This paper is an exposition and evaluation of the Agustín Rayo's views about the epistemology and metaphysics of mathematics, as they are presented in his book The Construction of Logical Space.

Thomas Hofweber takes the semantic paradoxes to motivate a radical reconceptualization of logical validity, rejecting the idea that an inference rule is valid just in case every instance thereof is necessarily truth-preserving. Rather than this “strict validity”, we should identify validity with “generic validity”, where a rule is generically valid just in case its instances are truth preserving, and where this last sentence is a generic, like “Bears are dangerous”. While sympathetic to Hofweber’s view that strict validity should be replaced (...) by something allowing for exceptions, I argue that this should instead be truth-conduciveness, a matter of a large majority of instances being truth-preserving. The fact that inference rules have uncountably many instances, I argue, can be handled by defining truth-conduciveness as relative to finite sets of instances. Moreover, I argue that Hofweber’s position, while seemingly radical, may be less so under closer scrutiny. For the mere claim that classical rules and unrestricted truth rules are generically valid (or truth-conducive) is not in itself controversial. Also, if there is an answer to the question of which of these are also strictly valid, then the claim that generic validity is the central notion in logic is at most an interest-relative matter, since there is then also a fact of the matter as to which inference rules are (not) strictly valid. If no solution operating with strict validity to the paradoxes can be had, however, then the claim that validity should be identified with a weaker notion is better motivated. I argue that it is reasonable, in view of past failures, to conjecture that no ordinary solution will score high enough relative to standard (uncontroversial) desiderata to merit justified belief. Hence, it is unknowable which solution is correct. I further argue that this is best explained by its being metaphysically indeterminate which solution is correct. If this conjecture is true, then we ought instead to think of validity as allowing exceptions, and then take the “true logic” to be one that takes both the classical rules and the truth rules to be valid, i.e., truth-conducive. This logic scores very high on the desiderata on logics, and is therefore preferable to any logic operating with strict validity. (shrink)

This paper begins by raising a puzzle about what function our use of the word ‘rational’ could serve. To solve the puzzle, I introduce a view I call Epistemic Communism: we use epistemic evaluations to promote coordination among our basic belief-forming rules, and the function of this is to make the acquisition of knowledge by testimony more efficient.

Are there any things that are such that any things whatsoever are among them. I argue that there are not. My thesis follows from these three premises: (1) There are two or more things; (2) for any things, there is a unique thing that corresponds to those things; (3) for any two or more things, there are fewer of them than there are pluralities of them.

This paper defends the claim that although ‘Superman is Clark Kent and some people who believe that Superman flies do not believe that Clark Kent flies’ is a logically inconsistent sentence, we can still utter this sentence, while speaking literally, without asserting anything false. The key idea is that the context-sensitivity of attitude reports can be - and often is - resolved in different ways within a single sentence.

Dialetheists believe some sentences are both true and false. Objectors have argued that this makes it unclear how people can disagree with each other because, given the dialetheist’s commitments, if I make a claim and you tell me my claim is false, we might both be correct. Graham Priest (2006a) thinks that people disagree by rejecting or denying what is said rather than ascribing falsehood to it. We build on the work of Julien Murzi and Massimiliano Carrara (2015) and show (...) that Priest’s approach cannot succeed: given the same dialetheist’s commitments you may be correct to reject a claim that I correctly believe. We argue further that any attempt to solve the problem by identifying a new attitude of disagreement will also fail. The culprit, we claim, is the attempt to find a pair of attitudes that satisfy ‘exclusivity’—that is, attitudes such that both cannot be simultaneously correct. Instead of identifying disagreement by the kinds of attitudes involved, we propose dialetheists focus on the normative landscape and identify it in part by whether parties have reasons to change their attitudes. We offer our own normative theory of disagreement to help dialetheists with this challenge. (shrink)

