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> All of math is a byproduct of our brains. It doesn't exist, out there, in some Platonic World. Anyone who thinks so, I'm looking at you Max Tegmark, is mistak

> All of math is a byproduct of our brains. It doesn't exist, out there, in some Platonic World. Anyone who thinks so, I'm looking at you Max Tegmark, is mistaking the map for the territory. I could brashly say the exact opposite and would have proven just as much as you. Fictionalists often attempt to shunt the Platonic realm into an ill-conceived emanation of the mental realm (which just so happens to itself be an accident of matter). Somehow all of this works by virtue of following a kind of mathematical logic that just so happens to not exist or something. I suspect the fundamental problem here is some kind of neurosis that psychologically compels people to reduce the quality of their thought until hard problems disappear. I hope we one day are able to build a catalog of all the ways thought goes wrong so as to prevent such nonsense from proliferating in at least some section of the world. I think a reasonably compelling way to teach yourself how to actually see The Problem (tm) is to view it from the perspective of Roger Penrose's three worlds ( https://hrstraub.ch/en/the-theory-of-the-three-worlds-penrose/ https://hrstraub.ch/en/the-theory-of-the-three-worlds-penros... ) and actually think through the implications in a contemplative, meditative way over the course of several hours. Any analysis of this issue that doesn't involve a sustained look at both logic and phenomenology is a waste of time.

smokel 3y ago
Thank you for that reference! It is indeed not so simple. If I continue my thought experiments about sets not being universal or foundational, I run into a myriad of problems. For one, how can one reason about anything when rejecting concepts? How can one conclude anything when rejecting logic? How can one infer anything when rejecting time? These problems seem to point to some recursive or symmetric (or circular as the article suggests) dependency between the realist and non-realist perspectives. I don't yet fully understand why there would have to be three worlds -- I'd intuitively say that two (e.g. physical and mental) suffice. The platonic world might simply follow from the mental one, or vice versa. I'll put in several hours of thought and report back in the next post that touches upon this subject. I concluded for myself that logic, science, nor philosophy are going to be of much help with this. I therefore turned to contemporary art, where such thought still has some kind of validity. Let's see where that leads me :) Edit: It seems that the "three world" idea is originally an idea by Karl Popper. Wikipedia [1] explains this in some detail, from which it becomes clear why the thought experiment has three, not two worlds. [1] https://en.m.wikipedia.org/wiki/Popper%27s_three_worlds https://en.m.wikipedia.org/wiki/Popper%27s_three_worlds
- zehaeva 3y ago
  Part of the reason that you're going to run into trouble with sets being universal, or foundational, rightly found in a theorem that was birthed from set theory, Gödel's Incompleteness Theorem[0]. I will confess that when I took discrete in college I was seduced by set theory. I literally had the, naive, thought to myself "you could prove all of math with just sets!". As my education continued I found out, much to my chagrin, and Hiblert's[1], that I was very, very, mistaken. This hasn't stopped everyone from trying to continue Hilbert's program, though with a bit more limited scope[2][3]. By and large, all math is undergirded by a set of axioms that have to be taken as true with no proof. Even as far back as Euclid's Elements basically starts with a set of axioms and then proceeds from there. Strange that something that is so real must have a bunch of rules given as true with no proof of their validity beyond "well, everyone can see that it's true". In a final, ish, dig, I'll just say leave it up to Penrose to take Popper's sensible cosmology and turn it into a quasi-religious one. [0] https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_... [1] https://en.wikipedia.org/wiki/Hilbert%27s_program https://en.wikipedia.org/wiki/Hilbert%27s_program [2] https://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_theory https://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_t... [3] https://en.wikipedia.org/wiki/Reverse_mathematics https://en.wikipedia.org/wiki/Reverse_mathematics
  - 2snakes 3y ago
    I wonder if you could prove it all with G. Spencer Brown's Laws of Form?
zehaeva 3y ago
You could brashly say that the Platonic world does exist? I must be from Missouri, show it to me! Do that and you can bring me to your, and Max Tegmark's, side. Show me a Tree that has the pure essence of tree, show me a One, show me the pure ideal of a triangle. I do take umbrage at your insinuation that I have not actually thought "through the implications in a contemplative, meditative way over the course of several hours" on this subject. I have spent many years, and not a few semesters of college, contemplating this very subject. Consider this, where would your platonic world go if there were no sentient beings in the universe? Would it sit there, on some "higher plane" awaiting discovery by no one? Would the pure idea of a Tree get lonely? We're very into "does a tree fall in the forest with no one to hear it does it make a sound?" territory, however I think this is extremely important when trying to decide what is Real. Plato, a man who lived ~2,400 years ago, decided that ideas were Real with zero proof and you're just going to accept his word on this, I'm supposed to just accept this? This does strike me as extremely life-centric, for lack of a better, all encompassing, term. If all life in the universe disappeared, the universe itself does not suddenly vanish in a puff of smoke. Stars will still fuse the elements, blackholes will still gobble up matter, the earth will continue to orbit the sun until it's consumed by the sun or is disrupted by some massive interstellar traveler. But the world of ideas wouldn't exist because there would be nothing to think of them. Mathematics wouldn't exist, because there would be nothing to conceive of them. If you assume the platonic realm exists, sure, I would grant you all of Penrose's Three Worlds, I would grant Tegmark's belief that somewhere out there is a physical Platonic realm. I'd also probably believe in a lot of other things with out evidence as well. But, maybe I'm just from Missouri. You're gonna have to show me.
- smokel 3y ago
  Playing devil's advocate here. Mathematics and concepts can be shown in the regular way: in books, or in configurations of bits. Their meaning is generally lost though, unless there is someone to interpret it. I think we should be careful about the contexts that we are discussing things in. If we consider, for example, a string of text that contains the King James Bible, and we assume that the string "exists", that does not imply that the actual stories in the text exist, let alone that the characters featuring in it exist. In the above example, existence has three different meanings. It would be great if philosophy would be able to use strict type checking on their arguments :) It would also be nice if I could simply state my philosophical dependencies in a plain text file.
mjan22640 3y ago
> I could brashly say the exact opposite and would have proven just as much as you. go ahead

