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Comment by sonusario | Hacker News Reader

> Propositions are in the same category as sentences, as far as their dependency on representation is concerned.

What evidence do you have of this being the case?

Think about what it would mean for the truth of "Snow is white" if it was dependent upon how it was represented. If you can represent something in more than one way, then that thing is not dependent upon its representation.

> Take a random proposition that you think would have evaluated to true in the past, before humans existed, if an entity capable of evaluating the proposition had been around. Now, subtract from the concept that you have in your mind everything that is simply the (physical) world as it is (i.e., the "testable"/empirical aspects referenced by the proposition). What do you have left that could be considered to exist in any meaningful sense, absent a (physical) representation expressing the abstraction?

You would have nothing, but you removed the physical world and have removed the propositions that go along with that world. The proposition "Snow is white" depends on the existence of snow being white, and it does not depend on the sentence "Snow is white".

That being said, the proposition "1 < 2" does not depend on anything physical. So you can removed all physical things, and "1 < 2" will still be true under the Peano axioms.

>> What evidence do you have that establishes this as true?

> "It has not been demonstrated that you can use the testable patterns to demonstrate the existence of untestable abstract ideas."

Not to be a burden, but to respond to your question could you give me a refresh: What are you considering to be a testable pattern? What are you considering to be an untestable abstract idea?

>> To have objective reality or being.

> And how would you define "objective reality" and "being"?

Objective reality: not influenced by personal feelings or opinions in considering and representing facts regarding the world or the state of things as they actually exist, as opposed to an idealistic or notional idea of them.

> Those seem to me more like synonyms than definitions!?

Uhh... the composition of words in a definition is synonymous with what they are defining. If you only use one word to define something, then that word is a synonym... I don't understand the point of this complaint. If you think the definition is wrong or obscure then please state why.

Perhaps you don't like the definition because you are trying to find something that implies physicality? I got the definition straight from google... Is there some other dictionary you'd like to suggest?

>> I did not define "potential" as "possible", I defined it as "possible state".

> So ... where you wrote "potential state", you meant "possible state state"?! ... Or in other words: a state can not be current and possible at the same time. What did I miss?

Oof, cleaning up it is... let's start from scratch (the "same time" stuff has been removed as I am acknowledging that it made no sense):

(Potential = possibility; actually = currently)

===========================================================================================================================================================

A) If it is not the case that the potential for the universe being in a different state actually exists, then it is not the case that the universe can change states.

B) The universe can change states.

C) If the potential for the universe being in a different state is physical, then the potential for the universe being in a different state would be observable.

D) If the potential for the universe being in a different state is observable, then the potential for the universe being in a different state would have qualities which can be scientifically observed.

E) It is not the case that the potential for the universe being in a different state has qualities which can be scientifically observed.

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F) The potential for the universe being in a different state actually exists. (modus tollens A,B)

G) It is not the case that the potential for the universe being in a different state is observable. (modus tollens D,E)

H) It is not the case that the potential for the universe being in a different state is physical. (modus tollens C,G)

I) The potential for the universe being in a different state actually exists, and it is not the case that the potential for the universe being in a different state is physical. (conjunction introduction F,H)

===========================================================================================================================================================

>> Morality: Principles concerning the distinction between right and wrong or good and bad behavior.

> Well, as above: How would you define "right", "wrong", "good", and "bad" (in this context)?

Right/Good behavior is an act which is in accordance with what God wills.

Wrong/Bad behavior is and act which is not in accordance with what God wills.

View on HN

> What evidence do you have of this being the case?

Well, the thought experiment that followed?

> Think about what it would mean for the truth of "Snow is white" if it was dependent upon how it was represented. If you can represent something in more than one way, then that thing is not dependent upon its representation.

Nah, that's not what I mean. My point is not that the content of the concept depends on how it is represented, but that the existence of the concept depends on the concept being represented. It doesn't matter how it is represented, the point is that if it is not represented at all, there is no basis for the claim that it exists.

> You would have nothing, but you removed the physical world and have removed the propositions that go along with that world. The proposition "Snow is white" depends on the existence of snow being white, and it does not depend on the sentence "Snow is white".

Nah, that's also not what I mean. The idea isn't to change the world to not have any physical reality. The idea is to remove from your conception of "snow is white" all the aspects that mirror physical reality (though I think that's a bad example for this because it's kinda difficult to see how to do that).

> That being said, the proposition "1 < 2" does not depend on anything physical. So you can removed all physical things, and "1 < 2" will still be true under the Peano axioms.

You mean you could evaluate "1 < 2" to "true" using the Peano axioms ... without representing the Peano axioms anywhere? Doing an immaterial computation? I am not sure I have any concept of what you are trying to construct here.

> Not to be a burden, but to respond to your question could you give me a refresh: What are you considering to be a testable pattern? What are you considering to be an untestable abstract idea?

By a testable pattern I mean essentially "a description of physical reality", by an abstract idea I mean "a description of a made-up system of rules". As in, "9 apples + 1 apple = 10 apples" is a description of a pattern in physical reality, which is also testable, in that you can take 9 apples, and add another apple, and then check whether you failed to get 10 apples (which would falsify the claim). "9 + 1 = 10" on the other hand is a description of a made-up system of rules, which you can only evaluate for consistency against the system of rules (so, you could check whether "9 + 1 = 10" can be proved based on the (implied by convention unless specified otherwise) Peano axioms, or any other axioms).

> Objective reality: not influenced by personal feelings or opinions in considering and representing facts regarding the world or the state of things as they actually exist, as opposed to an idealistic or notional idea of them.

It's kinda unfortunate that you used "exist" in defining "objective reality", which was supposed to define "exist" ... ?!

> Uhh... the composition of words in a definition is synonymous with what they are defining. If you only use one word to define something, then that word is a synonym... I don't understand the point of this complaint. If you think the definition is wrong or obscure then please state why.

Sure, there is nothing wrong with your definition per se (and I don't really care much whether it's obscure or "wrong", I am just trying to understand what you are trying to say), it just doesn't seem to be any less ambiguous than what I was asking about. So, yeah, synonyms are perfectly fine definitions in principle, but I was asking for a definition because "exist" is a pretty ambiguous word, and a synonym doesn't really help with that--rather, I am trying to understand which specific meaning you have in mind when you are using it here. (And, after all, I can look up generally used synonyms myself ;-)

> Perhaps you don't like the definition because you are trying to find something that implies physicality? I got the definition straight from google... Is there some other dictionary you'd like to suggest?

No, it's just about understanding what you mean when you say "exists" (in this context), and to make sure we aren't running into any equivocation where it's used with two different meanings in different places in the argument.

> B) The universe can change states.

I see quite a few potential flaws in that whole argument, but I think I'll start with this one:

How do you know that, if not as a result of the scientific observation of the physical process of the universe changing states? Or am I misunderstanding your claim here?

> Right/Good behavior is an act which is in accordance with what God wills.

> Wrong/Bad behavior is and act which is not in accordance with what God wills.

OK ... so, under that definition(!!!): Why should I, or anyone, care about morality?

>>> Propositions are in the same category as sentences, as far as their dependency on representation is concerned. >> What evidence do you have of this being the case? > Well, the thought experiment that followed?

The thought experiment was scientific evidence?

> My point is not that the content of the concept depends on how it is represented, but that the existence of the concept depends on the concept being represented.

Ah, well I am referring to the proposition as the content of the concept, and the content of the concept as not being dependent on its representation conceptually or syntactically. How something is conceptualized in the mind is not of current concern for my position.

