One's Modus Ponens: Modality,Coherence and Logic

Recently, there has been a shift away from traditional truth‐conditional accounts of meaning towards non‐truth‐conditional ones, e.g., expressivism, relativism and certain forms of dynamic semantics. Fueling this trend is some puzzling behavior of modal discourse. One particularly surprising manifestation of such behavior is the alleged failure of some of the most entrenched classical rules of inference; viz., modus ponens and modus tollens. These revisionary, non‐truth‐conditional accounts tout these failures, and the alleged tension between the behavior of modal vocabulary and classical logic, as data in support of their departure from tradition, since the revisionary semantics invalidate some of these patterns. I, instead, offer a semantics for modality with the resources to accommodate the puzzling data while preserving classical logic, thus affirming the tradition that modals express ordinary truth‐conditional content. My account shows that the real lesson of the apparent counterexamples is not the one the critics draw, but rather one they missed: namely, that there are linguistic mechanisms, reflected in the logical form, that affect the interpretation of modal language in a context in a systematic and precise way, which have to be captured by any adequate semantic account of the interaction between discourse context and modal vocabulary. The semantic theory I develop specifies these mechanisms and captures precisely how they affect the interpretation of modals in a context, and do so in a way that both explains the appearance of the putative counterexamples and preserves classical logic.     

Future Contingents,Indeterminacy and Context

In Facing the Future, Belnap et al. reject bivalence and propose double time reference semantics to give a pragmatic response to the following assertion problem: how can we make sense of assertions about future events made at a time when the outcomes of those events are not yet determined? John MacFarlane employs the same semantics, now bolstered with a relative‐truth predicate, to accommodate the following apparently conflicting intuitions regarding the truth‐value of an uttered future contingent: at the moment of utterance, if asked to evaluate the truth‐value of the asserted future contingent one has the intuition that the assertion is neither true nor false, yet later, at the moment of the predicted event, one has the intuition that the assertion was, already, either true or false. Both MacFarlane and Belnap assume that assertions of future contingents have complete propositional content – the traditional propositional contents that, according to him ‘are the contents of assertions and beliefs’. This assumption is challenged.     

The evidence for relativism

The aim of this paper is to examine the kind of evidence that might be adduced in support of relativist semantics of a kind that have recently been proposed for predicates of personal taste, for epistemic modals, for knowledge attributions and for other cases. I shall concentrate on the case of taste predicates, but what I have to say is easily transposed to the other cases just mentioned. I shall begin by considering in general the question of what kind of evidence can be offered in favour of some semantic theory or framework of semantic theorizing. In other words, I shall begin with the difficult question of the empirical significance of semantic theorizing. In Sect. 2, I outline a relativist semantic theory, and in Sect. 3, I review four types of evidence that might be offered in favour of a relativistic framework. I show that the evidence is not conclusive because a sophisticated form of contextualism (or indexical relativism) can stand up to the evidence. However, the evidence can be taken to support the view that either relativism or the sophisticated form of contextualism is correct.     

A Contextualist Approach to Higher‐Order Vagueness

According to contextualism about vagueness, the content of a vague predicate is context sensitive. On this view, when item a is in the penumbra of the vague predicate ‘F’, speakers may (truly) utter ‘Fa’, or they may (truly) utter ‘not‐Fa’, without contravening the literal meaning of ‘F’. Unlike its more popular variants, the version of contextualism I defend rejects the principle of tolerance, a principle according to which small differences should not affect the applicability of a vague predicate. My goal is to show how such a rejection allows for a plausible treatment of higher‐order vagueness, and for a dissolution of paradoxes of higher‐order vagueness.     

In defence of a perspectival semantics for ‘know’

Relativism offers an ingenious way of accommodating most of our intuitions about ‘know’: the truth-value of sentences containing ‘know’ is a function of parameters determined by a context of use and a context of assessment. This sort of double-indexing provides a more adequate account of the linguistic data involving ‘know’ than does standard contextualism. However, relativism has come under recent attack: it supposedly cannot account for the factivity of ‘know’, and it entails, counterintuitively, that circumstances of evaluation have features that cannot be shifted by any intensional operator. I offer replies to these objections on behalf of the relativist. I then argue that a version of contextualism can account for the same data as relativism without relativizing sentence truth to contexts of assessment. This version of contextualism is thus preferable to relativism on methodological grounds.     

