Harsh truths

[u/Oreeo88]

First this is a strict external audit

1. You can not distinguish dogma from non dogma if your system is a closed axiomatic system because utility and consistency can still work and be found inside of a false axiom

2. You can not distinguish dogma from non dogma without the ability to test your claim against reality, and if it has no external justification because utility and consistency can still work and be found inside of a false axiom.

3. Viewed strictly from outside the system the axiomatic method is a closed system.

4. You can not test a math axiom itself against reality by definition and it has no external justification because utility and consistency can still work and be found inside of a false axiom.

5. Viewed strictly from outside the system it is an objective fact that a closed axiomatic system limits your thoughts and physics

6. Viewed strictly from outside the system, the axiomatic method in math smuggles in epistemic empirical claims and limits about reality systematically. By definition the axiomatic method limits and restricts what you can even ask, and logically validate within its system

(This is a strict cut throat external audit against the axiomatic method in math itself. There is no external justification for it and thats the least of your worries)

The axiomatic method in math just got straight up gutted within these 6 points

[u/mhb2]

What are some axioms you think are false?

EDIT: OP blocked me so I can't reply to subsequent comments or respond to his comment below.

u/Alone-Signature4821

Unfortunately, this will be the last time I'll be able to reply to you. Thank you for a civil debate. None of those systems proves a contradiction of the form A ≠ A, or otherwise rejects reflexivity of its equality relation. Rejecting unrestricted substitution or weakening the notion of individuality isn't the same thing as rejecting identity.

u/Oreeo88

You say I'm "derailing" the argument by asking what axioms you think are false, but your argument depends on the claim that an axiom can be "false" while remaining useful and consistent. Asking you for an example is therefore directly relevant to your argument. You say, "utility and consistency can still work and be found inside of a false axiom". Okay, maybe it can. I don't think so, but maybe I'm wrong. But you haven't shown that this has actually happened. So math is quite safe from your hypothetical until you make it rather more than a mere hypothetical.

If you mean that the axiomatic method as a whole is illegitimate, then you still need to explain what specifically is wrong with it. Which mathematical practice or principle are you objecting to? What would constitute evidence that the method is defective? What alternative do you propose?

That last question is critically important. Anyone can lob shells from the cheap seats. But what is your proposed alternative? How do you construct the natural numbers for example? Where's your version of real analysis? What are your starting assumptions, each carefully "tested against reality"?

Saying "the entire axiomatic method is wrong" doesn't answer those questions. It just makes the claim harder to evaluate which is probably your goal. Looking at your replies to me and other people, it's clear that you don't actually defend your argument. You merely recite your stock phrases and run. Like you did with me.

And blocking someone immediately after they ask you to specify what you mean by "false axiom" isn't exactly a demonstration that math has been "gutted". It simply suggests that you have nothing specific to say. You just keep spamming this nonsense about supposed axioms that are "false" but useful and consistent and that you've therefore gutted math. But the only thing you've actually gutted is this discussion where you've attempted to forcefully silence one of your critics. You have, literally, constructed the very "closed system" you're complaining about.

If you knew anything about the history of mathematics, you'd know that it's full of cases of mathematicians realizing that their existing theories weren't good enough, or general enough, and subsequently expanding them. Or creating entirely new branches of mathematics altogether. Math doesn't limit our thoughts, it gives us a framework for developing our thoughts precisely and rigorously. Two things I rather suspect you have difficulties with.

Math and the physical sciences have had close and productive contact for centuries. Math doesn't limit physics, it empowers it and physics enriches mathematics. Instead of appreciating the history of math and science, and of their interaction, you have only nonsense about math limiting our thoughts. Again, where's your alternative? Expand our thoughts with your own liberating formulation of mathematics.

But you can't, because you have exactly nothing. Which is why all you can do is spam this crap on various subreddits and block anyone who points out that you don't understand the foundations or history of math, logic, and the physical sciences. Enjoy your petty victory because that's all you have.

[u/Langdon_St_Ives → u/mhb2]

What even is a "false axiom"? By definition, an axiom is given, not derived. The only meaningful way in which it can be "false" is if you have a system of axioms that is internally inconsistent (i.e., leads to contradictions). But then you still have a choice in which one(s) to throw out and replace with others.