> You mean you could evaluate "1 < 2" to "true" using the Peano axioms ... without representing the Peano axioms anywhere? Doing an immaterial computation? I am not sure I have any concept of what you are trying to construct here.

No, 'you' and 'evaluate/compute' is not in the picture. I can do an evaluation, and that would require representation, but my evaluation is to find that it is true, not to make it true. I agree that immaterial computation is not possible, but computation is not what is being discussed. Do you think that the statement "'1 < 2' is true under the Peano axioms" is dependent on something material?

> It's kinda unfortunate that you used "exist" in defining "objective reality", which was supposed to define "exist" ... ?!

Well its not my definition. Is there a definition that satisfies you that I could consider co-opting?

> ... "exist" is a pretty ambiguous word ...

Hmmm, interesting. I hadn't thought that it might be ambiguous. Why do you think it's ambiguous?

> ... to make sure we aren't running into any equivocation where ["exists" is] used with two different meanings in different places in the argument.

Well, if it is any consolation, you may note that I use "exists" in only one phrase that is used three times: "The potential for the universe being in a different state actually exists".

>> B) The universe can change states.

> I see quite a few potential flaws in that whole argument, but I think I'll start with this one:

> How do you know that, if not as a result of the scientific observation of the physical process of the universe changing states? Or am I misunderstanding your claim here?

That "the universe can change states" is known by observation.

>> Right/Good behavior is an act which is in accordance with what God wills.

>> Wrong/Bad behavior is and act which is not in accordance with what God wills.

> OK ... so, under that definition(!!!): Why should I, or anyone, care about morality?

Define "should".

> The thought experiment was scientific evidence?

Well, I guess you could even look at it that way (it is a question about thought that we are trying to answer, after all), but I'd tend to think that that is a category error, strictly speaking, in that we are dealing with a formal (language) system, so it's more on the proof side of things. Unless you consider it a question of finding agreement about definitions, in which case that thought experiment is simply an exercise in (empirically) determining the definition that you are using.

> Ah, well I am referring to the proposition as the content of the concept, and the content of the concept as not being dependent on its representation conceptually or syntactically. How something is conceptualized in the mind is not of current concern for my position.

Yes, I agree that how it is conceptualized is not (very) relevant (it kindof is, because complexity theory, essentially, but maybe we don't need to get into that?).

But it is relevant that it is represented, or at least I don't see any reason to think that representation is optional. That is to say: I have no idea what you are talking about when you are talking about immaterial Peano axioms. Every instance of Peano axioms that I can think of has a physical representation, just as every instance of cake that I can think of has physical representation. Making the assumption that there is such a thing as immaterial Peano axioms seems to me as reasonable as making the assumption that there is such a thing as immaterial cake. It is grammatically perfectly fine English to say "immaterial cake", but that's it, there is no content to those words.

> Well its not my definition. Is there a definition that satisfies you that I could consider co-opting?

Well, that's difficult, as ...

> Hmmm, interesting. I hadn't thought that it might be ambiguous. Why do you think it's ambiguous?

... there are so many ways in which people vary what exactly they mean by "exist".

As a random example, some people think that things that exist for a span of time that has no extent (like, 0 seconds) can be said to exist. In my book, that is a pretty useless definition, because it makes for a concept that cannot distinguish anything, but if that is your definition, an otherwise wrong argument might actually be correct--even though it doesn't tell you anything about useful notions of existence. And the argument that you are making seems to be of the kind where those details can make the difference between true and false.

> Well, if it is any consolation, you may note that I use "exists" in only one phrase that is used three times: "The potential for the universe being in a different state actually exists".

Which seems to be a central claim in all of this? But, I dunno, maybe we can try approaching it from the other end, and maybe that'll give me an idea what aspects of "existence" to ask for clarification on:

> That "the universe can change states" is known by observation.

Then ... in which sense isn't that scientific observation demonstrating the existence of the potential for the universe to be in different states?!

(Though I want to note that I probably would not use the word "existence" to describe the situation, as it smells a bit like a category error, specifically it smells like fallacious reification.)

> Define "should".

Haha, sorry, I didn't mean to sneak in another reference to morality or anything like that ;-)

I simply meant which reasons you would give to anyone who was interested, or possibly to humanity as a whole, to try and convince them to care about morality under that definition.

>> The thought experiment was scientific evidence?

> Well, I guess you could even look at it that way (it is a question about thought that we are trying to answer, after all), but I'd tend to think that that is a category error, strictly speaking, in that we are dealing with a formal (language) system, so it's more on the proof side of things. Unless you consider it a question of finding agreement about definitions, in which case that thought experiment is simply an exercise in (empirically) determining the definition that you are using.

Let me see if I can show you what I am getting at (looking for yes/no answers but I'm not going to stop you from digging deeper, lol): Are all claims about reality scientifically testable?

> I don't see any reason to think that representation is optional.

Can't something be true regardless of whether or not it's being represented?

> Every instance of Peano axioms that I can think of has a physical representation, just as every instance of cake that I can think of has physical representation.

Wouldn't that be because you can't think of those things without a representation, not because they are dependent upon a representation?

> Making the assumption that there is such a thing as immaterial Peano axioms seems to me as reasonable as making the assumption that there is such a thing as immaterial cake.

So what material(s) are the Peano axioms composed of?

> ... some people think that things that exist for a span of time that has no extent (like, 0 seconds) can be said to exist ...

Heh, yeah I don't even know what that means...

> In my book, that is a pretty useless definition...

Do you have any definition for "exist" that you consider useful?

>> That "the universe can change states" is known by observation.

> Then ... in which sense isn't that scientific observation demonstrating the existence of the potential for the universe to be in different states?!

Yes.

> I simply meant which reasons you would give to anyone who was interested, or possibly to humanity as a whole, to try and convince them to care about morality under that definition.

I'd probably say a reason for someone to care about morality would be if they cared to maximize joy/happiness in themselves and others.

> Let me see if I can show you what I am getting at (looking for yes/no answers but I'm not going to stop you from digging deeper, lol): Are all claims about reality scientifically testable?

I am not quite sure I understand what you are getting at. I mean, it's obviously possible for someone to make the claim "I own a real undetectable pet dragon" ... so, given that such claims can be made, not all claims about reality are scientifically testable?! The only possible objection to that that I can see would be that if you define "reality" to require testability, then "real undetectable" is a category error--but then, that's just a matter of definition, and either definition seems to be in common use, and usefully so, in different contexts, so there is no general answer--you only have to be careful to not construct false equivocations due to this ambiguity.

> Can't something be true regardless of whether or not it's being represented?

That's a question with a lot of potential for false equivocations. The most problematic seems to be "be", as that tends to be quite ambiguous, and while that is seldom a problem in day-to-day language use, it causes lots of confusion on such questions. For example, "be" in statements like "is A and B true?" usually means "does A and B evaluate to true?" If that is what you mean: How would you evaluate a proposition without having it represented anywhere? If that is not what you mean: Well, what do you mean then?

Or are we maybe talking about something like a thought experiment of the sort "suppose you could time travel 3 billion years into the past, what would you evaluate 'true and false' to then?"? While that's a perfectly fine thought experiment that can be insightful, you must not lose sight of the pretty wild assumption of time travel and the fact that it implies a human being present in that hypothetical scenario when you then try to generalize that insight: While a lot of generalizations can be made just fine while ignoring that you made those rather unrealistic assumptions, it is easy to be carried away into territory where suddenly the result is just an artefact of those assumptions.

