If we come up with a language that can be used to describe what’s true—that’s just how languages work.
the so-called “surprising effectiveness” is not that formal languages can describe reality. as you point out, that’s a property of any descriptive language. no, the surprise which must be explained is that many of our specific sentences in those languages later turned out to be physically relevant.
i don’t necessarily agree with the surprising effectiveness crowd, but you misrepresent their point.
i guess my comment was unclear. i’m just saying that “mathematics is a language, so of course it can be used to describe reality” is arguing against something the surprising-effectiveness crowd does not claim. they do not say “it is surprising that mathematical language can be used to describe reality”, but rather that “it is surprising that specific mathematical objects of interest to mathematicians often end up useful in physics or other empirical sciences.”[1]
i feel the original essay—in this section—elides the difference between “mathematical language” and “mathematical object”, and thereby argues against a strawman.
note that i’m making a very narrow point, here. for example, i think the next section of the essay is strong: mathematics has catalogued a LOT of true statements, and it’s not necessarily surprising that some of them can be used in models of reality.
to your direct question: no, of course not? any description of reality is physically relevant.
the distinction between mathematical language and object is fuzzy. mathematics is happy to treat languages themselves as objects of study. nonetheless, while we’re speaking philosophically, i think we can allow it.
i’m just saying that “mathematics is a language, so of course it can be used to describe reality” is arguing against something the surprising-effectiveness crowd does not claim. they do not say “it is surprising that mathematical language can be used to describe reality”, but rather that “it is surprising that specific mathematical objects of interest to mathematicians often end up useful in physics or other empirical sciences.”[1]
Do I understand correctly that you claim that the surprising part is that mathematical objects are “discovered” first for their own sake and only later are revealed to be physically relevant? Because if this is the case, I address this here:
We can still be somewhat surprised if the language has necessary words to describe certain parts of reality before they were encountered. But this is an improbability of a much smaller degree, reduced by the fact that creating new words in this language is an interesting and rewarded activity, which people tend to do for its own sake, as exactly is the case with mathematics.
I’ve met people just generally confused why math can describe reality at all. And math being a language is a part of the answer here. I think Lorenzo Elijah, whose post I’m answering to, is confused in a similar manner. He acknowledges that math is a language but then thinks this is problematic and uses the middle-earth-planaet analogy which would make sense only if math was a story. So I think it’s totally appropriate to point that math is a language and not a story and that this resolves the huge part of the apparent improbability, before addressing the smaller improbability related to the order in which mathematical objects are invented/discovered.
i feel the original essay—in this section—elides the difference between “mathematical language” and “mathematical object”, and thereby argues against a strawman.
Mathematical objects are parts of the language. Like words pr other semantic constructions. I think it’s pretty straightforward.
the so-called “surprising effectiveness” is not that formal languages can describe reality. as you point out, that’s a property of any descriptive language. no, the surprise which must be explained is that many of our specific sentences in those languages later turned out to be physically relevant.
i don’t necessarily agree with the surprising effectiveness crowd, but you misrepresent their point.
Can you come up with an example of a mathematical statement that describes reality while not being physically relevant?
sorry, i think we misunderstand each other.
i guess my comment was unclear. i’m just saying that “mathematics is a language, so of course it can be used to describe reality” is arguing against something the surprising-effectiveness crowd does not claim. they do not say “it is surprising that mathematical language can be used to describe reality”, but rather that “it is surprising that specific mathematical objects of interest to mathematicians often end up useful in physics or other empirical sciences.”[1]
i feel the original essay—in this section—elides the difference between “mathematical language” and “mathematical object”, and thereby argues against a strawman.
note that i’m making a very narrow point, here. for example, i think the next section of the essay is strong: mathematics has catalogued a LOT of true statements, and it’s not necessarily surprising that some of them can be used in models of reality.
to your direct question: no, of course not? any description of reality is physically relevant.
the distinction between mathematical language and object is fuzzy. mathematics is happy to treat languages themselves as objects of study. nonetheless, while we’re speaking philosophically, i think we can allow it.
Do I understand correctly that you claim that the surprising part is that mathematical objects are “discovered” first for their own sake and only later are revealed to be physically relevant? Because if this is the case, I address this here:
I’ve met people just generally confused why math can describe reality at all. And math being a language is a part of the answer here. I think Lorenzo Elijah, whose post I’m answering to, is confused in a similar manner. He acknowledges that math is a language but then thinks this is problematic and uses the middle-earth-planaet analogy which would make sense only if math was a story. So I think it’s totally appropriate to point that math is a language and not a story and that this resolves the huge part of the apparent improbability, before addressing the smaller improbability related to the order in which mathematical objects are invented/discovered.
Mathematical objects are parts of the language. Like words pr other semantic constructions. I think it’s pretty straightforward.