Le premier livre des Topiques constitue une sorte d’introduction théorique à la compilation de stratégies dialectiques présentée dans les livres centraux de cette œuvre. Nombre des notions principales employées dans les règles d’inférence contenues dans les τόποι sont systématiquement exposées et ordonnées dans ce premier livre. Parmi elles, l’exemple le plus clair est celui des « prédicables ». Il y a, néanmoins, d’autres notions, dont l’exposition doctrinale doit être recherchée dans les Catégories. Par exemple, les diverses sortes d’opposition entre termes, (...) qui sont abondamment utilisées dans les Topiques, mais ne s’y trouvent pas définies. Dans cet article, je présente une analyse formelle des deux définitions des relatifs que l’on trouve dans Cat. 7, pour montrer ensuite comment elles sont employées dans les τόποι qui impliquent la prédication essentielle des relatifs, démontrant ainsi la cohérence de cette théorie et la dépendance étroite entre les deux œuvres. (shrink)

The difficulties encountered by attempts to treat identity as a relation between an object and itself are well-known: "...the sentence 'The morning star is...the morning star' is analytic and a truism, while...'The morning star is the evening star' is synthetic and represents a 'valuable extension of our knowledge'... But if {the morning star} and {the evening star} are the same object, and identity is taken as a relation holding between this object and itself, then it is impossible to explain how (...) the two sentences can differ in cognitive content... ". Russell's solution to these difficulties rejects the identification of logical with grammatical form, in effect denying that such sentences assert relations between the morning star and itself. The logical representations which the Russellian proposes, contain quantifiers, predicate letters, and individual variables, but no expressions standing for particulars. The Fregean solution, while admitting logical representations whose nominal expressions stand for particulars, insists that the meaning of such expressions is different from their reference. Frege-Russell analyses thus both deny that the morning star is involved qua particular in the meaning of the sentences in question. ;Rather than replace the morning star as ontological subject of these sentences, I suggest that their difference in meaning arises from the kind of particular that the identity-relation relates--a particular which, unlike its Frege-Russell counterpart, is two-sided and multi-faceted. Such a particular requires an ambiguous singular term. In Chapter 1, I utilize such a term to provide a surfacist account of belief-context ambiguity requiring neither differences in relative scope nor distinctions between sense and reference. In Chapter 2, I go on to provide an account of negative existentials, necessity- and identity-statements which resolves philosophical problems that Russell-Frege analyses only avoid. To solve these problems, I show that it is necessary to reject two canons of philosophical logic, the Law of Identity and the Indiscernibility of Identicals. (shrink)

Meontology of Gorgias vs. Nihilism. The purpose of this paper is to challenge Gorgias’ image of a “nihilist existentialist”. The original thesis ouden estin, too frequently rendered as „nothing exists”, thus reducing the verb “to be” to denote “bare” existence, and ouden to denote “nothingness”. On close inspection, it turns out that, in Gorgias, neither do we have a negation of reality nor an affirmative treatment of the word “nothingness”.Therefore, ouden” should not be understood as a negation of all reality (...) or a kind of affirmative “nothingness”, whereas “estin” should not be reduced to “bare” existence. (When existence is negated what we obtain is annihilation). Such practices still affect the various translations of Gorgias’ treaty On the non-being or on Nature. Gorgias’ “sophist” thought is typically interpreted as a joke or a parody of dialectical thinking of the Eleatics. In fact, as it turns out, he made no parody of dialectic but applied the elenctic, apagogic method in Zeno’s masterly manner. He did so not for an artificial purpose but to prove the absurdity of the hypothesis of absolute, transcendent (hence incognizable) one Truth-Being, which eliminates the non-being of becoming as absolute non-being. Gorgias argued in earnest in favour of relative being as such, Becoming as the only reality, which from the point of view of absolute being is after all non-being, but not-this-being, or relative non-being but not non-relative non-being, as the Eleatics had claimed. Gorgias’ positions appears to be an apologia of non-being which is, that is of Becoming. We do not transform the “nothing” into a “no thing”. The main question of the treaty is: what is predicated by the word “nothing”? Gorgias’ position can be recapitulated as “nothing is sc. true, there is no criterion because, after all, everything is opinion. It is reinforced further by meontological, i.e. anti-eleatic Gorgias’ emphasis: “No thing is Being (substance)”, because everything is Becoming. Thus the title if Gorgias’ treaty can thus be treated as as an antithesis to that of Melissos’, which – in our opinion – is to emphasize the “non-beingness” of nature, the non-substantiality of things. Therefore, if Gorgias’ text was polemical, and it questioned (while at the same time maintaining the positivity of Becoming as non-being) only the immutability of things, and thus we cannot speak of the existence or the cognizability of natures or of essences of things. In sum, the reasoning of Zeno and Melissos was of a kind that is apt to cut both ways, and that is what Gorgias showed. The argument given as peculiar to himself was to this effect. “What is not” is not, so, it is just as much as “what is”. It is as if the onset of the issues that Plato will take up in The Sophist as the problem of non-being understood as difference. The axis of Gorgias’s anti-eleatic critique, in our view, is his polemic with Parmenides’ famous thesis B3 regarding the relationship of identity or equality between noein and einai. It is an additional and perhaps the most important point of his critique that aims at demonstrating that such relationship is impossible. In brief, things are not words just as thoughts are not words. (shrink)

