work of art as both outside of and in time. The work of art is a singular point in time, but at the same time it is continually in process. In the borderland between form and non-form, between creation and destruction, it shimmers like a fata morgana . The work is done but at the same time undone. It is only there as a cry in response to the inability to come into being. Akin to the etching is the drawing, but while both, of course, use the stroke or line as their main instrument, the paper does not resist the line in the same sense as the metal-plate of the etching. As a result in Lage’s drawings the stroke frolics in a space with almost no tension at all. There is nothing there to keep the pencil stroke at bay, but at the same time this means that there is nothing there to keep it together. One of the more expressive examples of this is found in an untitled drawing from Tegninger og Text ( Drawings and Text ) from 1999. The drawing consists of one unbroken pencil stroke. It is as if the stroke is confused—it darts around on the paper making doodles on the way or gathers itself in more straight lines in the center of the paper. It is in this manner that the semblance of a body is established. A couple of small circles serve as eyes and are the reason that the rest can be read as both face and body instead of pure abstraction. In fact the unbroken stroke serves as both abstraction and figuration as on the one hand it is the stroke that seemingly outlines the shape of a figure, while on the other hand the unbroken stroke dissolves any truly recognizable figuration by continuously, without end or aim, overflowing the boundaries of the figure. Seen again here is a doubleness to the stroke and the act of creation. In the etching it was all about the tension between the resistance of the material which created the doubleness. Here it is the opposite. It is the lack of tension. The stroke is free to do anything, but has no aim: without some kind of resistance, there is nothing to hold figuration together. It threatens to dissolve into nothingness. Conversely, the drawing can also be seen as a process of becoming. Like a form of automatic writing, the pencil darts around until it finds a point of densification. But even in such an interpretation of the drawing, the figuration appears artificial—it points to itself as the result of the artistic act of creation. The stroke is primarily stroke and only secondarily figuration. With its wild movement it calls attention to itself as stroke. Thus the figuration never becomes something in its own right. It points to the basic principle of creation: Someone has drawn me, I am the result of artistic endeavors, and therefore I am not for myself but always overflowing the boundaries that contain me. It is the stroke that in the very same movement creates figuration and dissolves it. Leif Lage, Untitled , 1999 (drawing) THE LIGHTNESS OF COLOR, THE DENSITY OF PAPER Often the watercolor is used as a precursor for larger paintings, because it has an immediacy in which one can quickly paint the main lines of a composition. However, Lage’s watercolors are not temporary points in a process leading to another final painting. They are not sketches, later to be filled with details in another material. For him watercolor is an end in itself. This also implies that he doesn’t try to work against the paper’s absorption of the water color and its tendency to absorb detail. On the contrary, he examines the possibilities inherent in this blurring of the line and absorption of color. As in the previous examples, there are of course recognizable shapes in Lage’s water colors. But these shapes are rarely separable from color, line or even paper. In other words: the figurative and the abstract more or less become one. One of the reasons for this is that Lage often works on wetted paper which means that the paper hungrily absorbs color into its fabric instead of it being on top of the paper. The paper becomes line because it is the absorption of the color which, together with the brush stroke itself, separates the colors from each other. The line is also color and the color is also line, because there is no separation between the different colors other than the colors themselves. At times this results in almost complete abstraction. In such cases Lage add lines with a pencil as if he wants to hold some sort of figuration together. At other times it is the other way around: the strokes of the pencil are a being dissolved by the water color blurring out the figuration. Untitled 1 from 1999 displays various tones of green. The contour of the colors appears unusually rough. Most of all it is reminiscent of a shoreline which has found its form through the work of thousands of years between water and land. Pockets of resistance surface as islands not yet drowned in color—as paper or color not yet consumed by the dominant color. The shape of the colors does not seem created by the hand of the artist, but rather by the inner workings of the watercolor: color against color over time has resulted in this very image, as if it is all a part of a natural process of change and decay. Despite the fact that there are no strong differences in color there seems to be a struggle taking place in the watercolor. For example, inexplicable holes in the dark color, which cover most of the right side of the watercolor, appear as if the underlying color is eating away the dark color, or that the dark color is in the process of covering up the underlying color. The small pockets of resistance