> I don't really know yet what assumptions to build on that you would share.
Then just start with something, and if I don't agree with your assumptions then we can decide where to go from there. It doesn't have to be perfectly formal, but at least needs to flow via enumerated propositions. I fail to see how avoiding to produce a formal argument for your position isn't an attempt at equivocation. Why else attempt to only argue informally where the informality is more likely to generate greater ambiguity?
> Yes. Example: ...
Is it possible that a testable claim could be true and imply another claim that is not testable?
===
> ... I mean, unless you really do happen to have the evidence that everyone has been waiting for ...
Flat earthers may say the same to anyone whom tells them that there is great evidence that the earth is an oblate spheroid. Simply thinking that evidence isn't sufficient doesn't mean that it isn't.
> I don't understand what the distinction is that you are making here.
Science is a method. Doing science is to use the scientific method. The scientific method involves testing claims. Using the scientific method on non-testable claims is contradictory. The scientific method and the claims it has proven can co-exist with claims that can't be tested so long as those claims don't contradict the scientific claims. While those claims that can't be tested can co-exist with the scientific method, the incompatibility is in attempting to do science with those claims.
===
> Well, let's see ...
Thanks :-)
===
> And mind you that not much reliability is necessary in order to bootstrap this, because you can largely test that, too.
I get what bootstrapping means in compiler terms, but regarding methods of discerning truth, the notion of bootstrapping would seem to fly in the face of Gödel.
> But when you think about it, you'll notice that that assumption isn't actually necessary ... And as soon as there is even a little bit of structure to reality that you could figure out, building on your senses is going to outperform ignoring your senses.
Still sounds like your relying on the assumption that our senses are reliable... Like, you wouldn't know that using your senses out performs ignoring your senses unless you were already relying on your senses to determine that.
===
> More precisely, because a statement about math is not a statement about reality, other than that math is part of (human) reality.
When you apply the name "John" to one person and the name "Jack" to another, there are physical criterion to distinguish between John and Jack allowing us to verify via testing that a claim only about John is not a claim about Jack. Unless there are physical criterion that allows us to distinguish between math and reality, you've made a false analogy.
> The answer is simply: They didn't.
The conclusion I'm looking for is "They couldn't" and in particular "They couldn't intelligibly mean 'claims only about math are claims about reality'" and I want to know why. Only saying "they didn't" leaves the door open for someone else who could.
===
> Yes, those axioms, evaluations and derivations (well, particular aspects of them). Just the same way that 'Game of Thrones' has a referent, given the series, and characters of that series have a referent, given the series.
>>>>> The point is: A bunch of axioms and what results from them.
Under this axiomatic context: Do distances, spaces, cardinalities, and sets symbolically or conceptually exist absent of any physical representation?
===
> No, you haven't. At best, you have shown that holding that position is not justified (arguably, you haven't done that either, but it doesn't really matter for this). ... Well, see above. You have to show that it is impossible for something to be unexplainable, not just that we don't know whether something is unexplainable.
Explain how I haven't. You're just saying I haven't. Where is the misstep in my argument (formalized below)?
==========
1 ) If X has no explanation, then X can't be explained.
2 ) If X can't be explained, then X is unintelligible.
3 ) If X is unintelligible and X is a part of reality, then the claim "reality as a whole is unintelligible" can be truthfully asserted.
4 ) If the claim "reality as a whole is unintelligible" can be truthfully asserted, then all claims about reality as a whole are unintelligible.
5 ) If all claims about reality as a whole are unintelligible, then the claim "reality as a whole is unintelligible" is unintelligible.
6 ) If the claim "reality as a whole is unintelligible" is unintelligible, then the claim "reality as a whole is unintelligible" cannot be truthfully asserted.
----------
7 ) X is a part of reality and X has no explanation (ASSUME for RAA)
8 ) X is a part of reality (Conjunction Elimination from 7)
9 ) X has no explanation (Conjunction Elimination from 7)
10) X can't be explained (Conditional Elimination from 1, 9)
11) X is unintelligible (Conditional Elimination from 2, 10)
12) X is unintelligible and X is a part of reality (Conjunction Introduction 11, 8)
13) The claim "reality as a whole is unintelligible" can be truthfully asserted (Conditional Elimination from 3, 12)
14) All claims about reality as a whole are unintelligible (Conditional Elimination from 4, 13)
15) The claim "reality as a whole is unintelligible" is unintelligible (Conditional Elimination from 5, 14)
16) The claim "reality as a whole is unintelligible" cannot be truthfully asserted (Conditional Elimination from 6, 15)
17) The claim "reality as a whole is unintelligible" can be truthfully asserted and The claim "reality as a whole is unintelligible" cannot be truthfully asserted (Conjunction Introduction 13, 16)
18) Therefore: It is not the case that X is a part of reality and X has no explanation (Reductio Ad Absurdum from 7 to a contradiction on 17)
---------
Rephrasing of the Conclusion: Either X is not a part of reality or X has an explanation (De Morgan)
Rephrase of the Rephrasing: If X is a part of reality then X has an explanation (Implication)
==========