Applies the ‘Conformal Framework’ developed in Ch. 2 to some problems of the classical theory of reference, namely, to the question of how the reference of expressions in specific problem categories, in particular, proper names, observational predicates, and natural kind terms, is determined. McCarthy proposes interpretationally motivated accounts of the reference of these terms that cut across the conflicting accounts presented by causal and descriptive theories of reference. The striking feature of these accounts is their ‘local holism’: in each of (...) the three cases under consideration, the answer provided takes the form of saying how the reference of expressions of the given sort is fixed relative to the interpretations of expressions in one or both of the other sorts. The reference mechanisms suggested stand in a dialectical relation to the Conformal Framework, in the sense that they are justified by the latter and at the same time lend support the Framework's constitutive principles proposed in Ch. 2. (shrink)

Relative essentialism is the novel metaphysical theory that there can be multiple objects occupying the same space at the same time each with its own de re modal truths. Relative essentialism is motivated by Davidson’s semantics and his denial that nature itself is divided into a privileged domain of objects. Relative essentialism was first presented by Samuel C. Wheeler. I argue that Wheeler’s approach to the Davidsonian program needs to be elaborated in terms of various types of preconceptual intentional relations. (...) This elaboration is already largely implicit in Davidson’s own later work and in Wheeler’s relaunching of Davidsonian metaphysics. More specifically, I argue that relative essentialism is ultimately founded not on predication narrowly construed but on intentionality broadly construed. Following Wheeler’s suggestion, comparisons are made between relative essentialism and work within the phenomenological tradition. (shrink)

This article reports that some robustness of the notions of predicativity and of autonomous progression is broken down if as the given infinite total entity we choose some mathematical entities other than the traditionalω. Namely, the equivalence between normal transfinite recursion scheme and newdependent transfinite recursionscheme, which does hold in the context of subsystems of second order number theory, does not hold in the context of subsystems of second order set theory where the universeVof sets is treated as the given (...) totality. (shrink)

Ordinary language contains groups of related predicates with different arities. Interpreting utterances that appear to contain an n-place predicate by using an n+m-place predicate to dissolve merely apparent disagreements and other misunderstandings is an established practice in everyday discourse. This paper aims to present hermeneutical maxims to guide and evaluate these interpretations through arity raising. In interpreting utterances by using a higher-place predicate, we should use only expressions that their authors themselves reasonably could have used and which would have been (...) suitable to achieve their supposed purposes. The goal is to achieve a charitable, accurate reading that also maximizes the text's transparency to improve our understanding of it. (shrink)

Marxism proved and developed the theory of the infinite process of the increase of absoluteness in relative truth ; and this, together with the introduction of the dialectical materialist concept of practice into gnoseology , led to a fundamental change in the entire theory of knowledge, elevating it to the level of a theory of ascent toward genuine knowledge of the objectively real world via contradiction.

In this paper I shall attempt to enter part of the way into the microstructure of the account of truth in the Parmenidean fragment 8, and to reveal that account as a dialectical sequence of affirmation and denial involving various kinds of modal utterance. The sequence will then be put into parallel with the first four hypotheses of the second half of Plato’s Parmenides as well as with Zeno and some of the later tradition.

In recent work on context­dependency, it has been argued that certain types of sentences give rise to a notion of relative truth. In particular, sentences containing predicates of personal taste and moral or aesthetic evaluation as well as epistemic modals are held to express a proposition (relative to a context of use) which is true or false not only relative to a world of evaluation, but other parameters as well, such as standards of taste or knowledge or an agent. Thus, (...) a sentence like chocolate tastes good would express a proposition p that is true or false not only at a world of evaluation, but relative to the additional parameter as well, such as a parameter of taste or an agent. I will argue that the sentences that apparently give rise to relative truth should be understood by relating them in a certain way to the first person. More precisely, such sentences express what I will call first­person­based genericity, a form of generalization that is based on or directed toward an essential first­person application of the predicate. The account differs from standard relative truth account in crucial respects: it is not the truth of the proposition expressed that is relative to the first person; the proposition expressed by a sentence with a predicate of taste rather has absolute truth conditions. Instead it is the propositional content itself that requires a first­personal cognitive access whenever it is entertained. This account, I will argue, avoids a range of problems that standard relative truth theories of the sentences in question face and explains a number of further peculiarities that such sentences display. (shrink)

Whether a predicate is a referential expression depends upon what reference is conceived to be. Even if it is granted that reference is a relation between words and worldly items, the referents of expressions being the items to which they are so related, this still leaves considerable scope for disagreement about whether predicates refer. One of Frege's great contributions to the philosophy of language was to introduce an especially liberal conception of reference relative to which it is unproblematic to suppose (...) that predicates are referring expressions. According to this liberal conception, each significant expression in a language has its own distinctive semantic role or power, a power to effect the truth-value of the sentences in which it occurs. (shrink)

