| > Brut facts. Principle of Sufficient Reason. I am getting a vocabulary bump here. I spent some time further expanding my vocabulary on related concepts on Wikipedia. Glad to hear it. I'm not an expert on these topics, so it's probably best to be skeptical on this. You may find the paper and some of the names I've mentioned (ie: Carrol) worth reading/ listening to. > Some truths are the result of co-constraint. This is a fine claim to make and it's not totally insane or unheard of. The concept of simultaneous causality, for example, is definitely something people argue. > Reality must have this form of being. This is a claim, and a fine one to make. It's still a claim though. I think it's worth reminding you that I haven't actually said anything other than that it's not really reasonable to assert things like randomness not being scientific, or that all things have a cause, etc - that most physicists probably disagree with that is notable. It's your position that those claims are true, and that's fine, but it's just notable that you're plainly asserting rather controversial claims. > (2) It cannot be determined by infinite regress, because there is no where beyond reality to regress. And obviously FWIW you can actually just say that you accept infinite regress. That'd be fine. You would have some other metaphysical commitments there, but it's a move you can make. > Contradictions are contradictions regardless of priors. You can also just reject the law of non-contradiction. Or I could. Or you have to assert it. > in terms of being (1) self-consistent, (2) consistent with hosting a region with what we know of our local physics, and (3) to avoid simply being a circular argument, demonstrate that alternatives to the explanation necessarily are contradictory. It's probably notable that all of these are just assertions. Consistency is a property that you're claiming. (2) seems reasonable. (3) I'm not sure of. And again, law of non-contradiction would have to be shown as being necessary. Neither of us is right or wrong, which is sort of my point - these are valid metaphysical theories. Your view is not unreasonable. A lot of people hold to the strong PSR, it's just notable that it's controversial. > I think it is fair to say, while some may believe a theory of everything with unexplained brut facts can be valid (some things being just what they are), few or none would be unsatisfied with a theory that demonstrated all facts were well determined, was consistent, could be shown to be compatible with our region of reality, and could not be altered without creating a contradiction. Sure. A theory with no axioms would be desirable. But also, like, we wanted that in mathematics and accepted that it was impossible too. Would we have preferred otherwise? Well yeah. But we know it's not the case. |
Yes, I am confident. But not ambiguous that my confidence is backed up with some aesthetic factors, not just squeezing out the hand waving.
> FWIW you can actually just say that you accept infinite regress.
I think my claim that everything that has a specific value, has been constrained to it, is very strong. And the inverse, that where something isn't constrained, it will appear in all its forms.
In that sense, I admit brut facts. We don't need to explain a specific, if we know its alternatives play out disjointly. Exhaustion instead of determination.
(The possibilities in that survey didn't include exhaustion! A much simpler explanation than evolutionary universes, or inverting the arrow of the anthropic principle.)
Superposition and entanglement are an exact example of mutual determination/exhaustion. Along with cancellation as a direct expression of conservation.
But my view that finite regions are potentially always characterizable with an unbounded finite region it is embedded in, as apposed to characterized by an infinity of other independent specifics, is easily my weakest conjecture.
> You can also just reject the law of non-contradiction.
I think contradiction is a category error for primitives of reality. Conservation is the right view.
I make a clear distinction between descriptions, partial models, conjectured models, etc. Contradictions can occur in our descriptions. But I don't believe reality is constrained by logical primitives. Just conservation. And with primitives whose generative/reductive properties are not constrained by logic, because there are not even "virtual" contradictions to prune.
I expect logic to be necessary for us to reason about primitives. But that logic is the wrong way to think of basis elements. Those are very different things.
> A theory with no axioms would be desirable.
I think this is necessary. I am 100% confident in that, for what that is worth to anyone else. Realty is able to exist precisely because it requires no priors, and has structure because it creates nothing, destroys nothing (conservation). Tautological anti-axioms that become axioms.
> But also, like, we wanted that in mathematics and accepted that it was impossible too.
This is not nearly as well established as is assumed. Whether we look at Russell's Paradox, or Gödel/Turings incompleteness theorems, there is a repeated issue. The proofs are about machines (or sets) that return (or are defined by) true or false. But any logical system with open (cycle) expressions admits two more possibilities, undetermined and contradictory statements. Not for some deep reason, but because notation is not reality, and we can trivially say things with notation that are undetermined or contradictory. "x in {x}, is unknown". "x in { logical x = not(x) }" is a contradiction. A universal mathematical discriminator needs to be defined as first, determining whether a statement is unknown or a contradiction. Then decide true or false for remaining expressions.
Note that the problem is implicitly collapsing unknown into true (i.e. "satisfiable") and contradiction into false ("unsatisfiable"), but then still treating those values as if they were just primitive true and false, which they no longer are.
To be concrete: If M is the mathematic machine, and we defined it reduce expressions (any kind of reducable structure, including 4-valued logic, not just Boolean truth), and it is tasked with evaluating a copy of itself operating on a self-referencing contradiction "M will say this is false", it is trivial to show M(M("M will say this is false")) = M("M will say this is false") = <contradiction>. No inconsistency, and no window to rework the statement into a problematic alternate, because we have avoided a special dependency, inconsistent treatment (t/f vs. u/c), or premature limitation around logic.
M may still have limits, but Gödel's incompleteness is not one of them.
This is another indicator to me, that a fundamental description of math (as with reality), needs to be based on sub-logical primitives. Another big clue is that Boolean logic is not reversible. Logic will be easily created from the fundamental relationship, but it creates a premature deadend to start there.
There are a number of well accepted famous theorems with this limited scope problem. They are absolutely solid proofs. But they define something more restricted than it needs to be, then knock it down. Leaving trivial possibilities unrestricted.
Cantors diagonalization proof for cardinality of R being greater than for N, is also trivially defanged. But there are better reformulations of it, and I haven't had the time to work though them yet.
I find that mathematicians, like everyone else, have trouble truly seeing what they looking at. I could go on and on.
Well thanks for pushing me, I am sure I have taken up enough of your time. But, I am now aware of more philosophical viewpoints on the big questions!