Relativism,Disagreement and Testimony

This article brings together two sets of data that are rarely discussed in concert; namely, disagreement and testimony data. I will argue that relativism yields a much more elegant account of these data than its major rival, contextualism. The basic idea will be that contextualists can account for disagreement data only by adopting principles that preclude a simple account of testimony data. I will conclude that, other things being equal, we should prefer relativism to contextualism. In making this comparative point, I will also defend self‐standing relativist accounts of disagreement and testimony data.     

MORAL CONTEXTUALISM AND MORAL RELATIVISM

Moral relativism provides a compelling explanation of linguistic data involving ordinary moral expressions like 'right' and 'wrong'. But it is a very radical view. Because relativism relativizes sentence truth to contexts of assessment it forces us to revise standard linguistic theory. If, however, no competing theory explains all of the evidence, perhaps it is time for a paradigm shift. However, I argue that a version of moral contextualism can account for the same data as relativism without relativizing sentence truth to contexts of assessment. This version of moral contextualism is thus preferable to relativism on methodological grounds.     

Epistemic Contextualism and the Semantics-Pragmatics Distinction

Contextualism, in its standard form, is the view that the truth conditions of sentences of the form ‘S knows that P’ vary according to the context in which they are uttered. One possible objection to contextualism appeals to what Keith DeRose calls a warranted assertability maneuver (or WAM), according to which it is not our knowledge sentences themselves that have context-sensitive truth conditions, but what is pragmatically conveyed by the use of such sentences. Thus, proponents of WAMs argue, the context sensitivity of knowledge attributions is not a semantic phenomenon but a pragmatic one. I examine a number of WAMs and show that each (i) is seriously flawed, or (ii) undercuts standard contextualism if we hold a minimalist conception of semantic content. I propose an alternative form of contextualism that accommodates minimalism and is immune to the second type of WAM, and show that this new form of contextualism shares the virtues of standard contextualism.     

On the Logic of Nonmonotonic Conditionals and Conditional Probabilities: Predicate Logic

In a previous paper I described a range of nonmonotonic conditionals that behave like conditional probability functions at various levels of probabilistic support. These conditionals were defined as semantic relations on an object language for sentential logic. In this paper I extend the most prominent family of these conditionals to a language for predicate logic. My approach to quantifiers is closely related to Hartry Field's probabilistic semantics. Along the way I will show how Field's semantics differs from a substitutional interpretation of quantifiers in crucial ways, and show that Field's approach is closely related to the usual objectual semantics. One of Field's quantifier rules, however, must be significantly modified to be adapted to nonmonotonic conditional semantics. And this modification suggests, in turn, an alternative quantifier rule for probabilistic semantics.     

Two-Valued Logics of Intentionality: Temporality,Truth, Modality,and Identity

The essay introduces a non-Diodorean, non-Kantian temporal modal semantics based on part-whole, rather than class, theory. Formalizing Edmund Husserl’s theory of inner time consciousness, §3 uses his protention and retention concepts to define a relation of self-awareness on intentional events. §4 introduces a syntax and two-valued semantics for modal first-order predicate object-languages, defines semantic assignments for variables and predicates, and truth for formulae in terms of the axiomatic version of Edmund Husserl’s dependence ontology (viz. the Calculus [CU] of Urelements) introduced by The Ontology of Intentionality I & II. It then uses the §3 results to define the modalities of truth, and §5 extends the semantics to identity claims. §6 defines and contrasts synthetic a priori truths to analytic a priori truths, and §7 compares Brentano School noetic semantic and Leibnizian possible-world semantic perspectives on modality. The essay argues that the modal logics it defines semantically are two-valued, first-order versions of the type of language which Husserl viewed as the language of any ontology of experience (i.e. of any science), and conceived as the logic of intentionality.     

Contextualism,Invariantism and Semantic Blindness

Epistemic contextualism, many critics argue, entails that ordinary speakers are blind to the fact that knowledge claims have context-sensitive truth conditions. This attribution of blindness, critics add, seriously undermines contextualism. I show that this criticism and, in general, discussions about the error theory entailed by contextualism, greatly underestimates the complexity and diversity of the data about ordinary speakers’ inter-contextual judgments, as well as the range of explanatory moves that are open to both invariantists and contextualists concerning such judgments. Contextualism does entail that some speakers suffer from semantic blindness; however, at its roots, this blindness concerns not the context-sensitivity of knowledge claims, but the question whether knowledge sentences possess context-independent truth conditions. I argue that this blindness should not be deemed problematic, but that invariantism entails an error theory that is, by comparison, much more troubling.     