This paper is devoted to the formulation and investigation of a dynamic semantic interpretation of the language of first-order predicate logic. The resulting system, which will be referred to as ‘dynamic predicate logic’, is intended as a first step towards a compositional, non-representational theory of discourse semantics. In the last decade, various theories of discourse semantics have emerged within the paradigm of model-theoretic semantics. A common feature of these theories is a tendency to do away with the principle of compositionality, (...) a principle which, implicitly or explicitly, has dominated semantics since the days of Frege. Therefore the question naturally arises whether non-compositionality is in any way a necessary feature of discourse semantics. Since we subscribe to the interpretation of compositionality as constituting primarily a methodological principle, we consider this to be a methodological rather than an empirical question. As a consequence, the emphasis in the present paper lies on developing an alternative compositional semantics of discourse, which is empirically equivalent to its non-compositional brethren, but which differs from them in a principled methodological way. Hence, no attempts are made to improve on existing theories empirically. Nevertheless, as we indicate in section 5, the development of a compositional alternative may in the end have empirical consequences, too. First of all, it can be argued that the dynamic view on interpretation developed in this paper suggests natural and relatively easy to formulate extensions which enable one to deal with a wider range of phenomena than can be dealt with in existing theories. Moreover, the various approaches to the model-theoretic semantics of discourse that have been developed during the last decade, have constituted a ‘fresh start’ in the sense that much of what had been accomplished before was ignored, at least for a start. Of course, this is a justified strategy if one feels one is trying to develop a radically different approach to recalcitrant problems. However, there comes a time when such new approaches have to be compared with the older one, and when an assessment of the pros and cons of each has to be made. One of the main problems in semantics today, we feel, is that a semantic theory such as Montague grammar, and an approach like Kamp’s discourse representation theory, are hard to compare, let alone that it is possible to unify their insights and results.. (shrink)

The Dialectical Forge identifies dialectical disputation as a primary formative dynamic in the evolution of pre-modern Islamic legal systems, promoting dialectic from relative obscurity to a more appropriate position at the forefront of Islamic legal studies. The author introduces and develops a dialectics-based analytical method for the study of pre-modern Islamic legal argumentation, examines parallels and divergences between Aristotelian dialectic and early juridical jadal-theory, and proposes a multi-component paradigm—the Dialectical Forge Model—to account for the power of jadal in shaping (...) Islamic law and legal theory.In addition to overviews of current evolutionary narratives for Islamic legal theory and dialectic, and expositions on key texts, this work shines an analytical light upon the considerably sophisticated “proto-system” of juridical dialectical teaching and practice evident in Islam’s second century, several generations before the first “full-system” treatises of legal and dialectical theory were composed. This proto-system is revealed from analyses of dialectical sequences in the 2nd/8th century Kitāb Ikhtilāf al-ʿIrāqiyyīn / ʿIrāqiyyayn through a lens molded from 5th/11th century jadal-theory treatises. Specific features thus uncovered inform the elaboration of a Dialectical Forge Model, whose more general components and functions are explored in closing chapters. (shrink)

The purpose of this paper is to give an account and a rational reconstruction of the heuristic advice provided by Aristotle in the Topics and Prior Analytics in regard to the difficulty or ease of strategic planning in the context of a dialectical dialogue. The general idea is that a Questioner can foresee what his refutational syllogism would have to look like given the character of the thesis defended by the Answerer, and therefore plan accordingly. A rational reconstruction of this (...) advice will be attempted from three perspectives: strategic planning based on the acceptability of Answerer’s thesis, strategic planning based on the predicational form of the thesis, strategic planning based on the logical form of the thesis. In addition, we will provide an illustration of the potential of this heuristic advice as we apply it to the interpretation of a fragment from Plato, presuming that, in a similar way, a reading of this kind might be more generally applicable in the interpretation of the Platonic dialogues. (shrink)

We formulate Suppes predicates for various kinds of space-time: classical Euclidean, Minkowski's, and that of General Relativity. Starting with topological properties, these continua are mathematically constructed with the help of a basic algebra of events; this algebra constitutes a kind of mereology, in the sense of Lesniewski. There are several alternative, possible constructions, depending, for instance, on the use of the common field of reals or of a non-Archimedian field (with infinitesimals). Our approach was inspired by the work of Whitehead (...) (1919), though our philosophical stance is completely different from his. The structures obtained are idealized constructs underlying extant, physical space-time. (shrink)

ABSTRACTWide-ranging semantic flexibility is often considered a magic cure for contextualism to account for all kinds of troubling data. In particular, it seems to offer a way to account for our intuitions regarding embedded perspectival sentences. As has been pointed out by Lasersohn [2009. “Relative Truth, Speaker Commitment, and Control of Implicit Arguments.” Synthese 166 : 359â374], however, the semantic flexibility does not present a remedy for all kinds of embeddings. In particular, it seems ineffective when it comes to embeddings (...) under operators with truth evaluative adverbs such as ‘correctly believes that’ and ‘incorrectly believes that’ and under factive verbs. This paper takes a closer look at the problematic embedding data with respect to predicates of personal taste. It argues that there is indeed no semantic solution for contextualism but a pragmatic way out. (shrink)