> Wouldn't that be because you can't think of those things without a representation, not because they are dependent upon a representation?

Yeah, sure! But the same applies for cake, then, doesn't it? After all, I am not making the claim that "immaterial axioms" cannot mean anything, nor that "immaterial cake" cannot mean anything. The point is: How would we know? Maybe we can, I don't know, but wouldn't you agree that in order to build an argument on it, there should be more to show than "I can put the words 'immaterial cake' together", when all the cake we've ever seen was material?

> So what material(s) are the Peano axioms composed of?

That's a category error? What material(s) are movies composed of? Or would you say that movies are immaterial (obviously, "immaterial" here meaning "existing without being represented in matter", just as I used it for the Peano axioms)?

> Do you have any definition for "exist" that you consider useful?

Really, I don't. Or rather, I guess I do, somehow (I mean, I do use the word, so I better have some idea what I mean by it when I use it ;-), but I have no clue how to comprehensively dump that into text. Plus, there are multiple useful definitions, depending on the context. I think it is easier to clarify ambiguous aspects of what I mean in a particular use than to write down a general definition.

>> Then ... in which sense isn't that scientific observation demonstrating the existence of the potential for the universe to be in different states?!

> Yes.

I take it that you mean that it is scientific observation demonstrating the existence of the potential for the universe to be in different states?

So ... do you agree then that that is not an example of non-physical reality (which is what you originally proposed it as)?!

> I'd probably say a reason for someone to care about morality would be if they cared to maximize joy/happiness in themselves and others.

Hu? How did we get there?! I mean, that sure sounds like a good reason to care about something if it gets you there, I just don't see how this reason is connected to your definition!?

Let me try and construct an analogous dialog:

A: X is a pleasure to eat.

B: Please provide evidence for the claim that X is a pleasure to eat, or if you think that asking for evidence is a category error, define what you mean by "being a pleasure to eat".

A: Yeah, it's a category error. "A pleasure to eat" concerns the distinction between what tastes good and what tastes bad.

B: Please define what you mean by "tastes good" and "tastes bad".

A: What tastes good is food that you eat in accordance with what Jane wills. What tastes bad is food that you eat not in accordance with what Jane wills.

B: OK ... so, under that definition(!!!): Which reasons would you give to anyone who was interested to try and convince them to care about eating things that are a pleasure to eat under that definition.

A: A reason for someone to care about eating things that are a pleasure to eat would be if they cared about enjoying what they eat.

How does something being enjoyable to eat connect to Jane's will? It seems to me like the whole part about why anyone should be convinced that eating what Jane wants them to eat is going to be enjoyable is missing?

Also, isn't joy and happiness quite accessible to empirical study? Aren't you implicitly saying that it is a category error to ask for evidence that certain acts increase or diminish joy or happiness? Or what would you suggest people to do when they do as Jane/God wants, but they observe decrease in joy and happiness? Do it anyway, because otherwise they aren't eating what is pleasurable/they aren't moral? Or stop eating what they observe to be causing them to puke because a definition of "a pleasure to eat" that makes them puke is kinda useless?

> I am not quite sure I understand what you are getting at.

I was asking my first question in a potential series.

How do you determine whether a claim is about reality?

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>> Can't something be true regardless of whether or not it's being represented?

> How would you evaluate a proposition without having it represented anywhere? If that is not what you mean: Well, what do you mean then?

Again, as I've stated before (and asked a question that you didn't answer, which turns out to be pertinent here):

>>>> I can do an evaluation, and that would require representation, but my evaluation is to find that [something] is true, not to make it true. I agree that immaterial computation is not possible, but computation is not what is being discussed. Do you think that the [truth of the] statement "'1 < 2' is true under the Peano axioms" is dependent on something material?

To add to my previous statement on this having nothing to do with evaluation, and to provide a realistic thought experiment: If someone says "A diamond is on the moon", either it is true or it is not, regardless of its representation or evaluation. Evaluating the claim as true would require observing the diamond on the moon, but that "A diamond is on the moon" is either true or not before such an observation takes place.

So, my question "Can't something be true regardless of whether or not it's being represented?" is attempting to ask if the truth of some claim is true or false regardless of its symbolic or conceptual representation.

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>>> Every instance of Peano axioms that I can think of has a physical representation, just as every instance of cake that I can think of has physical representation.

>> Wouldn't that be because you can't think of those things without a representation, not because they are dependent upon a representation?

> ... How would we know? Maybe we can, I don't know, ...

By the reasons I've been giving... By the fact that symbols and concepts are not the things they represent.

> ... wouldn't you agree that in order to build an argument on it, there should be more to show than "I can put the words 'immaterial cake' together", when all the cake we've ever seen was material?

Where have I put the words 'immaterial' and 'axioms' together without first attempting to build up a reason to do so?

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>> So what material(s) are the Peano axioms composed of?

> That's a category error?

Are you asking me or telling me? If you're telling me it is a category error, why?

> What material(s) are movies composed of?

Image frames. How is this a challenge to my question?

> (obviously, "immaterial" here meaning "existing without being represented in matter", just as I used it for the Peano axioms)

Do you think that the Peano axioms are material or not material?

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> I take it that you mean that it is scientific observation demonstrating the existence of the potential for the universe to be in different states?

Yes.

> So ... do you agree then that that is not an example of non-physical reality (which is what you originally proposed it as)?!

No. The existence of non-physical reality has been demonstrated by scientific observation. The non-physical reality itself was not observed in order to do so.

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>> I'd probably say a reason for someone to care about morality would be if they cared to maximize joy/happiness in themselves and others.

> Hu? How did we get there?! I mean, that sure sounds like a good reason to care about something if it gets you there, I just don't see how this reason is connected to your definition!?

Implicit in my reason is the claim that when one acts according to God's will they will attain maximal joy/happiness.

> Also, isn't joy and happiness quite accessible to empirical study?

The effects of joy and happiness, yes, joy and happiness itself, I don't know.

> Aren't you implicitly saying that it is a category error to ask for evidence that certain acts increase or diminish joy or happiness?

No.

> Or what would you suggest people to do when they do as Jane/God wants, but they observe decrease in joy and happiness? Do it anyway, because otherwise they aren't eating what is pleasurable/they aren't moral? Or stop eating what they observe to be causing them to puke because a definition of "a pleasure to eat" that makes them puke is kinda useless?

Not as mechanical as this, but to answer your question in short: "the global maximum of joy/happiness is achieved through acting according to God's will for your entire life, so don't let dips in local joy/happiness deter you from abiding by God's will".

> I was asking my first question in a potential series.

Sure, I wasn't objecting, it just made it a bit unclear what you meant by that first question ...

> How do you determine whether a claim is about reality?

By looking for statements that as input for their evaluation depend on something that is not just a matter of definition. (And if something is ambiguous by asking for clarification ...)

> Again, as I've stated before (and asked a question that you didn't answer, which turns out to be pertinent here):

I considered that answered by my answer to the preceding paragraph, but let's see ...

> To add to my previous statement on this having nothing to do with evaluation, and to provide a realistic thought experiment: If someone says "A diamond is on the moon", either it is true or it is not, regardless of its representation or evaluation. Evaluating the claim as true would require observing the diamond on the moon, but that "A diamond is on the moon" is either true or not before such an observation takes place.

Yes, I agree.

