Let a Thousand Flowers Bloom: A Tour of Logical Pluralism

Abstract

Logical pluralism is the view that there is more than one correct logic. In this article, I explore what logical pluralism is, and what it entails, by: (i) distinguishing clearly between relativism about a particular domain and pluralism about that domain; (ii) distinguishing between a number of forms logical pluralism might take; (iii) attempting to distinguish between those versions of pluralism that are clearly true and those that are might be controversial; and (iv) surveying three prominent attempts to argue for logical pluralism and evaluating them along the criteria provided by (ii) and (iii). Relativism Versus Pluralism 1One is a relativist about a particular phenomenon X if and only if one thinks that the correct account of X is a function of some distinct set of facts Y. Thus, relativism about X amounts to acceptance of the following schema: Philosophy Compass 5/6 (2010):For our purposes, we can define a formal logic (hereafter, simply 'logic') to be any pair <L, Þ> where L is a formal language (i.e., L consists of a nonempty set of primitive symbols and a set of formation rules -typically recursive -that delineate which sequences of primitive symbols are 'well-formed') and Þ (the formal consequence relation of the logic) is a relation holding between a set of statements from L (the premises) and a single statement from L (the conclusion). Þ can be given in terms of a system of proof, or a formal semantics, or primitively -the pluralist debate hinges primarily on how many such relations there might be, and not on how these relations are presented to us.This definition is, strictly speaking, both too narrow and too wide: On the one hand, it ignores logics, such as many formulated within the sequent calculus, that allow multiple conclusions (see Gentzen 1965). On the other hand, it includes mathematical structures with bizarre or random formal consequence relations (e.g., those that do not validate Let a Thousand Flowers Bloom 493 ª

Informational Semantics as a Third Alternative?

“…Hence, the outcome is misleading and this is due to the philosophical application of a formalism that doesn't provide a real insight into intuitionist logic (but see Aberdein and Read (2009) for a more extensive treatment of the different attitudes one may adopt). We recognise the philosophical difference between relevant and intuitionist logic, and do not want to obliterate the substantive 15 Strictly speaking, if we follow the characterisation of Cook (2010), pluralism still implies a form of relativism in the sense that logical consequence is relative to a prior choice of a degree of logical discrimination. disagreement between intuitionist and classical logic.…”

A New Interpretation of Carnap’s Logical Pluralism

“…It will be useful to explain carefully why the typical slogan about Carnap's view takes him to be claiming that change in logic requires a change in connective meanings. Authors who often seem to be making use of such a slogan to describe Carnap's position include Cook (2010), Hellman (2006) and Restall (2002). Shapiro (2014) makes this claim more prominently.…”

A plea for KR

“…There is currently a lively debate about logical pluralism-whether multiple distinct logics are equally correct. (See Beall and Restall (2006) and Cook (2010) for more on logical pluralism.) If logical pluralism is right, then there is no single universal standard for evaluating deductive arguments.…”