This paper argues that truth values of sentences containing predicates of “personal taste” such as fun or tasty must be relativized to individuals. This relativization is of truth value only, and does not involve a relativization of semantic content: If you say roller coasters are fun, and I say they are not, I am negating the same content which you assert, and directly contradicting you. Nonetheless, both our utterances can be true (relative to their separate contexts). A formal semantic theory (...) is presented which gives this result by introducing an individual index, analogous to the world and time indices commonly used, and by treating the pragmatic context as supplying a particular value for this index. The context supplies this value in the derivation of truth values from content, not in the derivation of content from character. Predicates of personal taste therefore display a kind of contextual variation in interpretation which is unlike the familiar variation exhibited by pronouns and other indexicals. (shrink)

In this paper, we show that the predicate logics of consistent extensions of Heyting's Arithmetic plus Church's Thesis with uniqueness condition are complete $\Pi _{2}^{0}$. Similarly, we show that the predicate logic of HA*, i.e. Heyting's Arithmetic plus the Completeness Principle (for HA*) is complete $\Pi _{2}^{0}$. These results extend the known results due to Valery Plisko. To prove the results we adapt Plisko's method to use Tennenbaum's Theorem to prove 'categoricity of interpretations' under certain assumptions.

The general consensus emerging from decades of empirical investigation of metaphor processing is that, when appropriately contextualised, metaphorically used language is no more demanding of processing effort than literally used language. However, there is a small number of studies which contradict this position, notably Noveck, Bianco, and Castry (2001): they maintain that relevance-based pragmatic theory predicts increased cognitive costs incurred in deriving the extra effects that metaphors typically yield, and they provide experimental results that support this prediction. In our study, (...) we first surveyed and assessed the tasks and stimulus materials of many experiments on metaphor processing from the 1970's to the present day. The most telling result was an apparent disparity between the processing of metaphorical language used predicatively versus referentially. We then ran two self-paced reading experiments to test our hypothesis that when used as a predicate, metaphorical language is no more costly than literal language, but when used referentially, it does incur extra costs, even given a preceding biasing context. In the first experiment, all metaphorical referring expressions were in subject position so occurred early in the sentence; in the second experiment, we controlled for any effect of sentence position by placing metaphorical referring expressions in object position, thus later in the sentence, similar to the predicate metaphors. In both cases, metaphorical referring incurred significantly greater costs relative to literal equivalents than did metaphorical predication, with no effect of sentence position. We end with a brief analysis of why the referential use of metaphor is special and effort-demanding. (shrink)

Here I propose a coherent way of preserving the identity of material objects with the matter that constitutes them. The presentation is formal, and intended for RSL. An informal presentation is in preliminary draft! -/- Relative-sameness relations—such as being the same person as—are like David Lewis's "counterpart" relations in the following respects: (i) they may hold between objects that aren't identical (I propose), and (ii) there are a multiplicity of them, different ones of which may be variously invoked in different (...) contexts. They differ from counterpart relations, however, in that they are weak equivalence relations (transitive, symmetric and weakly reflexive). The likenesses to counterpart relations make them suitable for an analysis of de-re temporal and modal predications. The difference renders the resulting counterpart theory immune to standard criticisms of Lewis's Counterpart Theory (e.g., in Hazen 1979, and Fara and Williamson 2005). (shrink)

In the framework of set theory we cannot distinguish between natural and non-natural predicates. To avoid this shortcoming one can use mathematical structures as conceptual spaces such that natural predicates are characterized as structurally nice subsets. In this paper topological and related structures are used for this purpose. We shall discuss several examples taken from conceptual spaces of quantum mechanics (orthoframes), and the geometric logic of refutative and affirmable assertions. In particular we deal with the problem of structurally distinguishing between (...) natural colour predicates and Goodmanian predicates like grue and bleen. Moreover the problem of characterizing natural predicates is reformulated in such a way that its connection with the classical problem of geometric conventionalism becomes manifest. This can be used to shed some new light on Goodman's remarks on the relative entrenchment of predicates as a criterion of projectibility. (shrink)

This paper is an informal presentation of the ideas presented formally in ”Relative-Sameness Counterpart Theory”. Relative-sameness relations -- such as being the same person as -- are like David Lewis’s “counterpart” relations in the following respects: (i) they may hold over time or across worlds between objects that aren’t cross-time or cross-world identical (I propose), and (ii) there are a multiplicity of them, different ones of which may be variously invoked in different contexts. They differ from his counterpart relations, however, (...) in that they are weak equivalence relations (transitive, symmetric and weakly reflexive). The likenesses to counterpart relations make them suitable for an analysis of de-re temporal and modal predications. The difference renders the resulting counterpart theory immune to standard criticisms of Lewis’s Counterpart Theory (e.g., in Hazen 1979, and Fara and Williamson 2005). The use of sameness as opposed to similarity relations in the analysis of de-re temporal and modal predication renders the resulting truth conditions as statable in terms that proponents of Kripke’s identity-based analysis can accept. (shrink)

