Hacker News Reader

Comment by codebolt | Hacker News Reader

One thing this hypothesis has going for it, from a purely armchair metaphysics perspective, is that it gives some kind of answer to the question 'why does anything exist'. 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.

It also explains why all physical laws are mathematical and all physical properties are quantifiable ('mathematics is the language of the universe' as Galileo said).

I still don't believe in it for several reasons. But I believe that it is the only logical conclusion of a purely materialist worldview.

View on HN

> 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.

Indeed; I managed to independently arrive at this part of the idea, I think even before the Mathematical Universe Hypothesis was published.

It's even more cognitively unstable than Boltzmann brains, but maths is also the only thing I can think of that doesn't need to be caused in order to exist.

https://kitsunesoftware.wordpress.com/2018/08/26/mathematica...

> maths is also the only thing I can think of that doesn't need to be caused in order to exist

I never understood this line of argument. Plainly, there is something at the beginning of the universe (or an eternal existence in some other way) which doesn't need to be caused in order to exist. So then, why do we take this notion that everything needs to have a cause to exist as some kind of rule, when it is self-evidently broken?

The argument is "only X has property Y, therefore this other thing of unknown nature with property Y must also be an X".

Well, except for the bit where X is cognitively unstable, and also for the other bit where I don't seriously believe the fact that I personally can't imagine alternatives means they don't exist.

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.

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.

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

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?

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?)

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.

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.

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.

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.

You either have causality/time component [...]

I don't understand what you mean.

  1. causality and time component
  2. causality or time component
  3. causality and time component are two words for the same thing
  4. causality and time component are deeply connected, maybe depend on each other or imply each other
  5. something else

And what does time component mean, I would guess component in the sense of a vector component, i.e. a time dimension, right? Assuming that is true, having a time dimension does probably not imply that there is causality, i.e. all events could be independent. Does having causality imply having a time dimension as causality depends on time. I would guess so, at least in the common understanding of the term.

If you get distracted by a message on your phone and hit a tree with your car, the person sending you the message caused you to be distracted which caused you to hit the tree. But did not also your driving teacher cause this because he did not get you to understand to not use your phone while driving well enough? And your parents because without them you would not exist and be driving a car? And the phone designers and manufactures because without them there would be no phone to distract you. And no car without the car manufacturer. And no tree without the person planting it exactly where you hit it?

Causality is at the very least a really tricky concept, we usually just pick something pretty arbitrarily and declare it the cause. And what about the relationships between time, space, change, events, correlation, cause, and effect - what comes first, what depends on what? Does time enable change or does change define time? Does causality cause change or does change define causality? Does causality even exist fundamentally, after all cause and effect are no where to be found in the fundamental laws of physics? Is it just a human abstraction to talk about the world? What does the theory of relativity tell us as the ordering of events is observer dependent?

[...] and can derive some basic axioms that get you existence or not existence (boolean) or you don't.

Derive axioms from what, causality and time? And does deriving axioms even make sense, are they not the things that you just postulate as true without further justification? And who said that existence - or anything for that matter - has to be binary? From the law of excluded middle which is an axiom and not even universally accepted in our universe? And what does existence even mean? Is there only one kind of existence or are there several? Does wetness exist in the same way as the keyboard I am just typing on?

If you have the former, we have turing completeness, and there we go.

What is the former and how on earth did we get from whatever the former is to Turing completeness and why does it matter?

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.

I don't think it really matters whether it interesting or not, but this sounds a bit like you are just dismissing my main point in a single sentence - if there could be universe where our logic does not apply or is even wrong, how can we call our logic and the math on top of it true and assign some kind of Platonic existence or whatnot to it, if it is at best true relative to our universe?

Maybe I am overthinking it but I would counter that you are underthinking it.

From [0]:

"Something like this view is defended by philosophers such as James Ladyman and Don Ross in their book 'Every Thing Must Go: Metaphysics Naturalized', and by the physicist Max Tegmark. I have a lot to say about Ladyman and Ross’s project in the forthcoming 'Aristotle’s Revenge'[1], all of it critical. Suffice it for present purposes to note that this sort of view essentially identifies the physical world with a kind of Platonic abstract object. Ladyman and Ross try to deal with this problem by denying that there is a clear distinction between abstract and concrete. As I argue in the book, this position is incoherent and the arguments for it are entirely question-begging. Moreover, even apart from that it doesn’t really solve the problem at all, because (as the Aristotelian would argue) Platonism itself essentially blurs the distinction between the abstract and the concrete. For a Platonic Form is characterized both as a universal (and hence as abstract) and as a substance (and hence as concrete). To blur the abstract/concrete distinction is to fall deeper into Platonism, rather than to avoid it."

[0] https://edwardfeser.blogspot.com/2019/01/materialism-subvert...

[1] https://a.co/d/6JNDiCH

Reply on news.ycombinator.com