The liar paradox is still an open philosophical problem. Most contemporary answers to the paradox target the logical principles underlying the reasoning from the liar sentence to the paradoxical conclusion that the liar sentence is both true and false. In contrast to these answers, Buddhist epistemology offers resources to devise a distinctively epistemological approach to the liar paradox. In this paper, I mobilise these resources and argue that the liar sentence is what Buddhist epistemologists call a contradiction with one’s own (...) words. I situate my argument in the works of Dignāga and Dharmakīrti and show how Buddhist epistemology answers the paradox. (shrink)

Roache has raised a new objection to cohabitation theories of personal fission. According to these theories, in cases of personal fission the pre-fission body is cohabited by (at least) two persons. She claims such cohabitants cannot be concerned for their survival in the way ordinary non-cohabitants can. I will offer criticism of Roache’s argument and conclude she doesn’t establish this claim.

An old and well-known objection to non-classical logics is that they are too weak; in particular, they cannot prove a number of important mathematical results. A promising strategy to deal with this objection consists in proving so-called recapture results. Roughly, these results show that classical logic can be used in mathematics and other unproblematic contexts. However, the strategy faces some potential problems. First, typical recapture results are formulated in a purely logical language, and do not generalize nicely to languages containing (...) the kind of vocabulary that usually motivates non-classical theories—for example, a language containing a naïve truth predicate. Second, proofs of recapture results typically employ classical principles that are not valid in the targeted non-classical system; hence, non-classical theorists do not seem entitled to those results. In this paper, we analyze these problems and provide solutions on behalf of non-classical theorists. To address the first problem, we provide a novel kind of recapture result, which generalizes nicely to a truth-theoretic language. As for the second problem, we argue that it relies on an ambiguity and that, once the ambiguity is removed, there are no reasons to think that non-classical logicians are not entitled to their recapture results. (shrink)

The paper tries to spell out a connection between deductive logic and rationality, against Harman's arguments that there is no such connection, and also against the thought that any such connection would preclude rational change in logic. One might not need to connect logic to rationality if one could view logic as the science of what preserves truth by a certain kind of necessity (or by necessity plus logical form); but the paper points out a serious obstacle to any such (...) view. (shrink)

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. (shrink)

We investigate the philosophical significance of the existence of different semantic systems with respect to which a given deductive system is sound and complete. Our case study will be Corcoran's deductive system D for Aristotelian syllogistic and some of the different semantic systems for syllogistic that have been proposed in the literature. We shall prove that they are not equivalent, in spite of D being sound and complete with respect to each of them. Beyond the specific case of syllogistic, the (...) goal is to offer a general discussion of the relations between informal notions—in this case, an informal notion of deductive validity—and logical apparatuses such as deductive systems and (model-theoretic or other) semantic systems that aim at offering technical, formal accounts of informal notions. Specifically, we will be interested in Kreisel's famous 'squeezing argument'; we shall ask ourselves what a plurality of semantic systems (understood as classes of mathematical structures) may entail for the cogency of specific applications of the squeezing argument. More generally, the analysis brings to the fore the need for criteria of adequacy for semantic systems based on mathematical structures. Without such criteria, the idea that the gap between informal and technical accounts of validity can be bridged is put under pressure. (shrink)

Minimalism about truth is one of the main contenders for our best theory of truth, but minimalists face the charge of being unable to properly state their theory. Donald Davidson incisively pointed out that minimalists must generalize over occurrences of the same expression placed in two different contexts, which is futile. In order to meet the challenge, Paul Horwich argues that one can nevertheless characterize the axioms of the minimalist theory. Sten Lindström and Tim Button have independently argued that Horwich’s (...) attempt to formulate minimalism remains unsuccessful. We show how to properly state Horwich’s axioms by appealing to propositional functions that are given by definite descriptions. Both Lindström and Button discuss proposals similar to ours and conclude that they are unsuccessful. Our new suggestion avoids these objections. (shrink)