We formulate Suppes predicates for various kinds of space-time: classical Euclidean, Minkowski's, and that of General Relativity. Starting with topological properties, these continua are mathematically constructed with the help of a basic algebra of events; this algebra constitutes a kind of mereology, in the sense of Lesniewski. There are several alternative, possible constructions, depending, for instance, on the use of the common field of reals or of a non-Archimedian field. Our approach was inspired by the work of Whitehead, though our (...) philosophical stance is completely different from his. The structures obtained are idealized constructs underlying extant, physical space-time. (shrink)

Peter Geach famously holds that there is no such thing as absolute identity. There are rather, as Geach sees it, a variety of relative identity relations, each essentially connected with a particular monadic predicate. Though we can strictly and meaningfully say that an individual a is the same man as the individual b, or that a is the same statue as b, we cannot, on this view, strictly and meaningfully say that the individual a simply is b. It is difficult (...) to find anything like a persuasive argument for this doctrine in Geach's work. But one claim made by Geach is that his account of identity is the account most naturally aligned with Frege's widely admired treatment of cardinality. And though this claim of an affinity between Frege's and Geach's doctrines has been challenged, the challenge has been resisted. William Alston and Jonathan Bennett, indeed, go further than Geach to argue that Frege's doctrine implies Geach's. If Alston and Bennett are right, then those who favor a broadly Fregean treatment of cardinality have no choice but to adopt Geach's doctrine of relative identity. And because contemporary set-theoretic accounts of cardinality are essentially Fregean in all respects relevant to this issue (see §11 below), it follows from Alston and Bennett's claim that virtually every standard modern treatment of cardinality requires a 'relativized' treatment of identity. The purpose of this paper is to argue against the implication claimed by Alston and Bennett. Despite some superficial similarities between Frege's treatment of cardinality and Geach's treatment of identity, the two doctrines are fundamentally opposed. Frege's account of cardinality, and its set-theoretic descendants, are all inconsistent with the claim that identity is 'relative' in Geach's sense. (shrink)

Along with many other languages, English has a relatively straightforward grammatical distinction between mass-occurrences of nouns and their countoccurrences. As the mass-count distinction, in my view, is best drawn between occurrences of expressions, rather than expressions themselves, it becomes important that there be some rule-governed way of classifying a given noun-occurrence into mass or count. The project of classifying noun-occurrences is the topic of Section II of this paper. Section III, the remainder of the paper, concerns the semantic differences between (...) nouns in their mass-occurrences and those in their count-occurrences. As both the name view and the mixed view are, in my opinion, subject to serious difficulties discussed in Section III.1,I defend a version of the predicate view. Traditionally, nouns in their singular count-occurrences are also analyzed as playing the semantic role of a predicate. How, then, does the predicate view preserve the intuitive difference between nouns in their mass- and those in their count-occurrences? I suggest, in Section III.2, that there are different kinds of predicates: mass-predicates, e.g. ‘is hair’, singular count-predicates, e.g. ‘is a hair’, and plural count-predicates, e.g. ‘are hairs’. Mass-predicates and count-predicates, in my view, are not reducible to each other. The remainder of Section III takes a closer look at the differences and interrelations between these different kinds of predicates. Mass-predicates and count-predicates differ from each other truth-conditionally, and these truth-conditional differences turn out to have interesting implications, in particular concerning the part-whole relation and our practices of counting. But mass- and count-predicates are also related to each other through systematic entailment relations; these entailment relations are examined in Section III.4. (shrink)

ON A GENERAL READING of the Metaphysics and the treatises of the so-called Organon, the types of assertion which Aristotle would allow as genuine predications seem relatively straightforward. According to the Categories, for instance, a species is characteristically predicated of the individuals falling under it, while genera and differentiae are predicated both of the relevant species and their associated individuals. The predicates are, in these instances, universals in a familiar Aristotelian sense. Furthermore, these intra-categorial predications, such as "Socrates is a (...) man" and "white is a color," are not the only instances of categorial acts. Aristotle also admits certain cross-categorial predications as logically well-formed; for example, "Socrates is white" and "Socrates is in the marketplace". These latter predications are at first glance also intelligible enough, though there are in both cases questions yet to be faced about the logical structure and ontological commitments of such ways of speaking. For Aristotle, one metaphysical theme presented even on the face of these linguistic appearances is the possibility that being a substrate for predication counts as a criterion for ontological primacy or, more generally, that being an ultimate substrate for meaningful discourse is grounds for being primarily real. An obvious corollary to this line of thought is the thesis that whatever might be said of or predicated of such primary substrata is ontologically dependent upon them. Just such a criterion seems to be at work in disqualifying universals from their claim to be substance in a significant sense. Therefore, it would be somewhat surprising to find primary substance appearing anywhere as a predicate. (shrink)

