5 ms·

If mathematics (or the underlying 'thing' that math describes) is objectively true or real, then it could have a platonic existence by power of its own self ref

If mathematics (or the underlying 'thing' that math describes) is objectively true or real, then it could have a platonic existence by power of its own self reference. My response would be, that math is not true. It is build on top of logic, which is not universally true. x && !x == false, sounds right, doesn't it? In one place at one time it either rains or it does not rain. But this is, I would argue, an observed fact about our universe, not some universal truth. Imagine a different universe, something like the Everett multiverse where all possibilities actually happen and where the inhabitants of that universe experience all the different branches. For them it could be raining and not raining at the same time in the same place, their logic might say x && !x == true.

codebolt 3y ago
Would you agree that an alien civilization completely separate from humans but equally intelligent would also be likely to discover Pythagoras theorem (with a different name and different symbolics)? To me that would imply that its truth is independent of human perception.
- disconcision 3y ago
  i don't find this argument convincing. it depends, at minimum, on bounding 'aliens' to mean something reasonably close to humans. if we allow aliens to be arbitrarily different, than i don't see a reason to bound their abstract symbolic technical development any more than arbitrarily distant to human development. otoh, if we assume that aliens are significantly similar to humans in some specific respects, then it seems likely to me that their technical development will also have substantial similarities, including but not limited to their abstract symbolic development. the space of abstractions seems large, and our particular path through it is historically contingent in both obvious and likely non-obvious ways; likewise for the formal inferential constructs which we use to parameterize this space
- danbruc 3y ago
  Math and logic are fundamentally some kind of game, you make up some rules and axioms and then you figure out the consequences. So the interesting question is which rules and axioms you pick and I would guess aliens in our universe would pick similar rules and axioms as we did because they will want to describe the same universe. And they would probably discover the Pythagorean theorem. But in a different universe without space dimensions or multiple time dimensions or discrete space dimensions or something completely incomprehensible to us for which we do not even have concepts and words, there I am not sure that they would certainly come up with the axioms of Euclidean space and discover the Pythagorean theorem, or it might be a very esoteric mathematical structure to them at best. So it seems there is still something universal in there, the idea of inventing rules and axioms and figuring out the consequences, which could maybe essentially boil down to computations or something like that. But even there I am not so sure that it is truly universal, the original idea of a Turing machine is an abstraction of repeatedly modifying some state over time, and can we not imagine a universe where updating state over time makes no sense?
jerf 3y ago
To be honest, I'm not even particularly impressed by the claim that the only mathematical universes that can exist are the self-consistent ones. I think that is mostly stipulated in these theories for post hoc reasons. So some of them aren't consistent... so what? Do the consistency police come along and strip you of your "existence"? How? Why? We humans use inconsistent logics all the time. When confronted by inconsistencies we often just fix them up, either with some other logic or just plain ad hoc new rules. Inconsistent universes can similarly each be rescued by an infinite number of "fixups", up to and including uncountably infinite functions that simply brute force resolve the inconsistencies. This renders the term "inconsistent" meaningless in this context because rather than an inconsistent universe not being able to "exist" it instead represents some infinite class of existing universes with some fixups applied. The main problem I have with this line of argumentation is that in its zeal to explain why anything exists, it actually goes all the way to the other end of the spectrum and can't explain why anything doesn't exist. But clearly there are things that don't exist, by virtue of the fact that the subjective experience of being in a universe where literally everything exists would be one of total chaos; in any given moment, the countably-infinite possible futures where the next subjective instant is "reasonable" to you is dwarfed by the uncountably infinite possible futures that contain an embedding of "you" and your next subjective instant is not reasonable to you. (And if you're objecting to my casual assertion that your next instant is at best countably infinite, I'm already erring on the side of giving grace to the argument; I'd personally characterize them as straight-up finite.) Things exist; some things also don't exist. The mathematical universe hypothesis covers the first at the cost of failing the second. Math isn't parabolas and conic sections and tiny integers getting added together; math is uncountably infinite functions of uncountably infinite structures being mapped to other uncountably infinite structures with no pattern, out of which we carve our little niches that are useful and comprehensible and mistake them as being the rule, rather than than the vanishingly tiny exception. Something isn't just causing things to exist, it is also holding back the incomprehensible chaos of total, undifferentiated existence. (The fine tuning of the physical universe is a nearly insignificant mystery next to this. How is reality reasonable to any degree at all? Forget the question of life, how does there exist any structure that has a reasonable subjective existence rather than total, utter chaos beyond any capability we have to imagine?)
speak_plainly 3y ago
If you look carefully at Frege’s original notations you’ll see that all logical connectives are simply if-then statements with the exception of ‘not’. Logic is just formalized cause and effect, partly inspired by Hume. Cause and effect seems to reflect some deep truth about the universe.
VirusNewbie 3y ago
How can that even make sense without any axioms. You can’t say logic doesn’t work because i proved a true statement is false.
- danbruc 3y ago
  You mean how can I do any kind of reasoning if I think the logic I use for reasoning does work or at the very least is kind of an arbitrary choice? I have no answer for that. And that is very similar to something else that always bothered me. I think there is no free will, everything in the universe just mindlessly follows the laws of physics. But if that is the case, how can anyone do any meaningful reasoning? If you just think, write and say what the laws of physics make you think, write or say, what guarantees that your thoughts or words follow any logic? I have no good answer, at best some extremely vague idea of consistency, that the laws of physics in our universe have some logic to them or maybe better that they imply some logic that is useful to reason about them and that this implied logic gets imprinted onto composit systems in the universe. But even if that was true, you would end up with new questions, why is it true and does it have to be true? And I can think of at least one more instance of a similar problem, namely what guarantees that your perception of the the world is in any way linked to an actually existing world that you inhabit? How do you know that you are not just hallucinating the universe into existence? There the usual answer is, I think, to just assume it, otherwise any reasoning would be doomed right from the beginning as you can never know whether there is any real universe or whether you are just making it up. The lesson is probably that reasoning from the inside - from your mind about your mind, from inside the universe about the universe, with logic about logic - is really hard, in the same way that Gödel's incompleteness theorems tell us about the limits of reasoning with math about math.
  - VirusNewbie 3y ago
    You're way over thinking it. You either have causality/time component, and can derive some basic axioms that get you existence or not existence (boolean) or you don't. If you have the former, we have turing completeness, and there we go. If you don't, well, sure, whose to say there isn't a universe where you can't have both presence, absence, and a time component but it's not all that interesting.

