Not just axioms, but all mathematical proofs are not testable by science.
> ... that's simply a category error because axioms are not claims about reality.
Are you saying that math on its own doesn't pertain to reality at all?
Either way I'd imagine you find math useful, and if you take it as a category error to test mathematics with science, then you've stumbled across my exact point. It would be a category error to test all religious claims with science, and unless a religion has made an explicit scientific claim that IS false, whether known or not, then that religion can't be said to be incompatible with science without making a categorical error.
> Not just axioms, but all mathematical proofs are not testable by science.
By virtue of being derived from axioms?
> Are you saying that math on its own doesn't pertain to reality at all?
No, I am saying exactly what I am saying: Axioms, and thus all of mathematics, because all of mathematics is derived from axioms, do/does not make claims about reality. "1 + 9 = 10" is not a claim about reality, it's simply a statement that is consistent with the Peano axioms.
> Either way I'd imagine you find math useful
Yes, very much so. Because it so happens that it can be used to describe models of reality. But whether given mathematical structure is a good fit for describing some aspect of reality is testable. In fact ,that is the only reason why it is rational to believe that mathematics can be used to model reality.
While "1 + 9 = 10" is not a claim about reality, "1 apple + 9 apples = 10 apples" is, and a very testable one at that.
> It would be a category error to test all religious claims with science
Why?
> and unless a religion has made an explicit scientific claim that IS false, whether known or not
How do you decide whether a given claim made by a religion is a scientific claim? Is it "not scientific" just because they say so? Or is there come criterion by which to distinguish scientific religious claims from "not scientific" religious claims?
>> Not just axioms, but all mathematical proofs are not testable by science.
> By virtue of being derived from axioms?
No, but by virtue of not being able to perform scientific observation on a mathematical proof. Math has no color, smell, taste, feel, nor affect on other material objects from which we can observe.
> "1 + 9 = 10" is not a claim about reality
This is wrong. If "1 + 9 = 10" is true and truth is that which pertains to reality, then "1 + 9 = 10" is a claim about reality albeit a mathematical one (i.e. science is not the only way to talk about reality). I'd agree that it's not a claim about PHYSICAL reality though.
>> It would be a category error to test all religious claims with science
> Why?
Because not all religious claims are claims about physical reality, some are about moral reality. Just like "1 apple + 9 apples = 10 apples" is not a claim about physical reality, but is an application of mathematics to physical reality, "You must not steal" is not a claim about physical reality, but is an application of morals to persons in physical reality.
Moral claims are not testable by science. It would be a categorical error to try to discover the color, smell, taste, feel, or affect of morality.
> How do you decide whether a given claim made by a religion is a scientific claim? Is it "not scientific" just because they say so? Or is there come criterion by which to distinguish scientific religious claims from "not scientific" religious claims?
If you can perform direct or indirect physical observation to verify a religious claim, then it is a claim that science can deal with.
The former has no content for me (like, no text on the page), so only referring to the latter:
Isn't it strange how the whole criticism is based on a completely unfounded assumption?
How does the author come to the conclusion that Anthony Magnabosco does not use the same methods to question his own beliefs? Unless he actually asked him questions about his beliefs, how does he know how he justifies his beliefs and whether he does have good justifications, or at least justifications that he himself considers good justifications?
And even stranger: How is it even relevant whether he personally uses it on anything else? He has advocated many times for religious people to adopt it as well to go out and question others' beliefs on religious matters. If he maybe has a blind spot on some of the things he believes (as people tend to have), then maybe it's on those who see the blind spots to use street epistemology on him? I mean, if anything, that's the whole point, to have a non-confrontational, constructive method to make other people aware of possible blind spots in their reasoning that they themselves can't see, for they are blind spots?
In one sentence, that criticism reads to me as "How dare he questions other people's blind spots and suggests everyone should be doing the same to help everyone see the blind spots they couldn't possibly find by themselves ... when he hasn't found his own blind spots by himself yet!" How is that anything but a completely nonsensical statement?
But the point is that it isn't true. It is consistent with and implied by the Peano axioms, that's it. If you make the completely arbitrary assumption (as far as pure mathematics is concerned) that the Peano axioms are true (that is to say, you consider them to be axioms), then it follows that "1 + 9 = 10" is also true. If you reject the Peano axioms, then it's not true anymore. That is, until you accept some alternate axioms that also imply "1 + 9 = 10". Or you simply make "1 + 9 = 10" an axiom, then it's true simply because it's an axiom. The fact that the truth of that statement is completely dependent on your arbitrary choice of axioms should tell you that it's not a statement about reality.