> So, my question "Can't something be true regardless of whether or not it's being represented?" is attempting to ask if the truth of some claim is true or false regardless of its symbolic or conceptual representation.

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.

But claims about mathematical definitions are not about anything unless there is someone/something to define them. Mathematics is a formal construct made up of definitions by humans, and evaluated based on rules made up by humans. Claims about mathematics are inherently linked to those definitions, and to those rules of evaluation. 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?

> By the reasons I've been giving... By the fact that symbols and concepts are not the things they represent.

Well, but that seems to be exactly what your argument is built on?! Though I think we might also have been talking past each other on this, but that might be cleared up by what's below ...

> Where have I put the words 'immaterial' and 'axioms' together without first attempting to build up a reason to do so?

I don't think you did. But all the attempts at building up reason to do so seem to not succeed, and in part because some of them seem to just be elaborate ways to put the words together.

> Are you asking me or telling me? If you're telling me it is a category error, why?

I am telling you, because axioms are not made of a material.

> Image frames. How is this a challenge to my question?

It is a demonstration of the same category error, or so I would think ... I am slightly confused by your answer, though.

So, you think that images frames are a material, and movies are made of this material? So, like, MPEG files contain a material substance called "image frames" (which constitute the movie)?

> Do you think that the Peano axioms are material or not material?

I would tend towards saying that they are not material, in the same way that I would say that movies are not material. But that does not mean that I think that the Peano axioms can be said to exist absent a material representation, just as I wouldn't think that movies can be said to exist absent a material representation.

The point is that when you refer to a DVD as "a movie", you are expressing that you are talking about properties of that DVD that are not dependent on that specific DVD, or even on a DVD at all. You are talking about properties that can be mapped to an almost arbitrary material, hence the specific material is not significant to the discussion of the movie, hence the concept of a movie does not concern itself with materials. But that is no reason to believe that a movie could exist without material representation.

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.

> No. The existence of non-physical reality has been demonstrated by scientific observation. The non-physical reality itself was not observed in order to do so.

Oh, that's where you are coming from, I see!

Would you also say that electrons are part of non-physical reality, for example? Mind you, we have never observed electrons themselves!

> Implicit in my reason is the claim that when one acts according to God's will they will attain maximal joy/happiness.

Well, sure, but then that's still mostly just the same claim using different words, not a reason to be convinced it's actually true?

> Not as mechanical as this, but to answer your question in short: "the global maximum of joy/happiness is achieved through acting according to God's will for your entire life, so don't let dips in local joy/happiness deter you from abiding by God's will".

And the global maximum of eating pleasure is achieved through eating according to Jane's will for your entire life, so don't let dips in local pleasure deter you from abiding by Jane's will.

Are you convinced yet that eating the way Jane wants you to is the way to go? If not, why not?

> Sure, I wasn't objecting, it just made it a bit unclear what you meant by that first question ...

Sorry about that, I wasn't explicit with that as part of my intention.

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> By looking for statements that as input for their evaluation depend on something that is not just a matter of definition.

How would a claim only depending on something that is just a matter of definition indicate that it is not about reality?

How do you determine whether a claim depends on something that is not just a matter of definition?

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")?

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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).

Is this to say that the diamond is its representation?

> 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.

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?

> Claims about mathematics are inherently linked to those definitions, and to those rules of evaluation.

Are definitions and rules of evaluation physical?

> 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?

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>>>>> Making the assumption that there is such a thing as immaterial Peano axioms seems to me as reasonable as making the assumption that there is such a thing as immaterial cake.

>>>> So what material(s) are the Peano axioms composed of?

>>> That's a category error?

>> Are you asking me or telling me? If you're telling me it is a category error, why?

> I am telling you, because axioms are not made of a material.

>> Do you think that the Peano axioms are material or not material?

> I would tend towards saying that they are not material, in the same way that I would say that movies are not material. But that does not mean that I think that the Peano axioms can be said to exist absent a material representation, just as I wouldn't think that movies can be said to exist absent a material representation.

> 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"?

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> Would you also say that electrons are part of non-physical reality, for example? Mind you, we have never observed electrons themselves!

Depends on how you are defining "observe". Regarding electrons, the effects they produce indicates interactions that are physical in nature.

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>> Implicit in my reason is the claim that when one acts according to God's will they will attain maximal joy/happiness.

> Well, sure, but then that's still mostly just the same claim using different words, not a reason to be convinced it's actually true?

You never asked for reasons to be convinced it's true. You asked for reasons to care.

> And the global maximum of eating pleasure is achieved through eating according to Jane's will for your entire life, so don't let dips in local pleasure deter you from abiding by Jane's will.

> Are you convinced yet that eating the way Jane wants you to is the way to go? If not, why not?

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.

To parallel:

If you cared to attain maximum joy/happiness and you believed of God that the maximum joy/happiness could be achieved through acting according to God's will your entire life, the God's will would be the way to go.

> How would a claim only depending on something that is just a matter of definition indicate that it is not about reality?

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?

> ... "definition" is defined to mean an arbitrary assignment of semantics to symbols, with no requirement that those semantics in any way connect to reality ...

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.

> 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?

> Nothing does, because that is exactly what it is?

So, we can only agree or disagree, and there is no reason to believe your definition of 'definition'?

> 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.

How might we empirically determine whether such agreements exist without having agreement on what the term 'agree' means?

> Well, yeah?

How do you determine that there are actual unresolved references, and that it is not just a deficiency in your definitions?

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> Either consistent with reality or derived from axioms.

Why is that your definition of "true"?

Also what are your definitions of "consistent" and "derived"?

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

Agreed.

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> So, in that sense, every 'formal truth' is a 'real truth' about evaluators in the world...

You may need to go into more depth for me because this seems to walk back on previous statements you've made. Above you defined "true" as "Either consistent with reality or derived from axioms". It seems that you agree with calling 'consistent with reality' a 'real truth' and 'derived from axioms' a 'formal truth'. Now you've stated that "... every 'formal truth' is a 'real truth' ...". Wouldn't that in some way negate the most of the emphasis provided by the term 'formal truth'?

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> How about 'a more abstract word'?

A number is 'a more abstract word'??

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> 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.

Does that mean that the math isn't a model of reality though?

> The existence of a thought and the content of that thought are two distinct things.

Does that establish that the content of a thought doesn't really exist though?

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> But it is not a(n existing) movie anymore when you destroy all representations of it.

Are you making a distinction between a representation and the thing being represented? It seems that your definition of 'representation' also includes the thing being represented, but that is a definition you deny later on when you state "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")".

>>>> 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 "[...]"

> In which way?

"... the same way that movies aren't physical." and "... all movies we have ever encountered so far had a physical representation.", and now also "But it is not a(n existing) movie anymore when you destroy all representations of it."

To paraphrase my understanding of your position:

"All movies encountered have had physical representation." K

"Definitions are not physical in the same way that movies aren't physical." Contradicts the previous line a bit...

"When all representations of a movie are destroyed, that movie no longer exists." Wait, if there are only physical representations of movies, then, even if I'm confusing abstraction and representation, how can movies be non-physical in any way?

Again this could be another case of confusing abstraction and the underlying representation, and if that is the case, what is 'abstraction', what does it mean for something to be an abstraction, and do particular abstractions have physical representation?

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> 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).

This back-and-forth between us started off of me having stated "Math is not testable with the scientific method, but it is obviously compatible with science" and you had replied "If you mean that axioms are not testable, that's simply a category error because axioms are not claims about reality."

