> All of those say pretty much the same, in so far as they are applicable to the situation?

Do you think they mean the same thing as your definition? If so why, otherwise where did you get your definition of 'incompatible with science' from?

> ... it is non-scientific methods that are (potentially) incompatible with [science].

Is this to say that non-scientific methods are not necessarily incompatible with science?

> Using science.

How is science demonstrated to be reasonably reliable for determining the truth of a claim?

Is that to say that science can demonstrate the reliability of a methodology that is used to determine the truth of non-scientific claims?

> Because science is concerned with reality, and determining what is true about reality, and formal claims don't say anything about reality.

Define reality.

How do you know that formal claims don't say anything about reality?

Is science the only method that can determine what is true about reality?

> Yes, obviously?

Then, how do you know that mathematical claims are not about reality when it may simply be the case that the rules that derive them have not been demonstrated to be reasonably reliable for determining the real truth of such a claim?

> As far as this discussion is concerned, it's the idea that methods you use to justify claims about reality should be demonstrably reliable.

What about this definition determines that not being testable is "about as incompatible with science as you can get"?

Why define 'science' this way over utilizing some form of the top definitions of 'science' resulting from a quick google search (e.g. "the intellectual and practical activity encompassing the systematic study of the structure and behaviour of the physical and natural world through observation and experiment", "such knowledge or such a system of knowledge concerned with the physical world", "systematic knowledge of the physical or material world gained through observation and experimentation", "is the pursuit and application of knowledge and understanding of the natural and social world following a systematic methodology based on evidence")?

===

> Distances (in spaces) and cardinality (of sets).

What is distance?

What are spaces?

What is cardinality?

What are sets?

> If we can what? Distinguish the word 'mathematics' from the concept of mathematics?

Not the word but mathematics itself. Just like you can distinguish a rock from the concept of a rock.

> No ...

Then why state "... (by mathematicians)" rather than "(by some mathematicians)" (though that still wouldn't seem to help assert your case)? It seams like your using the intent of mathematicians to assert that axioms are not claims about reality when you don't know the intent of all mathematicians. Do you have a more solid way to stake your claim?

> Which might be because they are not all talking exclusively about mathematics?

Then from where are you drawing your definition?

> But really, I don't get what the point of all this even is. ... I have pointed out that those categories can be distinguished, and that showing something for one of those categories does not demonstrate truth for the other categories.

We have singled out formal truths from real truths to highlight your position that distinguishes them. I have yet to agree that formal truths are not real truths because I don't think that you have established that as fact.

> Well, yes and no.

So you don't know whether your defining 'axiom' however you want and whether the statement "axioms are not claims about reality" simply conforms with your definition?

> No, in that I used the definition that is commonly accepted...

What is, and from where are you drawing, your definition of axiom?

> No. It is not obvious that there is such a thing as "given the Peano axioms", absent humans (or possibly more generalized evaluators).

So, it is not obvious to you that '1 < 2' does or does not have a referent, because the Peano axioms that '1 < 2' is derived from may or may not be a purely artificial construct of humans (or possibly more generalized evaluators)?

> That depends on the definition of "exists".

What is your definition?

> As far as the most commonly used definition is concerned, the non-physical does not exist, because existence by definition implies physicality

"You constantly want to make this assumption, but that assumption really is just the assumption of the [non-]existence of the immaterial, and as such it's not a useful basis for demonstrating the [non-]existence of the immaterial, because every false claim could be assumed to be true in order to demonstrate that it is true, and thus assuming a claim in order to demonstrate that it is true is not a reliable method for determining the truth of a claim.

> because existence by definition implies physicality (when a normal person says "there exists no grocery store in this street", they are not excluding the possibility that a non-physical grocery store exists in the street)

How do you know 'existence' is implying physicality in this scenario over 'grocery store' implying physicality?

===

> ... Or what?

Read 'can be'.

> Hu?! I mean, yeah, we can observe changes in state, I guess, but then we also can observe changes in state that we don't have explanations for, can't we? So ... no?

Not having an explanation now doesn't mean that there can't be one. Science has yet to fail in giving us further explanations for things. So, unless you want to deny the effectiveness of science you have no case.

> Well ... maybe? It smells like a setup for equivocation ...

If a wall was painted completely blue and then someone added a spec of orange somewhere, then wall as a whole would not be blue.

> Well ... yeah? The point being? Has anyone made the claim that reality is not entirely intelligible?

You asked "Couldn't there be mechanisms by which something changes state that can not be determined by science?". My point is "No" for the aforementioned reasons.

> Could you explain then what there is to this potential to change the state of the electric field beyond what is described by the theory of the electron and other charged particles (I used only "electron" before for simplicity, but I guess some more precision is appropriate here)?

There is nothing to the "potential to change the state of the electric field" that goes beyond what is described by the theory of the electron and other charged particles. The theory incorporates notions of change. Stating that something can change is to state that the potential for that thing to change exists. So, the "potential to change the state of the electric field" doesn't go beyond the theory.

> As far as I can tell, "the potential to change" generally is simply a way to describe certain attributes of a thing, and you haven't demonstrated that that isn't all that's going on here.

This sounds like a claim against my definition. If that's what it is, then you'll need to substantiate that your definition is something I need to deny, but... You yourself rightly noted to me that it doesn't make sense to ask if a definition is true. Are you now saying that I need to argue against a definition, one that, as far as I can tell, you made up?

Or perhaps you are saying that your definition is the generally accepted one, and you are asking me to argue that your definition isn't the generally accepted one. In which case I'd ask you to substantiate your claim that your definition is the generally accepted one?

> When someone says "this lamp has the potential to change color", there isn't a thing in addition to the lamp that we call "the potential to change color", neither a physical nor a non-physical one

Soooo, you don't think a lamp can change color?

> it's simply a way of expressing the fact that it has colored light filters built in, or uses different-colored LEDs, and that there are controls or something to influence in which proportions those are used to produce light.

And not to express that a lamp can change color...?

> If you think there is something like "the essence of the potential to change color" that has some sort of existence beyond what is described by the mechanism of the lamp, that would be for you to demonstrate.

Again, like with the electric field, "the essence of the potential to change color" does not exist beyond what is described by the mechanism of the lamb because the mechanism of the lamp is in part described by change. To be able to change color is "the essence of the potential to change color", which of course exists, otherwise you'd be saying something tantamount to "lamps can't change color".

That "non-physical potential(s) of particular physical things exists" is the conclusion to my 'potential' argument. You have yet to substantiate any objection against it.

===

> So, you think they ought to follow their belief even though they demonstrably (I think you would agree?) will achieve the exact opposite of their stated goal by doing so?

Long story short: It is immoral to do what you think is immoral even if it is moral, so you'll be better off doing what you think is moral even if it is immoral. That being said we are obligated to correct our neighbors' incorrect moral beliefs and to be open to being corrected.

Looking back, all of my statements regarding the scenarios were ambiguous to my intent because they were all meant to be tied to morality but I didn't explicitly state it as such. My bad.

> Well, yeah ... so there is no reason to care about morality under your definition, then?

Does a person not substantiating a claim mean that the claim is not true?

Out of curiosity, what would you say is a reason to care about science?