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> Exist or not exist, why does it matter? Yes, that's exactly how pragmatists[1] answer the question. It depends entirely on what you mean by exists and what y

> Exist or not exist, why does it matter? Yes, that's exactly how pragmatists[1] answer the question. It depends entirely on what you mean by exists and what you mean by exists always depends on what you're trying to do, i.e. your goal. That's what the whole squirrel* anectdote that William James came up with was about. 1. https://plato.stanford.edu/entries/pragmatism https://plato.stanford.edu/entries/pragmatism * The squirrel thing is in section 1 of the linked article.

paganel 5y ago
I've generally found Pragmatism to be pretty parochial and limited, I mean, looking at general statements like this one: > that a claim is true if and only if it is useful one cannot be judged for thinking "what good is there for any quest for true/false if all that matters is the usefulness of the thing/action itself?". I find pragmatism to be too anchored in this socio-material reality of ours, one in which things/actions have to be "useful" (the fact that many of the pragmatists come from the Anglo world, so obsessed with usefulness and utility generally speaking, also helps accentuate this). Back to the post per se, I think "the exist or not exist" issue/problem when it comes to mathematics is a subconscious sociologic-related plot (I'm only half-joking) of the people studying maths and believing in the power of maths so that they would impose on the rest of us, the non-maths people, the statement which says something like "what we, mathematicians, are studying does indeed exist and stands at the roots of the (scientific) world as we know it! Give us symbolic power in return!". Tell some lay-person that what a mathematician studies is in effect just a figment of his/her imagination, and one of the questions posed in return by that lay-person might be: "why should we believe what mathematicians say more than what poets say?".
- guerrilla 5y ago
  It sounds like you could have a narrower idea of what utility is than I do. For me, this is really about definitions relative to systems and those systems serving out goals. That's where utility comes in: Whether something is true or not depends on the system in which we judge it (i.e. relativism) and what system we use will depend on our goal. Our goals obviously depend on what we like and want, so axiology is clearly the root here. You'll run into this immediately when you study logics and find out that different ones can prove different theorems thus they have varying use cases, similar to the way programming languages do. If you want to predict the future, science is the tool you want but if you want to court someone then maybe poetry is your tool. It's not that anything has to be useful, it's just that analyzing concepts in terms of utility can clarify what we mean and illuminate the criteria necessary to decide certain questions. I agree with your second-to-last paragraph. Everyone wants what they study to be proven to be "real." It protects the prestige of the field. I always figure there's a conflict of interest going on when you find most mathematicians are Platonists but this unanimity doesn't carry over into philosophy where careers and social lives don't ride on that result [1]. I hope my previous paragraphs clarified when I think the layperson should trust the mathematician. 1. https://philpapers.org/surveys/results.pl https://philpapers.org/surveys/results.pl
  - paganel 5y ago
    > If you want to predict the future, science is the tool you want but if you want to court someone then maybe poetry is your tool. I agree and I definitely see your point, what I'm saying (or what I'm trying to say, at least, English not being my mother-tongue and me not being a mathematician nor a philosopher) is that going one (or two steps) back one may ask him/herself about the very concept/idea of utility, more exactly on what "premise" (so to speak) we assign "goals" to the "reality" surrounding us, why do we assume there is an "utility", why do we assume there should be "goals"? Why should we instrumentalize said "reality" by seeing it through the prism of "utility" and "goals"? I know that taking that many steps back from "natural" concepts like "utility" and achieving "goals" risks turning everything into empty metaphysics and, worse (from the pov of a mathematician or of a scientist more generally speaking) into mysticism, but imo at the higher level the mysticism of the neoplatonists (i.e. Plato's ideas taken several steps further with some pre-socratic elements added in) plus the ideas of some pre-socratics themselves are more closer to the "reality" of it all than what we ended up adopting (basically Aristotle whom we refined/corrected in some specific points). Basically I think a guy like Heraclitus was closer to grasping the "reality" around us than Aristotle ever was, but had we gone the way of Heraclitus we wouldn't have had computers and rockets and all, computers and rockets that were made possible by Aristotle's logic (and by the way how he perceived the logic process per se). Again, imo, Plato stands between the pre-socratics and Aristotle, but because we chose Aristotle's way and we basically built our world on Aristotle's way of thinking when we read Plato we tend to focus only on the part of his philosophy that in a way confirms this "world" that we built, so to speak (with this correlation between Plato's ideas and mathematics being just an example for that). Anyway, these are just some ramblings :)
    - guerrilla 5y ago
      > more exactly on what "premise" (so to speak) we assign "goals" to the "reality" surrounding us, why do we assume there is an "utility", why do we assume there should be "goals"? Why should we instrumentalize said "reality" by seeing it through the prism of "utility" and "goals"? We don't assume. It's just an empirical fact of our life that we have desires and goals. Don't you have desires and goals? I do. > Basically I think a guy like Heraclitus was closer to grasping the "reality" around us than Aristotle ever was, but had we gone the way of Heraclitus we wouldn't have had computers and rockets and all, computers and rockets This is an interesting idea. It reminds me of the Two-Truths Doctrine of Buddhism as interpreted by the Madhyamaka school. They believed that there was a provisional truth useful for doing doing daily stuff (like how you see Aristotle) and then an ultimate truth (like how you see the pre-Socatics.) I think there are monists in Western traditions who have similar views but I couldn't name any.
- sorokod 5y ago
  During my uni days I had a math lecturer who stated that it was a matter of great pride to him that all the math he created was pure and had absolutely no practical applications. With this in mind what does usefulness has to do with truth? Alternatively, his results where doubtlessly useful to other mathematitians in their research, does that make them more true?