This paper presents a new approach to the class-theoretic paradoxes. In the first part of the paper, I will distinguish classes from sets, describe the function of class talk, and present several reasons for postulating type-free classes. This involves applications to the problem of unrestricted quantification, reduction of properties, natural language semantics, and the epistemology of mathematics. In the second part of the paper, I will present some axioms for type-free classes. My approach is loosely based on the Gödel–Russell idea (...) of limited ranges of significance. It is shown how to derive the second-order Dedekind–Peano axioms within that theory. I conclude by discussing whether the theory can be used as a solution to the problem of unrestricted quantification. In an appendix, I prove the consistency of the class theory relative to Zermelo–Fraenkel set theory. (shrink)

There are three questions associated with Simpson’s paradox (SP): (i) Why is SP paradoxical? (ii) What conditions generate SP? and (iii) How to proceed when confronted with SP? An adequate analysis of the paradox starts by distinguishing these three questions. Then, by developing a formal account of SP, and substantiating it with a counterexample to causal accounts, we argue that there are no causal factors at play in answering questions (i) and (ii). Causality enters only in connection with action.

What requirements must deflationary formal theories of truth satisfy? This chapter argues against the widely accepted view that compositional and Tarskian theories of truth are substantial or otherwise unacceptable to deflationists. First, two purposes that a formal truth theory can serve are distinguished: one descriptive, the other logical (i.e., to characterise the correctness of inferences involving ‘true’). The chapter argues that the most compelling arguments for the incompatibility of compositional and Tarskian theories concern descriptive theories only. -/- Second, two requirements (...) that any deflationist truth theory intended to serve a logical purpose must satisfy are put forward. These requirements, it is argued, suggest that (i) many well-known compositional and Tarskian theories are acceptable from a deflationist standpoint (including CT); (ii) certain other popular theories of truth (including KF and FS) are not similarly acceptable; (iii) there are no conclusive reasons to impose a conservativeness requirement on deflationary theories of truth. (shrink)

The paper provides an alternative interpretation of ‘pair points’, discussed in Beall et al., "On the ternary relation and conditionality", J. of Philosophical Logic 41(3), 595-612. Pair points are seen as points viewed from two different ‘perspectives’ and the latter are explicated in terms of two independent valuations. The interpretation is developed into a semantics using pairs of Kripke models (‘pair models’). It is demonstrated that, if certain conditions are fulfilled, pair models are validity-preserving copies of positive substructural models. This (...) yields a general soundness and completeness result for a variety of (positive) substructural logics with respect to multimodal Kripke frames with binary accessibility relations. In addition, an epistemic interpretation of pair models is provided. (shrink)

The historical consensus is that logical evidence is special. Whereas empirical evidence is used to support theories within both the natural and social sciences, logic answers solely to a priori evidence. Further, unlike other areas of research that rely upon a priori evidence, such as mathematics, logical evidence is basic. While we can assume the validity of certain inferences in order to establish truths within mathematics and test scientifi c theories, logicians cannot use results from mathematics or the empirical sciences (...) without seemingly begging the question. Appeals to rational intuition and analyticity in order to account for logical knowledge are symptomatic of these commitments to the apriority and basicness of logical evidence. This chapter argues that these historically prevalent accounts of logical evidence are mistaken, and that if we take logical practice seriously we fi nd that logical evidence is rather unexceptional, sharing many similarities to the types of evidence appealed to within other research areas. (shrink)

In this paper we explain our pretense account of truth-talk and apply it in a diagnosis and treatment of the Liar Paradox. We begin by assuming that some form of deflationism is the correct approach to the topic of truth. We then briefly motivate the idea that all T-deflationists should endorse a fictionalist view of truth-talk, and, after distinguishing pretense-involving fictionalism (PIF) from error- theoretic fictionalism (ETF), explain the merits of the former over the latter. After presenting the basic framework (...) of our PIF account of truth-talk, we demonstrate a few advantages it offers over T-deflationist accounts that do not explicitly acknowledge pretense at work in the discourse. In turning to the Liar Paradox, we explain how the quasi-anaphoric functioning that our account attributes to truth-talk provides a diagnosis of the Liar Paradox (and other instances of semantic pathology) as having no content—in the sense of not specifying any of what we call M-conditions. At the same time, however, we vindicate the intuition that we can understand liar sentences, thereby avoiding one standard objection to “meaningless strategy” responses to the Liar Paradox. With this diagnosis in place, we then, by way of treatment, introduce a new predicate, ‘semantically defective’, and show how the explanation we give for its application allows for a consistent, yet revenge-immune, (dis)solution of the Liar Paradox, and semantic pathology generally. (shrink)

