Comment: 1: “The assumption, alone, that the physical universe must be consistent is insufficient to show that there is a separate MU.
The assumption that the physical universe must be consistent, plus the assumption of MR, plus the assumption that consistency doesn't matter for MU's is sufficient to show that there is a separate MU.”
Response 1: Thanks for clarifying what you mean here. I hear you, but I have been clear in the manuscript that I take the assumption of MR. And then, for assumption of the physical universe needing to be consistent isn’t really assumed, but it’s discussed, and I bring to bear a practicality argument - that it’s actually a semantic... (read 1342 more words →)
Comment: "That is necessary, but insufficient , at best. If mathematical entities don't have real existence, as fictionalists cliaim, then there is also no real inconsistency."
Response: Can you say that more precisely, what is necessary but insufficient, for what?
What I stated was, from this work, based on the assumptions as laid out in the manuscript, I can verbally summarise the result by the statement that ‘abstract objects can be demonstrated to be in a distinct universe from ours, as the set of both of them together cannot be defined in a consistent way logically.’
Do you mean that these assumptions, together with the steps, don't show that these abstract objects to be in... (read more)
Responses:
Context: When you state ‘If MR is true, then the mathematical universe is obviously bigger than the physical universe,just because most maths isn’t physical’ doesn’t follow, in my view. Why would MR being true mean that the mathematical universe is necessarily bigger than the physical universe?
Comment 1: "Because most maths isn't physically applicable, as I stated, and you agreed."
Response 1: I do agree that most maths isn't physically applicable, but that doesn't mean that for MR, the MU is obviously bigger (to clarify, for MU here, do you mean physical+maths, I am assuming not). For example, I might have many physical objects in my universe, and not all being mapped to by... (read 715 more words →)
Responses:
Context: I haven’t thought of how to construct an Ansatz in a framework built from an arbitrary metaphysic
Comment 1: "I have. There's almost nothing to it, if Ansatz means nothing more than some guessed-at mathematical descriptions turning out to be right.. and that is the . description of Ansaztz you give here:- (etc) ..then, so long as some things are mathematically describable, some mathematical descriptions will describe them, even if guessed randomly"
Response 1: Hang on, what I mean is, constructing an Ansatz completely from scratch, without any assumed structure doesn't sound like something there would be 'nothing to it' - I would expect that if you have one, you'd need to be... (read 1175 more words →)
Responses to questions, also thank you for your patience - there seems to be a misunderstanding under the surface that we are both approaching, perhaps in terms of terminology that is causing some of the disagreement:
Comment 1: "The universe meaning the physical universe? But that's an argument against MR."
Response 1: Yes, the universe meaning the physical universe, and I am taking Mathematical Realism to mean that the mathematical statements are real (they exist) but not in the physical universe. If one defined Mathematical Realism as compelling the inclusion of mathematical objects into the physical universe, then I don't hold that. This position is about demonstrating how the putting together of mathematical objects... (read 1357 more words →)
Cont'd (2)
8. "You seem to be blurring "whether mathematical realism is true" and "what are they implications of MR". If MR is true , then the mathematical universe is obviously bigger than the physical universe,just because most maths isn't physical."
I wasn't able to perceive the blur between these two items in my quote: "!!!! That’s not at all obvious, in fact, I’d never heard it before until I began looking into this. If it’s obvious now to many people, that’s great! Perhaps the cultural mindset is different compared to my younger days. Certainly the most common view I run into among academics ‘spoken’ is that maths is included in the physical universe... (read 1057 more words →)
(Cont’d) apologies, this is taking some time and I will do this in parts as I will run out of time here and there. Bear with me.
Did you read the paper? It’s not the existence of a mathematical universe that is used to show it, but, given the framework, I use a cardinality argument - so there’s more work and proofs and theorems in the paper - I just summarise the cliff notes in this post for the lay audience. What I... (read 478 more words →)
... (read 357 more words →)For a mathematical universe, it only isn’t obviously contradictory if it is constrained in a way to avoid the Cantor problem. But what I mean is, people are clearly accessing many mathematical truths beyond that that don’t specifically exhibit in the universe, (aside: unless you count the thought process itself as the exhibition, but then as its a question of will and enterprise, it could be arbitrarily expanded with effort which still puts the bound
Yes - fair enough — to clarify that, in that quoted sentence, when I said ‘non-mathematical entities’ I actually meant physical entities, rather than eg non-truths/falsehoods within mathematics (eg contradictory theorems and so forth).
That is a good pickup, and a good fix as I try to describe it in english language terms.
Your sentence is clearer.
Introduction
One of the topics that seems to come up from time to time on Lesswrong is the supernatural vs a naturalistic explanation for the universe.
I felt that I could make a contribution to this discussion as a theoretical physicist (now moved into a different area), which actually came about from a discussion I had with a particular esteemed professor from the University of Melbourne, in 2012. Prior to this moment, I had slowly (perhaps nascently) been developing a metaphysical philosophy that was a little closer to Functionalism than Physicalism (these two metaphysics are compatible with one another), but since Functionalism was shown by Prof. Searle to be 'incomplete' in a certain sense... (read 3294 more words →)
Hi Tag, I didn’t hear back from you so I suppose I can assume that my explanations were satisfactory and I had now resolved the qualms as previously raised. Thank you for your attention.