@brimstoneSalad
brimstoneSalad wrote: ↑Sat May 12, 2018 2:41 pm
Sure, but now we just know more about which metaphysics are invalid. That does nothing to classical logic, which isn't committed to any invalid metaphysics.
I would be very careful with such statements. In the case of QM it's not that determinism is invalid, but the most popular interpretation (which is metaphysical anyway) invalidates it. What physicist really do here is they pick more elegant interpretation.
The classical logic is not committed to any metaphysics, it's just a formal system. It's interpretation when we try to model statements about the reality in natural language is.
brimstoneSalad wrote: ↑Sat May 12, 2018 2:41 pm
What? No. It was the moment I introduced metaphysical premises to deal with the metaphysical implications in the statement.
Yes, you said "the claim "Tomorrow will be a sea battle" is also the claim that there is a single universe in (...)", at least that's what I'm referring to. To make sense of the statement about the sea battle you switch to modal logic.
brimstoneSalad wrote: ↑Sat May 12, 2018 2:41 pm
Modal logic can be useful since it's not making any specific metaphysical commitments, but failing to make those metaphysical commitments means it doesn't necessarily map to reality (even if it may represent the ambiguity of natural language better, that doesn't mean anything).
If you introduce those necessary premises, however, modal logic can be circumvented and we know (as long as those premises are true) that it's going to map well to reality.
By introducing those premises (universes and such) you already model statements in the natural language on the reality by modal logic. Explicitly. You think you are circumventing it, but you don't.
brimstoneSalad wrote: ↑Sat May 12, 2018 2:41 pm
You can add on more axioms if you want to, in order to deal with these things, or you can handle it by making some metaphysical commitments.
I fail to see how these two differ significantly, if they result in essentailly the same thing.
brimstoneSalad wrote: ↑Sat May 12, 2018 2:41 pm
My point is only that your claim that classical logic is inherently inadequate isn't true.
It's not my claim.
brimstoneSalad wrote: ↑Sat May 12, 2018 2:41 pm
Or they're just naturally incoherent, and you have to bootstrap on some extra ad hoc axioms which you can't substantiate without making the very metaphysical commitments that if used in classical logic can make those statements coherent.
Not seeing the benefit here.
What do you mean by naturally incoherent? In natural language as long as a statement is gramatically correct (i.e. it's a well formed formula), it's OK. It's interpretation in a certain logic may be incoherent, and then statement on the reality modelled by that logic may have no sense.
Ad the second part. I just notice, that for future contingents to work in the classical logic one has to accept logical determinism. You bring all these new assumptions, because you have it backwards - you assume indeterminism (suggested for example by the common interpretation of QM, or for no apparent reason) then break down the statement with respect to your metaphysical assumptions, and declare it's incoherent. And you do this
de facto via modal logic (explicitly using possible universes), although you don't want to admit it for some reason. Or I don't undestand something.
brimstoneSalad wrote: ↑Sat May 12, 2018 2:41 pm
Modal logic was even developed after the inception of MWI, so it was technically never needed to make sense of QM... although of course I understand that information probably moves slowly from cutting edge theoretical physics to philosophy (MWI is only just gaining significant ground among physicists).
Not really, modal logic dates to 30' of the last century and MWI was introduced in 50' I believe (quick search through Internets, don't blame me

).
brimstoneSalad wrote: ↑Sat May 12, 2018 2:41 pm
And what substantiates the extra axioms you must assume to legitimize it?
Hmm...
The same substantiation applied as a premise in classical logic can carry the same load. Occam's razor would prefer classical logic since it CAN do the same thing if you just include the relevant metaphysical premises. You need fewer axioms.
Again, I fail to see they differ. Why do you think making metaphysical premises trumps introducing different model of underlying logic? Especially if you can transfer one into another, while you metaphysical premises reformulate the original statement? Why would Occam's razor prefer mataphysical assumptions over axioms of logic?
brimstoneSalad wrote: ↑Sat May 12, 2018 2:41 pm
Now if you just want something cleaner to work with that's fine, but you can't claim it's superior. That's like using Newtonian physics to solve your problem within a certain margin of error; that's perfectly acceptable, but you're missing something.
I think it's the other way around. Modal logic is like the Copernican model, and the classical logic is like the model of Ptolemeus - you can patch the holes with additional metaphysical premises (epicycles), or come up with different model (with circular orbits).
What am I missing?
@Cirion Spellbinder
Starting from scratch, I would advice going through some basic course of the set theory (there is a bible "Set Theory" by Thomas Jech, though it's a dense read) mathematical logic ("Introduction to mathematical logic" by Enderton comes to mind) to get familiar with concepts. Some background in algebra and topology woudln't hurt, since some notions are very similar and it's easier to understand with wider view. Then feel free to choose any introduction to the modal logic. There is a free book by Goldblatt "Logic of time and computation" for example.
Cirion Spellbinder wrote: ↑Sat May 12, 2018 3:38 pm
Can it explain an infinite number of steps using finite words, like the golden ratio or rational repeating decimals?
We have induction for this. For "golden ratio" you define Fibonacci sequence of F(n) and take the limit of F(n+1)/F(n).
Cirion Spellbinder wrote: ↑Sat May 12, 2018 3:38 pm
Agreed, but to have a meaningful discussion about reality do you think it would be worthwhile to arbitrarily select those premises and definitions or only give half the effort into selecting them carefully?
I don't know. Almost every back and forth in (honest) discussions boils down to different assumptions tacitly made by each party, so maybe we should be very careful.
Cirion Spellbinder wrote: ↑Sat May 12, 2018 3:38 pm
Coherence, mostly. Basically that what we discuss will always be understandable by having no contradictions and if we had the full picture, would allow for all true statements to be deduced.
The problem is usually with the full picture though, so we have to speculate.
Cirion Spellbinder wrote: ↑Sat May 12, 2018 3:38 pm
Experiments rely on induction as well, just meaning that induction in a controlled environment will probably be stronger than in an uncontrolled one. I'm not sure how that is vague outside of induction itself.
Vague in the sense it seems paradoxical relying on induction, but defending paradigms of the theory at the same time. There are no clear criterions when the theory really collapses, or just needs to be refined. Sometimes theories are accepted beside the fact that there are experimental disproofs of the theory (it was the case for Copernican theory).