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)

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)

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)

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)

This paper explores the possibility of developing a hybrid version of dispositional theories of aesthetic values. On such a theory, uses of aesthetic predicates express relational second-order dispositional properties. If the theory is not absolutist, it allows for the relativity of aesthetic values. But it may be objected to on the grounds that it fails to explain disagreement among subjects who are not disposed alike. This paper explores the possibility of adapting recent proposals of hybrid expressivist theories for moral predicates (...) to the case of aesthetic predicates. Hybrid expressivist theories make no explicit commitment about the kind of property expressed by the predicate, but make explicit commitments to implicated (or presupposed)expressive content. It is argued that dispositionalism about the properties expressed by aesthetic predicates, combined with expressive implicatures (or presuppositions), can account for aesthetic disagreements even in cases where subjects are not relevantly alike. (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)

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)

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)

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)

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)

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)

Recent arguments for relativist semantic theories have centered on the phenomenon of “faultless disagreement.” This paper offers independent motivation for such theories, based on the interpretation of predicates of personal taste in certain attitude contexts and presuppositional constructions. It is argued that the correct interpretation falls out naturally from a relativist theory, but requires special stipulation in a theory which appeals instead to the use of hidden indexicals; and that a hidden indexical analysis presents problems for contemporary syntactic theory.

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)

Lifschitz introduced the notion of defining extensions of predicate default theories not as absolute, but relative to a specified domain. We look specifically at default theories over a countable domain and show the set of default theories which possess an ω -extension is Σ 2 1 -complete. That the set is in Σ 2 1 is shown by writing a nearly circumscriptive formula whose ω -models correspond to the ω -extensions of a given default theory; similarly, Σ 2 1 (...) -hardness is established by a method for translating formulas into default theories in such a way that ω -models of the circumscriptive formula correspond to ω -extensions of the default theory. (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)

The nature of moral judgments, and, more specifically, the question of how they relate, on the one hand, to objective reality and, on the other, to subjective experience, are issues that have been central to metaethics from its very beginnings. While these complex and challenging issues have been debated by analytic philosophers for over a century, it is only relatively recently that more interdisciplinary and empirically-oriented approaches to such issues have begun to see light. The present chapter aims to make (...) a contribution of that kind. We will present the results of an empirical – specifically, corpus linguistic – study that offers evidence that moral predicates exhibit hallmarks of subjectivity at the linguistic level, but also, that they differ significantly from paradigmatically subjective predicates. (shrink)

One way to study and understand the notion of truth is to examine principles that we are willing to associate with truth, often because they conform to a pre-theoretical or to a semi-formal characterization of this concept. In comparing different collections of such principles, one requires formally precise notions of inter-theoretic reduction that are also adequate to compare these conceptual aspects. In this work I study possible ways to make precise the relation of conceptual equivalence between notions of truth associated (...) with collections of principles of truth. In doing so, I will consider refinements and strengthenings of the notion of relative truth-definability proposed by Fujimoto (2010): in particular I employ suitable variants of notions of equivalence of theories considered in Visser (2006) and Friedman & Visser (2014) to show that there are better candidates than mutual truth-definability for the role of sufficient condition for conceptual equivalence between the semantic notions associated with the theories. In the concluding part of the paper, I extend the techniques introduced in the first and show that there is a precise sense in which ramified truth (either disquotational or compositional) does not correspond to iterations of comprehension. (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)

Solving expressivism’s Frege-Geach problem requires specifying the attitudes expressed by arbitrarily complex moral sentences. Nicholas Unwin emphasizes the problems that arise in doing so for even the relatively simple case of negated atomic sentences. Terry Horgan and Mark Timmons believe that contrary-forming predicate negation offers a solution to this negation problem. I argue that their solution is incomplete.

Within a weak system \ of intuitionistic analysis one may prove, using the Weak Fan Theorem as an additional axiom, a completeness theorem for intuitionistic first-order predicate logic relative to validity in generalized Beth models as well as a completeness theorem for classical first-order predicate logic relative to validity in intuitionistic structures. Conversely, each of these theorems implies over \ the Weak Fan Theorem.