> I'd agree that it's not a claim about PHYSICAL reality though.
So, can you demonstrate that there is a non-physical reality?
> Because not all religious claims are claims about physical reality, some are about moral reality
What is moral reality and how do you demonstrate that it exists (and is distinct from physical reality)?
> Just like "1 apple + 9 apples = 10 apples" is not a claim about physical reality, but is an application of mathematics to physical reality
Uh ... what? Did I maybe just not express myself clearly? Let me rephrase: When you have one apple in a basket, and you put another 9 apples into the same basket, you will have 10 apples in that basket. That is a statement about (physical) reality, wouldn't you agree? That's what I meant.
> "You must not steal" is not a claim about physical reality, but is an application of morals to persons in physical reality.
It's simply not a claim at all, and therefore it's just yet another category error? "Electrons must have a mass of 5 tons" is also not a claim about physical reality, because it's also not a claim. "Electrons do have a mass of 5 tons" is a claim, and it's also a claim about reality, and it's testable. And equally "having and enforcing a social norm of not stealing provides such and such benefits for human societies" is a claim, and it's also a claim about reality, and it's also testable.
The problem with your example is not that it's somehow about morals, the problem is that you simply didn't make a claim, but a command. And that is not because it is impossible to make claims about morals, but because you intentionally avoided making a claim.
> Moral claims are not testable by science. It would be a categorical error to try to discover the color, smell, taste, feel, or affect of morality.
So, you think it is a category error to try and discover the effects of moral norms, because it is impossible to observe the effects of moral norms, because moral norms don't affect (physical) reality?
> If you can perform direct or indirect physical observation to verify a religious claim, then it is a claim that science can deal with.
What would be an example of a religious claim that is "not scientific", other than claims about an afterlife?
> ... If you make the completely arbitrary assumption ...
What do you mean by an "arbitrary assumption". The first definition that comes up for "arbitrary" is "Based on random choice or personal whim, rather than any reason or system". If you agree with this definition, then do you also think that there is "completely" NO REASON to assume that the Peano axioms are true? If so, is this because the Peano axioms are merely assumptions, and not themselves proven?
> If you reject the Peano axioms, then it's not true anymore.
How would someone rejecting axioms, make statements consistent with those axioms untrue?
> The fact that the truth of that statement is completely dependent on your arbitrary choice of axioms should tell you that it's not a statement about reality.
I'll agree that the truth of any mathematical statement is dependent upon the framework under which you view it, but that doesn't stop the statement from being true or false under those frameworks regardless of which frameworks a person chooses to use. Those frameworks don't depend on human minds, so even before mathematical axioms were formulated by humans "1 + 9 = 10" was still true under the Peano axioms, and that will still be true after humans have died off. That which is true is "in accordance with fact or reality".
> So, can you demonstrate that there is a non-physical reality?
Yes.
(Note: Potential is possible state, actual is current state)
A) If potential states of the universe do not exist, then the universe can't change states.
B) The universe can change states.
C) If potential states of the universe are physical, then potential states of the universe would be observable hear and now.
D) If potential states of the universe are observable hear and now, then potential states of the universe would be actual and potential at the same time.
E) Potential states of the universe are not actual and potential at the same time.
-----------------------------------------------------------------------------------
F) Potential states of the universe exist. (modus tollens A,B)
G) Potential states of the universe are not observable hear and now. (modus tollens D,E)
H) Potential states of the universe are not physical. (modus tollens C,G)
I) Potential states of the universe exist and potential states of the universe are not physical. (conjunction introduction F,H)
> The problem with your example ["You must not steal"] is not that it's somehow about morals, the problem is that you simply didn't make a claim, but a command. And that is not because it is impossible to make claims about morals, but because you intentionally avoided making a claim.
Saying I intentionally avoided making a claim is disingenuous, you may have merely misinterpreted what I was trying to say. How might you respond to a rephrasing such as "It is immoral to <X>"?
> What would be an example of a religious claim that is "not scientific", other than claims about an afterlife?