demonstrate a process and development that, almost as a happy accident, evokes a couple of small eyes and a large mouth. Behind the colors a few slanted lines can be discerned, but the hand of the artist has long ago disappeared behind the life of the colors. Thus the watercolor seems to be held at precisely the point in time where figuration randomly appears. The small eyes and wide mouth seemingly express the realization of the figuration’s temporality. It is just a moment in time, soon to be consumed again in the life of the colors. The nature, the background it stems from and is part of, moves on undeterred, continuing its everlasting process of creation and decay. In this sense, the watercolor provides an experience of how neither artist nor man is able to transcend the materiality they consist of. The colors of man, the materials man consists of are “becoming” and “progress” but also “decay” and “disappearance”. The artist’s pencil strokes have been eaten up long ago, and the figuration is living on borrowed time. Human or artistic activity is about creating form, transcending mere matter by shaping and applying meaning to it. But Untitled 1 shows the doubleness of such creation: the transience and fragility of human life. Should the figuration come into being, should it rise and transcend the material, which binds it to its temporal existence, it would become nothing because its very existence is conditioned by the life and work of the colors. In the same sense man cannot escape his own temporality. He too, for better or worse, must accept a life in the volatility of sensation. Leif Lage, Untitled 1 , 1999 (watercolor) In most of Lage’s watercolors there seem to be a stronger artistic control than in Untitled 1 . Most often both the arrangement of colors and the technique in which they are painted express the hand of the artist. An example of this is Untitled 2 from 1999. While figuration in Untitled 1 seemed to appear as a happy accident, the figuration is much more “created” in Untitled 2 . Here the most important parts of the figuration, the eyes, the mouth and part of the skull, are colored black and painted on top of the background’s play of colors. The background primarily consists of blue and yellow tones. Only parts of the paper are covered in color, however, which yet again stresses the act of painting: There is a surface which is being filled by color by an artist. The blue tones are concentrated in the figuration, while the yellow tones surround it. All this means that the figuration stands out more clearly in this watercolor. This is also underlined by the fact that the blue and dark tones cover part of the yellow tones as spots here and there. Thus it is not a background which is in the process of consuming figuration, but rather the emerging figuration which blots out the background. Such an understanding is even suggested by how the mouth and eyes are placed in the larger blue color field. The eyes and mouth are in the center of the watercolor, while the blue color field is placed from center out towards the left side. This gives the impression of a face turned slightly to the right and slightly upwards, which again makes the mouth appear to emerge from the paper. It also helps that the mouth cuts the center axis of the watercolor. In other words, the arrangement of the blue and black colors create some depth and perspective which gives the illusion of a figuration, seen partially in profile, emerging from the background. Seen in profile, the eyes and mouth seem extroverted—they almost seem as if they are put on top of the face. But at the same time they are painted as black holes, sucking in the gaze of the onlooker. The watercolor is even more challenging if one follows what may be the faint outline of the skull, which, on the right side of the watercolor, no longer works together with the blue color, but rather alone postulates the outline of the skull. If not the blue color field, but this line, is the outline of the skull, then all of a sudden the face is not in profile but “en face”—staring directly towards the onlooker. Outline and color seemingly work against each other and establish two different expressions. Without the slightly upward tilted expression of the profile, the eyes and mouth do not seem to emerge from the paper. On the contrary, seen “en face,” the eyes and mouth are really gaping pits of darkness. In this sense Untitled 2 is at the same time surface and depth of perspective. The line gives form but at the same time it dissolves the form created by the colors, and vice versa. Leif Lage, Untitled 2 , 1999 (watercolor) As the last example of Lage’s artistic method, I have chosen another untitled work (as indeed nearly all of Lage’s artworks are)—this time from 2000. This is perhaps one of the most figurative watercolors Lage has created, though that doesn’t tell us too much. The painting depicts a human face in blue and green tones on a yellow toned background. The colors create a clear demarcation between the figure and the background, which compensate for the watercolor’s lack of outline. Beneath the face darker tones imply the beginning of the torso, and nuances of color even hint at something which could be a collar. The hair is in even darker tones and its structure is emphasized using pencil strokes on top of the water color. One eye is marked by a brown spot with a darker spot in the middle, while the other eye is added by pencil. The mouth is a round, red dot. In Untitled from 2000 the work between abstraction and figuration is much