Jamie Tappenden was one of the first authors to entertain the possibility of a common treatment for the Liar and the Sorites paradoxes. In order to deal with these two paradoxes he proposed using the Strong Kleene semantic scheme. This strategy left unexplained our tendency to regard as true certain sentences which, according to this semantic scheme, should lack truth value. Tappenden tried to solve this problem by using a new speech act, articulation. Unlike assertion, which implies truth, articulation only (...) implies non-falsity. In this paper I argue that Tappenden’s strategy cannot be successfully applied to truth and the Liar. (shrink)

This paper develops the idea that valid arguments are equivalent to true conditionals by combining Kripke’s theory of truth with the evidential account of conditionals offered by Crupi and Iacona. As will be shown, in a first-order language that contains a naïve truth predicate and a suitable conditional, one can define a validity predicate in accordance with the thesis that the inference from a conjunction of premises to a conclusion is valid when the corresponding conditional is true. The validity predicate (...) so defined significantly increases our expressive resources and provides a coherent formal treatment of paradoxical arguments. (shrink)

This anthology of the very latest research on truth features the work of recognized luminaries in the field, put together following a rigorous refereeing process. Along with an introduction outlining the central issues in the field, it provides a unique and unrivaled view of contemporary work on the nature of truth, with papers selected from key conferences in 2011 such as Truth Be Told, Truth at Work, Paradoxes of Truth and Denotation and Axiomatic Theories of Truth. Studying the nature of (...) the concept of ‘truth’ has always been a core role of philosophy, but recent years have been a boom time in the topic. With a wealth of recent conferences examining the subject from various angles, this collection of essays recognizes the pressing need for a volume that brings scholars up to date on the arguments. Offering academics and graduate students alike a much-needed repository of today’s cutting-edge work in this vital topic of philosophy, the volume is required reading for anyone needing to keep abreast of developments, and is certain to act as a catalyst for further innovation and research. (shrink)

Per il dialeteismo ci sono contraddizioni vere. Questa concezione filosofica ha assunto una forma chiara e definita a partire dal lavoro del filosofo e logico Graham Priest – uno dei suoi padri fondatori, nonché uno dei suoi più strenui difensori. Questo libro intende portare il dialeteismo all’attenzione di un ampio pubblico, che non sia solo quello degli addetti ai lavori. Il volume è suddiviso in due parti. La prima include le cinque lezioni su "Dialeteismo e storia della filosofia" tenute da (...) Priest e Filippo Casati a Padova nel 2016, in occasione del Corso di Eccellenza per il dottorato in filosofia dell’Università di Padova. La seconda contiene quattro contributi sul dialeteismo di autori italiani. (shrink)

This book provides a detailed commentary on the classic monograph by Alfred Tarski, and offers a reinterpretation and retranslation of the work using the original Polish text and the English and German translations. In the original work, Tarski presents a method for constructing definitions of truth for classical, quantificational formal languages. Furthermore, using the defined notion of truth, he demonstrates that it is possible to provide intuitively adequate definitions of the semantic notions of definability and denotation and that the notion (...) in a structure can be defined in a way that is analogous to that used to define truth. Tarski’s piece is considered to be one of the major contributions to logic, semantics, and epistemology in the 20th century. However, the author points out that some mistakes were introduced into the text when it was translated into German in 1935. As the 1956 English version of the work was translated from the German text, those discrepancies were carried over in addition to new mistakes. The author has painstakingly compared the three texts, sentence-by-sentence, highlighting the inaccurate translations, offering explanations as to how they came about, and commenting on how they have influenced the content and suggesting a correct interpretation of certain passages. Furthermore, the author thoroughly examines Tarski’s article, offering interpretations and comments on the work. (shrink)

