[HN Gopher] Is Mathematics Real? (2020)
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Is Mathematics Real? (2020)
Author : happy-go-lucky
Score : 10 points
Date : 2021-01-24 13:52 UTC (9 hours ago)
(HTM) web link (theconversation.com)
(TXT) w3m dump (theconversation.com)
| sunstone wrote:
| Mathematics is not embodied by any of the entities of physics and
| to that extent it is not real.
| victor106 wrote:
| what are some good resources/books to learn the
| thoughts/debates/ideas that forced us to create/discover say for
| example concepts like complex numbers or logarithms or calculus
| etc.,
| teucris wrote:
| "God made the integers, all else is the work of man"
|
| I'm not sure if even that is true. Integer counts and succession
| seem like human constructs to me. An apple isn't fundamentally a
| single unit. If I take a bite out of it, is it still one apple?
| bluepoint wrote:
| I think this is a really good comment. Are you implying that
| the concept of integer is a consequence of the abstraction of
| an apple, an abstraction which is entirely human? I really like
| this point of view.
| teucris wrote:
| That's exactly what I'm saying. I'm glad you like it!
| LambdaTrain wrote:
| This quote is neither true nor false. The author called it a
| "sentiment", but I think when Kronecker made this statement, he
| took it as some kind of principle to work out the foundation of
| modern mathematics.
|
| Basically the mathematical notion of integer is trying to make
| sense of our idea of a discrete unit. Taking a bite of apple
| makes it non-unit, but I think you would agree that the notion
| of "one apple" or "two dogs" makes common sense.
|
| Also when reading someone's quote, I would always consider its
| context. I think Kronecket had the axiomatic construction of
| real number in mind. The idea of rational number and real
| number can be investigated by just assuming the idea of
| increment by one is solid.
|
| These mathematical concepts are usually covered in a
| undergraduate analysis class. For more information, see
| Cauchy's construction and Dadekind's construction.
| LambdaTrain wrote:
| Add: so the idea is that once we have integers, we can
| construct rationals and even real numbers instead of talking
| about reals as granted. Now when taking a bite out of an
| apple, we can say it takes, say 1/3, of an apple, while we
| only assume the idea of integers.
| teucris wrote:
| > assuming the idea of increment by one is solid.
|
| Therein lies the rub! Succession is a human concept. All math
| is a magnificent city built upon that one stone.
| sound1 wrote:
| Well at least according to the friends I have beer with over
| the weekends, real world is a subset of math we invented. It is
| a tool we invented to describe the universe, but I am not sure
| if everything we derive from the axioms is true. (eg.
| discontinuous functions make me a little uncomfortable)
|
| Disclaimer: I am very poor at math but eager to learn :)
| ukj wrote:
| Category theorist: What is the universal property for "realness"?
|
| https://en.wikipedia.org/wiki/Universal_property
| MikeBVaughn wrote:
| I've always been interested by the Platonist-vs-anti-Platonist
| debate. I generally disagree with finitist mathematicians, but I
| really do find their position interesting, and as a computer
| scientist I'm not unsympathetic to their perspective.
|
| At the end of the day, though, I always go back to an old joke my
| undergrad philsophy professor told me:
|
| Analytic Philosopher A: "Hey, do you believe in baptism?"
|
| Analytic Philsopopher B: "Believe in it? Hell, I've been to one."
| klyrs wrote:
| Me: I believe in any number that I can represent with my
| computer
|
| Professor: I am suddenly concerned that my PhD student does not
| believe in induction
|
| Me: I am suddenly concerned that my PhD supervisor does not
| know the difference between converse and contrapositive
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