smokel 3y ago

Thank you for that reference! It is indeed not so simple. If I continue my thought experiments about sets not being universal or foundational, I run into a myriad of problems. For one, how can one reason about anything when rejecting concepts? How can one conclude anything when rejecting logic? How can one infer anything when rejecting time? These problems seem to point to some recursive or symmetric (or circular as the article suggests) dependency between the realist and non-realist perspectives. I don't yet fully understand why there would have to be three worlds -- I'd intuitively say that two (e.g. physical and mental) suffice. The platonic world might simply follow from the mental one, or vice versa. I'll put in several hours of thought and report back in the next post that touches upon this subject. I concluded for myself that logic, science, nor philosophy are going to be of much help with this. I therefore turned to contemporary art, where such thought still has some kind of validity. Let's see where that leads me :) Edit: It seems that the "three world" idea is originally an idea by Karl Popper. Wikipedia [1] explains this in some detail, from which it becomes clear why the thought experiment has three, not two worlds. [1] https://en.m.wikipedia.org/wiki/Popper%27s_three_worlds https://en.m.wikipedia.org/wiki/Popper%27s_three_worlds

zehaeva 3y ago
Part of the reason that you're going to run into trouble with sets being universal, or foundational, rightly found in a theorem that was birthed from set theory, Gödel's Incompleteness Theorem[0]. I will confess that when I took discrete in college I was seduced by set theory. I literally had the, naive, thought to myself "you could prove all of math with just sets!". As my education continued I found out, much to my chagrin, and Hiblert's[1], that I was very, very, mistaken. This hasn't stopped everyone from trying to continue Hilbert's program, though with a bit more limited scope[2][3]. By and large, all math is undergirded by a set of axioms that have to be taken as true with no proof. Even as far back as Euclid's Elements basically starts with a set of axioms and then proceeds from there. Strange that something that is so real must have a bunch of rules given as true with no proof of their validity beyond "well, everyone can see that it's true". In a final, ish, dig, I'll just say leave it up to Penrose to take Popper's sensible cosmology and turn it into a quasi-religious one. [0] https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_... [1] https://en.wikipedia.org/wiki/Hilbert%27s_program https://en.wikipedia.org/wiki/Hilbert%27s_program [2] https://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_theory https://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_t... [3] https://en.wikipedia.org/wiki/Reverse_mathematics https://en.wikipedia.org/wiki/Reverse_mathematics
- 2snakes 3y ago
  I wonder if you could prove it all with G. Spencer Brown's Laws of Form?

zehaeva 3y ago

You could brashly say that the Platonic world does exist? I must be from Missouri, show it to me! Do that and you can bring me to your, and Max Tegmark's, side. Show me a Tree that has the pure essence of tree, show me a One, show me the pure ideal of a triangle. I do take umbrage at your insinuation that I have not actually thought "through the implications in a contemplative, meditative way over the course of several hours" on this subject. I have spent many years, and not a few semesters of college, contemplating this very subject. Consider this, where would your platonic world go if there were no sentient beings in the universe? Would it sit there, on some "higher plane" awaiting discovery by no one? Would the pure idea of a Tree get lonely? We're very into "does a tree fall in the forest with no one to hear it does it make a sound?" territory, however I think this is extremely important when trying to decide what is Real. Plato, a man who lived ~2,400 years ago, decided that ideas were Real with zero proof and you're just going to accept his word on this, I'm supposed to just accept this? This does strike me as extremely life-centric, for lack of a better, all encompassing, term. If all life in the universe disappeared, the universe itself does not suddenly vanish in a puff of smoke. Stars will still fuse the elements, blackholes will still gobble up matter, the earth will continue to orbit the sun until it's consumed by the sun or is disrupted by some massive interstellar traveler. But the world of ideas wouldn't exist because there would be nothing to think of them. Mathematics wouldn't exist, because there would be nothing to conceive of them. If you assume the platonic realm exists, sure, I would grant you all of Penrose's Three Worlds, I would grant Tegmark's belief that somewhere out there is a physical Platonic realm. I'd also probably believe in a lot of other things with out evidence as well. But, maybe I'm just from Missouri. You're gonna have to show me.

smokel 3y ago
Playing devil's advocate here. Mathematics and concepts can be shown in the regular way: in books, or in configurations of bits. Their meaning is generally lost though, unless there is someone to interpret it. I think we should be careful about the contexts that we are discussing things in. If we consider, for example, a string of text that contains the King James Bible, and we assume that the string "exists", that does not imply that the actual stories in the text exist, let alone that the characters featuring in it exist. In the above example, existence has three different meanings. It would be great if philosophy would be able to use strict type checking on their arguments :) It would also be nice if I could simply state my philosophical dependencies in a plain text file.

mjan22640 3y ago

> I could brashly say the exact opposite and would have proven just as much as you. go ahead