• gurugeorge
    I'd rather put it this way. One modern view of logic boils down to: logic is really just using symbols consistently in some symbol-shuffling game (or algorithm: recipe for symbol-shuffling). In this sense, logic is thought of as pure syntax, intrinsically detached from semantics (or the "interpretation" of those symbols, which makes the symbols stand for things in the world).

    In that case, it's just happenstance that some dreamed-up algorithm happens to fit reality.

    But then a lot of people go an illegitimate further step, and think that means logic isn't inherent in nature, isn't bundled into semantics.

    But if a dreamed-up algorithm fits reality,it really fits. i.e. nature really, objectively hasthat particular pattern. So in fact, the syntax of logical statements that do happen to actually describe the world is derived from semantics (which is another way of saying what the later Wittgenstein was banging on about, the sort of thing Sime talks about above). Even though we can extend logic and play with patterns that are divorced from anything real, the starting point is the logic of the middle-sized furniture of the world that we commonly interact with from birth - just the standard logic. What logically follows from what depends on the nature of the things being symbolized.

    The upshot is that you can't demonstrate the validity of logic in general (because logic is just dreamed-up consistent play patterns that may or may not fit some reality). But for any given logic that does fit the world as we find it, the world as we find it necessarily has that logic, that nature, that flow, that grain.

    However, of course while that's obvious in principle, in practice, since the scope of our knowledge is limited, there may be any number of unknown factors that could make our deduction wrong, unbeknownst to us.

    And this is really what makes the difference between induction and deduction. Induction isn't actually any different from deduction - rather, it's deduction that's aware of knowledge limitations, hence it's expressed in terms of probabilities. Induction is the punting of a specific nature or identity for experience, then the deducing of necessary conclusions (for experience) from that nature or identity. This is the process of science, in essence - we think up a possible character for things, and see if experience bears out the logical implications of the character we've posited for the things. But because of knowledge limitations, we have to hedge our bets ("all things being equal", "presuming no confounding factors", "it is probable/possible/likely that ..." etc.).

    Just one final thought: it's unproblematic to think of logic as innate to some degree. It's pretty obvious that we bootstrap ourselves all the way from childhood into adult knowledge not from a pure blank slate position, but from an innate understanding of some basic logical primitives. However, that understanding has to be drawn out from us (in the Platonic sense of anamnesis), it's not in front of us reflectively from infancy, rather it's just innate in the way we act from infancy (e.g. reaching out expecting to touch something), and comes to conscious reflection as a result of interaction with the world. (Rather analogous to the way genes are expressed in the phenotype, in fact.)
  • Banno
    Yes, except
    ...and our intentions...sime
    happens too fast.

    It's not clear that bringing intent into the discussion helps; why not stop at behaviour?

    If I accelerate towards a red light, but my car stalls so that I stop at the light, haven't I obeyed the traffic rule despite my intent?
  • TheMadFool
    n that case, it's just happenstance that some dreamed-up algorithm happens to fit reality.gurugeorge

    Speaking for myself, I think logic is derived from the world outside. I've read a few books on logic and all of them make a similar point - that logic is essentially about finding truths about the world. Isn't it obvious then that our logic (its structure) must mirror the structure of reality itself? I don't think this is "just happenstance".

    Just one final thought: it's unproblematic to think of logic as innate to some degree.gurugeorge

    I agree but here too I believe evolution has played a part. From all the different possible brain structures only those that conform to the rules of the world have been selected. All the other types of brain structures, with logical components that didn't reflect the world's structure, were culled.
  • TheMadFool
    Why not?

    Also, where did "mustn't" come from?

    It's my understanding that any logical system developed must be useful in the sense that it can find truths about the world. I agree that we can arbitrarily choose the axioms of a logical system BUT the systems with axioms that lead to nothing must be discarded. Right?
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