The view you ascribe to Martin Gardner (a friend of my Dad, btw), that math (including logic) describes an abstract aspect of reality, is called Platonism and it is the standard view, held by about 95% of philosophers of logic and mathematics. A few others are conventionalists, who think we make it all up; others are intuitionists, who think that only what can be proved is true, and then there are handful of Milleans who think that math and logic are empirical in something like the way that biology is empirical.
The logic and math that are in our heads when we use them may be psychological, that is, there may be a psychological realization of fragments of these formal languages in something like the way that when we think in words natural language is psychological. But if Platonism is true, math and logic are no more psychological in virtue of being occasionally partly realized in thought than they are machine states in virtue of being partly realized in physical computing systems. One way to see these on both counts: human thinkers and silicon computers can make mistakes, but mathematical and logical truth is what it is regardless of our errors. Anyway, fun as phil of math can be, it really hasn't anything to do with Hegel's Logik. But we seem to agree on that point. --- "Devine, James" <[EMAIL PROTECTED]> wrote: > > Logic -- modern mathematical logic, descending > from > > Frege -- is not psychological and does not pretend > to > > be. It is a branch of mathematics. ... > > Yes, but logic is psychological (or "in our heads" > as I said) when we _use_ it. As is math. > > There's a big question of whether math (including > logic) exists independent of the version that's in > our heads (or that our heads arrange to have put on > paper or other media). I'll leave that aside. (I > must admit that I like Martin Gardner's view that > there's an ontological basis for math & logic, i.e., > that math describes the abstract aspect of reality. > But I don't know if that view is defensible or not.) > > > If Hegel's Logik -- no relation to either modern > math > > logic or the Aristotlean syllogistic -- is > > psychological, it is not a matter of individual > > psychology. ... > > Again, it's psychological (in our heads) when we use > it. > > > The Logik is really what modern philosophers call > > metaphysics, about substantive concepts like being > and > > nonbeing, substance and accident, and the like. It > > only confuses things to think that Hegel was > trying to > > do badly what Kant or Frege was doing well in > thinking > > abour logic -- that is the mathematical theory of > > formal validity. Hegel was instead doing, possibly > > well, what Leibniz and Spinoza were doing when > they > > were thinking about the ultimate structure of > reality > > abstractly described. > > that makes sense to me. > > > Hegel, btw, doesn't think that whatever is, is > > rational in the sense that everything is always > hunky > > dory and this is always the best of all possible > > worlds. > > nor did I say that he was saying such a thing. > Rather, it was that there was a "correspondence > between mental > states (dialectical 'logic') and empirical reality." > > > ... A more charitable reading is that the real is > > _intelligible_, that we with the equipment of the > > Logik we can make sense out of whatever is real, > > without necessarily thinking it is perfect. > > that's what I was talking about, though Hegel's > mature view leaned toward Panglossism. > JD > > > > > _______________________________ Do you Yahoo!? Declare Yourself - Register online to vote today! http://vote.yahoo.com