Now, if you're not saying "that all representations are physical", and are saying "that no non-physical representation has ever been demonstrated", wouldn't that, at the very least, leave the question open to axioms being claims about reality?

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>> 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.

Why are you equating the "symbolic or conceptual representation" of '1 < 2' to the "evaluation rules" of '1 < 2'?

> '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.

I have no qualms with ending our discussion if your taking the middle ground of "I don't know". I could go on, but I really don't care to. You initially challenged my assertion regarding math and science, my claims namely being on the grounds of math not being physical, by claiming that I was making a category error (at the time from my vantage point, you seemed to be saying only the physical exists). My goal has been to bring things to a middle ground, but if you haven't been or are no longer making claims against the non-physical, then we are at where I wanted to be. You can challenge claims of the non-physical, to be sure, but at this juncture I prefer to shoot down claims that assert the non-physical doesn't exist, of which you no longer appear to me to be claiming.

>> 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.

Your paragraph here is a valid challenge. Your pointing out of an unjustified assumption was not explicit previously.

What makes "'1 < 2' has a referent" an unjustified assumption in the context of my argument? Yes I have not established it, but what would make me unjustified in assuming it?

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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?

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

What did you mean by "instances of movies"?

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

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

No. The potential for the universe being in a different state is not a mechanism by which the universe changes state.

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> ... why I should care about morality under the definition you gave (i.e., why I should use that version of morality for anything).

First "care" and "use" are two very different questions. Again, define should ;).

Why should you use the version of morality of which I am speaking? Because it is the true one (I recognize that I have not established this).

> 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?

Absolutely not.

[part 1]

> So, we can only agree or disagree, and there is no reason to believe your definition of 'definition'?

I'm not really sure what you are asking?!

I am telling you what I think the generally accepted definition is. That's an empirical claim, and it's up to you whether you take my word for it, check other sources, or do an investigation yourself, just as with every other empirical claim?

> How might we empirically determine whether such agreements exist without having agreement on what the term 'agree' means?

By not using the term 'agree' in the empirical investigation?! Though I don't quite see what the point of that limitation is? If there is agreement on what 'agree' means, as seems to be common among users of the English language, then why would you want to avoid the term?

> How do you determine that there are actual unresolved references, and that it is not just a deficiency in your definitions?

I am not quite sure what you mean by "deficiency in the definitions"?

If you mean that there are terms in the statement that I have no definition for, then I try to obtain a definition for those terms. So, if I can ask whoever made the statement, I might ask them for the definition they were using. If that isn't an (easy) option, I might look it up in dictionaries. Or I might try to derive it from the context in which the statement was made (in particular when I do know definitions, but it's multiple mutually-exclusive ones).

If you mean that my definitions are not the ones that the person making the statement meant ... well, then I get the wrong idea of what they were saying?

But mind you that when I said "there are unresolved references remaining", I don't mean "unresolved references to definitions". When I evaluate "Polar bears are green", then "polar bear", for example, refers to a concept that refers to an observable entity. So, I can resolve "polar bear" to that concept using the definition of "polar bear". But at the end there remains the reference to the observable thing. That's what I am talking about.

> Why is that your definition of "true"?

Because that is the generally accepted definition, and as such it is useful to have a definition that matches what other people understand when you use the term. Also, it's probably the generally accepted definition because those two concepts are useful, even though having them both use the same label maybe is unfortunate.

> Also what are your definitions of "consistent" and "derived"?

In this particular context:

Consistent: Not leading to contradictions.

Derived: Arrived at by applying transformations/identities specified by the axioms. You could also say proven using the axioms.

> It seems that you agree with calling 'consistent with reality' a 'real truth' and 'derived from axioms' a 'formal truth'.

Seemed like a useful short hand, so I went with it, sure.

> Now you've stated that "... every 'formal truth' is a 'real truth' ...". Wouldn't that in some way negate the most of the emphasis provided by the term 'formal truth'?

No, that is just a confusion of layers of abstraction. Within the framework of mathematics, noone empirically investigates whether "1 + 9 = 10", because that would be a category error, simply by definition. Within mathematics, 1 + 9 = 10 is defined to be formally true (unless explicitly stated that standard axioms don't apply), but noone is making a claim about real truth, which is why investigating that question empirically is a category error: Empirical investigation applies to claims of real truth, not to claims of formal truth, just as proofs apply only to formal truths, but not to real truths.

But that doesn't mean that the claim that "'1 + 9 = 10' is a formal truth in mathematics" isn't an empirical claim. For every supposed formal truth in mathematics, you can investigate empirically whether that is indeed the case, namely by investigating what the consensus on definitions among mathematicians is.

> A number is 'a more abstract word'??

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.

> Does that mean that the math isn't a model of reality though?

Yes, of course, that's exactly what it means!

Mind you though that that doesn't mean that some parts of mathematics can't be used to model some aspects of reality. But that is a matter of empirical investigation.

Does Newton's law of gravity predict the movement of masses that don't collide? That is an empirical question of whether a particular mathematical structure is useful for modeling an aspect of reality. As it turned out, it is quite useful indeed. But as it later also turned out, it's not actually a (perfect) model of reality, and the theory of relativity gives more accurate results, even though it uses a quite different mathematical structure. But then, there is no reason to think that that is a perfect model of reality either.

> Does that establish that the content of a thought doesn't really exist though?

I'm not sure what you are trying to say here? What do you mean by "really exist"? Are you saying that someone who is hallucinating doesn't have those ideas that we usually call "hallucinations"?

> Are you making a distinction between a representation and the thing being represented?

Well, yes?!

> It seems that your definition of 'representation' also includes the thing being represented, but that is a definition you deny later on when you state "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")".

I'm not sure where you see a contradiction here?! I am just pointing out that no matter how you prefer to generally define 'representation' (and different definitions are useful in different contexts), you can distinguish between things representing themselves and things representing other things, i.e., you can (conceptually) distinguish a rock from a picture of a rock or from the word "rock".

> Again this could be another case of confusing abstraction and the underlying representation, and if that is the case, what is 'abstraction', what does it mean for something to be an abstraction, and do particular abstractions have physical representation?

I suppose it is.

When you say "movie X is funny", it is completely irrelevant to the meaning of that statement how that movie is physically represented. The thing that you refer to as "the movie" here is a concept that is not concerned with material aspects. You can use pretty much any object (as long as it has sufficient degrees of freedom) to encode that movie into it, and that statement would still have the same meaning.

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. Really, as far as the abstraction is concerned, things would still work perfectly fine with a movie that had no physical representation--if that were a thing somehow.

As for what an abstraction is, I think the summary at the top of the wikipedia article is a good one:

https://en.wikipedia.org/wiki/Abstraction

In the specific case, the material representation has no subjectively valued purposes to the concept of a movie.

As to whether particular abstractions have physical representation: Well, given that our brains constantly operate using abstractions (all of language is nothing but abstractions), I would say that obviously yes?!

Mind you, none of this is about "empirical properties of movies" or anything of that sort. The claim isn't "if you take a DVD and put it under the microscope, you will find that it is immaterial" or anything like that. It's simply a matter of what abstractions are concerned with by definition, and the definition of "movie" simply is not concerned with physical representation.

> Now, if you're not saying "that all representations are physical", and are saying "that no non-physical representation has ever been demonstrated", wouldn't that, at the very least, leave the question open to axioms being claims about reality?

