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?
>> 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.
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"?
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> "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...
What is your definition of "true"?
If "To be in accordance with reality implies being true", then I can replace "in accordance with reality" with "true" in a sentence. Now, if I am understanding you correctly, according to you I can't do that the other way around. In either case I can still rephrase what you've said.
"'to be true is to be in accordance with reality' is not something I would agree with" then becomes "'to be true is to be true' is not something I would agree with" which follows from "To be in accordance with reality implies being true". So, either you're just wrong, because true is true, or there is some separate word or adjective we need to use while we speak of truth.
> 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.
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?
If so, is "consistent with a formal system" a reality or a derivation from a formal system?
In other words: is the word 'true' in the statement "It is true that '1+9=10' is consistent with the Peano axioms" referring to derivation from a formal system, or is it referring to being in accord with reality?
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'?
> 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.
You didn't change anything though. Saying "now it is false" implies that something changed of either the axioms themselves or the statement '1 + 9 = 10'. '1 + 9 = 10' is true under the Peano axioms and false under the '(1 + 9 = 10) = false' axiom. Without proper context '1 + 9 = 10' is not able to be evaluated. With proper context it is always true of false depending on that context.
Another question that I think is pertinent to our conversation regarding '1 + 9 = 10': What is a number?
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> ... I don't see a reason to think that axioms, and thus mathematics, can exist absent a physical/material medium ...
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?
>> Are definitions and rules of evaluation physical?
> For definitions: No, the same way that movies aren't physical.
This seems to fly in the face of you stating "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 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?
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>>> The problem with your analogy is that that diamond (or its absence) is represented, in the form of the diamond (or its absence). It's a claim about external reality, or a description of a pattern in external (physical) reality. That pattern is there, even without anyone conceptualizing it. ... A closer analogy would be about "a diamond on the moon", with "the moon" having no referent. Does "a diamond is on the moon" have a truth value if there is no moon?
>> 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.
I analogized "1 < 2" being true or false regardless of its symbolic or conceptual representation 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.
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". You drawing a "closer analogy" would seem to indicate that you intended to claim that "1 < 2" has no referent as a challenge to my analogy. Which is the case?
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>>> An expression of the form "movies are not material" only says something about which aspects are relevant to the abstraction, not about the underlying reality of instances of movies.
>> 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.
What, then, constitutes an instance of an axiom that is analogous to an instance of a movie?
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> 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!?
The potential for the universe being in a different state does not effect anything.
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> Isn't being convinced it's true a requirement for caring?
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. 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.
>> 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.