In a series of works, Pablo Cobreros, Paul Égré, David Ripley and Robert van Rooij have proposed a nontransitive system (call it ‘_K__3__L__P_’) as a basis for a solution to the semantic paradoxes. I critically consider that proposal at three levels. At the level of the background logic, I present a conception of classical logic on which _K__3__L__P_ fails to vindicate classical logic not only in terms of structural principles, but also in terms of operational ones. At the level of (...) the theory of truth, I raise a cluster of philosophical difficulties for a _K__3__L__P_-based system of naive truth, all variously related to the fact that such a system proves things that would seem already by themselves repugnant, even in the absence of transitivity. At the level of the theory of validity, I consider an extension of the _K__3__L__P_-based system of naive validity that is supposed to certify that validity in that system does not fall short of naive validity, argue that such an extension is untenable in that its nontriviality depends on the inadmissibility of a certain irresistible instance of transitivity (whence the advertised “final cut”) and conclude on this basis that the _K__3__L__P_-based system of naive validity cannot coherently be adopted either. At all these levels, a crucial role is played by certain metaentailments and by the extra strength they afford over the corresponding entailments: on the one hand, such strength derives from considerations that would seem just as compelling in a general nontransitive framework, but, on the other hand, such strength wreaks havoc in the particular setting of _K__3__L__P_. (shrink)

This paper sketches an understanding of conflation and vagueness according to which the latter is a special kind of the former. First, I sketch a particular understanding of conflation. Then, I go on to argue that vague concepts fit directly into this understanding. This picture of vagueness is related, but not identical, to a number of existing accounts.

This paper presents and motivates a new philosophical and logical approach to truth and semantic paradox. It begins from an inferentialist, and particularly bilateralist, theory of meaning---one which takes meaning to be constituted by assertibility and deniability conditions---and shows how the usual multiple-conclusion sequent calculus for classical logic can be given an inferentialist motivation, leaving classical model theory as of only derivative importance. The paper then uses this theory of meaning to present and motivate a logical system---ST---that conservatively extends classical (...) logic with a fully transparent truth predicate. This system is shown to allow for classical reasoning over the full (truth-involving) vocabulary, but to be non-transitive. Some special cases where transitivity does hold are outlined. ST is also shown to give rise to a familiar sort of model for non-classical logics: Kripke fixed points on the Strong Kleene valuation scheme. Finally, to give a theory of paradoxical sentences, a distinction is drawn between two varieties of assertion and two varieties of denial. On one variety, paradoxical sentences cannot be either asserted or denied; on the other, they must be both asserted and denied. The target theory is compared favourably to more familiar related systems, and some objections are considered. (shrink)

Nicholas Smith argues that an adequate account of vagueness must involve\ndegrees of truth. The basic idea of degrees of truth is that while\nsome sentences are true and some are false, others possess intermediate\ntruth values: they are truer than the false sentences, but not as\ntrue as the true ones. This idea is immediately appealing in the\ncontext of vagueness--yet it has fallen on hard times in the philosophical\nliterature, with existing degree-theoretic treatments of vagueness\nfacing apparently insuperable objections. Smith seeks to turn the\ntide in (...) favor of a degree-theoretic treatment of vagueness, by motivating\nand defending the basic idea that truth can come in degrees, by arguing\nthat no theory of vagueness that does not countenance degrees of\ntruth can be correct, and by developing a new degree-theoretic treatment\nof vagueness--fuzzy plurivaluationism--that solves the problems plaguing\nearlier degree theories. (shrink)

Kit Fine distinguishes between inexact and exact truthmaking. He argues that the former can be defined from the latter, but not vice versa, and so concludes that truthmaker semanticists should treat the exact variety of truthmaking as primitive. I argue that this gets things backwards. We can define exact truthmaking in terms of inexact truthmaking and we can’t define inexact truthmaking in terms of exact truthmaking. I conclude that it’s inexact truthmaking, rather than exact truthmaking, that truthmaker semanticists should treat (...) as the primitive semantic relation. (shrink)

1. The label conjunctive paraconsistency has been adopted to mean a consequence relation whereby ‘p and not p’ does not imply ‘p’ and ‘not p’ separately, so that Simplification in case of contradic...