codebolt 3y ago

Would you agree that an alien civilization completely separate from humans but equally intelligent would also be likely to discover Pythagoras theorem (with a different name and different symbolics)? To me that would imply that its truth is independent of human perception.

disconcision 3y ago
i don't find this argument convincing. it depends, at minimum, on bounding 'aliens' to mean something reasonably close to humans. if we allow aliens to be arbitrarily different, than i don't see a reason to bound their abstract symbolic technical development any more than arbitrarily distant to human development. otoh, if we assume that aliens are significantly similar to humans in some specific respects, then it seems likely to me that their technical development will also have substantial similarities, including but not limited to their abstract symbolic development. the space of abstractions seems large, and our particular path through it is historically contingent in both obvious and likely non-obvious ways; likewise for the formal inferential constructs which we use to parameterize this space
danbruc 3y ago
Math and logic are fundamentally some kind of game, you make up some rules and axioms and then you figure out the consequences. So the interesting question is which rules and axioms you pick and I would guess aliens in our universe would pick similar rules and axioms as we did because they will want to describe the same universe. And they would probably discover the Pythagorean theorem. But in a different universe without space dimensions or multiple time dimensions or discrete space dimensions or something completely incomprehensible to us for which we do not even have concepts and words, there I am not sure that they would certainly come up with the axioms of Euclidean space and discover the Pythagorean theorem, or it might be a very esoteric mathematical structure to them at best. So it seems there is still something universal in there, the idea of inventing rules and axioms and figuring out the consequences, which could maybe essentially boil down to computations or something like that. But even there I am not so sure that it is truly universal, the original idea of a Turing machine is an abstraction of repeatedly modifying some state over time, and can we not imagine a universe where updating state over time makes no sense?

