The Hard Problem of Gravity

yy2bggggs said:
The logical extension of those relationships either includes, or does not include, SCGC.
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If it does, then GC is false, and if it does not, then GC is true, right? I just want to make sure what we are saying here.

yy2bggggs said:
Sure, and unicorns and fairies are isomorphic in the same sense. They are isomorphic. It's perfectly true that they are. But it has absolutely nothing to do with whether or not there are unicorns, or whether or not there are fairies. You're just saying, essentially, that everything we say here involves internet protocols. Big deal.

Yes, it's no longer what you were talking about, once we consider whether or not there actually are unicorns, or whether or not there actually are fairies, or whether or not there actually does exist an SCGC. But I really don't care--it was never what you were talking about. That itself is the entire point I was bringing up.
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It isn't? This whole debate got started because westprog claimed that mathematical statements and physical statements are different.

But if any purely theoretical purely abstract mathematical statement can be reduced to a simple (albeit large) statement about physical reality -- and they all can, because of the isomorphism -- he is wrong and all mathematical statements are in fact physical statements.

yy2bggggs said:
What a navel gazer! Either this is true or that is true. Has it ever occurred to you that they are completely different kinds of things, and they are both true? And that only the "discover" thing has anything to do with what mathematics is, just like only that actual creature with the horn has to do with what a unicorn is?

This "cop out"--this thing other than the "view" you take--that is not "the other view". That is another true thing.
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Yeah I wasn't clear enough -- the first view is that there happens to be a world of mathematics out there that is independent of physical reality.

There is simply no evidence that could possibly support such a statement.
 
rocketdodger said:
If it does, then GC is false, and if it does not, then GC is true, right? I just want to make sure what we are saying here.
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Correct. GC is true iff there does not exist SCGC, almost by definition.
It isn't? This whole debate got started because westprog claimed that mathematical statements and physical statements are different.
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And you disagree, so you're trying to show that they are the same.

The problem is, you shouldn't be showing that they are the same. You should be showing that they are not different. westprog is only wrong if they are not different.

Apples and garlic, for example, are different. But all apples are food, and all garlic is food. Since they are both food, they are the same kind of thing--foods. But that doesn't show they aren't different.
But if any purely theoretical purely abstract mathematical statement can be reduced to a simple (albeit large) statement about physical reality -- and they all can, because of the isomorphism
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What isomorphism are you talking about, exactly? The only mapping I'm aware that necessitates that mathematical statements be physical somehow, is that the description of any given mathematical statement that a person gives must necessarily have a representation in their head. I can certainly see a mapping from physical statements to mathematical ones. But I have no expectations that there should be, say, an uncountably infinite number of particles, or anything in particular (because there's a concept of that in mathematics), or that I should find a Klein bottle somewhere, or that I should be able to actually find an SCGC. I'm quite sure that without exception all of these are somehow in the brain, because I'm conceiving them with one--but that is the concept, not the thing it's about. The particular salient point about SCGC is that we currently don't know if there is such a thing.
-- he is wrong and all mathematical statements are in fact physical statements.
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Right, but I don't think you've actually shown anything more than that both physical statements and mathematical statements are statements. You haven't yet shown me a Klein bottle, for example.

Furthermore, math is about abstractions, and your allegations that all mathematical statements should be physical sets my reification alarm to full alert.
Yeah I wasn't clear enough -- the first view is that there happens to be a world of mathematics out there that is independent of physical reality.
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You mean in the sense that abstract statements are not concrete?
There is simply no evidence that could possibly support such a statement.
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Reification.
 
yy2bggggs said:
What isomorphism are you talking about, exactly? The only mapping I'm aware that necessitates that mathematical statements be physical somehow, is that the description of any given mathematical statement that a person gives must necessarily have a representation in their head.
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Yes, that one.

Although I don't know why you say "description of any given mathematical statement" instead of just "any given mathematical statement."

yy2bggggs said:
Right, but I don't think you've actually shown anything more than that both physical statements and mathematical statements are statements. You haven't yet shown me a Klein bottle, for example.
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But, because of the above, the mathematical definition of a klein bottle must be ismorphic to some behavior of a set of physical particles.

And that is all I am arguing. If there is a computational theory, then there is necessarily a physical system that behaves in a way isomorphic to that theory.
 
rocketdodger said:
Yes, that one.

Although I don't know why you say "description of any given mathematical statement" instead of just "any given mathematical statement."
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It's because I'm an idiot. I should have said descriptive aspect.

But there's the description, and there's the thing being described. The latter is part of what is meant by statement. Here's a quick argument summarizing why this is true...

A statement is, formally, a sentence that has, associated with it, a definite truth value. If your sentence does not have a definite truth value (that is, it is either true, or it is false), then you do not have a statement.

The thing that gives statements truth values is the thing meant by the statement, and that involves some sort of claim about something. That something is the thing being described.