One of the characteristic features of contemporary logic is that it incorporates the Frege‐Russell thesis according to which verbs for being are multiply ambiguous. This thesis was not accepted before the nineteenth century. In Aristotle existence could not serve alone as a predicate term. However, it could be a part of the force of the predicate term, depending on the context. For Kant existence could not even be a part of the force of the predicate term. Hence, after Kant, existence (...) was left homeless. It found a home in the algebra of logic in which the operators corresponding to universal and particular judgments were treated as duals, and universal judgments were taken to be relative to some universe of discourse. Because of the duality, existential quantifier expressions came to express existence. The orphaned notion of existence thus found a new home in the existential quantifier. (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.

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 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)

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)

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)

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)

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)

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 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)

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)

As is well-known, the formal system in which Frege works in his Grundgesetze der Arithmetik is formally inconsistent, Russell's Paradox being derivable in it. This system is, except for minor differences, full second-order logic, augmented by a single non-logical axiom, Frege's Axiom V. It has been known for some time now that the first-order fragment of the theory is consistent. The present paper establishes that both the simple and the ramified predicative second-order fragments are consistent, and that Robinson arithmetic, Q, (...) is relatively interpretable in the simple predicative fragment. The philosophical significance of the result is discussed. (shrink)

I discuss the interest-relative account of vagueness and argue for a distinction between relational vague predicates and non-relational vague predicates depending on the kind of properties expressed by them. The strategy rests on three arguments arising from the existence of clear cases of a vague predicate, from contexts in which a different answer is required for questions about whether a vague predicate applies to an item, and whether such an item satisfies the interest of an agent, and from cases (...) where an object changes up to the point of becoming P, where P is a vague predicate. In the second part of the paper, I distinguish between relational properties and non-relational properties, and I argue for the view that some vague predicates can express non-relational properties, comparative relational properties and interest-relative properties. On the basis of these arguments, I conclude that vagueness cannot be reduced to interest-relativity. (shrink)

An account of assertion along truth-relativistic lines is offered. The main lines of relativism about truth are laid out and the problematic features that assertion acquires in the presence of relative truth are identified. These features are the possibility of coherently formulating norms of assertion and the possibility of grounding a rational practice of assertion upon relative truth. A solution to these problems is provided by formulating norms for making and assessing assertions that employ a suitably relativized truth (...) predicate and a perspectival notion of correctness. Two potential objections to this proposal are addressed. (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)

The purpose of this paper is to argue that assessment relativism entails the assessment-sensitivity of the sentential truth-predicate, but not of the propositional truth-predicate. The central idea of assessment relativism is that a single token claim evaluated within a single world can have different truth-values when considered in different contexts of assessment. John MacFarlane in Assessment Sensitivity: Relative Truth and its Applications and also Max Kölbel in the article ‘Global relativism and self-refutation’ have argued that this position leads to (...) relativism about the propositional truth-predicate. I argue that this is not the case—it entails relativism only about the sentential truth-predicate. (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)

This article examines instances of the pu relative construction in Modern Greek in which the semantic role of the head is underspecified by the syntax. Such cases include sentences whose nominal head corresponds to some complement of the relative clause predicate and sentences in which the head does not have any sort of syntactic relationship with the relative. The latter, which are characteristic of oral, informal discourse, have been completely ignored in the previous literature, which has defined (...) relatives on the basis of exclusively structural criteria. It is argued that a unified account of the pu-construction (including gapped and gapless relatives) can be achieved if we analyze it as a conventional instruction for a particular kind of conceptual integration. Semantic and pragmatic factors influencing successful construal (one which leads to the construction of a unique blend) are systematically examined. The lack of a clear cut-off point in acceptability for such utterances tallies with the conclusion reached here, namely that the constraints governing such uses are constraints on interpretability. (shrink)

