Comment Re:They've already proved it isn't a game: Gö (Score 1) 496
The formalists thought it was a "game" -- which is to say a formal system interesting mainly because of the relations between various components in the system.
maths is a game /= formal systems interesting because of the relations between its elements. besides, all systems have this quality, not just formal systems, so this alone wouldn't qualify them as interesting.
Unfortunately, that was only fun for a little while until Gödel's Incompleteness Proof successfully proved that not all truths of arithmetic could be proved using the rules of arithmetic.
godel's incompleteness theorem is not just about this. it states that any systems that are complex enough to refer to itself are either inconsistent/contradictory, or contains axioms (i.e., propositions that cannot be deducted/proved from within the system and are accepted without proof). now this has nothing to do with maths (or formal systems) being fun. or if it does, it only added to its fun, as it made people embrace the thitherto much hated paradoxes. paradoxes *are* interesting, they can set the mind to work like few things can. in fact, godel used epimenides's paradox: epimenides was a cretan, and he stated that "all cretans are liars". this was the statement that godel formalized thereby creating the incompleteness theorem.
So the real question here is "Are all sports games?" If so, and it seems quite reasonable, then quite objectively the answer to "Is mathematics a sport?" is no. (Ok, so only if all games are formal systems...)
i don't see your logic. this is true, yes: 1) all sports are games 2) all games are formal systems C) maths is a sport (implicit premise: math is a formal system, but i think we'd accept that)
but the fact that the above conclusion is true doesn't mean that the opposite is true either. check it out: 1) all sports are games ("if so...") 2) not all games are formal systems Conclusion: maths is not a sport.
there's no way you can draw such a conclusion based on logic (esp. "quite objectively").
now this would also bring up the question of the definition of "game," which is yet to be created. no soothing definition of game has been created yet (though there're many passable ones). now what is sport? the word derives from "disport." in fact, it was a variant of that word up until modern english. disport literally meant to carry, which suggests that there's an element of physical work involved. later, however, it became to mean to play, or to amuse. so according to etymology, maths can well be a sport.
but, really, this all comes down to tradition. what people are used to mean under sport. some people now might oppose, but their children might learn the word to include all kind of mental activities as well (not just chess).
maths is a game
Unfortunately, that was only fun for a little while until Gödel's Incompleteness Proof successfully proved that not all truths of arithmetic could be proved using the rules of arithmetic.
godel's incompleteness theorem is not just about this. it states that any systems that are complex enough to refer to itself are either inconsistent/contradictory, or contains axioms (i.e., propositions that cannot be deducted/proved from within the system and are accepted without proof). now this has nothing to do with maths (or formal systems) being fun. or if it does, it only added to its fun, as it made people embrace the thitherto much hated paradoxes. paradoxes *are* interesting, they can set the mind to work like few things can. in fact, godel used epimenides's paradox: epimenides was a cretan, and he stated that "all cretans are liars". this was the statement that godel formalized thereby creating the incompleteness theorem.
So the real question here is "Are all sports games?" If so, and it seems quite reasonable, then quite objectively the answer to "Is mathematics a sport?" is no. (Ok, so only if all games are formal systems...)
i don't see your logic. this is true, yes: 1) all sports are games 2) all games are formal systems C) maths is a sport (implicit premise: math is a formal system, but i think we'd accept that)
but the fact that the above conclusion is true doesn't mean that the opposite is true either. check it out: 1) all sports are games ("if so...") 2) not all games are formal systems Conclusion: maths is not a sport.
there's no way you can draw such a conclusion based on logic (esp. "quite objectively").
now this would also bring up the question of the definition of "game," which is yet to be created. no soothing definition of game has been created yet (though there're many passable ones). now what is sport? the word derives from "disport." in fact, it was a variant of that word up until modern english. disport literally meant to carry, which suggests that there's an element of physical work involved. later, however, it became to mean to play, or to amuse. so according to etymology, maths can well be a sport.
but, really, this all comes down to tradition. what people are used to mean under sport. some people now might oppose, but their children might learn the word to include all kind of mental activities as well (not just chess).