Against the identification of assertoric content with compositional value

This essay investigates whether the things we say are identical to the things our sentences mean. It is argued that these theoretical notions should be distinguished, since assertoric content does not respect the compositionality principle. As a paradigmatic example, Kaplan??s formal language LD is shown to exemplify a failure of compositionality. It is demonstrated that by respecting the theoretical distinction between the objects of assertion and compositional values certain conflicts between compositionality and contextualism are avoided. This includes the conflict between eternalism and the semantics of tense, the embedding problems for contextualism about epistemic modals and taste claims, and the conflict between direct reference and the semantics of bound pronouns (and monstrous operators). After presenting the theoretical picture which distinguishes assertoric content from compositional semantic value, some objections to the picture are addressed. In so doing, the objection from King (Philos Perspect 17(1):195?C246, 2003) stemming from apparent complications with the interaction of temporal expressions and attitude reports is assessed and shown to be non-threatening.     

The Dizzying Turn of Epistemic Contextualism

The debate concerning epistemic contextualism represents a kind of linguistic turn in epistemology, where the focus has shifted from theorising about knowledge to theorising about knowledge attributions. Such a shift may well prove valuable, but only if we are clear on what the relationship is between a semantic analysis of knowledge attributions and a philosophical analysis of knowledge. One plausible approach is to claim that the semantic analysis entails and is entailed by the philosophical analysis. Yet this view—referred to here as the default view—has been explicitly adopted by few in the contextualism debate. This paper considers a form of argument in favour of the default view, and then considers the challenges that arise from either accepting or rejecting the default view.     

Aristotle on Predication

A predicate logic typically has a heterogeneous semantic theory. Subjects and predicates have distinct semantic roles: subjects refer; predicates characterize. A sentence expresses a truth if the object to which the subject refers is correctly characterized by the predicate. Traditional term logic, by contrast, has a homogeneous theory: both subjects and predicates refer; and a sentence is true if the subject and predicate name one and the same thing. In this paper, I will examine evidence for ascribing to Aristotle the view that subjects and predicates refer. If this is correct, then it seems that Aristotle, like the traditional term logician, problematically conflates predication and identity claims. I will argue that we can ascribe to Aristotle the view that both subjects and predicates refer, while holding that he would deny that a sentence is true just in case the subject and predicate name one and the same thing. In particular, I will argue that Aristotle's core semantic notion is not identity but the weaker relation of constitution. For example, the predication ‘All men are mortal’ expresses a true thought, in Aristotle's view, just in case the mereological sum of humans is a part of the mereological sum of mortals.     

Theories of Truth without Standard Models and Yablo’s Sequences

The aim of this paper is to show that it’s not a good idea to have a theory of truth that is consistent but ω-inconsistent. In order to bring out this point, it is useful to consider a particular case: Yablo’s Paradox. In theories of truth without standard models, the introduction of the truth-predicate to a first order theory does not maintain the standard ontology. Firstly, I exhibit some conceptual problems that follow from so introducing it. Secondly, I show that in second order theories with standard semantics the same procedure yields a theory that doesn’t have models. So, while having an ω- inconsistent theory is a bad thing, having an unsatisfiable theory of truth is actually worse. This casts doubts on whether the predicate in question is, after all, a truthpredicate for that language. Finally, I present some alternatives to prove an inconsistency adding plausible principles to certain theories of truth.     

Now is the time

The aim of this paper is to consider some logical aspects of the debate between the view that the present is the only ‘real’ time, and the view that the present is not in any way metaphysically privileged. In particular I shall set out a language of first-order predicate tense logic with a now predicate, and a first order (extensional) language with an abstraction operator, in such a way that each language can be shewn to be exactly translatable into the other. I shew that this translation is preserved at the metalinguistic level, so that equivalent truth conditions can be defined in a tensed metalanguage or an indexical metalanguage. I then make some remarks about the connection between proofs of relative consistency and metaphysical truth; and some historical remarks about Arthur Prior's use of formal logic in expressing his presentist views.