less pronounced than in the previous examples cited here. Nonetheless the watercolor has a delicacy to it which almost makes the figuration disappear, even as it appears. This has something to do with the fact that all the individual brush strokes have dissolved. The only outlines are those created by the clash of colors. Even the red mouth seems to be more paint than mouth—unable to be formed truly as anything other than a speck of color with some small semblance to a mouth. In contrast to the other watercolors, there is no movement, no progress or decay, just a vibrating standstill. The figure is not emerging or disappearing but embedded in and as surface, and as such it makes the figure seem stuck in its condition rather than freed by the act of giving form: mouth open as a wound. Pencil strokes add detail and life to the hair as an attempt to help the figure emerge. But all this does is create two levels in the watercolor: The pencil strokes are put on top of the figuration rather than being part of it. Thus they end up highlighting the endless distance between the movement and form-giving of the pencil strokes and the static and stuck figure behind these strokes. Leif Lage, Untitled , 2000 (watercolor) MAN AND THE VIEW OF THE ONLOOKER Lage’s works seem at the same time to be an examination of tensions between form and material in art and a display of an image of man full of the same tensions. This is because the people who are emerging in Lage’s images are not just in his works, They are his works. This means that man is not something emerging from a background but is part of this background and vice versa. The art of Lage inscribes man in its surroundings and background. Man is not the ruler of nature. Man does not rise above matter; there is no truly transcendent position for man to occupy in the art of Lage. Instead man is a part of the very matter, it, at the same time, tries to distance itself from in order to distinguish itself from its surroundings. Man emerges in an attempt not to be line, stroke, color. In an attempt to free itself of matter. Should it succeed in this, however, it would turn into nothing. On the other hand, if man fully accepted itself as mere matter it would disappear in it—in instincts, urges and lack of reflection. The appearance of man is thus subject to a state of being in-between. Only in the tension between material and its negation can the outlines of man be traced. However this also means that in the art of Lage man is never something in itself but always in process—on the way to its freedom and its loss. However, Lage’s art is not just about showing the tensions inherent in man but also about showing such tension on the verge of breaking point. In the moment before everything is done, or when nothing yet has been done, the delicate tension between form and material has been stretched to its utmost in such a way that man’s character of process emerges and is contained on the paper or canvas. Therefore, Lage’s art contain traces of human life. Not only is it an autonomous unity of tensions where man is stretched out between its singularity and the surroundings it is a part of. It is also this pulsation between figuration and material which brings about the traces of human endeavor and activity. Even when man almost seems to have disappeared into the material, strokes and lines are still there as a reminder of human activity and potential creative power—as a reminder that hope is still possible and that man is still there. The view of the onlooker seeks out forms and meaning. It seeks outlines and edges. But first and foremost it is the eyes in Lage’s works of art that allow the onlooker to decode the figuration at play. This creates a distinctive relationship between the onlooker and the artwork. The onlooker tries to wrest the enigma from the artwork, tries to reduce it to solid, meaningful form. But the very same moment that hints at such a possibility sees the view of the onlooker confronted with a gaze of its own. The eyes of the figure in the work of art are most often dark pits, as if they were an illustration of the violence committed against the eyes of the onlookers and their search for meaning. Or as if they were a dark reflection of the onlooker’s failed attempts to delineate the traces of life in the artwork to a solid meaningful form. Therefore, the gaze of the figuration speaks not only of its own powerlessness but also of the powerlessness of the onlooker. When the view or sight has trouble finding solid meaningful forms, it has something to do with the fact that the precondition for sight, light, no longer stems from something transcendent. In Lage’s art there is nothing outside the works of art, nothing outside of human life, and as such nothing to shed light on the works of art or human life and reveal solid meaningful forms. All light comes from within. In a western context, light as a medium for sight is central to the understanding of meaning. People speak of the clarity of thought, while knowledge is tied together with enlightenment, and so forth. But the light no longer originates from a divine point of view. It originates from man, who has created himself in the image of God. The problem with this is that light always covers up its own base. Light illuminates something but at the same time it hides itself. 