2 ms·

Math is not about truths, at least not by the meaning of "truth" as a word in daily use. Math has been almost purely arbitrary since ~ late 19th/early 20th cen

Math is not about truths, at least not by the meaning of "truth" as a word in daily use. Math has been almost purely arbitrary since ~ late 19th/early 20th century. There are uncountably many correct mathematical theorems. Almost all of them can't even be written in symbols. Even if you have a tape with infinite length (which is already longer than the whole physical universe!) filled with theorems, they are still only 0% of all correct theorems. That's how arbitrary math is. > The area of a triangle Yes, even this is arbitrary. The rigorous definition of triangle is arbitrary. People just subconsciously choose something that vaguely approximates their physical intuition.

GPerson 2mo ago
The tastes and interests, and cultural pretext, of human beings are not arbitrary just because they’re not easily described.
- ziiinq 2mo ago
  Yes and therefore? You seem to be vaguely waving in the general direction of a point, without making any concrete claims or bothering to engage with the GP’s argument. The tastes and interests of humans are absolutely not arbitrary. They are dictated by fate, the sun and the moon gods. Or maybe by the unitary evolution of the universe’s quantum state. Or by the probability distribution of finding ourselves in a particular branch of the universe. What bearing does this have on whether math is a collaborative endeavor? And what is unique to math, that your argument wouldn’t apply equally to physics, sociology or financial markets? All, “truth seeking” disciplines.
  - GPerson 2mo ago
    You seem rather aggressive so replying to you feels pointless and uncomfortable. Nonetheless, the person writes, “ Math has been almost purely arbitrary”. This is simply a misusage of the word arbitrary, which is a word with a specific meaning you can look up if you are unaware, since mathematics is (obviously) not arbitrary in the sense this person wants to convey, in part for the reasons I state. Humans are not choosing arbitrary logical statements to prove true or false.
loicd 2mo ago
> There are uncountably many correct mathematical theorems. Almost all of them can't even be written in symbols. What are you talking about? A theorem is a statement that has been proved from some axioms. A statement itself is a finite sequence of symbols satisfying some syntactical rules. The set of symbols for set theory, arithmetic, etc is finite, so the set of statements, and a fortiori the set of theorems, is at most countable. Where do you get the uncountability? I suspect you are confusing theorems and theories. Assuming the set theory ZF (for instance) is consistent, then a consequence of Gödel's incompleteness theorem is that there are indeed uncountably many inequivalent extensions of ZF that are complete and consistent. Also, not a single one of these extensions can be described in symbols in the sense that there does not exist a computer program that enumerates a possible set of axioms for the extension. As for your general point about arbitrariness, the late 19th century was a period when mathematicians started being concerned with the rigorous formalization of mathematics. Sure, there are some arbitrariness in the particular choice of formalization in the same way that the particular form of a programming language like C is arbitrary. However, the Gödel stuff has nothing to do with that arbitrariness, it is about the limit of formalization itself. The programming analogue is the undecidability of the halting problem. Saying that mathematics are arbitrary sounds to me a bit like saying that an algorithm like Quicksort is arbitrary because you saw an implementation in C and the particular form of the C language is arbitrary. Obviously, if you don't like the C language, you can implement Quicksort in another language. The same is true for mathematics. If some day, somebody finds a contradiction in ZF, or simply a new formalization that people find more convenient, then most mathematics will simply get translated and very little will change.

GPerson 2mo ago

The tastes and interests, and cultural pretext, of human beings are not arbitrary just because they’re not easily described.

ziiinq 2mo ago
Yes and therefore? You seem to be vaguely waving in the general direction of a point, without making any concrete claims or bothering to engage with the GP’s argument. The tastes and interests of humans are absolutely not arbitrary. They are dictated by fate, the sun and the moon gods. Or maybe by the unitary evolution of the universe’s quantum state. Or by the probability distribution of finding ourselves in a particular branch of the universe. What bearing does this have on whether math is a collaborative endeavor? And what is unique to math, that your argument wouldn’t apply equally to physics, sociology or financial markets? All, “truth seeking” disciplines.
- GPerson 2mo ago
  You seem rather aggressive so replying to you feels pointless and uncomfortable. Nonetheless, the person writes, “ Math has been almost purely arbitrary”. This is simply a misusage of the word arbitrary, which is a word with a specific meaning you can look up if you are unaware, since mathematics is (obviously) not arbitrary in the sense this person wants to convey, in part for the reasons I state. Humans are not choosing arbitrary logical statements to prove true or false.

loicd 2mo ago

> There are uncountably many correct mathematical theorems. Almost all of them can't even be written in symbols. What are you talking about? A theorem is a statement that has been proved from some axioms. A statement itself is a finite sequence of symbols satisfying some syntactical rules. The set of symbols for set theory, arithmetic, etc is finite, so the set of statements, and a fortiori the set of theorems, is at most countable. Where do you get the uncountability? I suspect you are confusing theorems and theories. Assuming the set theory ZF (for instance) is consistent, then a consequence of Gödel's incompleteness theorem is that there are indeed uncountably many inequivalent extensions of ZF that are complete and consistent. Also, not a single one of these extensions can be described in symbols in the sense that there does not exist a computer program that enumerates a possible set of axioms for the extension. As for your general point about arbitrariness, the late 19th century was a period when mathematicians started being concerned with the rigorous formalization of mathematics. Sure, there are some arbitrariness in the particular choice of formalization in the same way that the particular form of a programming language like C is arbitrary. However, the Gödel stuff has nothing to do with that arbitrariness, it is about the limit of formalization itself. The programming analogue is the undecidability of the halting problem. Saying that mathematics are arbitrary sounds to me a bit like saying that an algorithm like Quicksort is arbitrary because you saw an implementation in C and the particular form of the C language is arbitrary. Obviously, if you don't like the C language, you can implement Quicksort in another language. The same is true for mathematics. If some day, somebody finds a contradiction in ZF, or simply a new formalization that people find more convenient, then most mathematics will simply get translated and very little will change.