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article

Instability and Contraction

Elia Zardini

Journal of Philosophical Logic > 2019 > 48 > 1 > 155-188

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.

article

HYPE: A System of Hyperintensional Logic (with an Application to Semantic Paradoxes)

Hannes Leitgeb

Journal of Philosophical Logic > 2019 > 48 > 2 > 305-405

This article introduces, studies, and applies a new system of logic which is called ‘HYPE’. In HYPE, formulas are evaluated at states that may exhibit truth value gaps (partiality) and truth value gluts (overdeterminedness). Simple and natural semantic rules for negation and the conditional operator are formulated based on an incompatibility relation and a partial fusion operation on states. The semantics...

article

Model-theoretic semantics and revenge paradoxes

Lorenzo Rossi

Philosophical Studies > 2019 > 176 > 4 > 1035-1054

Revenge arguments purport to show that any proposed solution to the semantic paradoxes generates new paradoxes that prove that solution to be inadequate. In this paper, I focus on revenge arguments that employ the model-theoretic semantics of a target theory and I argue, contra the current revenge-theoretic wisdom, that they can constitute genuine expressive limitations. I consider the anti-revenge...

article

Further Reflections on Sentences Saying of Themselves Strange Things

Elia Zardini

Logic and Logical Philosophy > 2017 > 26 > 4 > 563–581

Milne [2005] argued that a sentence saying of itself that it does not have a truthmaker is true but does not have a truthmaker. López de Sa and Zardini [2006] worried that, by parity of reasoning, one should conclude that a sentence saying of itself that it is not both true and short is true but not short. Recently, Milne [2013] and Gołosz [2015] have replied to López de Sa and Zardini’s worry, arguing...

article

Provably True Sentences Across Axiomatizations of Kripke’s Theory of Truth

Carlo Nicolai

Studia Logica > 2018 > 106 > 1 > 101-130

We study the relationships between two clusters of axiomatizations of Kripke’s fixed-point models for languages containing a self-applicable truth predicate. The first cluster is represented by what we will call ‘$$\fancyscript{PKF}$$ PKF -like’ theories, originating in recent work by Halbach and Horsten, whose axioms and rules (in Basic De Morgan Logic) are all valid in fixed-point models; the second...

article

On the Costs of Nonclassical Logic

Volker Halbach, Carlo Nicolai

Journal of Philosophical Logic > 2018 > 47 > 2 > 227-257

Solutions to semantic paradoxes often involve restrictions of classical logic for semantic vocabulary. In the paper we investigate the costs of these restrictions in a model case. In particular, we fix two systems of truth capturing the same conception of truth: (a variant) of the system KF of Feferman (The Journal of Symbolic Logic, 56, 1–49, 1991) formulated in classical logic, and (a variant of)...

article

Naive Modus Ponens and Failure of Transitivity

Andreas Fjellstad

Journal of Philosophical Logic > 2016 > 45 > 1 > 65-72

In the recent paper “Naive modus ponens”, Zardini presents some brief considerations against an approach to semantic paradoxes that rejects the transitivity of entailment. The problem with the approach is, according to Zardini, that the failure of a meta-inference closely resembling modus ponens clashes both with the logical idea of modus ponens as a valid inference and the semantic idea of the conditional...

article

Solving Multimodal Paradoxes

Federico Pailos, Lucas Rosenblatt

Theoria > 81 > 3 > 192 - 210

Recently, it has been observed that the usual type‐theoretic restrictions are not enough to block certain paradoxes involving two or more predicates. In particular, when we have a self‐referential language containing modal predicates, new paradoxes might appear even if there are type restrictions for the principles governing those predicates. In this article we consider two type‐theoretic solutions...

article

The Logics of Strict-Tolerant Logic

Eduardo Barrio, Lucas Rosenblatt, Diego Tajer

Journal of Philosophical Logic > 2015 > 44 > 5 > 551-571

Adding a transparent truth predicate to a language completely governed by classical logic is not possible. The trouble, as is well-known, comes from paradoxes such as the Liar and Curry. Recently, Cobreros, Egré, Ripley and van Rooij have put forward an approach based on a non-transitive notion of consequence which is suitable to deal with semantic paradoxes while having a transparent truth predicate...

article

The Opacity of Truth

Elia Zardini

Topoi > 2015 > 34 > 1 > 37-54

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...

article

Peter Crockaert on Self-Reference

Petr Hanke

Acta Comeniana (International review of Comenius studies and early modern... > 2014 > 28 > 145-167

The Dominican philosopher and theologian Peter Crockaert, also known as Peter of Brussels (c. 1460–1514), was a former member of the nominalist circle of John Mair. Having received nominalist training from one of the prominent post-medieval scholastic logicians, he entered the Dominican order and adopted a Thomist identity. As a result, his sentential semantics combines thirteenth-century Thomist...

article

Intuitionism and the liar paradox

Nik Weaver

Annals of Pure and Applied Logic > 2012 > 163 > 10 > 1437-1445

The concept of informal mathematical proof considered in intuitionism is apparently vulnerable to a version of the liar paradox. However, a careful reevaluation of this concept reveals a subtle error whose correction blocks the contradiction. This leads to a general resolution of the classical semantic paradoxes.This paper is an expanded version of parts of Weaver [10]

article

ZÁKLADY EXPLIKACE SÉMANTICKÝCH POJMŮ

Jiří Raclavský

Organon F. medzinárodný časopis pre analytickú filozofiu > 2012 > 19 > 4 > 488 – 505

It is a truism that semantic concepts (concepts of meaning, denotation, reference and even truth, etc.) are relative to language. I distinguish two their kinds in accordance to their relativity to language L; the relativity is either explicit (“true in L”), or implicit (“trueL”). If language is explicated, the concepts of the former kind can be easily explicated in a plausible way and we resist semantic...

article

PARADOXES, TRUTH, AND CORRESPONDENCE IN ROGER SWYNESHED'S SEMANTICS (Paradoxy, pravdivost a korespondence v semantice Rogera Swynesheda)

Miroslav Hanke

Organon F. medzinárodný časopis pre analytickú filozofiu > 2011 > 18 > 1 > 40-61

The present paper is concerned with an exposé of the basic general-semantic theses presented in the tract called 'De insolubilibus' written by the 14th century British logician Roger Swyneshed. Swyneshed's semantics is analysed as a highly specific theory of truth, correspondence and facts (truth-makers). Swyneshed's theory revises the correspondence theory of truth and rejects the principle of bivalence,...

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