No. 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. It's simply a matter of definition: Axioms are defined to be unproved statements that are assumed to be (formally) true for the purpose of making derivations from them.

When I say "Joe is a baker", that doesn't leave the question open whether I am talking about John, and when a mathematician says "I will assume that 1 is a natural number", that doesn't leave the question open whether it's an assumption.

That doesn't mean that John isn't a baker, nor that the structure that can be derived from the Peano axioms can't be used to model aspects of reality. But that's not what either of those claims is about.

> Why are you equating the "symbolic or conceptual representation" of '1 < 2' to the "evaluation rules" of '1 < 2'?

I am not. I am saying that there is no such thing as the meaning of a statement in a formal language absent the rules of that formal language. It's like asking "is a pun funny regardless which language it is in?" It's a category error. The pun is a property of the language, or possibly of a family of related languages: If you remove the language from it, there is no pun left. "A pun in English, but absent English" has no referent.

Given how long it can take to make responses, for us to start dipping into doing two part posts when we aren't making much progress is likely a waist time for the both of us (I wouldn't say no progress because we have still been defining and attempting to understand each other's terms).

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.

===

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"?

===

> 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?

===

>> 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.

===

> 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.

[part 1 ... again ... ;-)]

> Given how long it can take to make responses, for us to start dipping into doing two part posts when we aren't making much progress is likely a waist time for the both of us [...]

Sure, I felt a bit like doing that as well, especially when I couldn't submit my previous response in one piece ;-)

> What does it mean for something to be incompatible with science?

Well, I guess that's a question that can be answered in a million ways, depending on the context, but the relevant aspect to this discussion probably is this:

To be incompatible with science means to be making factual (as in real/non-formal) claims based on methodology that is not demonstrated to be reasonably reliable for determining the truth of such a claim.

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

The definition of what science/"the scientific method" is?

> 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?

No, and that is for the simple reason that "having no reason to believe any definition is true" is a category error, and hence the question doesn't even make sense.

Let's say I define that X = 5. Is that definition true? Does it even make sense to ask whether me defining X as 5 is true?

The act of assigning meanings to labels is not in the category of things that have a truth value. You might as well be asking whether pouring juice into a glass is true. Or whether singing a song is true. When someone says "I will use the word 'apple' to refer to large, grey animals with trunks" (i.e., they give you the definition they are using), and you ask "but is that definition true?", that is simply a non-sequitur. It's as sensible as asking in response to "I will use 'X' to refer to 5" with "but is that definition true?".

And just to make sure this doesn't cause confusion: That does not mean that asking for the truth value of "'apple' as a word for large, grey animals with trunks is commonly accepted in the English language" is a category error. Whether something is a commonly accepted definition for a word in a widely used language is in the category of things that have a truth value, more specifically a "real truth" value, and obviously in this particular case that truth value is false.

> How is it really a succinct description if "lots of mathematical objects would fall under that definition that are not usually considered numbers"?

Well, then it's not. Combined with what I added after that, it still is, so what's the point of harping on this? I gave you a definition, you think half of that definition is not good enough ... well, how about you use the full definition, then? Especially when I obviously kindof agree that the first part is pretty ambiguous, which presumably is why I added the second part?

> 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 am simply trying to avoid the pitfall of hard solipsism. After all, every rock you see is mediated through a picture of that rock on your retina. If there actually is a retina, that is. So, can you really distinguish a rock from a picture of a rock?

I think none of that is really all that relevant to the question at hand, and it's kindof enough that you can conceptualize the difference, which is why I added the "(conceptually)", to avoid that possible distraction--but if you agree that we can distinguish a rock from a picture of a rock, then you might as well ignore it.

> 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.

Yeah, sure.

> Can or can you not do the same with mathematics, and why or why not?

Well, obviously not the same, as there is no such thing as "a picture of a mathematics"?! But obviously, we can, say, distinguish mathematics from the word "mathematics". So, I guess I am not really sure what the question is?

> So, in that sense, would you agree that the non-physical exists in reality?

I agree that instances of abstractions that are not concerned with physical representation do exist in reality. That does not mean that I agree that instances of those same abstractions exist without physical representation, for lack of evidence of that being a thing.

> How do you know that mathematicians don't intend to make statements about reality when they declare axioms?

Because that is how "axiom" is defined (by mathematicians)?

> Even if they don't intend to make claims about reality, couldn't mathematicians intend to do so?

You mean whether a hypothetical mathematician could be intending to make a claim about reality when declaring it an "axiom"?

Well, yes, in the sense that anyone can obviously redefine words however they want? It's the same sense in which I could be talking about a mammal when I say 'apple'. The point is, that still doesn't make elephants a fruit, so the question is kindof pointless. Even if you somehow manage to make someone apply the label 'axiom' to a claim about reality, that helps you nothing with trying to show that all of the not-a-claim-about-reality axioms are claims about reality.

> 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...

Well, if that is how you use the term, then that's how you use the term, I guess, but it seems to me that it's more appropriate for someone taking a position that is meaningfully on a scale between two other positions--which is very much distinct from not coming to a conclusion.

> 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.

Sure. Though it's just as much just an expression of how convincing you find someone's arguments as it is some claim of an objective measure of substantiation.

> 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, you can read it that way. But ultimately, in a discussion between two, it's about how convincing your arguments are to the other party, so it's kindof besides the point?

> Sure, but be careful to substantiate your rejections.

Yeah, I think I am. That is, I explain why your arguments are not convincing (unless they are ...).

> The assumption it self is unjustified, yes, but why am I unjustified in assuming it?

My point was that you are neither justified nor unjustified (in the sense of being (in)sufficiently justified), because that's a category error. To make an assumption means to declare that you will treat whatever you are saying you assume as true (for the purposes of a particular statement/discussion/argument/whatever), regardless whether there is justification for it or not. Assumptions are not in the category of things that have a level of sufficient justification. If you give a justification for a statement, that that by definition makes it not an assumption. "Justified assumption" is a contradiction in terms like "wet dryness".

> Arguments can't be made without assumptions, but the assumptions of arguments should be obvious.

And they should be something the other party agrees with, if you goal is to convince. If you assume something to be true that the other party doesn't (yet) think is true, any arguments that you build on that assumption will be unconvincing.

Which also means that if the other party challenges your assumption, you then should justify it (making it no longer an assumption).

> 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)).

Well, but that is what this is all about? If the Peano axioms are a purely artificial construct of humans, then "'1 < 2' absent humans" has no referent, and your hypothetical scenario that you were asking about was roughly the equivalent of that, arguably.

Also, it doesn't really make too much sense to respond to an objection to an assumption with "it should be obvious". I mean, you might have thought that, and that's why you made the assumption, and that's all fine. But the moment the other party tells you they don't agree with your assumption, the equivalent of "but I think you should agree" is not really going to help anyone.

> If you think that is not obvious, why?

Why I think that it is not obvious that '1 < 2' absent an evaluator aware of the Peano axioms (and more) has a referent? Because as far as I can see that is a statement in a formal system, which has no meaning without that formal system.

> If you think arguments shouldn't make assumptions at all, then tell me why and give me an example argument with no assumptions.

I am not saying that at all. It just doesn't make sense to make "justified assumptions", because that's a contradiction in terms.

> So if the "copies" are material, are the "originals" also material?

How would I know? I mean, I have only ever experienced material (in the farthest sense) copies and originals, so I see no reason to think that non-material ones are a thing. But who knows, maybe you have the evidence for non-material copies of movies?!

