Given the context of some of the things we've discussed and being aware of how each of us is defining terms, I'm going to start from where our discussion began and see if we can come to a quicker agreement/disagreement.
I've still answered what I consider highlights of our discussion from your last reply, but I'll be putting more stock into the starting point of our discussion, attempting to be more careful with any assumptions made.
As always if you think I'm intentionally avoiding something by my skimming, feel free to bring it up.
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zAy> Being untestable is about as incompatible with science as you can get.
I replied "Math is not testable with the scientific method, but it is obviously compatible with science".
Instead, this time I'll ask two questions:
What does it mean for something to be incompatible with science?
and
What determines that not being testable is "about as incompatible with science as you can get"?
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> I'm not really sure what you are asking?!
I'm asking whether I am following your statements correctly. You, to paraphrase, seemed to have stated that we can only agree or disagree on definitions, having no reason to believe any definition is true because all definitions are arbitrary "by definition". Does this sum up your position correctly?
> Seems like a pretty succinct description? Though, as I also wrote, it probably needs to be usable for measuring or counting, otherwise lots of mathematical objects would fall under that definition that are not usually considered numbers.
How is it really a succinct description if "lots of mathematical objects would fall under that definition that are not usually considered numbers"?
> you can (conceptually) distinguish a rock from a picture of a rock or from the word "rock".
What do you intend to mean by adding the modifier "conceptually" to "distinguish"? I probably agree, but I want to make sure I'm understanding you correctly. I would add that you can distinguish a rock from a picture of a rock, from the word "rock", and from the concept of a rock.
Can or can you not do the same with mathematics, and why or why not?
> So, movies are not material in the sense that any statement that you make about a movie retains its meaning no matter what representation you choose for the movie/the statement applies to all representations of it that there are, have been, or will be.
So, in that sense, would you agree that the non-physical exists in reality?
> What claims are about is a matter of intention, and mathematicians don't intend to make statements about reality when they declare axioms, thus they are not claims about reality.
How do you know that mathematicians don't intend to make statements about reality when they declare axioms?
Even if they don't intend to make claims about reality, couldn't mathematicians intend to do so?
> When someone makes some outlandish claim and you ask "How is that true?", to which they they respond "Why are you saying that I am wrong?", and you say "I am not saying you are wrong, I don't know whether you are wrong, but your claim is unsubstantiated, and since it is your claim, it is up to you to substantiate it." ... would you say that you have taken some sort of middle ground on the outlandish claim?
Yes, asking them to substantiate their claim does not mean that you are taking the opposite view point. Having not taking the affirmative or negative position means that you are taking the middle ground...
That being said, asking someone to substantiate their claim does mean that you are claiming that their claim is unsubstantiated, meaning that you are not taking the middle ground regarding the evidence they do or don't have to back up their claim.
> I have only objected to your unsubstantiated claims that the non-physical exists because they are unsubstantiated.
Your objection, that my claim is unsubstantiated, is an unsubstantiated claim. (This claim hear is unsubstantiated because I have given no evidence to support it. Evidence for or against it might be found in previous replies)
> Well, sure, but be careful to not confuse rejections of unsubstantiated claims with counter-claims.
Sure, but be careful to substantiate your rejections.
> Hu? What would make you unjustified in assuming it? The fact that you are assuming it? The definition of "assumption" is "to be accepted as true without justification"? So, if you were giving a justification, it wouldn't be an assumption anymore?! I really don't understand what you are asking me here ...
The assumption it self is unjustified, yes, but why am I unjustified in assuming it? Arguments can't be made without assumptions, but the assumptions of arguments should be obvious. I think that "'1 < 2' has a referent" is an obvious assumption in light of the Peano axioms (in part since we both think that the Peano axioms exist (ignoring what we think regarding the nature of the Peano axioms and their derivations)). If you think that is not obvious, why?
If you think arguments shouldn't make assumptions at all, then tell me why and give me an example argument with no assumptions.
> I guess you could say "copies" instead of "instances".
So if the "copies" are material, are the "originals" also material?
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>> No. The potential for the universe being in a different state is not a mechanism by which the universe changes state.
> How did you determine that?
The mechanisms by which something changes state can be determined by science.
> I don't see the fundamental difference between "the potential for the universe being in a different state" and "the potential for the electric field being in a different state"
There isn't a fundamental difference between those two statements. I used the word "universe" as a catch-all. You could substitute "universe" for just about anything else, if not all things, physical.
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> Yeah, and "care" and "listen to" are two different questions as well. If you care about what someone is saying, "listening to" is how you express that. If you care about someone's version of morality, "using it" is how you express that. That is what caring about something means.
Fair.
> And then you certainly also recognized that you haven't given reasons to be convinced, right?
Yes... I explicitly stated this, albeit in different terms.
> OK, so: Are you saying that if you believe that the global maximum of eating pleasure is achieved through eating according to Jane's will for your entire life, then if you eat according to Jane's will for your entire life, you will indeed achieve the global maximum of eating pleasure?
Absolutely not.