This dissertation concerns the foundations of epistemic modality. I examine the nature of epistemic modality, when the modal operator is interpreted as concerning both apriority and conceivability, as well as states of knowledge and belief. The dissertation demonstrates how phenomenal consciousness and gradational possible-worlds models in Bayesian perceptual psychology relate to epistemic modal space. The dissertation demonstrates, then, how epistemic modality relates to the computational theory of mind; metaphysical modality; deontic modality; logical modality; the types of mathematical modality; to the (...) epistemic status of undecidable propositions and abstraction principles in the philosophy of mathematics; to the apriori-aposteriori distinction; to the modal profile of rational propositional intuition; and to the types of intention, when the latter is interpreted as a modal mental state. Examining the nature of epistemic logic itself, I develop a novel approach to conditions of self-knowledge in the setting of the modal μ-calculus, as well as novel epistemicist solutions to Curry's, the liar, and the knowability paradoxes. Solutions to previously intransigent issues concerning the first-person concept; the distinction between fundamental and derivative truths; and the unity of intention and its role in decision theory, are developed along the way. (shrink)

The paper offers a critical examination of a prominent, “quasi-deflationist” argument advanced in the contemporary debate on the semantic paradoxes against non-naive and non-transparent theories of truth. The argument claims that truth unrestrictedly fulfils certain expressive functions, and that its so doing requires the unrestricted validity of naivety and transparency principles. The paper criticises the quasi-deflationist argument by considering some kinds of cases in which transparency and naivety arguably fail. In some such cases truth still fulfils the relevant expressive functions (...) without being transparent or naive; in some other such cases, truth does not fulfil the relevant expressive functions and other conceptual resources must be called upon. Thus, in different ways, all such cases belie the quasi-deflationist argument’s insistence that naivety and transparency should be unrestrictedly valid for truth unrestrictedly to fulfil the relevant expressive functions. There might however be other reasons for solving the semantic paradoxes by revising classical logic, and the paper in effect closes by offering versions of the liar paradox that rely on compelling but opacity-friendly truth-theoretic principles. (shrink)

The concept of truth arguably plays a central role in many areas of philosophical theorizing. Yet, what seems to be one of the most fundamental principles governing that concept, i.e. the equivalence between P and , is inconsistent in full classical logic, as shown by the semantic paradoxes. I propose a new solution to those paradoxes, based on a principled revision of classical logic. Technically, the key idea consists in the rejection of the unrestricted validity of the structural principle of (...) contraction. I first motivate philosophically this idea with the metaphysical picture of the states-of-affairs expressed by paradoxical sentences as being distinctively . I then proceed to demonstrate that the theory of truth resulting from this metaphysical picture is, in many philosophically interesting respects, surprisingly stronger than most other theories of truth endorsing the equivalence between P and (for example, the theory vindicates the validity of the traditional laws of excluded middle and of non-contradiction, and also vindicates the traditional constraint of truth preservation on logical consequence). I conclude by proving a cutelimination theorem that shows the consistency of the theory. (shrink)

The paper is concerned with a logical difficulty which Lionel Shapiro’s deflationist theory of logical consequence (as well as the author’s favoured, non-deflationist theory) gives rise to. It is argued that Shapiro’s non-contractive approach to solving the difficulty, although correct in its broad outlines, is nevertheless extremely problematic in some of its specifics, in particular in its failure to validate certain intuitive rules and laws associated with the principle of modus ponens. An alternative non-contractive theory is offered which does not (...) suffer from the same problem. (shrink)

A new semantic paradox developed by Richard Heck and relying on very minimal logical and truth-theoretic resources is rehearsed. A theory of truth restricting the structural metarule of contraction is presented and some of the theory's relevant features are made explicit. It is then shown how the theory provides a principled solution to the paradox while preserving the extremely compelling truth-theoretic principles at stake, thus bringing out a significant advantage that the theory enjoys over virtually all other non-dialetheic theories. It (...) is finally argued that such advantage is amplified by theoretical considerations made available by the adoption of a correspondentist perspective in the philosophy of truth. (shrink)

In other works, I’ve proposed a solution to the semantic paradoxes which, at the technical level, basically relies on failure of contraction. I’ve also suggested that, at the philosophical level, contraction fails because of the instability of certain states of affairs. In this paper, I try to make good on that suggestion.

