| ▲ | kenjackson 4 hours ago |
| "new kind of math" Well I think the point is there is no "new kind of math". There's just types of math we've discovered and what we haven't. No new math is created, just found. |
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| ▲ | grey-area 4 hours ago | parent | next [-] |
| The map is not the territory. |
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| ▲ | cthalupa 3 hours ago | parent [-] | | I don't know what you're even trying to argue here. We're not comparing math to reality (though there's a strong argument to be made that reality has a structure that is mathematical in nature - structural realism didn't die a scientific philosophy just because someone came up with a pithy saying), we're talking about if math is discovered or invented. Most mathematicians would argue both - math is a language, we have created operations, axioms are proposed based on human creativity, etc., but the actual laws, patterns, etc. are discovered. Pi is going to be pi no matter if you're a human or someone else - we might represent it differently with some other number system or whatever, but that's a matter of representation, not mathematical truth. | | |
| ▲ | Koshkin 2 hours ago | parent [-] | | > we have created operations It seems that addition (for instance) was "created" long before us. On the other hand, it seems highly unlikely that a civilization similar to ours could "invent" an essentially different kind of mathematics (or physics, etc.) |
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| ▲ | black_knight 3 hours ago | parent | prev | next [-] |
| Where does this mathematics exist before we discover it? I know of no realm where mathematical objects live except human minds. No, it seems clear to me that mathematics is a creation of our minds. |
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| ▲ | hackinthebochs 2 minutes ago | parent [-] | | If it were merely a creation, there would be no reason for two independent mathematicians to land on the same creation given some directed effort. But of course we do see that. There is an objectivity to mathematics that must be accounted for. "Where" mathematics exists is in the abstract combinatorical space of an infinite repeating application of logical rules. This space doesn't exist in a substantive sense, but it is accessible/navigable by studying the consequences of logical rules. It is the space of possible structure. |
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| ▲ | bbor 4 hours ago | parent | prev [-] |
| Does that correction matter, tho…? Discovered or created, it would be new to us, and is clearly not easy to reach! |
