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> No, I'm not conflating them. Earlier you said "¼ and 1/4 are the same symbol" but now you're saying that symbols are physical things that unambiguously map o

by kmill 5y ago

> No, I'm not conflating them. Earlier you said "¼ and 1/4 are the same symbol" but now you're saying that symbols are physical things that unambiguously map onto a single equivalence class called a "concept." If they're the same, you're conflating signifier and signified. If they're not the same, then I'll leave you to your workshopping of your own philosophies of math and semiotics. (It would be more interesting if you'd relate what you're saying to established philosophies. I've mentioned a few, and it's a bit frustrating that they were overlooked.) Formalism is a legitimate philosophy of math, but I think it's rather absurd to declare that it serves as a definition of math. I like how Simon Stevin translated mathematics (Latin) into Dutch, wiskunde "the knowledge/art of what is certain." Symbolic calculation is certainly a way to be certain of something.

lisper 5y ago
I think we're dealing the limitations of communication via unicode text. When I say that ¼ and 1/4 are "the same symbol" what I mean is that they are the same symbol with respect to their visual appearance, not with respect to their numerical representations are unicode code points (or, in the case of 1/4, three unicode code points). And I shouldn't have used the word "concept". That just muddied the waters. Imagine if we were standing in front of a white board and I wrote 1/4 twice. The physical appearance of those two batches of dry-erase marker ink would be slightly different. They would have slightly different shapes. They would be in different physical locations on the board. They might even have different colors. They might even be individually multicolored. None of those things would matter. Both of them would be the "same symbol" because they would both be members of a single equivalence class (with respect to the conventions of mathematical notation). > Formalism is a legitimate philosophy of math, but I think it's rather absurd to declare that it serves as a definition of math. How would you define it then?

by kmill 5y ago

lisper 5y ago

I think we're dealing the limitations of communication via unicode text. When I say that ¼ and 1/4 are "the same symbol" what I mean is that they are the same symbol with respect to their visual appearance, not with respect to their numerical representations are unicode code points (or, in the case of 1/4, three unicode code points). And I shouldn't have used the word "concept". That just muddied the waters. Imagine if we were standing in front of a white board and I wrote 1/4 twice. The physical appearance of those two batches of dry-erase marker ink would be slightly different. They would have slightly different shapes. They would be in different physical locations on the board. They might even have different colors. They might even be individually multicolored. None of those things would matter. Both of them would be the "same symbol" because they would both be members of a single equivalence class (with respect to the conventions of mathematical notation). > Formalism is a legitimate philosophy of math, but I think it's rather absurd to declare that it serves as a definition of math. How would you define it then?