Footnote 4Ĭonnexive logics, in contrast, ask for more validities than classical logic gives us. In all other well-known cases, the non-classical logic rejects something that is valid in classical logic, such as the Law of Excluded Middle, Explosion or some other classical principle. That is what makes connexive logic a topic in non-classical logic, but the pattern is interestingly different from that of other non-classical logics. The connexive principles, Footnote 3 although that surprises many students even after a thorough introductory course in logic, are not valid in classical logic. Let me also take the opportunity to sketch my personal view on how to think about connexivity, as it will be helpful to know the perspective from which this paper is written. Before we get there, though, let me say a little bit more about the peculiar status of connexive logics in the landscape of present day philosophical logic. These principles surely seem plausible when the connectives are read with their usual meaning, and it is the aim of this paper to get clear about where that feeling of plausibility comes from. Part I: Connexive Logic and Connexive IntuitionsĬonnexive logics Footnote 1 are non-classical logics that are characterized by the following principles:Īristotle: \((\lnot A\rightarrow A)\) are valid.īoethius: \((A\rightarrow B)\rightarrow \lnot (A\rightarrow \lnot B)\) and \((A\rightarrow \lnot B)\rightarrow \lnot (A\rightarrow B)\) are valid. What is common to all of them is that they can make a claim to do justice to the intuitions motivating connexivity, and that they entail changes to commonly held assumptions about logic, semantics and/or pragmatics. Some of them will require adopting a connexive logic, others will not. I will present a range of options, and though I find some of these more plausible than others, I believe they can all be incorporated into a generally feasible theory of conditionals which will, in particular, all have some success in accommodating the connexive intuitions. Second, although I am sympathetic to the aims of the lately invigorated and growing connexive community, I try to conduct this investigation without any foregone conclusions in mind (however, I will allow myself some opinionated comments at the very end of the essay). As a result, the material is not heavy on formal technicalities in fact, I hope that even philosophers of language and linguists who are not particularly interested in logic at all might be able to get something of value, especially out of the part on pragmatics. My aim is to get the goal into clearer focus, how to get there is beyond the scope of this piece. Two remarks about what to expect: First, from a logical point of view the paper is quite programmatic in nature, in that it discusses rather general features of semantic and logical theories rather than particular systems. Lastly, a third part surveys the upshots for logic choice of such an explanation and thus supplies my answer to Q-Revision, this time a resounding “It depends”. The second part will discuss the pragmatic features of conditionals that might help explain those intuitions and present my answer to Q-Pragmatic: I will argue that such an explanation works for indicative conditionals, but not for counterfactuals. I will show that the intuitions are equally strong for indicative and counterfactual conditionals. The outline of the paper is as follows: In a first part, I will introduce the principles of connexive logic and supply a first analysis of the intuitions that lie behind their plausibility.
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