Varieties of Logic

by Stewart Shapiro

Logical pluralism is the view that different logics are equally appropriate, or equally correct. Logical relativism is a pluralism according to which validity and logical consequence are relative to something. In Varieties of Logic , Stewart Shapiro develops several ways in which one can be a pluralist or relativist about logic. One of these is an extended argument that words and phrases like 'valid' and 'logical consequence' are polysemous or, perhaps better, are cluster concepts. The notions can be sharpened in various ways. This explains away the 'debates' in the literature between inferentialists and advocates of a truth-conditional, model-theoretic approach, and between those who advocate higher-order logic and those who insist that logic is first-order.

A significant kind of pluralism flows from an orientation toward mathematics that emerged toward the end of the nineteenth century, and continues to dominate the field today. The theme is that consistency is the only legitimate criterion for a theory. Logical pluralism arises when one considers a number of interesting and important mathematical theories that invoke a non-classical logic, and are rendered inconsistent, and trivial, if classical logic is imposed. So validity is relative to a theory or structure.

The perspective raises a host of important questions about meaning. The most significant of these concern the semantic content of logical terminology, words like 'or', 'not', and 'for all', as they occur in rigorous mathematical deduction. Does the intuitionistic 'not', for example, have the same meaning as its classical counterpart? Shapiro examines the major arguments on the issue, on both sides, and finds them all wanting. He then articulates and defends a thesis that the question of meaning-shift is itself context-sensitive and, indeed, interest-relative. He relates the issue to some prominent considerations concerning open texture, vagueness, and verbal disputes.

Logic is ubiquitous. Whenever there is deductive reasoning, there is logic. So there are questions about logical pluralism that are analogous to standard questions about global relativism. The most pressing of these concerns foundational studies, wherein one compares theories, sometimes with different logics, and where one figures out what follows from what in a given logic. Shapiro shows that the issues are not problematic, and that is usually easy to keep track of the logic being used and the one mentioned.

Genres: Logic, Philosophy

240 pages, Paperback

First published September 4, 2014

Reviews

[Sofia · Rating 4 out of 5]

TERMINEI! Esse livro foi / é muito importante pra minha pesquisa, esclareceu as ideias e as organizou de forma didática. Como não especialista e quase leiga, não achei super facinho de ler, mesmo tendo 200 e poucas páginas demorei mais que o normal, porém é um dos livros mais acessíveis que achei sobre pluralismo lógico, recomendo demais.

É legalzinho que o autor parece conversar contigo, direto faz umas "bad puns" (que são divertidas) e chama sua atenção. Também vale notar que os exemplos são inclusivos, geralmente ele usa "she" para dar exemplos e falar de como alguém defende algo.

Ah, meio spoiler, mas a última frase deu uma leveza no final, e diz:

"The three of them may not be able to share all of their results with each other, in a straightforward homophonic manner, but that’s life."

recomendo 10/10

[Louna · Rating 4 out of 5]

from where B & R leaves