In this work we extend results from [4], [3] and [2] about propositional calculi with graded modalities to the predicative level. Our semantic is based on Kripke models with a single domain of interpretation for all the worlds. Therefore the axiomatic system will need a suitable generalization of the Barcan formula. We haven't considered semantics with world-relative domains because they don't present any new difficulties with respect to classical case. Our language will have, as in [1], constant and function symbols, (...) but they will have a rigid interpretation. In this instance the terms will be considered rigid designators, that is, their interpretations will be the same in all possible worlds (cfr. [5]). Nevertheless we will not consider languages with identity: in this way we avoid the problems of identity in modal contexts. On the other hand, we think that in that context would arise essentially the same problems which occur in classical predicative modal logic. Finally we will consider only denumerable languages because the extension to non denumerable ones isn't conceptually problematic. (shrink)

In nonstandard mathematics, the predicate ‘x is standard’ is fundamental. Recently, ‘relative’ or ‘stratified’ nonstandard theories have been developed in which this predicate is replaced with ‘x is y -standard’. Thus, objects are not standard in an absolute sense, but standard relative to other objects and there is a whole stratified universe of ‘levels’ or ‘degrees’ of standardness. Here, we study stratified nonstandard arithmetic and the related transfer principle. Using the latter, we obtain the ‘reduction theorem’ which states that arithmetical (...) formulas can be reduced to equivalent bounded formulas. Surprisingly, the reduction theorem is also equivalent to the transfer principle. As applications, we obtain a truth definition for arithmetical sentences and we formalize Nelson's notion of impredicativity. (shrink)

The aim of this paper is to connect the current debate on relative truth to the discussions of theories of truth in general, in which the so-called platitudes about truth have recently played a prominent role. Truth-relativists propose adding to the standard truth predicate an argument-place for an extra parameter over and above a possible world and they presume that the predicate that results from this relativization is a truth predicate. Yet this relativization arguably isn't just an innocuous extrapolation of (...) the Lewis-Kaplan line in semantics that naturally conserves the predicate's status as a truth predicate. This status has to be specifically established. I'll discuss arguments to the effect that truth-relativists fail on that score since relative truth doesn't satisfy certain basic platitudes about truth, in particular the Equivalence Schema and the normativity of truth. This suggests that a relativized truth predicate cannot play the role required of a truth predicate. I shall discuss the relativist's defensive strategies in detail, the most promising of which is to claim that it is legitimate to deny the Equivalence Schema by arguing that relativism introduces a revisionary concept of truth and so fundamentally revises semantics. However, I'll point out that solely invoking semantic revision doesn't suffice to justify a denial of the Equivalence Schema and that any further justification of such a denial is ad hoc or question begging. Moreover, I suggest that with respect to the normativity of truth the prospects of truth-relativism are equally dim. (shrink)

Lorenzo Valla (1407–1457) ranks among the greatest scholars and thinkers of the Renaissance. He secured lasting fame for his brilliant critical skills, most famously in his exposure of the “Donation of Constantine,” the forged document upon which the papacy based claims to political power. Lesser known in the English-speaking world is Valla's work in the philosophy of language—the basis of his reputation as the greatest philosopher of the humanist movement. Dialectical Disputations, translated here for the first time into any modern (...) language, is his principal contribution to the philosophy of language and logic. With this savage attack on the scholastic tradition of Aristotelian logic, Valla aimed to supersede it with a new logic based on the actual historical usage of classical Latin and on a commonsense approach to semantics and argument. Valla provides a logic that could be used by lawyers, preachers, statesmen, and others who needed to succeed in public debate—one that was stylistically correct and rhetorically elegant, and thus could dispense with the technical language of the scholastics, a “tribe of Peripatetics, perverters of natural meanings.” Valla's reformed dialectic became a milestone in the development of humanist logic and contains startling anticipations of modern theories of semantics and language. Volume 1 contains Book I, in which Valla refutes Aristotle's logical works on the categories, transcendentals, and predicables, with excursions into natural and moral philosophy and theology. (shrink)

This paper presents a precise semantics for incomplete predicates such as “ready”. Incomplete predicates have distinctive logical properties that a semantic theory needs to accommodate. For instance, “Tipper is ready” logically implies “Tipper is ready for something”, but “Tipper is ready for something” does not imply “Tipper is ready”. It is shown that several approaches to the semantics of incomplete predicates fail to accommodate these logical properties. The account offered here defines contexts as structures containing an element called a proposition (...) set, which contains atomic propositions and negations of atomic propositions. The condition under which “Tipper is ready” is true in a context is defined in terms of the contents of the proposition set for the context. On this account, the content of the context pertinent to a conversation must be determined not by what speakers have in mind but by relations of objective relevance. (shrink)