6 While it was previously God who was unknowable, now it is man. It is also problematic that sight and the medium of sight stem from the same place. Following this thought one can posit two final problems. Firstly, the immediacy and presence established by light by making forms and objects accessible to sight is fake. Light is not some independent entity which present things in a neutral manner for the onlooker. It is inextricably tied together with the gaze’s desire after meaning. In other words: Light perverts the appearance of things because it doesn’t originate from some objective entity which allows them to appear as they are. Instead light is based upon and originates from the subject and its conquering gaze, seeking out meaning and form constantly. Secondly, the joining of sight and light makes introspection within human life impossible. Everything can be illuminated by its use value for the subject but only as long as it is separated from the subject, as long as it is an object. But the subject itself cannot be illuminated. Lage’s art tears down such a dividing line between subject and matter, but it does so without reestablishing a divine position from where the light emanates. Therefore, the light in Lage’s art may not illuminate very well. It may not have the certainty presented by modern science or the religions of yesterday. But it does show what such light tries to hide, namely, the subject as it is in its material reality—inscribed in time and death, which are the basic conditions of materiality, but at the same time also full of life in its joy and will to create. For the onlooker the meeting of the gaze in Lage’s works of art is thus also a destruction of the view of the onlooker. The ability to see is challenged in a radical way. Those outlines will not solidify into static form, as if the light was too dim to see. Just as in Lage’s figurations, the view of the onlooker turns to black: turns towards the onlooker in recognition and becoming—or disappearance. NOTES Max Horkheimer and Theodor W. Adorno. Dialectic of Enlightenment . (Palo Alto: Stanford University Press, 2002): 4-5. Theodor W. Adorno. Aesthetic Theory . (London & New York, 2002): 176. Carsten Bach-Nielsen. “Mere glæde end gru.” Kristeligt Dagblad . September 24, 2002. Leif Hjernøe. “Den yderliggående inderlighed.” LEIF LAGE—Retrospektiv udstilling 1983 . (Copenhagen: Brøndum, 1983): 18. Ibid. Maurice Blanchot. The Infinite Conversation . (Minneapolis: University of Minnesota Press, 1993): 162-163. (shrink)

This paper investigates the question of characterizing first-order LFIs (logics of formal inconsistency) by means of two-valued semantics. LFIs are powerful paraconsistent logics that encode classical logic and permit a finer distinction between contradictions and inconsistencies, with a deep involvement in philosophical and foundational questions. Although focused on just one particular case, namely, the quantified logic QmbC, the method proposed here is completely general for this kind of logics, and can be easily extended to a large family of (...) quantified paraconsistent logics, supplying a sound and complete semantical interpretation for such logics. However, certain subtleties involving term substitution and replacement, that are hidden in classical structures, have to be taken into account when one ventures into the realm of nonclassical reasoning. This paper shows how such difficulties can be overcome, and offers detailed proofs showing that a smooth treatment of semantical characterization can be given to all such logics. Although the paper is well-endowed in technical details and results, it has a significant philosophical aside: it shows how slight extensions of classical methods can be used to construct the basic model theory of logics that are weaker than traditional logic due to the absence of certain rules present in classical logic. Several such logics, however, as in the case of the LFIs treated here, are notorious for their wealth of models precisely because they do not make indiscriminate use of certain rules; these models thus require new methods. In the case of this paper, by just appealing to a refined version of the Principle of Explosion, or Pseudo-Scotus, some new constructions and crafty solutions to certain non-obvious subtleties are proposed. The result is that a richer extension of model theory can be inaugurated, with interest not only for paraconsistency, but hopefully to other enlargements of traditional logic. (shrink)

The history of Physical Science appears to exhibit, periodically, a race between the acmulation of data and the ability of its codification to find a natural place for much of the empirical findings. If the codifying scheme is a mathematical theory, capable of interpolation and extrapolation, according to the rules of the particular branch of mathematics employed, the ablest handlers of the theory are frequently confronted with a situation in which mathematical computation alone does not suffice. In such a situation (...) the introduction of symbols, whose interpretation is not direct and simple is resorted to. This symbol is usually involved in a mathematical relation by a species of reasoning, which may be somewhat unfamiliar and remote from customary habits of thought. It is generally accepted as physically valid, if the mathematical formulation which involves it can produce results which account for the mass of data uncovered by experimenters. As an example of such a procedure we may mention the case of the Schrödinger Ψ-symbol, a symbol which was involved in Schrödinger's famous matter wave equation. The successes which such a theory enjoyed, particularly, in its initial stages, in formally relating the relative positions and intensities of spectral lines, with the atomistic concepts of gross matter which were inferred from the data of macroscopic measurement, such as the atomic mass, the electronic charge, Planck quantum of action, etc.,—these successes, gave a certain physical dignity to the Ψ-function itself. This dignity was further enhanced by the disclosure, by Schrödinger, of four functions of the Ψ-symbol which held the same place in the “continuity equation” as the classical charge density and the three components of current density. The successes accompanying this discovery for spectroscopic problems, in particular, are well known to Physicists. (shrink)