This dissertation is about the nature of perspectival thoughts and the context-sensitivity of the language used to express them. It focuses on two kinds of perspectival thoughts: ‘subjective’ evaluative thoughts about matters of personal taste, such as 'Beetroot is delicious' or 'Skydiving is fun', and first-personal or de se thoughts about oneself, such as 'I am hungry' or 'I have been fooled.' The dissertation defends of a novel form of relativism about truth - the idea that the truth of some (...) perspectival thought and talk is relative to the perspective of an evaluating subject or group. In Part I, I argue that the realm of ‘subjective’ evaluative thought and talk whose truth is perspective-relative includes attributions of knowledge of the form ’S knows that p.’ Following a brief introduction, chapter 2 presents a new, error-theoretic objection against relativism about knowledge attributions. The case for relativism regarding knowledge attributions rests on the claim that relativism is the only view that explains all of the empirical data from speakers' use of the word "know" without recourse to an error theory. In chapter 2, I show that the relativist can only account for sceptical paradoxes and ordinary epistemic closure puzzles if she attributes a problematic form of semantic blindness to speakers. However, in 3 I show that all major competitor theories - forms of invariantism and contextualism - are subject to equally serious error-theoretic objections. This raises the following fundamental question for empirical theorising about the meaning of natural language expressions: If error attributions are ubiquitous, by which criteria do we evaluate and compare the force of error-theoretic objections and the plausibility of error attributions? I provide a number of criteria and argue that they give us reason to think that relativism's error attributions are more plausible than those of its competitors. In Part II, I develop a novel unified account of the content and communication of perspectival thoughts. Many relativists regarding ‘subjective’ thoughts and Lewisians about de se thoughts endorse a view of belief as self-location. In chapter 4, I argue that the self-location view of belief is in conflict with the received picture of linguistic communication, which understands communication as the transmission of information from speaker's head to hearer's head. I argue that understanding mental content and speech act content in terms of sequenced worlds allows a reconciliation of these views. On the view I advocate, content is modelled as a set of sequenced worlds - possible worlds ‘centred’ on a group of individuals inhabiting the world at some time. Intuitively, a sequenced world is a way a group of people may be. I develop a Stalnakerian model of communication based on sequenced worlds content, and I provide a suitable semantics for personal pronouns and predicates of personal taste. In chapter 5, I show that one of the advantages of this model is its compatibility with both nonindexical contextualism and truth relativism about taste. I argue in chapters 5 and 6 that the empirical data from eavesdropping, retraction, and disagreement cases supports a relativist completion of the model, and I show in detail how to account for these phenomena on the sequenced worlds view. (shrink)

Along the same line as that in Ono (Ann Pure Appl Logic 161:246–250, 2009), a proof-theoretic approach to Glivenko theorems is developed here for substructural predicate logics relative not only to classical predicate logic but also to arbitrary involutive substructural predicate logics over intuitionistic linear predicate logic without exponentials QFLe. It is shown that there exists the weakest logic over QFLe among substructural predicate logics for which the Glivenko theorem holds. Negative translations of substructural predicate logics are studied by (...) using the same approach. First, a negative translation, called extended Kuroda translation is introduced. Then a translation result of an arbitrary involutive substructural predicate logics over QFLe is shown, and the existence of the weakest logic is proved among such logics for which the extended Kuroda translation works. They are obtained by a slight modification of the proof of the Glivenko theorem. Relations of our extended Kuroda translation with other standard negative translations will be discussed. Lastly, algebraic aspects of these results will be mentioned briefly. In this way, a clear and comprehensive understanding of Glivenko theorems and negative translations will be obtained from a substructural viewpoint. (shrink)

Sentences that ascribe action are logically related, but it is not always obvious why. According to event semantics, implications and non-implications result from referential relations between unpronounced constituents. Taking as starting point examples including free relative clauses, this paper advances the alternative view that examples as such present logical relations as forms of predicative dependence indicated with pronounced constituents. To this end, I argue that Verbal Phrases and verbal traces follow the pattern of Verbal Phrase Anaphora and, more controversially, (...) that they can be semantically interpreted in terms of higher-order quantification that represent actions as properties, but neither as events nor event-kinds. (shrink)

In “Unarticulated Comparison Classes” 2018 [2009], Richard Vallée adopts John Perry’s (2012 [2001]) reflexive-referential theory of meaning and content as well as his concept of unarticulated constituents (Perry 1986) to deal with certain context-sensitive elements of the truth-conditions of statements containing relative gradable predicates. I am sympathetic both with the general framework and with the assumption that unarticulated constituents are involved in the truth-conditions of bare positives such as “Monica is tall.” I do not share, however, Vallée’s main conclusions (...) on the examples he provides as pre-theoretical evidence. This leads me to disagree with some details of his proposal for the semantics and pragmatics of relative gradable adjectives. (shrink)