In this article I contrast in two ways those conceptions of semantic theory deriving from Richard Montague's Intensional Logic (IL) and later developments with conceptions that stick pretty closely to a far weaker semantic apparatus for human first languages. IL is a higher-order language incorporating the simple theory of types. As such, it endows predicates with a reference. Its intensional features yield a conception of propositional identity (namely necessary equivalence) that has seemed to many to be too coarse to be (...) acceptable. In the most usual expositions, it takes the object of linguistic explication to be the sentence in a context, as in Kaplan, 1977. This last has led to recent speculations about 'shifted' contexts. IL may be contrasted with a more linguistically (representationally) bound conception of propositions and interpretation of their predicational and functional parts, and with the explication, not of sentences in contexts, but of potential utterances, relative to the antecedent referential intentions of their speakers. We may then advance, as an empirical hypothesis about all human languages, that contexts never shift, and propose that apparent counterexamples stem from the misconstrual of linguistically coded anaphoric relations, relations that are wanted independently anyway. Donald Davidson's posthumous volume Truth and Predication mounts a sustained criticism of the notion of predicate reference. This criticism is not decisive. However, it may put the ball in the other court, insofar as it asks for a justification of what IL takes as given. Elaborations of IL using structured propositions, recently defended in King, 2007, recognize the problem of predicate reference, and the correlative issue of the 'unity of the proposition'; but I do not see that they can do better than bite the bullet already bitten in IL. I agree with Frege's insight that full justification of predicate reference pushes the boundaries of natural language, and to that extent may not be found within the semantic (as opposed to general scientific) enterprise. (shrink)

In addition to the familiar cardinal and proportional readings of many and few, there is yet another interpretation, the relative proportional reading. This reading, unlike the ordinary absolute proportional reading, is not conservative. Under the relative reading, 'Many ψs are φs' is true just in case the proportion of φs among ψs is greater than the proportion of φs among members of contextually given alternatives to ψ. I provide a definition of proportional readings that reduces the differences between absolute and (...) relative interpretations to the value of a single parameter.I argue that relative readings are not restricted to many and few, but are also exhibited by the adverbs often and seldom, and by generics. Interpretations of determiners that have been treated as "focus-affected readings," interpretations of adverbs of quantification that have been treated as "pure frequency readings," and interpretations of generics which have been claimed to be cases of "reverse interpretation" or "direct kind predication" are, in fact, instances of relative readings.A: Army reserve service is especially hard on people who own a small business.Q: Do many small-business owners serve in your regiment?A: I don't know what it's like in other regiments –Q: I am not asking you about other regiments.A: I know, but relatively speaking . . .(Interview on Israel Army Radio, June 8th, 2001). (shrink)

This book represents a study of Evelyn Underhill's premier work on mysticism, using Hegel's dialectics and Kant's theory of the sublime as interpretive tools. It especially focuses on two prominent features of Underhill's text: the description of the mystical life as one permeated by an intense love between the mystic and infinite reality, and the detailed delineation of stages of mystical development. Given these two features, the text lends itself to a construction of a valuable discourse predicated on dialecticism, (...) sublimity, and mysticism. The book also articulates a number of insights into the content and nature of the writings of Christian mystics. (shrink)

The purpose of this dissertation is to clarify Aristotle's conception of the nature and utility of the dialectical tools, as well as to help in establishing proof for the existence of a coherence between his logical theory and his philosophical practice. The first book of the Topics is unanimously considered to be Aristotle's introduction to his dialectical method. Thus, a certain familiarity with this book is necessary for whomever undertakes a study of one of its fundamental elements, such as the (...) tools. The first part of the dissertation is, therefore, devoted to this task. After situating the tools in the Topics, we will study Aristotle's proemium , especially as concerns the presentation of the dialectical argument and the goals of dialectic. For it is in order to procure such arguments that the tools are said to be useful, and it is how Aristotle uses the method for one of the aforesaid purposes that we will be studying later. We will then examine the chapters devoted to the parts of the dialectical argument . Among these are the predicables, which enter into the constitution of the propositions that will be laid down as dialectical problems, or taken as dialectical premises. Now, it is precisely because the tools furnish such premises that they allow us to obtain an abundance of arguments apt to solve such problems. These arguments can be syllogisms or inductions. We will next analyze Aristotle's presentation of the four tools . After which, we will propose a more essential and complete definition of them than is usually assigned. They are in fact described by Aristotle and his commentators in terms of the abundance of dialectical arguments they serve for. To my mind, however, it is better to speak of them as abilities ordered to obtaining probable premises. In the second part, we will examine the use made of the tools in certain sections of the De Anima and the Metaphysica. We will thus be in a better position to verify that when he is arguing dialectically, he is really using the tools as he described them in the Topics and as we explained them. Finally, we will propose a few explanations of the use of the tools in those passages where it seems that it is more a question of knowing than of dialectical reasoning. (shrink)

The article deals with the interpretation of propositional attitudes in the framework of modal predicate logic. The first part discusses the classical puzzles arising from the interplay between propositional attitudes, quantifiers and the notion of identity. After comparing different reactions to these puzzles it argues in favor of an analysis in which evaluations of de re attitudes may vary relative to the ways of identifying objects used in the context of use. The second part of the article gives this analysis (...) a precise formalization from a model-and proof-theoretic perspective. (shrink)