In his Lectures on the History of Philosophy, Hegel develops a subtle analysis of Megarian paradoxes: the Liar, the Veiled Man and the Sorites. In this paper, we focus on Hegel's interpretation of...

Stratified properties such as ‘happy unhappiness’, ‘ungrounded ground’, ‘fortunate misfortune’, and evidently ‘true falsity’ may generate dialetheias (true contradictions). The aim of the article is to show that if this is the case, then we will have a special, conjunctive, kind of dialetheia: a true state description of the form ‘Fa and not Fa’ (for some property F and object a), wherein the two conjuncts, separately taken, are to be held untrue. The particular focus of the article is on happy (...) unhappiness: people suffering from (or enjoying) happy unhappiness (if there is some situation or state of mind of this kind) cannot be truly said ‘happy’ or ‘unhappy’, but we can say they are both. In the first section three cases of conjunctive stratification are presented; in the second section the logic of stratified contradictions is explored. The last section focuses on eudemonistic ascriptions: stated that a is happy to be unhappy (or unhappy to be happy), should we say a is happy? unhappy? both? neither? (shrink)

This article is a preliminary presentation of conjunctive paraconsistency, the claim that there might be non-explosive true contradictions, but contradictory propositions cannot be considered separately true. In case of true ‘p and not p’, the conjuncts must be held untrue, Simplification fails. The conjunctive approach is dual to non-adjunctive conceptions of inconsistency, informed by the idea that there might be cases in which a proposition is true and its negation is true too, but the conjunction is untrue, Adjunction fails. While (...) non-adjunctivism is a well-known option, the other view is not so much studied nowadays, but it was not unknown in the tradition, and there are some positive suggestions, in recent literature, that the position is plausible and deserves to be developed. The article compares conjunctivism, non-adjunctivism and dialetheism, then focuses on some possible justifications, costs and benefits of the conjunctive view. (shrink)

Say that two sentences are factually equivalent when they describe the same facts or situations, understood as worldly items, i.e. as bits of reality rather than as representations of reality. The notion of factual equivalence is certainly of central interest to philosophical semantics, but it plays a role in a much wider range of philosophical areas. What is the logic of factual equivalence? This paper attempts to give a partial answer to this question, by providing an answer the following, more (...) specific question: Given a standard propositional language with negation, conjunction and disjunction as primitive operators, which sentences of the language should be taken to be factually equivalent by virtue of their logical form? The system for factual equivalence advocated in this paper is a proper fragment of the first-degree system for the logic of analytic equivalence put forward in the late seventies by R. B. Angell. I provide the system with two semantics, both formulated in terms of the notion of a situation’s being fittingly described by a linguistic item. In the final part of the paper I argue, contra a view I defended in my “Grounding and Truth-Functions”, that the logic for factual equivalence I advocate here should be preferred to Angell’s logic if one wishes to follow the general conception of the relationships between factual equivalence and the notion of grounding put forward in the 2010 paper. (shrink)

The principle of tolerance characteristic of vague predicates is sometimes presented as a soft rule, namely as a default which we can use in ordinary reasoning, but which requires care in order to avoid paradoxes. We focus on two ways in which the tolerance principle can be modeled in that spirit, using special consequence relations. The first approach relates tolerant reasoning to nontransitive reasoning; the second relates tolerant reasoning to nonmonotonic reasoning. We compare the two approaches and examine three specific (...) consequence relations in relation to those, which we call: strict-to-tolerant entailment, pragmatic-to-tolerant entailment, and pragmatic-to-pragmatic entailment. The first two are nontransitive, whereas the latter two are nonmonotonic. (shrink)

A dialetheia is a sentence, A, such that both it and its negation, A, are true (we shall talk of sentences throughout this entry; but one could run the definition in terms of propositions, statements, or whatever one takes as her favourite truth bearer: this would make little difference in the context). Assuming the fairly uncontroversial view that falsity just is the truth of negation, it can equally be claimed that a dialetheia is a sentence which is both true and (...) false. (shrink)

A dialetheia is a sentence, A, such that both it and its negation, ¬A, are true (we shall talk of sentences throughout this entry; but one could run the definition in terms of propositions, statements, or whatever one takes as her favourite truth-bearer: this would make little difference in the context). Assuming the fairly uncontroversial view that falsity just is the truth of negation, it can equally be claimed that a dialetheia is a sentence which is both true and false.