This is a very fine elementary-to-intermediate level text of mathematical logic. The initial chapter of the book consists of a good discussion of standard topics in modern formal logic including arguments and argument forms, logical functors, validity, proof, the axiomatic method, interpretations, and logical systems. The book then proceeds in subsequent chapters to a development of increasingly rich systems of sentential logic, systems of natural deduction, and a chapter on consistency and completeness of formal systems. This takes (...) the student through approximately one half of the book. The second half is devoted to more advanced topics such as non-standard systems of propositional logic, and predicate logic of the first order. Finally, there are chapters on higher functional calculi, the logical paradoxes, and non-standard functional systems. A good deal of attention is paid throughout to completeness and consistency properties, the decision problem for various systems, and algebraic structure. There are no frills or "gimmicks" in this book, but good intelligent discussions of important mathematical issues, and many theorems which are left as exercises to the student. Some items which one wishes had been included are normal forms, and elementary discussions of the theories of recursion and logical models.—H. P. K. (shrink)

Several authors have used the expression ‘formal asymmetry’ to characterize Einstein's method of introducing conceptual innovations. Prior to his use of formal asymmetries, however, Einstein relied upon analogy to introduce his major concepts, but without satisfactory results. He gradually refined another technique, reflection upon empirical problems, into the method of formal asymmetries, with impressive results. This historical study, based upon a textual analysis of Einstein's publications, raises a series of questions regarding the place of (...) class='Hi'>formal asymmetries in his work. (shrink)

Presumption of Equality requires that individuals be treated equally in the absence of relevant information that would discriminate between them. Our objective is to make this principle more precise, if viewed as a principle of fairness, and to determine why and under what conditions it should be obeyed. Presumption norms are procedural constraints, but their justification can be sought in the possible or expected outcomes of the procedures they regulate. This is the avenue pursued here. The suggestion is that in (...) the absence of information that would discriminate between the individuals, equal treatment minimizes the expected unfairness of the outcome. A related suggestion is that equal treatment under these circumstances also minimizes the maximal possible unfairness of the outcome. Whether these suggestions are correct or not depends on the properties of the underlying unfairness measure. The required properties are specified. (shrink)

Consciousness is defined as operating with the meanings of representations, which are what arises in mind under the influence of a stimulus (primary representations) as well as what arises as a result of their transformation (secondary, combined representations). In a first approximation, a representation is expressed by words. The concept of “representation” is a special case of the concept of “information-certainty”, which is the result of distinction. Any distinction is a distinction by a specific attribute and representation is the value (...) of the attribute. In relative ontology, distinction is an essential condition of being that is formalized quantitatively through the operation of ontological subtraction, which is a quantitative expression of representation in relation to consciousness. The finite set of representations for one attribute can always be sorted in ascending order of this attribute values. In the order constructed, each representation corresponds to an attribute number, the only difference of which from a number in mathematics is that the one is always associated with a specific attribute, and the other is not associated with any attribute. The meaning of a representation expressed by an attribute number has a place in an ordered quantitative series of other representations of the same attribute, which is the basis of distinction. Operating with meanings is operating with attributive numbers-meanings. This method of the meaning describing is called the relative method. All operations with the meanings of representations are performed in a multidimensional cognitive space. Each axis of the cognitive space corresponds to an attribute by which representations differ. On each axis there are attribute numbers corresponding to the meanings of representations for the attribute. This approach is a quantitative method of describing of all experimental processes of consciousness, which allows to build a scientific, i.e. quantitative, theory of consciousness with laws written down in a quantitative