3 ms·

This is either quite the claim or you have a non-standard definition of "symbol." Each of those three representations are obviously different, though they all

by kmill 5y ago

This is either quite the claim or you have a non-standard definition of "symbol." Each of those three representations are obviously different, though they all refer to the concept of "one-quarter," and I very much question the one made from @ signs. (And to be annoying, ¼ and 1/4 both have completely different UTF-8 representations, but I'd still associate them with the concept of "one-quarter.") It seems like you're conflating "signifier" with "signified". I'd say the whole point of symbols is that they play a role in semiosis, where an interpreter (us) receives meaning (the "signified") from decoding a symbol (the "signifier"). My own decoding apparatus gets the same roughly the same meaning from ¼ and 1/4. But the meaning's not a symbol in itself. What I was obliquely getting at earlier in bringing up intuitionism is that math seems to derive from pre-existing mental processes. Recognition and manipulation of symbols seems to be no more special than other mental processes. Rule-based manipulation seems to appeal to our understanding of causality, for example.

lisper 5y ago
> I very much question the one made from @ signs There are limits to what can be expressed in an HN comment. If we were standing at a whiteboard I could draw many more different variations on the theme than I can here. > you have a non-standard definition of "symbol." A symbol is a physical thing that can be unambiguously mapped into one of a finite set of equivalence classes. ¼ and 1/4 and even "one-quarter" can all be unambiguously mapped (within a particular context, i.e. people speaking English talking about math) onto a single concept which is denoted ¼ or 1/4 or "one-quarter" or "one-quarter". > It seems like you're conflating "signifier" with "signified". No, I'm not conflating them. It's just very hard to talk about these things because the only tool we have at our disposal is signifiers. I can't actually show you the thing that is signified by ¼ and 1/4 and "one-quarter", I can only talk about its properties (and I can only do that using signifiers). > math seems to derive from pre-existing mental processes That is a very human-centric view of things. It happens to arise in humans from pre-existing mental processes, but that doesn't mean that math necessarily or inherently arises that way. In fact, math arises in nature in myriad ways, many of which are not even mental processes at all. > Recognition and manipulation of symbols seems to be no more special than other mental processes. Oh, that is where you are very, very wrong, my friend. Manipulation of symbols is very special. There's a reason it's called the "computer revolution".
- 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 very much question the one made from @ signs There are limits to what can be expressed in an HN comment. If we were standing at a whiteboard I could draw many more different variations on the theme than I can here. > you have a non-standard definition of "symbol." A symbol is a physical thing that can be unambiguously mapped into one of a finite set of equivalence classes. ¼ and 1/4 and even "one-quarter" can all be unambiguously mapped (within a particular context, i.e. people speaking English talking about math) onto a single concept which is denoted ¼ or 1/4 or "one-quarter" or "one-quarter". > It seems like you're conflating "signifier" with "signified". No, I'm not conflating them. It's just very hard to talk about these things because the only tool we have at our disposal is signifiers. I can't actually show you the thing that is signified by ¼ and 1/4 and "one-quarter", I can only talk about its properties (and I can only do that using signifiers). > math seems to derive from pre-existing mental processes That is a very human-centric view of things. It happens to arise in humans from pre-existing mental processes, but that doesn't mean that math necessarily or inherently arises that way. In fact, math arises in nature in myriad ways, many of which are not even mental processes at all. > Recognition and manipulation of symbols seems to be no more special than other mental processes. Oh, that is where you are very, very wrong, my friend. Manipulation of symbols is very special. There's a reason it's called the "computer revolution".

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?