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> 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 becaus
by zAy0LfpBZLC8mAC 8y ago
> 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?
- sonusario 8y agoNote 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? Absolutely.