> To be incompatible with science means to be making factual (as in real/non-formal) claims based on methodology that is not demonstrated to be reasonably reliable for determining the truth of such a claim.

Why define 'incompatible with science' this way over utilizing some form of the top definitions of 'incompatible' resulting from a quick google search (e.g. "so opposed in character as to be incapable of existing along with science", "incapable of association or harmonious coexistence with science", "that which cannot coexist or be conjoined with science", "not able to exist or work with science")?

Also, are you saying that it is the "making" of the claim that is incompatible when using non-demonstrated methodology, or is it the claim itself that is incompatible?

How can a methodology be demonstrated to be reasonably reliable for determining the truth of a claim?

Why are formal claims excluded from being considered incompatible with science?

Is it possible that a claim could be really true even though the methodology used to arrive at that claim has not been demonstrated to be reasonably reliable for determining the truth of such a claim?

> The definition of what science/"the scientific method" is?

What is the definition of science/"the scientific method"?

===

> Well, then it's not. ... I obviously kindof agree that the first part is pretty ambiguous, which presumably is why I added the second part

Regarding the second part of your description of numbers, to what does "measuring or counting" refer (i.e. what is being measured or counted)?

> Well, obviously not the same, as there is no such thing as "a picture of a mathematics"?! But obviously, we can, say, distinguish mathematics from the word "mathematics". So, I guess I am not really sure what the question is?

When we distinguish a rock from a picture of a rock, from the word "rock", and from the concept of a rock, we are noting that the rock exists apart from a picture of it, a word of it, and a concept of it. Now that's not difficult to accept because a rock is physical. So when I ask if we can do the same of mathematics, I am seeking an acknowledgement of the non-physical and a reason why if we can, and for a reason why if we cannot.

> I agree that instances of abstractions that are not concerned with physical representation do exist in reality. That does not mean that I agree that instances of those same abstractions exist without physical representation, for lack of evidence of that being a thing.

Are you saying "not concerned with physical representation" is equivalent to "not material", as in "a movie is not material because it is not concerned with physical representation but is an instance of an abstraction which we have no evidence for or against being physical"?

> Because that is how "axiom" is defined (by mathematicians)

So all mathematicians agree that they don't intend to make statements about reality when they declare axioms?

What your definition of 'axiom'? The most readily available definitions I can find either roughly state that an axiom is "a self-evident truth", "a statement widely accepted as true", or "an assumption without proof for the sake of studying the consequences that follow". None of these indicate that axioms aren't intended to be statements about reality.

> Well, yes, in the sense that anyone can obviously redefine words however they want.

So would I be correct in stating that you could just be defining 'axiom' however you want, and the statement "axioms are not claims about reality" simply conforms with your definition?

> But the moment the other party tells you they don't agree with your assumption, the equivalent of "but I think you should agree" is not really going to help anyone.

I haven't only told you "I think you should agree" though. I also asked why you disagree...

> If the Peano axioms are a purely artificial construct of humans, then "'1 < 2' absent humans" has no referent ... ... Because as far as I can see ['1 < 2'] is a statement in a formal system, which has no meaning without that formal system.

So am I correct in that, given the Peano axioms, it is not obvious to you that '1 < 2' has a referent, because the Peano axioms may or may not be a purely artificial construct of humans.

> How would I know? I mean, I have only ever experienced material (in the farthest sense) copies and originals, so I see no reason to think that non-material ones are a thing. But who knows ...

So you acknowledge that you don't know whether non-physical things exist?

===

> How do you know that? Couldn't there be mechanisms by which something changes state that can not be determined by science? How do you know there aren't?

Because all of reality as we experience it can be intelligibly explained by science, and since changes in state can be observed by science then there are intelligible explanations for those changes.

If in reality there were some changes of state that could not be intelligibly explained, then reality taken as a whole wouldn't be intelligible. If reality as a whole was unintelligible, then it couldn't be fully and intelligibly asserted that "reality is not entirely intelligible". Such a statement is self defeating.

> And in the particular case: How did you determine that the mechanism by which the universe changes state can not be determined by science?

I don't know what this is asking.

> So, electrons are non-physical after all, then?

What have I said that lead you to this conclusion?

> I assume you agree that the electric field is physical? The potential to change the electric field is not observable, but it exists, therefore, it is non-physical? (I am paraphrasing, obviously, but I think that is roughly your argument applied to electrons?)

The electric field is physical, we can observe its effects and things that indicate it has been affected. The potential(s) for the electron field being in a different state is/are not observable via effects or things that indicate it has been affected.

> Exactly. So, why would you expect the same reason to be convincing when you use it?

What line of reasoning?! My agreement to the modification you gave to my scenario--"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"--was an assertion that a person ought to follow their beliefs.

Unless there is some ambiguity somewhere, "would be the way to go" doesn't bear much resemblance to "you will indeed attain".

You modified "then shooting yourself in the head would be the way to go" to say "you then shoot yourself in the head, [then] you will indeed attain maximum wealth", which seemed to become a line of questioning to determine whether I thought a person will get what is in line with their beliefs. It should be fairly obvious that I don't think that is the case, unless one's beliefs are in line with what is true. Have I established what I think is true: no.

I acknowledged that I had not substantiated a convincing argument to care about morality (given my definition) when you highlighted that "'care' and 'listen to' are two different questions as well".

[part 1 ... again!]

> Why define 'incompatible with science' this way over utilizing some form of the top definitions of 'incompatible' resulting from a quick google search (e.g. "so opposed in character as to be incapable of existing along with science", "incapable of association or harmonious coexistence with science", "that which cannot coexist or be conjoined with science", "not able to exist or work with science")?

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

> Also, are you saying that it is the "making" of the claim that is incompatible when using non-demonstrated methodology, or is it the claim itself that is incompatible?

Science is a "method for making/justifying claims", and as such, it is non-scientific methods that are (potentially) incompatible with it? Plus, obviously, you can justify claims that do have scientific justification via non-scientific methods (like, I dunno, "masses attract because I think 5 is a lucky number")--that justification is obviously non-scientific, but that doesn't change the fact that the claim that masses do attract does have scientific justification.

> How can a methodology be demonstrated to be reasonably reliable for determining the truth of a claim?

Using science.

> Why are formal claims excluded from being considered incompatible with science?

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

> Is it possible that a claim could be really true even though the methodology used to arrive at that claim has not been demonstrated to be reasonably reliable for determining the truth of such a claim?

Yes, obviously?

> What is the definition of science/"the scientific method"?

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

> Regarding the second part of your description of numbers, to what does "measuring or counting" refer (i.e. what is being measured or counted)?

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

> When we distinguish a rock from a picture of a rock, from the word "rock", and from the concept of a rock, we are noting that the rock exists apart from a picture of it, a word of it, and a concept of it. Now that's not difficult to accept because a rock is physical. So when I ask if we can do the same of mathematics, I am seeking an acknowledgement of the non-physical and a reason why if we can, and for a reason why if we cannot.

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

> Are you saying "not concerned with physical representation" is equivalent to "not material", as in "a movie is not material because it is not concerned with physical representation but is an instance of an abstraction which we have no evidence for or against being physical"?

No, it's not an equivalence, it is just one of the definitions of "not material". It is generally accepted usage to call concepts that are not concerned with material/physical aspects "not material". But there is also the usage of "something possessing attributes otherwise associated with the material, but also not being material", such as "an immaterial horse" or something along those lines. Those two definitions are not interchangeable.