The ArgumentThe purpose of this article is twofold. Firstly, I propose to analyze controversies using a “dialectical” model, in the sense described in Aristotle'sTopics. This approach presupposes that we temporarily disregard, for the sake of clarity, the concreteness of real life controversies in order to focus on their argumentative structure. From this point of view, the main advantage of controversies is that they allow the interlocutorsto testeach other's claims and therefore to arrive at relatively corroborated conclusions. This testing function in (...) a dialectical context is implemented through theassentto commonly accepted premises, and thenecessitywhich characterizes each step of the reasoning.Secondly, I shall apply this dialectical framework to the study of the controversy concerning the motion of the Earth, or rather a small episode of it. I shall examine an exchange of letters, written in 1616 and in 1624 respectively, between Galileo Galilei and Francesco Ingoli, one of his Aristotelian opponents. I shall then compare this exchange with the first day of Galileo'sDialogue Concerning the Two Chief Systems of the World, a fictional debate, where Galileo discusses some of the same arguments. While the first exemplifies what I call “negative” testing, and yields a refutation of the opponent's theses, the second exemplifies “positive” testing and yields a dialectical demonstration of the motion of the Earth. (shrink)

Hilary Putnam's doctrine of conceptual relativity sustains that there are many different incompatible, yet equivalent, descriptions of what have to be considered "the same" phenomena. This fact is reason to justify the idea that metaphysical realism is wrong and that a better general view of reality should be something like a "pragmatic realism." Putnam sustains further that the different incompatible and equivalent descriptions have to bear the same explanatory virtue. Here it is contended that there seems to be difficulties in (...) construing this requirement in a non-question begging way in an argument designed to show that metaphysical realism should be dismissed. Different descriptions can only be deemed to have the same explanative virtue if our knowledge of, for example, structures in the natural world, seems to be simply a form to "save the phenomena," but this is a characteristic anti-realist thesis that should not be taken for granted in the dialectical setting. (shrink)

Plato was the first philosopher to discover the metaphysical phenomenon of plural-subjects and plural-predication; e.g. you and I are two, but neither you, nor I are two. I argue that Plato devised an ontology for plural-predication through his Theory of Forms, namely, plural-partaking in a Form. Furthermore, I argue that Plato used plural-partaking to offer an ontology of related individuals without reifying relations. My contention is that Plato’s theory of plural-relatives has evaded detection in the exegetical literature because his account (...) of plural-subjects through the Theory of Forms had not been recognised for what it is. I further submit that Plato’s handling of related individuals through plural-predication is not only a “first” in philosophy, but also an “only”, having remained a unique account in the metaphysics of relations. I hope that Plato’s account will introduce a fresh approach to contemporary debates on the subject. (shrink)

This thesis has the following aims. First, to show that Deleuze can be situated clearly within the post-Kantian tradition. This is achieved through an analysis of the relations between Kant's transcendental idealism and Deleuze's transcendental empiricism. Second, to explore the criticisms of representational theories of difference which can be found in the work of Deleuze and Hegel. Representational theories are best understood as theories which rely on a logic which is governed by relations between entities which pre-exist those relations. Deleuze (...) argues that these logics presuppose the formal equivalent of a homogeneous space within which these relations can be construed. Hegel similarly understands representation as the utilisation of finite categories which rely on the fixity of the subject of predication. The third aim is to provide a rigorous explication of some of the key themes of Deleuzian ontology, particularly in relation to the problem of representation. This will involve looking at the logic of multiplicities, which attempts to provide a theory of difference that is non-oppositional. This logic will be clarified through a discussion of Deleuze's use of modern geometry, and his analysis of the foundations of the calculus. The fourth aim will be to contrast Deleuze's solution with that of Hegel, particularly with respect to their relationships to Kant and the calculus. This is achieved through the Deleuzian distinction between finite and infinite representation, the latter in Deleuze's view characterising the Hegelian attempt to bring the idea of transition into representation itself. Finally, having shown where Deleuze and Hegel differ in their respective projects, the thesis will explore whether either of these philosophies has the resources to provide a refutation of the other with reference to the dialectic of force and the understanding in the henomenology of Spirit, and the problem of the one and the many. (shrink)

The ancient semantic paradoxes were thought to undermine the rationalist metaphysics of Plato, and their modern relatives have been used by Russell and others to administer some severe logical and epistemological shocks. These are not just tricks or puzzles, but are intimately connected with some of the liveliest and most basic philosophical disputes about logical form, universals, reference and predication. Dr Cargile offers here an original and sustained treatment of this range of issues, and in fact presents an unfashionable defence (...) of a platonistic ontology. He argues that the paradoxes arise not from mistakes in classical assumptions about truth or from an ontology that includes propositions and properties, but from mistakes in describing what propositions and properties are conveyed by particular linguistic expressions. The book should interest, and may well surprise, philosophers and others concerned with semantics and the foundations of logic. (shrink)