Relevant Restricted Quantification

“…It can be shown, however, that a 'suitable' conditional weak enough not to trigger Curry's Paradox is bound not to validate certain Footnote 6 continued very intuitive principles about restricted quantification see e.g. Beall et al (2006), Field (2013), Ripley (2014), Zardini (2014c).…”

Section: Paradoxes Of Naïve Logical Propertiesmentioning

confidence: 99%

Paradox and Logical Revision. A Short Introduction

Murzi¹,

Carrara

2014

Topoi

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“…He argues that the 'the purpose of truth' is to be intersubstitutable. 4 Field holds that intersubstitutivity of truth is essential for it to serve its role as 'a device of quantification' (presumably, a device used along with quantification) in such sentences as (1): 1. If everything that the Conyers report says is true then the 2004 election was stolen.…”

Section: Partmentioning

confidence: 99%

“…The lack of a classical-like conditional in relevant logics leads to a familiar difficulty: relevant systems have trouble dealing with restricted quantification (see [4]), and the difficulty does not seem to be shared by Field's system. This is because of the failure, in relevant systems, of such inferences as A B → A, which holds in Field's system.…”

Section: Partmentioning

confidence: 99%

Book Reviews

Ripley¹

2010

Stud Logica

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Saving Truth From Paradox is both a detailed survey of approaches to the logic and philosophy of truth-related paradoxes and an exposition and defense of Field's favored approach to these paradoxes. It proceeds in five parts: first, it introduces the paradoxes, and discusses some background issues; second, it presents and criticizes classical approaches to the paradoxes (that is, approaches that hold to full classical logic); third and fourth, it presents, argues for, and considers the consequences of Field's preferred approach to the paradoxes, which involves a weakening of classical logic (in particular, a weakening of the logic of the conditional, along with rejection of excluded middle for some sentences); and fifth, it argues against another sort of non-classical approach to these paradoxes: dialetheism (or, as Field calls it, paraconsistent dialetheism).The book is sizeable (392 pp. of actual text) and chock-full of arguments; there's not space here to mention the half of it, and there are a number of important topics in the book that I'll skip here entirely. 1 Rather, I'll describe each of the four sections briefly in turn, and then offer some brief evaluative remarks.

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Relevant Restricted Quantification

Cited by 77 publications

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Paths to Triviality

Paths to Triviality

Paradox and Logical Revision. A Short Introduction

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