"God is a trinity of three divine persons each fully possessing one divine nature."
> If you agree with this definition, then do you also think that there is "completely" NO REASON to assume that the Peano axioms are true? If so, is this because the Peano axioms are merely assumptions, and not themselves proven?
Well, yes, that is what axioms are, by definition?
(And mind you, we are talking about pure mathematics here--there absolutely are good reasons for generally accepting certain axioms while rejecting others because of the applicability of the mathematics that can be derived from them, but that is where you enter the realm of the testable.)
> How would someone rejecting axioms, make statements consistent with those axioms untrue?
Well, how is truth of mathematical statements determined? How would you determine that "1 + 9 = 10" is mathematically true without the Peano axioms (and without new axioms that replace them, obviously)?
> I'll agree that the truth of any mathematical statement is dependent upon the framework under which you view it, but that doesn't stop the statement from being true or false under those frameworks regardless of which frameworks a person chooses to use. Those frameworks don't depend on human minds, so even before mathematical axioms were formulated by humans "1 + 9 = 10" was still true under the Peano axioms, and that will still be true after humans have died off. That which is true is "in accordance with fact or reality".
That sounds like one big category error?
Mathematics is pretty much like a language. You might as well be saying that "The sky is blue" was a meaningful sentence before English was invented. It seems like you are constantly crossing the border between pure mathematics (analogous to the grammar and vocabulary of a language) and its application (analogous to the semantics of a language). The sky was very much blue before English was a thing, but "The sky is blue" was not a meaningful sentence. In the same way, those things that we describe using mathematics had the same structure before mathematics was invented. When there was one rock in some place, and 9 rocks fell from the sky next to it, there were then 10 rocks in that place. But that is obviously a testable claim (about (physical) reality), not an untestable proof (derived from axioms).
If I were to try and boil down your argument, I think it would be this:
We use mathematics to describe physical reality. Physical reality with the patterns that we describe using mathematics existed before we existed. Therefore, mathematics existed before we existed.
And analogously:
We use English to describe physical reality. Physical reality with the patterns that we describe using English existed before we existed. Therefore, English existed before we existed.
Yes, the patterns existed. But the patterns are a perfectly testable thing. So, you can't use the testable patterns to demonstrate the existence of untestable abstract ideas.
> A) If potential states of the universe do not exist, then the universe can't change states
Could you define what you mean by the word "exist"?
> C) If potential states of the universe are physical, then potential states of the universe would be observable hear and now.
I can not observe the contents of your screen here and now. Does that mean that your screen is not physical?
> E) Potential states of the universe are not actual and potential at the same time.
So, the universe does not exist? (You defined "potential" as "possible", so if a state can not be actual and potential at the same time, all actual states are impossible, hence there is no state for the universe to be in, thus the universe can not exist, right?)
(And yeah, I suspect you mean something else, but it's kinda difficult to point out the flaws in an argument if you don't quite know what the argument is ...)
Overall, I suspect this is all one big exercise in false equivocation, but we'll first have to nail down some definitions and details before I can put my finger on it.
> Saying I intentionally avoided making a claim is disingenuous, you may have merely misinterpreted what I was trying to say.
Well, yeah, let me rephrase: You probably didn't have the intention of expressing something that is obviously identifiable as a claim (because it's a pretty strange way to formulate a sentence that is intended to express a claim)?
> How might you respond to a rephrasing such as "It is immoral to <X>"?
Assuming I didn't agree, I would probably ask you for the evidence to support that claim.
If you were to object that asking for evidence for moral claims is a category error (which I suspect is where you are going with this), I would ask you to define "morality".
> "God is a trinity of three divine persons each fully possessing one divine nature."
Does this god have any observable effects in physical reality?
Note I'm skimming over things because I think we are talking past each other about things that don't strike to the heart of our conversation. If there is anything in particular that I have skipped that you'd like me to comment on, let me know.
> You might as well be saying that "The sky is blue" was a meaningful sentence before English was invented.
You're not distinguishing between propositions and sentences.
"John is a bachelor" and "John is an unmarried man" are different sentences, but they express the same proposition. "Snow is white" and "Schnee ist weiss" are also different sentences--one is English, the other German--but they too express the same proposition. "The sky is blue" was not a meaningful sentence before English was invented, but the proposition it expresses was true before English was invented. Sentences that are claims about reality are labels for propositions. "2", "two, and "II" are just labels we use to talk about the number 2.
