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Jon, +2
Had been wracking my brain to imagine a simple reply to Paul Tyson's question, and couldn't figure out what to say in less than a few thousand words. Saying just a bit more than you, I would say that very thoughtful and smart people (as you imply) have devoted their lives primarily to this question, so it might just open up a can of worms to begin a discussion of it in an email. Indeed, a key such person now is John Corcoran, (whose student I have the good fortune to have been) in many papers and current discussions in academia.
First, it wasn't my question. It was Stan Ulam's, a supposedly
eminent mathematician of recent times.
How 'we' do think is mostly unsound -- most people seem to follow the fallacy of denying the antecedent, and even more the post hoc fallacy, and even more, almost always *argue* with each other based on different hidden premises, yet get enraged when these missing premises are pointed out. Preserving truth is how we ought to think, and mathematical logics are better or worse models of that.
Second, the point isn't about whether humans think logically or not, but whether mathematical logic is a useful model for any domain of human experience except, well, those that can be modeled by mathematical logic. Talk of "preserving truth" and "prescribing thought" worries me.
Regards,
--Paul
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Jon A> Had been wracking my brain to imagine a simple reply to Paul Tyson's...
Short answer: Nobody thinks in formal proofs, not even professional mathematicians.
But everybody -- including their pet cat or dog -- thinks in diagrammatic patterns that could be represented in mathematics. Writing down a formal proof is the last step *after* all the hard thinking has been done.
For details, see "Peirce, Polya,
and Euclid -- integrating logic,
heuristics, and geometry",
http://jfsowa.com/talks/ppe.pdf .
John
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On Aug 4, 2020, at 3:39 PM, John F. Sowa <so...@bestweb.net> wrote:
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<untitled-[2]>
I've nothing against mathematics, but would like ardent proponents of
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On Aug 6, 2020, at 3:48 AM, Chris Partridge <partri...@gmail.com> wrote:
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On Aug 6, 2020, at 8:28 AM, Chris Partridge <partri...@gmail.com> wrote:
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