Inclosure and Intolerance

[eng] Graham Priest has influentially claimed that the Sorites paradox is an Inclosure paradox, concluding that his favoured dialetheic solution to the Inclosure paradoxes should be extended to the Sorites paradox. We argue that, given Priest’s dialetheic solution to the Sorites paradox, the argument purporting to show that that paradox is an Inclosure is unsound, and discuss some issues surrounding this fact

Logical Predictivism

Motivated by weaknesses with traditional accounts of logical epistemology, considerable attention has been paid recently to the view, known as anti-exceptionalism about logic (AEL), that the subject matter and epistemology of logic may not be so different from that of the recognised sciences. One of the most prevalent claims made by advocates of AEL is that theory choice within logic is significantly similar to that within the sciences. This connection with scientific methodology highlights a considerable challenge for the anti-exceptionalist, as two uncontentious claims about scientific theories are that they attempt to explain a target phenomenon and (at least partially) prove their worth through successful predictions. Thus, if this methodological AEL is to be viable, the anti-exceptionalist will need a reasonable account of what phenomena logics are attempting to explain, how they can explain, and in what sense they can be said to issue predictions. This paper makes sense of the anti-exceptionalist proposal with a new account of logical theory choice, logical predictivism, according to which logics are engaged in both a process of prediction and explanation.publishedVersio

Inclosure and Intolerance

Graham Priest has influentially claimed that the Sorites paradox is an Inclosure paradox, concluding that his favored dialetheic solution to the Inclosure paradoxes should be extended to the Sorites paradox. We argue that, given Priest’s dialetheic solution to the Sorites paradox, the argument purporting to show that that paradox is an Inclosure is unsound, and discuss some issues surrounding this fact

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

Substructural Logics and Pragmatic Enrichment

In this dissertation, we argue for a Pragmatic Logical Pluralism, a pluralist thesis about logic which endorses Classical, Relevant, Linear, and Ordered logic. We justify that the formal languages of these four logics are legitimate codifications of the logical vocabulary and capture legitimate senses of logical consequence. This will be justified given a particular interpretation of the four formal languages: logical consequence and conditional, disjunction, and conjunction of the four different logics codify different and legitimate senses of ‘follows from’, ‘if...then’, ‘or’ and ‘and’ which diverge in their different pragmatic enrichments. The dissertation is twofold. First, we will explore the effect that the lack of structural rules has on logical connectives, in four substructural logics, and its connection with certain pragmatic enrichments. Second, we will defend a pluralist thesis according to which pragmatics has an important role for capturing the inferential role of logical vocabulary, both of the notions of ‘follows from’ and the logical constants, although classical logic preserves truth and captures their lit- eral meaning. In sum, we defend a version of logical pluralism based on the plurality of legitimate translations from natural language to formal languages, arguing that more than one translation is legitimate for logical vocabulary, which makes it possible to adopt more than one logic.En aquesta tesi presentem el Pluralisme Lògic Pragmàtic, una tesi pluralista sobre la lògica que accepta les lògiques Clàssica, Rellevant, Lineal i Ordenada. Justifiquem que els llenguatges formals d’aquestes quatre lògiques són codificacions legítimes del vocabulari lògic i capturen sentits legítims de la conseqüència lògica. Això es justificarà donant una interpretació particular dels quatre llenguatges formals: la conseqüència lògica i el condicional, la disjunció i la conjunció de les quatre lògiques acceptades codifiquen diferents i legítims sentits de ‘si...llavors’, ‘o’ i ‘i’, que es distingeixen pels diferents enriquiments pragmàtics que codifiquen. La tesi té dos vessants. Primer, explorem l’efecte que la falta de regles estructurals té en les connectives lògiques de les quatre lògiques presentades, i la seva connexió amb certs enriquiments pragmàtics. Segon, defensem una visió pluralista segons la qual la pragmàtica juga un rol important a l’hora de capturar el rol inferencial del vocabulari lògic, tant per la noció de conseqüència lògica com per les connectives, tot i que la lògica clàssica preserva la veritat i captura el seu significat literal. En resum, defensem una versió del pluralisme lògic basat en la pluralitat de traduccions legítimes del llenguatge natural al llenguatge formal, argumentant que més d’una traducció és legítima pel vocabulari lògic, la qual cosa ens permet adoptar més d’una lògica

Three Essays on Substructural Approaches to Semantic Paradoxes

This thesis consists of three papers on substructural approaches to semantic paradoxes. The first paper introduces a formal system, based on a nontransitive substructural logic, which has exactly the valid and antivalid inferences of classical logic at every level of (meta)inference, but which I argue is still not classical logic. In the second essay, I introduce infinite-premise versions of several semantic paradoxes, and show that noncontractive substructural approaches do not solve these paradoxes. In the third essay, I introduce an infinite metainferential hierarchy of validity curry paradoxes, and argue that providing a uniform solution to the paradoxes in this hierarchy makes substructural approaches less appealing. Together, the three essays in this thesis illustrate a problem for substructural approaches: substructural logics simply do not do everything that we need a logic to do, and so cannot solve semantic paradoxes in every context in which they appear. A new strategy, with a broader conception of what constitutes a uniform solution, is needed