3:AM: You’ve addressed the question about whether logic is a model of reason, correct thought, laws of thought and such like. So why are logic and reason completely different animals? PR: I’m not sure that I think they’re completely different animals, although there are plenty of reasons to think so, most of which have to do with the weird ways we actually use logic when we reason or the very different outcomes each can deliver in various scenarios – but I’ll talk more about those soon. What I’ve been interested in is exploring the idea that we may be better off if we draw back from the notion that logic is (or has to be) a model of correct reason. But this idea does not by itself mean that logic and reason must be completely different. For all the differences, there are a lot of similarities and a lot of shared features between the two. For example, correct reason (at least at times and in some contexts) shares with logic the goal to discover what follows from what or, at times, how and when the truth of certain ideas might entail the truth of others. Conversely, a drive toward clarity and rigor is something logic can share with reason. So, I’ve tried to challenge the idea that if logic does not describe or model the way we ought to reason, then it is in someway not doing its job or not being what it is supposed to be. This is in part because if we withdraw that idea we uncover a host of interesting questions which ought not, I think, be covered. Dislodging the underlying assumption that we know the relationship between reason and logic reveals the nature of that relationship, as well as of logic and reason themselves, as the open problems I suspect they ought to be. And, by withdrawing that assumption, we also further enable logic to freely develop as it will – perhaps in ways quite other to those we might anticipate while holding fast to any preconception of its proper role. For an example, the study of logic can include the exploration of the wealth of pure logical structures for their own sake, their fascinating interrelationships, and the many and various ways they relate to mathematical structures. I’m thinking here of work like that of Walter Carnielli and Marcelo Coniglio, who seem to me to explore abstract logical structures in much the same way pure mathematicians explore abstract mathematical structures. Carnielli and Coniglio look at translations between logics, and resultant new logics, using mathematical theories (particularly shelf theory and category theory) [SIC]. It seems to me that this sort of work follows the formalisms for their own sake in much the same way mathematics can – and, as has been demonstrated in mathematics, we can follow more freely if we don’t always have an eye on application or potentially suppressive canonical constraints. Some of higher order mathematics has no (known) application in the (known) physical world, but this does not stop it being interesting and important – nor does it stop mathematicians studying it. Logicians’ study of logical structures should, I think, be similarly unrestrained. -3ammagazine/3am/the-metaphysics-of-logic/?
Posted on: Sun, 07 Dec 2014 06:49:39 +0000
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