Is Mathematics Real? (2020)
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Is Mathematics Real? (2020)
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Re: Is Mathematics Real? (2020)
#2“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?
Re: Is Mathematics Real? (2020)
#3“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?
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 :)
Re: Is Mathematics Real? (2020)
#4“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?
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.
Re: Is Mathematics Real? (2020)
#5“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?
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 d…
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.
Re: Is Mathematics Real? (2020)
#6I'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."
Re: Is Mathematics Real? (2020)
#7Mathematics is not embodied by any of the entities of physics and to that extent it is not real.
Re: Is Mathematics Real? (2020)
#8what 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.,
Re: Is Mathematics Real? (2020)
#9“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?
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.
Re: Is Mathematics Real? (2020)
#10Category theorist: What is the universal property for “realness”?