To rephrase your boil down of my argument:
"We use mathematics to [label propositions that] describe physical reality. Physical reality with the patterns that [are described by propositions, we now label with mathematics,] existed before we existed. Therefore, [propositions, we now label with mathematics,] existed before we existed."
"And analogously:"
"We use English to [label propositions that] describe physical reality. Physical reality with the patterns that [are described by propositions, we now label with English,] existed before we existed. Therefore, [propositions, we now label with English,] existed before we existed."
> So, you can't use the testable patterns to demonstrate the existence of untestable abstract ideas.
What evidence do you have that establishes this as true?
>> A) If potential states of the universe do not exist, then the universe can't change states
> Could you define what you mean by the word "exist"?
To have objective reality or being.
>> C) If potential states of the universe are physical, then potential states of the universe would be observable hear and now.
> I can not observe the contents of your screen here and now. Does that mean that your screen is not physical?
Fair. Omit the words "here and now" from all of my statements.
>> E) Potential states of the universe are not actual and potential at the same time.
> So, the universe does not exist? (You defined "potential" as "possible", so if a state can not be actual and potential at the same time, all actual states are impossible, hence there is no state for the universe to be in, thus the universe can not exist, right?)
I did not define "potential" as "possible", I defined it as "possible state". I did not say "a state can not be actual and potential at the same time", I said "Potential states of the universe are not actual and potential at the same time".
> Overall, I suspect this is all one big exercise in false equivocation, but we'll first have to nail down some definitions and details before I can put my finger on it.
Sure, and I am more than willing to clean up how I am phrasing things if need be.
>> How might you respond to a rephrasing such as "It is immoral to <X>"?
> Assuming I didn't agree, I would probably ask you for the evidence to support that claim.
> If you were to object that asking for evidence for moral claims is a category error (which I suspect is where you are going with this), I would ask you to define "morality".
Correct. I would say it is a category error to seek out evidence for a moral claim itself. I would not say it is a category error to seek out evidence for why the moral claim should be accepted as true.
Morality: Principles concerning the distinction between right and wrong or good and bad behavior.
>> "God is a trinity of three divine persons each fully possessing one divine nature."
> Does this god have any observable effects in physical reality?
> You're not distinguishing between propositions and sentences.
Because it is not a useful distinction for the topic at hand. Propositions are in the same category as sentences, as far as their dependency on representation is concerned.
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?
> What evidence do you have that establishes this as true?
You are shifting the burden of proof. If you think that that is a reliable method, that is up to you to demonstrate. If you prefer, I'll rephrase to "It has not been demonstrated that you can use the testable patterns to demonstrate the existence of untestable abstract ideas."
> To have objective reality or being.
And how would you define "objective reality" and "being"? Those seem to me more like synonyms than definitions!?
> I did not define "potential" as "possible", I defined it as "possible state".
So ... where you wrote "potential state", you meant "possible state state"?!
> I did not say "a state can not be actual and potential at the same time", I said "Potential states of the universe are not actual and potential at the same time".
Except the latter implies the former? When I resolve your definitions, your statement reads "possible states of the universe are not current and possible at the same time". Or more formally: For any state that is possible, the state must also be either not current or not possible at any given time. A state that is possible obviously can not be not possible. Thus, to fulfill this condition, a state that is possible has to be not current (i.e., if a state is possible, that implies that it is not current). From that it follows that a state that is current hast to be not possible (i.e., if a state is current, that implies that it is not possible). Or in other words: a state can not be current and possible at the same time. What did I miss?
> 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)?
> 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):
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.
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)
> 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?
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?
>> 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.
>>> 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?
> 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.
>> 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?
> 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")?
> 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?
>>>>> 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"?
>> 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.
> ... "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"?
> "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?
> ... 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?
>>> 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?
>>> 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 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.
> 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.
> 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?
> 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'?
> 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?
> 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?
> 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?
>> 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?
>>>>> 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?
> ... 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?
That's either false or a category error.
If you mean that it is not testable whether a given mathematical structure models some aspect of observable reality, then that is obviously nonsense.
If you mean that axioms are not testable, that's simply a category error because axioms are not claims about reality.
> Like "multiverse" perhaps?
Yes?