paganel 5y ago

I've generally found Pragmatism to be pretty parochial and limited, I mean, looking at general statements like this one: > that a claim is true if and only if it is useful one cannot be judged for thinking "what good is there for any quest for true/false if all that matters is the usefulness of the thing/action itself?". I find pragmatism to be too anchored in this socio-material reality of ours, one in which things/actions have to be "useful" (the fact that many of the pragmatists come from the Anglo world, so obsessed with usefulness and utility generally speaking, also helps accentuate this). Back to the post per se, I think "the exist or not exist" issue/problem when it comes to mathematics is a subconscious sociologic-related plot (I'm only half-joking) of the people studying maths and believing in the power of maths so that they would impose on the rest of us, the non-maths people, the statement which says something like "what we, mathematicians, are studying does indeed exist and stands at the roots of the (scientific) world as we know it! Give us symbolic power in return!". Tell some lay-person that what a mathematician studies is in effect just a figment of his/her imagination, and one of the questions posed in return by that lay-person might be: "why should we believe what mathematicians say more than what poets say?".

guerrilla 5y ago
It sounds like you could have a narrower idea of what utility is than I do. For me, this is really about definitions relative to systems and those systems serving out goals. That's where utility comes in: Whether something is true or not depends on the system in which we judge it (i.e. relativism) and what system we use will depend on our goal. Our goals obviously depend on what we like and want, so axiology is clearly the root here. You'll run into this immediately when you study logics and find out that different ones can prove different theorems thus they have varying use cases, similar to the way programming languages do. If you want to predict the future, science is the tool you want but if you want to court someone then maybe poetry is your tool. It's not that anything has to be useful, it's just that analyzing concepts in terms of utility can clarify what we mean and illuminate the criteria necessary to decide certain questions. I agree with your second-to-last paragraph. Everyone wants what they study to be proven to be "real." It protects the prestige of the field. I always figure there's a conflict of interest going on when you find most mathematicians are Platonists but this unanimity doesn't carry over into philosophy where careers and social lives don't ride on that result [1]. I hope my previous paragraphs clarified when I think the layperson should trust the mathematician. 1. https://philpapers.org/surveys/results.pl https://philpapers.org/surveys/results.pl
- paganel 5y ago
  > If you want to predict the future, science is the tool you want but if you want to court someone then maybe poetry is your tool. I agree and I definitely see your point, what I'm saying (or what I'm trying to say, at least, English not being my mother-tongue and me not being a mathematician nor a philosopher) is that going one (or two steps) back one may ask him/herself about the very concept/idea of utility, more exactly on what "premise" (so to speak) we assign "goals" to the "reality" surrounding us, why do we assume there is an "utility", why do we assume there should be "goals"? Why should we instrumentalize said "reality" by seeing it through the prism of "utility" and "goals"? I know that taking that many steps back from "natural" concepts like "utility" and achieving "goals" risks turning everything into empty metaphysics and, worse (from the pov of a mathematician or of a scientist more generally speaking) into mysticism, but imo at the higher level the mysticism of the neoplatonists (i.e. Plato's ideas taken several steps further with some pre-socratic elements added in) plus the ideas of some pre-socratics themselves are more closer to the "reality" of it all than what we ended up adopting (basically Aristotle whom we refined/corrected in some specific points). Basically I think a guy like Heraclitus was closer to grasping the "reality" around us than Aristotle ever was, but had we gone the way of Heraclitus we wouldn't have had computers and rockets and all, computers and rockets that were made possible by Aristotle's logic (and by the way how he perceived the logic process per se). Again, imo, Plato stands between the pre-socratics and Aristotle, but because we chose Aristotle's way and we basically built our world on Aristotle's way of thinking when we read Plato we tend to focus only on the part of his philosophy that in a way confirms this "world" that we built, so to speak (with this correlation between Plato's ideas and mathematics being just an example for that). Anyway, these are just some ramblings :)
  - guerrilla 5y ago
    > more exactly on what "premise" (so to speak) we assign "goals" to the "reality" surrounding us, why do we assume there is an "utility", why do we assume there should be "goals"? Why should we instrumentalize said "reality" by seeing it through the prism of "utility" and "goals"? We don't assume. It's just an empirical fact of our life that we have desires and goals. Don't you have desires and goals? I do. > Basically I think a guy like Heraclitus was closer to grasping the "reality" around us than Aristotle ever was, but had we gone the way of Heraclitus we wouldn't have had computers and rockets and all, computers and rockets This is an interesting idea. It reminds me of the Two-Truths Doctrine of Buddhism as interpreted by the Madhyamaka school. They believed that there was a provisional truth useful for doing doing daily stuff (like how you see Aristotle) and then an ultimate truth (like how you see the pre-Socatics.) I think there are monists in Western traditions who have similar views but I couldn't name any.
sorokod 5y ago
During my uni days I had a math lecturer who stated that it was a matter of great pride to him that all the math he created was pure and had absolutely no practical applications. With this in mind what does usefulness has to do with truth? Alternatively, his results where doubtlessly useful to other mathematitians in their research, does that make them more true?