Further Reflections on Sentences Saying of Themselves Strange Things

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 in different ways that the worry is illfounded. In this paper, I’ll address these replies and argue that they fail to dispel López de Sa and Zardini’s worry, bringing out in the process some broader points concerning the use of self-referential sentences in arguments in philosophy of logic

Truth, demonstration and knowledge: a classical solution to the paradox of knowability

After introducing semantic anti-realism and the paradox of knowability, the paper offers a reconstruction of the anti-realist argument from the theory of understanding. The proposed reconstruction validates an unrestricted principle to the effect that truth requires the existence of a certain kind of “demonstration”. The paper shows that the principle fails to imply the problematic instances of the original unrestricted knowability principle but that the overall view still has unrestricted epistemic consequences. Appealing precisely to the paradox of knowability, the paper also argues, against BHK semantics, for the non-constructive character of the demonstrations envisaged by anti-realists, and contends that, in such a setting, one of the most natural arguments in favour of a revision of classical logic loses all its force

The Final Cut

In a series of works, Pablo Cobreros, Paul Egré, David Ripley and Robert van Rooij have proposed a nontransitive system (call it ‘K3LP’) 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 K3LP 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 K3LP-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 K3LP-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 K3LP-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 K3LP

What is a Paraconsistent Logic?

Paraconsistent logics are logical systems that reject the classical principle, usually dubbed Explosion, that a contradiction implies everything. However, the received view about paraconsistency focuses only the inferential version of Explosion, which is concerned with formulae, thereby overlooking other possible accounts. In this paper, we propose to focus, additionally, on a meta-inferential version of Explosion, i.e. which is concerned with inferences or sequents. In doing so, we will offer a new characterization of paraconsistency by means of which a logic is paraconsistent if it invalidates either the inferential or the meta-inferential notion of Explosion. We show the non-triviality of this criterion by discussing a number of logics. On the one hand, logics which validate and invalidate both versions of Explosion, such as classical logic and Asenjo–Priest’s 3-valued logic LP. On the other hand, logics which validate one version of Explosion but not the other, such as the substructural logics TS and ST, introduced by Malinowski and Cobreros, Egré, Ripley and van Rooij, which are obtained via Malinowski’s and Frankowski’s q- and p-matrices, respectively

Truth, Demonstration and Knowledge. A Classical Solution to the Paradox of Knowability

After introducing semantic anti-realism and the paradox of knowability, the paper offers a reconstruction of the anti-realist argument from understanding. The proposed reconstruction validates an unrestricted principle to the effect that truth requires the existence of a certain kind of “demonstration”. The paper shows that that principle fails to imply the problematic instances of the original unrestricted feasible-knowability principle but that the overall view underlying the new principle still has unrestricted epistemic consequences. Appealing precisely to the paradox of knowability, the paper also argues, against the BHK semantics, for the non-constructive character of the demonstrations envisaged by semantic anti-realism, and contends that, in such setting, one of the most natural arguments for a broadly intuitionist revision of classical logic loses all its force

Living on the slippery slope : the nature, sources and logic of vagueness

According to the dominant approach in the theory of vagueness, the nature of the vagueness of an expression ‘F’ consists in its presenting borderline cases in an appropriately ordered series: objects which are neither definitely F nor definitely not F (where the notion of definiteness can be semantic, ontic, epistemic, psychological or primitive). In view of the various problems faced by theories of vagueness adopting the dominant approach, the thesis proposes to reconsider the naive theory of vagueness, according to which the nature of the vagueness of an expression consists in its not drawing boundaries between any neighbouring objects in an appropriately ordered series. It is argued that expressions and concepts which do present this feature play an essential role in our cognitive and practical life, allowing us to conceptualize—in a way which would otherwise be impossible—the typically coarse-grained distinctions we encounter in reality. Despite its strong initial plausibility and ability to explain many phenomena of vagueness, the naive theory is widely rejected because thought to be shown inconsistent by the sorites paradox. In reply, it is first argued that accounts of vagueness based on the dominant approach are themselves subject to higher-order sorites paradoxes. The paradox is then solved on behalf of the naive theory by rejecting the unrestricted transitivity of the consequence relation on a vague language; a family of logics apt for reasoning with vague expressions is proposed and studied (using models with partially ordered values). The characteristic philosophical and logical consequences of this novel solution are developed and defended in detail. In particular, it is shown how the analysis of what happens in the attempt of surveying a sorites series and deciding each case allows the naive theory to recover a "thin" notion of a borderline case.Funding provided by an AHRC Fellowship and a Jacobsen Fellowship from The Royal Institute of Philosoph

Is Truth a Lie? Perspectives on the Semantic Paradoxes

Aquest treball ofereix una breu introducció, amb opinions de l’autor, a les paradoxes semàntiques i a algunes de les principals teories rivals que les estudien. El treball comença amb una clarificació de la noció de paradoxa semàntica i amb un esbós de la història de les paradoxes semàntiques. Després d’introduir el fenomen de l’autoreferència i els principis de la noció de veritat que les paradoxes semàntiques usen, el treball presenta en detall la més famosa de les paradoxes semàntiques, la paradoxa del Mentider. Un cop exposada la paradoxa del Mentider, el treball en classifica les solucions d’acord amb si revisen la nostra concepció tradicional de la noció de veritat o si revisen la nostra concepció tradicional de la lògica. Respecte les solucions del primer tipus, el treball discuteix, en particular, teories que substitueixen la propietat de la veritat per una jerarquia de propietats cadascuna de les quals s’assemblen parcialment a la noció de veritat, i teories que atribueixen la veritat a exemplars d’enunciats, en comptes de fer-ho a tipus d’enunciats. Respecte les solucions del segon tipus, el treball discuteix, en particular, teories que rebutgen la llei del terç exclòs, teories que rebutgen la llei de no contradicció i teories que rebutgen allò que en el treball s’anomena el principi de persistència.Paraules clau: lògiques no clàssiques, paradoxa del Mentider, paradoxes semàntiques, veritat.The article offers a short opinionated introduction to the semantic paradoxes and to some of the main competing theories about them. The article starts with clarifying the notion of semantic paradox and with providing a sketch of the history of the semantic paradoxes. After introducing the phenomenon of self-reference and the principles of truth exploited by the semantic paradoxes, the article proceeds to presenting in detail the most famous such paradox, the Liar paradox. With the Liar paradox on the table, the article classifies solutions to it according as to whether they revise our traditional conception of truth or our traditional conception of logic. As for solutions of the former kind, the article discusses in particular theories that replace the property of truth with a hierarchy of properties that partially resemble truth and theories that attribute truth to sentence tokens rather than sentence types. As for solutions of the latter kind, the article discusses in particular theories that reject the law of excluded middle, theories that reject the law of non-contradiction and theories that reject (what the article calls) the principle of persistence.Key words: non-classical logics, Liar paradox, semantic paradoxes, truth

Truth, demonstration and knowledge: a classical solution to the paradox of knowability

After introducing semantic anti-realism and the paradox of knowability, the paper offers a reconstruction of the anti-realist argument from the theory of understanding. The proposed reconstruction validates an unrestricted principle to the effect that truth requires the existence of a certain kind of “demonstration”. The paper shows that the principle fails to imply the problematic instances of the original unrestricted knowability principle but that the overall view still has unrestricted epistemic consequences. Appealing precisely to the paradox of knowability, the paper also argues, against BHK semantics, for the non-constructive character of the demonstrations envisaged by anti-realists, and contends that, in such a setting, one of the most natural arguments in favour of a revision of classical logic loses all its force