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Mathematics and physics are products of the mind, obviously. Mathematicians and physicists do their work by using their minds. They don't channel some divine tr

by asdflkj 16y ago

Mathematics and physics are products of the mind, obviously. Mathematicians and physicists do their work by using their minds. They don't channel some divine truth--they merely filter what their mind makes through certain criteria. I don't understand this common tendency, exemplified by your comment, to shift attention away from how mind makes things, to the criteria according to which we filter them before we call them "science" or "mathematics". I've studied mathematical logic, and it has been of little use to me in mathematics. Philosophy of mathematics has been of no use at all. The practice of mathematics can get by perfectly well without that stuff. So maybe it's time to put aside the mysticism, and start looking at how our brains actually make what they make. Especially since we are just now starting to understand what brains are and how they've evolved.

calibraxis 16y ago
On philosophy of mathematics, have you checked out Reuben Hersh? Or Lakatos? They're much more interesting to me than the usual platonism/formalism. I'm guessing platonism/formalism were popular in arguing against other ways of understanding the world, like folk science, authoritarianism and mysticism. (I'm not equating the last three.) Maybe also as a foundation myth for professional mathematics.
- asdflkj 16y ago
  Thanks--I'll check them out. I hope it's the kind of stuff that is only called philosophy, but actually falls under the purview of science, which doesn't yet have a framework to deal with it. That's the only kind of "philosophy" I've ever found of value.
calcnerd256 16y ago
I'm not talking about how we build them. I'm talking about what they are, and what they are is as they would be whether they were built by humans or computers or nature. That the theorems follow from their axioms is not a human invention, nor could it be. There is a difference between discovering something and inventing it. Man could not invent mathematics any more than man could invent electricity. When I say physics exists, I mean that the physical world exists and follows rules. If we discover those rules, it does not mean we have invented them.
- asdflkj 16y ago
  You're "not talking about how we build them", but you were responding to my post where I am talking about how we build them. I'm gonna say it again: I don't understand this tendency to shift attention away from the "how"--rather insistently, in your case.
  - calcnerd256 16y ago
    Either you're not just talking about how we build them or I misunderstand you, because the first thing you said was, "Mathematics is a product of the mind."

by asdflkj 16y ago

calibraxis 16y ago

On philosophy of mathematics, have you checked out Reuben Hersh? Or Lakatos? They're much more interesting to me than the usual platonism/formalism. I'm guessing platonism/formalism were popular in arguing against other ways of understanding the world, like folk science, authoritarianism and mysticism. (I'm not equating the last three.) Maybe also as a foundation myth for professional mathematics.

asdflkj 16y ago
Thanks--I'll check them out. I hope it's the kind of stuff that is only called philosophy, but actually falls under the purview of science, which doesn't yet have a framework to deal with it. That's the only kind of "philosophy" I've ever found of value.

calcnerd256 16y ago

I'm not talking about how we build them. I'm talking about what they are, and what they are is as they would be whether they were built by humans or computers or nature. That the theorems follow from their axioms is not a human invention, nor could it be. There is a difference between discovering something and inventing it. Man could not invent mathematics any more than man could invent electricity. When I say physics exists, I mean that the physical world exists and follows rules. If we discover those rules, it does not mean we have invented them.

asdflkj 16y ago
You're "not talking about how we build them", but you were responding to my post where I am talking about how we build them. I'm gonna say it again: I don't understand this tendency to shift attention away from the "how"--rather insistently, in your case.
- calcnerd256 16y ago
  Either you're not just talking about how we build them or I misunderstand you, because the first thing you said was, "Mathematics is a product of the mind."