jerf 3y ago

To be honest, I'm not even particularly impressed by the claim that the only mathematical universes that can exist are the self-consistent ones. I think that is mostly stipulated in these theories for post hoc reasons. So some of them aren't consistent... so what? Do the consistency police come along and strip you of your "existence"? How? Why? We humans use inconsistent logics all the time. When confronted by inconsistencies we often just fix them up, either with some other logic or just plain ad hoc new rules. Inconsistent universes can similarly each be rescued by an infinite number of "fixups", up to and including uncountably infinite functions that simply brute force resolve the inconsistencies. This renders the term "inconsistent" meaningless in this context because rather than an inconsistent universe not being able to "exist" it instead represents some infinite class of existing universes with some fixups applied. The main problem I have with this line of argumentation is that in its zeal to explain why anything exists, it actually goes all the way to the other end of the spectrum and can't explain why anything doesn't exist. But clearly there are things that don't exist, by virtue of the fact that the subjective experience of being in a universe where literally everything exists would be one of total chaos; in any given moment, the countably-infinite possible futures where the next subjective instant is "reasonable" to you is dwarfed by the uncountably infinite possible futures that contain an embedding of "you" and your next subjective instant is not reasonable to you. (And if you're objecting to my casual assertion that your next instant is at best countably infinite, I'm already erring on the side of giving grace to the argument; I'd personally characterize them as straight-up finite.) Things exist; some things also don't exist. The mathematical universe hypothesis covers the first at the cost of failing the second. Math isn't parabolas and conic sections and tiny integers getting added together; math is uncountably infinite functions of uncountably infinite structures being mapped to other uncountably infinite structures with no pattern, out of which we carve our little niches that are useful and comprehensible and mistake them as being the rule, rather than than the vanishingly tiny exception. Something isn't just causing things to exist, it is also holding back the incomprehensible chaos of total, undifferentiated existence. (The fine tuning of the physical universe is a nearly insignificant mystery next to this. How is reality reasonable to any degree at all? Forget the question of life, how does there exist any structure that has a reasonable subjective existence rather than total, utter chaos beyond any capability we have to imagine?)

speak_plainly 3y ago

If you look carefully at Frege’s original notations you’ll see that all logical connectives are simply if-then statements with the exception of ‘not’. Logic is just formalized cause and effect, partly inspired by Hume. Cause and effect seems to reflect some deep truth about the universe.

VirusNewbie 3y ago

How can that even make sense without any axioms. You can’t say logic doesn’t work because i proved a true statement is false.

danbruc 3y ago
You mean how can I do any kind of reasoning if I think the logic I use for reasoning does work or at the very least is kind of an arbitrary choice? I have no answer for that. And that is very similar to something else that always bothered me. I think there is no free will, everything in the universe just mindlessly follows the laws of physics. But if that is the case, how can anyone do any meaningful reasoning? If you just think, write and say what the laws of physics make you think, write or say, what guarantees that your thoughts or words follow any logic? I have no good answer, at best some extremely vague idea of consistency, that the laws of physics in our universe have some logic to them or maybe better that they imply some logic that is useful to reason about them and that this implied logic gets imprinted onto composit systems in the universe. But even if that was true, you would end up with new questions, why is it true and does it have to be true? And I can think of at least one more instance of a similar problem, namely what guarantees that your perception of the the world is in any way linked to an actually existing world that you inhabit? How do you know that you are not just hallucinating the universe into existence? There the usual answer is, I think, to just assume it, otherwise any reasoning would be doomed right from the beginning as you can never know whether there is any real universe or whether you are just making it up. The lesson is probably that reasoning from the inside - from your mind about your mind, from inside the universe about the universe, with logic about logic - is really hard, in the same way that Gödel's incompleteness theorems tell us about the limits of reasoning with math about math.
- VirusNewbie 3y ago
  You're way over thinking it. You either have causality/time component, and can derive some basic axioms that get you existence or not existence (boolean) or you don't. If you have the former, we have turing completeness, and there we go. If you don't, well, sure, whose to say there isn't a universe where you can't have both presence, absence, and a time component but it's not all that interesting.