Both KK-theory and cobordism theory are used in theoretical physics 
Actually, I don’t think there are any contexts in which I assign labels like “pretty much true” and “eh, sort of, not really.” Having said that, I guess I have to take it right back and say I will use those phrases as responses to claims sometimes. But I’ll generally have an account as to why the claim is strictly false, though I conjecture on conversational or practical (or whatever) grounds that there’s another claim “in the area” that’s strictly true.
I hope I’m not “fooling myself” about truth values here. I hope I’ve just got a different theory about them than you, even if it’s incorrect.
I don’t think I’ve said anything that implies otherwise, but the other guy in the conversation usually has a better idea about that. Have I said anything that implies otherwise?
I’m also not sure I agree with the claim. I just don’t think it’s truth or falsity has much to do with what I’ve been discussing.
Your points below about circles and about bivalence are well-taken. I guess I am surprised that the concept of “circle” has universal usefulness–after all, the concept is a tool that was forged in local, contingent conditions. But as I said about LNC and Commutativity, I can explain this to my satisfaction on the supposition that the concept “circle” is locally useful because its local usefulness is simply a consequence of its universal usefulness. But that just shifts the surprise. I’m no longer surprised that a locally produced tool is useful for its originally designed purpose in conditions wildly different than those it was designed in, but now I’m surprised that the conditions for its usefulness are universal. Why should those particular conditions have been universal?
Ultimately, and this is silly but, I’m just expressing amazement at the fact that the universe is actually amenable to induction. Most philosophical types don’t seem to share my amazement–but usually not because they have an account that explains it, but instead because they have more important things to think about and would rather not waste time. That’s fair enough. Your passage about the “universal applicability” of bivalence and everything that follows from a bivalent labelling system may offer an explanation that diffuses my amazement. Like you, I’m not sure if it meshes with my “measuring instrument” account or not.
All reasoning begins with induction. That’s how premises are formed.
ETA
Not to step on Indistinguishable’s toes. God knows that I do not qualify as gum on the bottom of his shoe. I advise that you pay careful attention to whatever he says whenever he says it. He may not always be right; but if you’re going to figure out what he’s wrong about, you’re going to have to dig like hell.
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I have been waiting for a while to point at the emporer’s schlong on this point: I see no reason to suppose that mathematics is “out there” or that it’s meaningful to describe the Universe as mathematical.
The standard argument seems to be: mathematics works. But I don’t think this ends the debate.
I mean, English “works”. We can invent words like “mountain” and define them to mean, say, “big hill”.
Then, using our new word, we can do abstraction and discuss the world in terms of things like “mountain ranges”. And what do you know? It works – any statement about mountains will also be true about big hills. Is this the Universe honouring the english language?
I don’t see how what mathematicians do is any different, other than being more complex. I’m not saying mathematics is not useful, just that it’s usefulness doesn’t demonstrate anything about nature, other than possibly that the universe is self-consistent.
Well, that last thing right there would be quite something already, in my opinion.
But, going back on your other points, isn’t it rather the case that, while English can be used to adequately describe the world, mathematics, apparently, can be used to model it? At least I cannot conceive of a way, using only the rules of English grammar and its vocabulary, to predict the behaviour of a system. You can make a logical deduction using English, but the rules you’re using then are logical ones, which are just as mysterious in their applicability to the world (and perhaps, one could make an argument that this is in some way the same as what one does in mathematical modelling – just that in that case the logical rules are expressed in the language of mathematics. But, frankly, I’m a bit hazy on whether one should consider logic to be in some way fundamental to mathematics, a branch of it, or if maybe the two aren’t really distinct at all, and mathematics is just an application of logic).
And it works.
Well yeah, Indistinguishable knows how highly I regard his posts.
And I Frylock’s. [Is there supposed to be a comma in writing that construction? Nah, I think I’m fine.]
I probably won’t be able to respond to anything substantive today, but looking back over wording, I do want to note, to stave off possible misunderstanding, that when I used (perhaps unfortunate) phrases like “if you think …, you’re probably fooling yourself” above, I wasn’t targeting these at anyone in particular, nor intending to make an accusation of shame-worthy willful delusion or any such thing. It was just a roundabout way of saying “I think … is a common but mistaken position”. Anyway, more later.
In response to the OP, as you study more and more complex systems, like the universe, you need higher forms of math to fully describe all the phenomena… you use multiple dimensions: this has a problem, I believe.
As you go to higher dimensions, and use imaginary numbers like i, the square root of -1, certain basic laws like commutative and assosiative identities no longer hold.
Paraphrasing from memory:
You could model the Solar System with Newton, only a two-body system with Einstein, have trouble with a single particle’s momentum and position with Quantum Mechanics, and cannot adequately use M-Theory to fully describe a Vacuum!
Well, it works for the purpose of formulating premises. But it does not work … um, generally. (That was a funny joke for those in the know.) It fails as often as it works. A person might form a premise that, because he has observed that almost every man in the room is bald, he is at a bald man’s convention. At least until he notices the sign that says he is at a convention for people undergoing chemotherapy.
He won’t like my saying this, but I simply must. I wouldn’t be surprised at all to discover that he is a member of Giga. In terms of sheer contribution, he is the Dope’s greatest asset, in my opinion.
Sorry to disappoint, but I barely know what Giga is (though I can guess from the name). Anyway, I’m flattered you enjoy my contributions so much, but I think you’re overdoing it with the praise.
I’ll attempt to tone it down in the future.
Well, now that the – not undeserved! – rounds of praise for Indistinguishable are apparently through, perhaps we can see if there’s some debate left in this topic.
For instance, having thought about it a little, I think I can’t really stand behind this statement:
Or rather, the implication that there’s a difference between describing and modelling. Specifically, I’m not sure that we actually learn something genuinely new about a system when we predict its behaviour using a mathematical model, that we get something out of it that we didn’t put in. Certainly, the rules of the evolution of the system are part of the model, and thus implicit when we say ‘model X applies to system Y’, which in itself is merely a descriptive statement, analogous to ‘the car is blue’.
That doesn’t quite dispel my wonder that reality is ‘modellable’ at all, though; I see no reason why it couldn’t be as random and incoherent as a dream, or hallucinations brought about by psychoactive substances, which often enough involve concepts that are not even expressible, or at least appear to do so. Yet, we seem to live in a universe nice and tidy enough to allow comparatively simple models to both exist and apply, which does strike me as being all sorts of amazing.