Now, what you have with this "isomorphism" is merely the description per se, along with just enough meaning to refer to something. All of that part of "there is an SCGC" is in my brain when I talk about the statement "there is an SCGC". But something is not in my brain about this. I know what I'm talking about, and I know what has to be the case for that statement to be true, or to be false, but I don't know if it is true, or if it is false. What's missing is that I don't have, in my brain, the logical chain that establishes whether or not there actually is an SCGC--the sequence of steps that goes from what I know to what I would like to know. This thing I don't have--the logical extension of relationships (you can call a particular connected chain a proof)--is the subject of mathematics.

This subject of mathematics is what makes the statement that there exists an SCGC have a definite truth value. It's not in my brain.

Where is it?
And that is all I am arguing. If there is a computational theory, then there is necessarily a physical system that behaves in a way isomorphic to that theory.
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Okay, but there are things in math that are not even in my brain. But they are part of mathematical statements that I can make, right now, today. They are, specifically, the part that gives the sentence its definite truth value--the part that qualifies the sentence for the next stage of precision of labeling... as a "statement".

It is not outside the realm of possibility for every single one of these to actually be manifest somehow in physical reality, by a mapping. But such is not necessarily true.

Going the other way--from all physical statements to mathematical statements--is much less problematic.
 
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This subject of mathematics is what makes the statement that there exists an SCGC have a definite truth value.
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The Incompleteness of mathematics means that it may not have a definite truth value.

One has to understand what "definite" means mathematically to see why.
 
Third Eye Open said:
Are you aware of being aware that you are aware of being aware?

Are you aware of that?

How far should I regress before you realize that this is not even a question?
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Well, your question my brain cannot make sense of. But "are you aware of being aware" I can make sense of. I am not aware of being aware, but I can make sense of the question.

Nick
 
Nick227 said:
That's idealism, as I read it.

Nick
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It may be - I don't claim to be philosophically trained - but I don't see how one can claim to believe in a material universe and not accept that it actually exists. If one accepts that it really exists, one has to accept that objective truth exists.
 
westprog said:
It may be - I don't claim to be philosophically trained - but I don't see how one can claim to believe in a material universe and not accept that it actually exists. If one accepts that it really exists, one has to accept that objective truth exists.
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Well, what we do know pretty much conclusively, I figure, is that the brain constructs our world for us according to outside stimuli and its programming. If an objective or mathematical truth is to exist outside of the brain it is, I imagine, going to have to exist either non-physically, or in some extension to physicality we don't know about, or somehow be implicate in the physical universe. I don't know much about these kinds of things but that's how it seems to me.

Nick
 
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AkuManiMani said:
I'm gunna venture a guess and say that he means that a mathematical description of a thing is not the thing itself, and that things IAOT may have properties and aspects that aren't part of a particular description.
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We're talking about describing shapes of objects. That the description is or is not the object itself is irrelevant.
 
Nick227 said:
westprog said:
No, it's exactly the opposite. I believe reality rests on objective truth. I don't think there can be any reality without objective truth.
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That's idealism, as I read it.

Nick
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I think there are two ways to read it, Nick.

If westprog means that "objective truth" has a separate existence, that truth (as in 'true' ideas) in some sense precedes and sustains reality, it is idealism (see Plato).

If westprog means that "objective truth" is in objects, that reality has definite, 'true', mind-independent properties and ideas only categorize those properties, it is materialism (see Aristotle).
 
blobru said:
I think there are two ways to read it, Nick.

If westprog means that "objective truth" has a separate existence, that truth (as in 'true' ideas) in some sense precedes and sustains reality, it is idealism (see Plato).

If westprog means that "objective truth" is in objects, that reality has definite, 'true', mind-independent properties and ideas only categorize those properties, it is materialism (see Aristotle).
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Yes. Fair enough.

Nick
 
cyborg said:
The Incompleteness of mathematics means that it may not have a definite truth value.
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No it doesn't.

Which of the incompleteness theorems do you think does say that the GC may not have a definite truth value?

ETA: Note that if the GC is false, there's a proof that it's false. It's only if GC is true that we run into a possible problem for proveability. The only way possible for us to not be able to prove that the GC is true or false would be a scenario in which the GC is true.
 
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yy2bggggs said:
It is not outside the realm of possibility for every single one of these to actually be manifest somehow in physical reality, by a mapping. But such is not necessarily true.
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It isn't?

Would you agree that all mathematical statements knowable to a physical entity are manifest in physical reality, by a mapping?

Because really, that is all that I care to show -- us being physical entities and all.
 
yy2bggggs, would you please weigh in on another issue?

Westprog contends that computation theory is not a physical theory.

But it is clear that, for example, there are many ways to build a physical turing machine. And since a turing machine is supposed to be able to compute anything that can be computed, by extension it seems to me that all of computation theory is then physical in this respect.

What is your opinion?
 
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