> What indicates to you that your definition of 'definition' isn't an arbitrary assignment of semantics to symbols, with semantics that don't in any way connect to reality?

Nothing does, because that is exactly what it is?

But mind you that that does not mean that whether there is a consensus on this definition is not a question of reality. Just because definitions are arbitrary, doesn't mean that you can't get together with other people and agree on a common definition, to make it useful for communication, nor that you can't empirically determine whether such an agreement exists.

> To rephrase, are you saying "a claim depends on something that is not just a matter of definition when evaluated using only definitions and there are remaining unresolved references"?

Well, yeah?

> What is your definition of "true"?

Either consistent with reality or derived from axioms.

> If "To be in accordance with reality implies being true", then I can replace "in accordance with reality" with "true" in a sentence.

If "To be a rat implies being a mammal", then I can replace "a rat" with "a mammal" in a sentence.

"'To be a mammal is being a rat' is not something I would agree with" then becomes "'To be a rat is being a rat' is not something I would agree with".

So, all mammals are rats then?

(In other words: No, you can't?)

> When you say "we also use the word 'true' to refer to statements derived from formal systems", would I be correct in saying that something is 'true' under a formal system, when it is consistent with that system?

I guess it depends on what exactly you mean by "consistent". A statement where neither that statement nor its negation can be derived/proven from a given formal system arguably can be considered consistent with that formal system (i.e., not inconsistent), in which case that implication isn't true.

> In other words yet again (regarding my above statement indicating that we may need a word or adjective to separate how we speak of truth): is the statement "It is true that '1 + 9 = 10' is consistent with the Peano axioms" 'formally true' or 'really true'?

That is 'formally true', I guess, though the statement is potentially ambiguous, because: Ultimately, behind every abstraction of a formal system that we have encountered so far, there is some physical evaluator or group of evaluators, and whether some proof is accepted as correct or not is ultimately decided by those evaluators/by a consensus of those evaluators.

So, in that sense, every 'formal truth' is a 'real truth' about evaluators in the world, and whether they agree on the evaluation result, in much the same way that every (arbitrary) definition is a 'real truth' about definers in the world, and whether they agree on a definition.

> Another question that I think is pertinent to our conversation regarding '1 + 9 = 10': What is a number?

How about 'a more abstract word'? (Plus, I guess, it needs to be usable for measuring and/or counting?)

> If math didn't exist absent a physical/material medium, then could you observe it? If so, then wouldn't all math be a reality, if not, then why consider it not able to exist absent a physical medium? Perhaps this is another case of confusing abstraction and the underlying representation, in which case, what is abstraction and how can it be represented in different ways but also be dependent on its representation?

That seems like another case of just that confusion, yeah.

Consider a hallucinating human. A hallucinating human has ideas that aren't real, right? But yet those ideas are real. That is to say: A hallucinating human is really hallucinating, hallucination is a somewhat physically observable phenomenon. But what they are thinking is not in any way a sensible model of reality, hence not real.

'Real' is used with two different meanings here, and conflating the two is fallacious equivocation. And in the same way, mathematicians can be observed doing math. But that doesn't mean that the math that they are doing is in any way a model of reality. The existence of a thought and the content of that thought are two distinct things.

Also, it is not dependent on its representation, it is dependent on a representation. You can not have a movie without representation. That doesn't mean that a movie must be a DVD. The movie is still the same movie when it is photons coming out of a projector. But it is not a(n existing) movie anymore when you destroy all representations of it.

> This seems to fly in the face of you stating "[...]"

In which way?

> Are you, summed together with the context of other things you've stated, saying: definitions and rules are non-physical, but there is no reason to think that there exists anything besides the representations of things, and all representations are physical?

No, I don't think so. For one, there is reason to think that things that are not (just) representations do exist, like, say, a rock (unless you count everything as a representation of itself, then I guess that's true by definition, but there is still a distinction between self-representation and "other-representation"). And also, I am not saying that all representations are physical, just that no non-physical representation has ever been demonstrated, and thus there is no reason to believe that that's a thing (yet).

> I analogized "1 < 2" being true or false regardless of its symbolic or conceptual representation

That simply seems to be a category error, which is the reason why I can't see a referent. '1 < 2' is an expression that can be evaluated using some formal system. Like, there are rules for transforming '1 < 2' into 'true'. You seem to be assuming that there is something left that '1 < 2' could refer to after you have removed the evaluation rules, but I don't see what that could be.

> to "There is a diamond on the moon" being true or false regardless of its symbolic or conceptual representation. You stated that a 'closer analogy would be about "a diamond on the moon", with "the moon" having no referent' because the objects in my diamond-moon analogy have physical presence and "1 < 2" does not.

'1 < 2' having a physical presence was not a requirement on my part. Not that I have any clue what a non-physical presence would look like, but that isn't my problem, because you are the one making the claim that there is such a thing, so it is up to you to demonstrate that.

> If you are "simply pointing out that there is no truth value if there is no referent" and not saying that "'1 < 2' has no referent", then you haven't challenged my analogy because you've only asserted "if".

That is actually a perfectly valid challenge, namely pointing out an unjustified assumption? Your argument builds on there being a truth value, and I have pointed out that you have not established that there is a truth value (because that is dependent on '1 < 2' having a referent, which you have not demonstrated), hence your argument fails, and it is now up to you to show that there is in fact a referent (and thus a truth value) if you want to continue using that argument, or to use a different argument, or to take back your claim.

> What, then, constitutes an instance of an axiom that is analogous to an instance of a movie?

I think I don't understand what you are asking.

> The potential for the universe being in a different state does not effect anything.

Doesn't it effect, you know, the universe changig its state?

Or is that simply a matter of naming? What if we called "the potential for the universe being in a different state" a "unichangetron" instead? A unichangetron is the mechanism that changes the state of the universe, much like an electron is a mechanism that changes the state of the electric field. Is the unichangetron a part of physical reality?

> Not necessarily. Morality is a topic. You can care about what someone has to say about morality without being convince of what they are saying. This conversation is an example. You care enough about what I have to say to continue asking what I have to say about morality, but, unless you've been holding out on me ;), you're obviously not convinced that what I am saying is true.

That's all true, but also completely besides the point? The question wasn't why I should care about what you have to say (i.e., why I should listen to what you say), but why I should care about morality under the definition you gave (i.e., why I should use that version of morality for anything).

> After caring about what I) had to say, you would only act toward following what I am saying regarding morality if you were convinced what I was saying was true.

Well, yeah. Which is why I am asking you to justify your assertions, so I can check whether your justifications are convincing. So far, as far as morality is concerned, there have been no justifications, only assertions, and obviously I am not going to be convinced by pure assertions that I wasn't convinced of before. So, if your goal is to convince, you have so far failed to present anything that would even fall into the category of "potentially convincing".

>> If you cared to attain maximum wealth, and you believed that maximum wealth could be attained through shooting yourself in the head, then shooting yourself in the head would be the way to go.

>> Do you agree?

> Absolutely.

So, are you saying that if you believe that shooting yourself in the head will make you attain maximum wealth, and you then shoot yourself in the head, you will indeed attain maximum wealth?