by Nevermark | 2026-03-05 19:29:25+00:00
> It's your position that those claims are true

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.

Superposition and entanglement are an exact example of that.

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, if the principles of reality are finitely describable.

> 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.

This is another indicator to me, that in a fundamental description of math (as with reality), needs to be based on sub-logical primitives. Another big clue is that logic as we formulate it, isn't 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 unaddressed.

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, has trouble really 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!