way. Based on this, it is possible to construct a quantitative calculation of this theory predictions. Such a prediction allows to make an accurate (unambiguous) experimental verification. Due to the quantitative way of describing the operation of meanings, such a theory of consciousness is easily modeled in information technologies, since the latter are also based on the numerical nature of all their processes. The main difference between the relative method and the vast majority of methods using information technologies for text processing is that the relative method, firstly, is not statistical, and secondly, conveys the meaning of the text fully and most adequately. The relative method is effective in operating not only with text data, but also with any data of a different nature, for example, with video data, audio data. (shrink)

In formal epistemology, we use mathematical methods to explore the questions of epistemology and rational choice. What can we know? What should we believe and how strongly? How should we act based on our beliefs and values? We begin by modelling phenomena like knowledge, belief, and desire using mathematical machinery, just as a biologist might model the fluctuations of a pair of competing populations, or a physicist might model the turbulence of a fluid passing through a small aperture. Then, (...) we explore, discover, and justify the laws governing those phenomena, using the precision that mathematical machinery affords. For example, we might represent a person by the strengths of their beliefs, and we might measure these using real numbers, which we call credences. Having done this, we might ask what the norms are that govern that person when we represent them in that way. How should those credences hang together? How should the credences change in response to evidence? And how should those credences guide the person’s actions? This is the approach of the first six chapters of this handbook. In the second half, we consider different representations—the set of propositions a person believes; their ranking of propositions by their plausibility. And in each case we ask again what the norms are that govern a person so represented. Or, we might represent them as having both credences and full beliefs, and then ask how those two representations should interact with one another. This handbook is incomplete, as such ventures often are. Formal epistemology is a much wider topic than we present here. One omission, for instance, is social epistemology, where we consider not only individual believers but also the epistemic aspects of their place in a social world. Michael Caie’s entry on doxastic logic touches on one part of this topic, but there is much more. Relatedly, there is no entry on epistemic logic, nor any on knowledge more generally. There are still more gaps. These omissions should not be taken as ideological choices. This material is missing, not because it is any less valuable or interesting, but because we v failed to secure it in time. Rather than delay publication further, we chose to go ahead with what is already a substantial collection. We anticipate a further volume in the future that will cover more ground. Why an open access handbook on this topic? A number of reasons. The topics covered here are large and complex and need the space allowed by the sort of 50 page treatment that many of the authors give. We also wanted to show that, using free and open software, one can overcome a major hurdle facing open access publishing, even on topics with complex typesetting needs. With the right software, one can produce attractive, clear publications at reasonably low cost. Indeed this handbook was created on a budget of exactly £0 (≈ $0). Our thanks to PhilPapers for serving as publisher, and to the authors: we are enormously grateful for the effort they put into their entries. (shrink)

세상에는 대부분 사람들이 믿는 통념이지만 실은 근거 없는 그런 견해도 있다. 우리나라 역사에 대해서도 근거 없이 믿고 있는 잘못된 신념들이 있다. 철학자인 나로서는 그런 신념을 만나면 먼저 개념(용법)분석을 시도한다. 분석 도구는 수학(연립방정식의 결정-과소결정(부정)-과잉결정(불능)), 자연과학(가설연역방법), 논리학(모순관계, 포함관계) 이다. 분석한 개념은 “주(炷: 심지)”와 “산(蒜: 달래)”, 단군의 “수(壽)”, 주몽의 아버지인 “해모수”와 “단군”의 용법, “해모수”의 세 가지 용법, “신기대보(神器大寶)” 등이다. 이 개념들을 분석해 보면 고대 한국 왕들이 장생불사(長生不死)의 철학을 믿었다는 것을 알 수 있다. 역사기록에 등장하는 용어를 그 당대 용법으로 이해하려면 엄격한 학문연구방법이 필요하다. 역사를 (...) 연구할 때 좀 더 치밀한 연구방법을 고민해야 한다. (shrink)

Presumption of Equality requires that individuals be treated equally in the absence of relevant information that would discriminate between them. Our objective is to make this principle more precise, if viewed as a principle of fairness, and to determine why and under what conditions it should be obeyed. Presumption norms are procedural constraints, but their justification can be sought in the possible or expected outcomes of the procedures they regulate. This is the avenue pursued here. The suggestion is that in (...) the absence of information that would discriminate between the individuals, equal treatment minimizes the expected unfairness of the outcome. A related suggestion is that equal treatment under these circumstances also minimizes the maximal possible unfairness of the outcome. Whether these suggestions are correct or not depends on the properties of the underlying unfairness measure. The required properties are specified. (shrink)

The aim of this article is to reconstruct Bocheński’s method of philosophical analysis as well as to clarify the purpose of that method and its basic elements. In the second part of the paper I will compare Bocheński’s method with the methods of modern applied ontology.