Because that is the definition of "definition"? "definition" is defined to mean an arbitrary assignment of semantics to symbols, with no requirement that those semantics in any way connect to reality, so you (a) only need to know those assignments in order to evaluate a statement that only references definitions, and (b) it would be a fallacy of equivocation to evaluate a reference to a definition as a reference to an object described by that definition, if there happens to be such a thing.
> How do you determine whether a claim depends on something that is not just a matter of definition?
By trying to evaluate the claim using only definitions as a source of information, and seeing whether any references remain unresolved this way?
> Isn't the claim "1 + 9 = 10" a claim about reality by virtue of it being a claim (because a claim asserts something as true, and to be true is to be in accordance with reality, so "1 + 9 = 10" is to say that "'1 + 9 = 10' is in accordance with reality")?
"to be true is to be in accordance with reality" is not something I would agree with. To be in accordance with reality implies being true, but the other way around is not true, because we also use the word "true" to refer to statements derived from formal systems, and formal systems are not reality. The difference between the two uses of the word is that truths in formal systems are only relative to that formal system, which itself is arbitrarily defined, which is why the same statement can be true relative to one formal system and at the same time false relative to another formal system.
As I mentioned earlier, '1 + 9 = 10' is not true. It is true under Peano axioms. Let's throw those away, an define a new axiom: '(1 + 9 = 10) = false'. Now, '1 + 9 = 10' is false.
> Is this to say that the diamond is its representation?
It's not so much "its" representation, as there can be many representations of the same information, but a diamond existing in some place certainly does represent the information that a diamond exists in that place, doesn't it? As in: You can potentially extract the information that a diamond exists in that place from the arrangement of matter that makes up the diamond!?
> Would this mean math doesn't exist outside of the brain because it doesn't have "a pattern in external (physical) reality"?
> Assuming only physical reality exists, wouldn't that make math a physical part of the brain?
That seems to me like a confusion of the abstraction and the underlying representation.
Yes, mathematics consists of axioms, and much like I see no reason to think that movies can exist absent a physical/material medium, I don't see a reason to think that axioms, and thus mathematics, can exist absent a physical/material medium--though I don't see why it would have to be a brain in either case, and DVDs and math textbooks seem to suggest that it doesn't, though either certainly can in principle be represented physically in a brain, sure.
But the abstraction of mathematics is about the physical representation just as much as movies are, and to avoid some potential distractions, let's assume we are talking about a cartoon: Does a cartoon have "a pattern in external (physical) reality", in the sense that there is a reality "out there" that is described by the cartoon?
Also, while there is nothing wrong with making the assumption that only physical reality exists for the argument's sake, there isn't really any need to. There is no problem with being open to the possibility that movies don't need physical representation to exist somehow. But there is no reason to believe that they in fact can until that has been demonstrated, when all movies we have ever encountered so far had a physical representation.
> Are definitions and rules of evaluation physical?
For definitions: No, the same way that movies aren't physical. For rules of evaluation: Well, for defined rules of evaluation, see definitions. But of course, you can look at the whole world as a computation, in which case the world is nothing but evaluation, and the rules of that evaluation essentially would be what makes up "the physical".
> Agreed. What indicates that the statement "1 < 2" has no referent?
You are shifting the burden of proof? I didn't claim that it has no referent, I am simply pointing out that there is no truth value if there is no referent, so if you want to make the claim that there is a truth value, you would have to demonstrate that there is a referent.
> Would the equivalent statement for axioms therefore say "An expression of the form "axioms are not material" only says something about which aspects are relevant to the abstraction, not about the underlying reality of instances of axioms"?
Sure.
> Depends on how you are defining "observe". Regarding electrons, the effects they produce indicates interactions that are physical in nature.
So, are you saying then that the effects of the potential of the universe to change state that we observe are not physical in nature? Because if they were physical, it seems you are saying, then the potential of the universe to change state would also be physical, wouldn't it? But if those effects aren't physical, wouldn't that then mean that we don't have scientific evidence for the potential of the universe to change state?
I am just wondering what distinguishes electrons from the potential of the universe to change state, that the effects of one scientifically establishes it as part of physical reality, while the effects of the other scientifically establishes it as part of non-physical reality!?
> You never asked for reasons to be convinced it's true. You asked for reasons to care.
Isn't being convinced it's true a requirement for caring? If someone said "You should do this work for me if you want to get paid by me" ... would you or anyone care if they weren't reasonably sure that the person making the claim actually had the money to pay them? I mean, how is that claim alone a reason to care if there is no reason to believe the consequence of being paid will actually materialize?
> If you cared to attain maximum eating pleasure and you believed of Jane that the maximum eating pleasure could be achieved through eating according to Jane's will your entire life, then Jane's will would be the way to go.
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?