The naive theory of vagueness holds that the vagueness of an expression consists in its failure to draw a sharp boundary between positive and negative cases. The naive theory is contrasted with the nowadays dominant approach to vagueness, holding that the vagueness of an expression consists in its presenting borderline cases of application. The two approaches are briefly compared in their respective explanations of a paramount phenomenon of vagueness: our ignorance of any sharp boundary between positive and negative cases. These (...) explanations clearly do not provide any ground for choosing the dominant approach against the naive theory. The decisive advantage of the former over the latter is rather supposed to consist in its immunity to any form of sorites paradox. But another paramount phenomenon of vagueness is higher-order vagueness: the expressions introduced in order to express in the object language the vagueness of the object language are themselves vague. Two highly plausible claims about higher-order vagueness are articulated and defended: the existence of “definitely ω ” positive and negative cases and the “radical” character of higher-order vagueness itself. Using very weak logical principles concerning vague expressions and the ‘definitely’-operator, it is then shown that, in the presence of higher-order vagueness as just described, the dominant approach is subject to higher-order sorites paradoxes analogous to the original ones besetting the naive theory, and therefore that, against the communis opinio, it does not fare substantially better with respect to immunity to any form of sorites paradox. (shrink)

The medieval Islamic solutions to the liar paradox can be categorized into three different families. According to the solutions of the first family, the liar sentences are not well-formed truth-apt...

In a recent paper, Jc Beall has employed what he calls ‘shriek rules’ in a putative solution to the long-standing ‘just false’ problem for glut theory. The purpose of this paper is twofold: firstly, I distinguish the ‘just false’ problem from another problem, with which it is often conflated, which I will call the ‘exclusion problem’. Secondly, I argue that shriek rules do not help glut theorists with either problem.

The pain of rejection, the sweetness of revenge Content Type Journal Article Pages 1-12 DOI 10.1007/s11098-011-9794-2 Authors Crispin Wright, Department of Philosophy, New York University, 5 Washington Place, New York, NY, USA Journal Philosophical Studies Online ISSN 1573-0883 Print ISSN 0031-8116.

The standard Kripkean semantic theories for quantified modal logic allow the individuals that exist at other worlds to vary from those that exist at the actual world. This causes a problem for those who deny the existence of non-actual individuals. I focus on two prominent strategies for solving this problem, due respectively to Bernard Linsky and Edward Zalta (who identify the possible individuals with the actual individuals) and Alvin Plantinga (who identifies the possible individuals with the individual essences). I argue, (...) contra various commentators, that both of these solutions are acceptable by the lights of those who deny the existence of mere possibilia. (shrink)

A natural suggestion and increasingly popular account of how to revise our logical beliefs treats revision of logic analogously to the revision of scientific theories. I investigate this approach and argue that simple applications of abductive methodology to logic result in revision-cycles, developing a detailed case study of an actual dispute with this property. This is problematic if we take abductive methodology to provide justification for revising our logical framework. I then generalize the case study, pointing to similarities with more (...) recent and popular heterodox logics such as naïve logics of truth. I use this discussion to motivate a constraint—logical partisanhood—on the uses of such methodology: roughly: both the proposed alternative and our actual background logic must be able to agree that moving to the alternative logic is no worse than staying put. (shrink)

I discuss Greg Restall’s attempt to generate an account of logical consequence from the incoherence of certain packages of assertions and denials. I take up his justification of the cut rule and argue that, in order to avoid counterexamples to cut, he needs, at least, to introduce a notion of logical form. I then suggest a few problems that will arise for his account if a notion of logical form is assumed. I close by sketching what I take to be (...) the most natural minimal way of distinguishing content and form and suggest further problems arising for this route. (shrink)

