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A philosophical discussion of logic in this decade should at least be aware of the Curry-Howard isomorphism and Linear Logic. This paper makes a passing mention

• empath75 8y ago
  > Philosophy without technical input is sophistry, technical developments without philosophy end up answering questions of no interest. This is such a great formulation.
  • danharaj 8y ago
    I should say, definitely not mine. I don't know where I got it, or where they got it.
• omon 8y ago
  Wholly irrelevant, the paper is specifically concerned with recovering a dialectic between W. O. Quine and M. Dummett. Even if the question was the more general, "Is Logic Metaphysics?", knowledge of formal logics isn't even of concern. It's trivial that we can construct a plethora of axioms with their own definitions, the problem remains: to even adhere to those definitions one is exercising another intuitive logic—even in the case of computation which is an engineered construction to proxy this very intuition, otherwise we would have never been concerned with the linear properties necessary for computation to begin with.
  • danharaj 8y ago
    What I'm saying is that linear logic is exactly a technical exploration directly pertinent to the questions Quine and Dummett considered. And who cares if the paper is specifically about Quine and Dummett? What's the point of resuscitating such a dialogue without informing it of modern developments? To do so seems like frolicking in the graveyard. But much like philosophy of mathematics (with some exceptions like [0]), philosophy of logic to me at least seems like it prefers dusty bones to fresh developments (if 40 years is fresh...). At the very least, modern logic and its myriad connections to other fields could shed light on whether it's even worth bothering to adjudicate the interplay of Quine and Dummet's metaphysical arguments. They might be completely irrelevant at this point in our understanding except as historical footnotes. Linear logic is in many ways a logic of logic. Both classical and intuitionistic logic can be decomposed into finer components in linear logic, which distills logical ideas into purer components of philosophical interest, like the exponentials. The links between linear logic and processes like computation makes it a much more interesting starting point for a discussion of metaphysics and logic: Its technical results tell us that not every bespoke Broccoli logic makes sense, that one can directly study the conditions of possibility of logic. It even has connections to fundamental physics [1]. > It's trivial that we can construct a plethora of axioms with their own definitions, the problem remains: to even adhere to those definitions one is exercising another intuitive logic—even in the case of computation which is an engineered construction to proxy this very intuition, otherwise we would have never been concerned with the linear properties necessary for computation to begin with. How are we to investigate this intuitive logic without probing the technical structure of logic and finding out what is really its essence? It's not, emphatically not trivial that one can cook up a bunch of axioms. Logic doesn't come from axioms, I think we agree about that, they are just an exigent way to surface it. There are most definitely inappropriate formulations of logic. For example, S4 is an OK modal logic of necessity and possibility but S5 is hardly a logic at all because it doesn't have cut elimination, the technical correlate of deduction. I think this attitude just serves to marginalize philosophy of logic. Technique and philosophy must be in dialogue or both will be marginalized. [0] https://www.urbanomic.com/book/synthetic-philosophy-of-contemporary-mathematics/ https://www.urbanomic.com/book/synthetic-philosophy-of-conte... [1] https://arxiv.org/abs/0903.0340 https://arxiv.org/abs/0903.0340