> So all mathematicians agree that they don't intend to make statements about reality when they declare axioms?

No, just as not all humans agree that the earth is a sphere.

> What your definition of 'axiom'? The most readily available definitions I can find either roughly state that an axiom is "a self-evident truth", "a statement widely accepted as true", or "an assumption without proof for the sake of studying the consequences that follow". None of these indicate that axioms aren't intended to be statements about reality.

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

But really, I don't get what the point of all this even is. You can distinguish claims in formal systems and claims about reality, right? And you can distinguish statements declared as assumptions from statements declared as derived or observed truth, right? So, who cares whether all mathematicians agree on the names for these things (no, they don't, if only because mathematicians speak differen languages)? 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. So, how about we get back to the substance of that, instead of trying to figure out what people call it?

> So would I be correct in stating that you could just be defining 'axiom' however you want, and the statement "axioms are not claims about reality" simply conforms with your definition?

Well, yes and no. No, in that I used the definition that is commonly accepted, and didn't mean to introduce any unusual definition. But also yes, in the sense that in so far as we are not primarily talking about what the generally accepted definitions are or what other people mean, it doesn't make much sense to do anything other than to go with "well, ok, that's what they mean when they use the word", as long as it is being used consistently.

> So am I correct in that, given the Peano axioms, it is not obvious to you that '1 < 2' has a referent, because the Peano axioms may or may not be a purely artificial construct of humans.

No. It is not obvious that there is such a thing as "given the Peano axioms", absent humans (or possibly more generalized evaluators). You constantly want to make this assumption, but that assumption really is just the assumption of the existence of the immaterial, and as such it's not a useful basis for demonstrating the 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.

> So you acknowledge that you don't know whether non-physical things exist?

That depends on the definition of "exists". As far as the most commonly used definition is concerned, the non-physical does not exist, 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). For a more general definition that you might find to be used by philosophers, I don't know.

> Because all of reality as we experience it can be intelligibly explained by science

Hu? Do you mean by that that there is nothing that's left unexplained by science? Or are you saying that whatever science doesn't have an explanation for yet, is (by definition) not part of reality? Or what?

> and since changes in state can be observed by science then there are intelligible explanations for those changes.

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?

> If in reality there were some changes of state that could not be intelligibly explained, then reality taken as a whole wouldn't be intelligible.

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

> If reality as a whole was unintelligible, then it couldn't be fully and intelligibly asserted that "reality is not entirely intelligible". Such a statement is self defeating.

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

> The electric field is physical, we can observe its effects and things that indicate it has been affected. The potential(s) for the electron field being in a different state is/are not observable via effects or things that indicate it has been affected.

Oh, so your claim is that the potential for the electric field to change state is something distinct from the electron? And analogously for the potential for the universe to change state?

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)?

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.

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, 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. 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.

> "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"--was an assertion that a person ought to follow their beliefs.

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?

[part 2]

> Unless there is some ambiguity somewhere, "would be the way to go" doesn't bear much resemblance to "you will indeed attain".

Seriously? You really didn't understand that "would be the way to go" in this context means roughly "would be how they would reach their goal"? And that the implied goal in this scenario was not to die, but to attain wealth? Are you absolutely sure that you are not intentionally not understanding the obvious that you would understand in any other conversation that is not about a god belief?

> You modified "then shooting yourself in the head would be the way to go" to say "you then shoot yourself in the head, [then] you will indeed attain maximum wealth", which seemed to become a line of questioning to determine whether I thought a person will get what is in line with their beliefs. It should be fairly obvious that I don't think that is the case, unless one's beliefs are in line with what is true. Have I established what I think is true: no.

Which primarily means that you have just completely missed the point of that part of the conversation?

> I acknowledged that I had not substantiated a convincing argument to care about morality (given my definition) when you highlighted that "'care' and 'listen to' are two different questions as well".

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

[part 2]

> The mechanisms by which something changes state can be determined by science.

How do you know that? Couldn't there be mechanisms by which something changes state that can not be determined by science? How do you know there aren't?

And in the particular case: How did you determine that the mechanism by which the universe changes state can not be determined by science?

> 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.

So, electrons are non-physical after all, then? I assume you agree that the electric field is physical? The potential to change the electric field is not observable, but it exists, therefore, it is non-physical? (I am paraphrasing, obviously, but I think that is roughly your argument applied to electrons?)

Also, it seems problematic that you are refering to "physical" here, in what for all intents and purposes is an attempt to define the distinction between the physical and the non-physical. And that doesn't seem to me to be a mere accident, but rather a symptom of the fact that you seem to build your argument on our current understanding of physics--when, really, the question is: What justifies our current understanding of physics? It is true that the electron is considered part of the physical world by physicists. But why is that? And what does that even mean? When you start with physics from a position where the existence of electrons has not been established yet, what were the steps to get from there to here?

> Yes... I explicitly stated this, albeit in different terms.

Well, possibly. But then, I asked for things that you would expect to be convincing. Stating that what you said isn't convincing still doesn't really make things convincing, does it?

> Absolutely not.

Exactly. So, why would you expect the same reason to be convincing when you use it?

[part 2]

> I have no qualms with ending our discussion if your taking the middle ground of "I don't know"

Well, it's obviously up to you what you want to discuss, but I would very much object to the idea that "I don't know" is some kind of middle ground.

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?

> My goal has been to bring things to a middle ground, but if you haven't been or are no longer making claims against the non-physical, then we are at where I wanted to be.

I don't think I have ever made claims against the non-physical, at least not intentionally. I have only objected to your unsubstantiated claims that the non-physical exists because they are unsubstantiated.

Though I do wonder: If you say that your goal was to bring things to a middle ground, and you consider "I don't know" to be some sort of middle ground ... do you agree then that we don't know of the existence of anything non-physical?

> You can challenge claims of the non-physical, to be sure, but at this juncture I prefer to shoot down claims that assert the non-physical doesn't exist, of which you no longer appear to me to be claiming.

Well, sure, but be careful to not confuse rejections of unsubstantiated claims with counter-claims.

> What makes "'1 < 2' has a referent" an unjustified assumption in the context of my argument? Yes I have not established it, but what would make me unjustified in assuming it?

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 ...

> What did you mean by "instances of movies"?

Like, a particular DVD, or blue-ray, or MPEG file, or series of pictures on a screen, or whatever ... I guess you could say "copies" instead of "instances". And likewise for axioms, them being remembered in a brain, written on a blackboard, printed in a book ...

> 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?

Like, I understand you are making this claim, but 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", or however else you could describe the electron, that would justify any fundamental distinction.

So, what are the criteria by which you decided that the potential for the universe being in a different state is not a mechanism by which the universe changes state, that would, when applied to the electron, get you to the conclusion that the electron is a mechanism by which the electric field changes state, which thus would justify the distinction? And the same for any other reasons you give.

So far, it seems more like you have the pre-conceived notion that one of those is physical and the other is not, and then you give reasons that seem consistent with either of those positions somehow. But what I am interested in is: Suppose we don't know yet which of those is physical or non-physical, how do we go about finding out?

> First "care" and "use" are two very different questions. Again, define should ;).

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.

> Why should you use the version of morality of which I am speaking? Because it is the true one (I recognize that I have not established this).

And then you certainly also recognized that you haven't given reasons to be convinced, right? Because that is what I explained I meant when you asked for a definition for "should". I am sorry, but this starts to feel like you are willfully missing the point.

> Absolutely not.

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?

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