In this video (https://www.youtube.com/watch?v=TrnteM9E2tI&t=6633s) about mathematics in the Wolfram Physics Project, Stephen Wolfram says at minute 1:49:37 something that seems contradictory:

He begins by apparently saying that the human observer determines what is true in mathematics and denies that, as Hilbert said, you can have axioms of all types (you can have axioms that talk about chairs and tables just as you can have axioms about integers) and that it is not true that there is a platonic object associated with whatever arbitrary thing that we can think of.

But then, just after that, he says that this platonic object would be the ruliad, and in other writings, such as this (https://writings.stephenwolfram.com/2022/03/the-physicalization-of-metamathematics-and-its-implications-for-the-foundations-of-mathematics/) he precisely says that all formal systems that we can think of would be platonic objects that would exist.

So this seems a bit contradictory to me: He first explains, apparently, that observers like us determine what axioms are true and what axioms are not and that there are no platonic objects associated with abstract things we can think of, but then he says that all axioms are equally valid and exist in the ruliad as some kind of platonic elements...

Perhaps I did not understand something and someone can clarify this a bit?

  • For Wolfram ruliad could be very concrete if not the most concrete, not abstract at all... Dec 26, 2022 at 0:34
  • @DoubleKnot I don't understand your comment, as Wolfram has clearly said multiple times that the ruliad is an abstract thing that necessarily exists and contains all possible abstract formal systems (see: writings.stephenwolfram.com/2021/11/the-concept-of-the-ruliad, writings.stephenwolfram.com/2022/03/…)
    – vengaq
    Dec 26, 2022 at 12:51
  • Formal systems/our "math" are not as abstract as the ruliad. As an analogy, human mathematics is like physicists working with stat mech instead of "raw" atoms. What makes stat mech true? The the most fundamental physics/the ruliad, which is beyond our limits forever. The "awkward" level of stat mech/human math is not false, but is not as abstract as deeper existence. Your attribution to W, "all axioms are equally valid and exist in the ruliad as some kind of platonic elements..," seems like a contradiction to his above language, but I can't find him saying that in your links.
    – J Kusin
    Dec 26, 2022 at 18:22
  • Just like we can never track physics down the the most fundamental level, even in heat death, the ruliad/absolute abstraction, "goes on forever, in effect continually generating “irreducible surprises"”. Rather than contradiction then (which I can't support from your links), I'd offer if he did say that, he was speaking hastily. He seems to consistently say that "abstract" is forever beyond human capabilities, and our products can only be more and more abstract, never absolute. If you can find a quote for your contradiction that would support your claim, but I cant find a textual contradiction
    – J Kusin
    Dec 26, 2022 at 18:23
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    @vengaq I mean, no formal system or mathematics humans have produced is at the fundamental level. Our formal systems and math are at the "awkward level" in his speak, and that awkward level exists because of the ruliad, but does not mirror it. When I said "are not in the ruliad" they are still part of existence, but not at the fundamental level - like statistical mechanics "exists", but its objects are not fundamental and don't mirror anything at the fundamental level of physics. They do not resemble/mirror/have a 1 to 1 relation to abstract objects and thus aren't abstract objects.
    – J Kusin
    Dec 30, 2022 at 22:50


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