Disagreement about logic from a pluralist perspective
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Disagreement about logic from a pluralist perspective Erik Stei1,2
Ó The Author(s) 2019
Abstract Logical pluralism is commonly described as the view that there is more than one correct logic. It has been claimed that, in order for that view to be interesting, there has to be at least a potential for rivalry between the correct logics. This paper offers a detailed assessment of this suggestion. I argue that an interesting version of logical pluralism is hard, if not impossible, to achieve. I first outline an intuitive understanding of the notions of rivalry and correctness. I then discuss a natural account of rivalry in terms of disagreement about validity claims and the argument from meaning variance that has been raised against it. I explore a more refined picture of the meaning of validity claims that makes use of the charactercontent distinction of classical two dimensional semantics. There are three ways in which pluralists can use that framework to argue for the view that different logics may be rivals but could nevertheless be equally correct. I argue that none of them is convincing. Keywords Logical pluralism Disagreement Rivalry Context-sensitivity Validity
1 Introduction Logics can be applied for a variety of purposes. They can be used for such diverse tasks as managing databases, simulating intelligent behaviour, analysing the grammatical structure of natural languages, or simplifying electronic circuits. It is & Erik Stei [email protected] 1
Department of Philosophy, Utrecht University, Janskerkhof 13, 3512 BL Utrecht, The Netherlands
2
Institut fu¨r Philosophie, Universita¨t Bonn, Bonn, Germany
123
E. Stei
therefore not surprising that there are many different logics. But even if we focus on more traditional applications like the study of valid arguments, there still are quite a number of different logics, each offering a theory of validity. This is still not very surprising. It is quite common, after all, that there are different theories about a domain subject to systematic study. A slightly more surprising thesis would be that more than one of those theories are correct. Call that the plurality thesis. Exactly how surprising the plurality thesis really is depends on how the theories in question relate to one another. This paper is concerned with those relations between different logics. More specifically, it is concerned with the question of whether an undoubtedly interesting version of the plurality thesis can be defended: a pluralism which claims that there are ‘‘at least two opposing, but equally correct, answers to the question of whether a single argument is valid’’ (Russell 2008, 609, emphasis added). Call this the interesting plurality thesis. In order to answer that question, we first need to get a grip on the notions of opposition (or rivalry) and of correctness (Sect. 2). I sketch a natural approach to rivalry between logics that focuses on the semantic conception of disagreement (Sect. 3) and I briefly discuss some familiar problems for the semantic approach (Sect. 4). Secti
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