I discuss Greg Restall’s attempt to generate an account of logical consequence from the incoherence of certain packages of assertions and denials. I take up his justification of the cut rule and argue that, in order to avoid counterexamples to cut, he needs, at least, to introduce a notion of logical form. I then suggest a few problems that will arise for his account if a notion of logical form is assumed. I close by sketching what I take to be (...) the most natural minimal way of distinguishing content and form and suggest further problems arising for this route. (shrink)

We discuss four distinct semantic consequence relations which are based on Strong Kleene theories of truth and which generalize the notion of classical consequence to 3-valued logics. Then we set up a uniform signed tableau calculus, which we show to be sound and complete with respect to each of the four semantic consequence relations. The signs employed by our calculus are,, and, which indicate a strict assertion, strict denial, tolerant assertion and tolerant denial respectively. Recently, Ripley applied the strict–tolerant account (...) of assertion and denial to develop a new approach to truth and alethic paradox, which we call the Strict–Tolerant Conceptionof Truth. The paper aims to contribute to our understanding of STCT in at least three ways. First, by developing the strict–tolerant calculus.Second, by developing a semantic version of the strict–tolerant calculus, which informs us about the assertoric possibilities relative to a fixed ground model. Third, by showing that the strict–tolerant calculus and assertoric semantics jointly suggest that STCT's claim that the strict and tolerant can be understood in terms of one another has to be reconsidered. (shrink)

Uzquiano (Analysis 70:39–44, 2010 ) showed that the Hardest Logic Puzzle Ever ( HLPE ) [in its amended form due to Rabern and Rabern (Analysis 68:105–112, 2008 )] has a solution in only two questions. Uzquiano concludes his paper by noting that his solution strategy naturally suggests a harder variation of the puzzle which, as he remarks, he does not know how to solve in two questions. Wheeler and Barahona (J Philos Logic, to appear, 2011 ) formulated a three question (...) solution to Uzquiano’s puzzle and gave an information theoretic argument to establish that a two question solution for Uzquiano’s puzzle does not exist. However, their argument crucially relies on a certain conception of what it means to answer self-referential yes–no questions truly and falsely . We propose an alternative such conception which, as we show, allows one to solve Uzquiano’s puzzle in two questions. The solution strategy adopted suggests an even harder variation of Uzquiano’s puzzle which, as we will show, can also be solved in two questions. Just as all previous solutions to versions of HLPE , our solution is presented informally. The second part of the paper investigates the prospects of formally representing solutions to HLPE by exploiting theories of truth. (shrink)

In a recent paper, Philip Kremer proposes a formal and theory-relative desideratum for theories of truth that is spelled out in terms of the notion of ‘no vicious reference’. Kremer’s Modified Gupta-Belnap Desideratum (MGBD) reads as follows: if theory of truth T dictates that there is no vicious reference in ground model M, then T should dictate that truth behaves like a classical concept in M. In this paper, we suggest an alternative desideratum (AD): if theory of truth T dictates (...) that there is no vicious reference in ground model M, then T should dictate that all T-biconditionals are (strongly) assertible in M. We illustrate that MGBD and AD are not equivalent by means of a Generalized Strong Kleene theory of truth and we argue that AD is preferable over MGBD as a desideratum for theories of truth. (shrink)

Many accounts of structural rationality give a special role to logic. This paper reviews the problem case of clear-eyed logical uncertainty. An account of rational norms on belief that does not give a special role to logic is developed: doxastic probabilism.

Revisionary theories of logic or truth require revisionary theories of mind. This essay outlines nonclassically based theories of rational belief, desire, and decision making, singling out the supervaluational family for special attention. To see these nonclassical theories of mind in action, this essay examines a debate between David Lewis and Derek Parfit over what matters in survival. Lewis argued that indeterminacy in personal identity allows caring about psychological connectedness and caring about personal identity to amount to the same thing. The (...) essay argues that Lewis's treatment of two of Parfit's puzzle cases—degreed survival and fission—presuppose different nonclassical treatments of belief and desire. (shrink)