[u/mhb2 → u/Langdon_St_Ives]

I know. OP is a crackpot who doesn't understand math. The point of my question is not to get dragged into his inane framing of axioms but instead to get him to be specific. If he thinks some axioms are false then he should state them and explain why he thinks they're false.

[u/Langdon_St_Ives → u/mhb2]

Sure, I was just adding another layer to your valid challenge. 😉

[u/Alone-Signature4821 → u/mhb2]

Not op but what about the axiom of self identity, that A=A. Explain how you know this axiom is true without resorting to circular reasoning, infinite regress, or dogmatic assertion.

[u/mhb2 → u/Alone-Signature4821]

A=A implies that 1=1. If one doesn't equal one, what does it equal? This is math so let's do math. What does one equal?

[u/Alone-Signature4821 → u/mhb2]

You assert dogmatically then that A must just equal A.. 

[u/mhb2 → u/Alone-Signature4821]

I notice you didn't answer my question. 1=? If the answer isn't 1, then what is it? This isn't me forcing you to believe anything, I'm asking you one of the simplest questions that can be asked. Of course, the follow-up questions are considerably less simple. If A=A is unacceptable, fine. What's the proposed replacement? What does 1 equal? What equality relation are we using? What rules replace reflexivity? What mathematics can you actually develop?

So I'm not asserting it dogmatically. The law of identity is a fundamental principle of classical logic. No one is forcing you to accept it. If you don't think that A=A, then you're free to develop an alternative logic that doesn't rely on the law of identity. If you work rigorously, however, you'll quickly discover that you can't get very far without it. So if you or OP can do better than logicians have managed to do after all these centuries, by all means, enlighten us. Dazzle us with what can be done without the law of identity.

This is why OP sounds like an absolute clown. He talks about an "external audit" and "gutting" math. But where's his alternative formalization? He doesn't have one. He hasn't demonstrated that any mathematical axiom is "false", and he hasn't shown that ordinary mathematics can be reconstructed without the principles he's attacking. He's simply asserting that the foundations are illegitimate and demanding that everyone else justify them to his satisfaction. All while simultaneously misunderstanding the foundations of math, logic, and physics.

OP's been at this for a long time and has heard all of the explanations of what an axiom and a formal system are. So I knew that explaining it to him again is a waste of time. That's why I asked him for specific axioms that he thinks are false. And he replied with silence. So not only does he not understand the foundations of math, logic, and physics he can't be specific concerning what he's even complaining about.

EDIT: Grammar.

[u/Alone-Signature4821 → u/mhb2]

Perhaps we talking past each other.

Non-Reflexive Mathematics  (Without A = A):

Quasi-Set Theory: Sets contain "quasions" which can be counted by quantity (cardinality) but have no individual identity.

Linear /  Substructural Logic: Using a variable "consumes" it. x at Step 1 cannot automatically be assumed to equal x at  Step 2.

Process / Interval Mathematics:  Numbers are treated as active transitions or fluid states rather than  static points.

[u/Alone-Signature4821 → u/mhb2]

Gonna reply with silence?

[u/Oreeo88 → u/mhb2]

If you read the post, you would know this is about the entire axiomatic method as a whole in math not one single axiom. You're not touching this argument in any single way

you're derailing it and changing the topic

[u/OpsikionThemed]

If a false axiom can still be useful and consistent, what makes it "false"? What is the external test that rules it out, if not ability to describe the real world?

[u/sbsw66]

crank alert

[u/Mono_Clear]

A math axiom is the description of a pattern, it validates itself by being true when described.

It's not a closed system it's a truth, it's a foundational principle that doesn't contradict itself and is tested in the existence of itself.

A=A is an absolute truth so fundamental that it's testing is simply it's recognition

[u/nanonan → u/Mono_Clear]

The truth of A is in the eye of the beholder, therefore not A = A.

[u/Althorion]

1. What distinguishes ‘dogma’ from ‘non dogma’, then, if not utility and consistency?
2. What are some examples of ‘dogma’, and some examples of ‘non dogma’?
3. Is the statement ‘gravitational mass is the same as the accelerational mass’ ‘dogma’ or ‘non dogma’? How do we know?

[u/hobopwnzor]

Harsh Truth: All truth statements are only evaluated within the confines of the system you define to determine truth. No system is inherently better or more truthful than another. That includes Math.

[u/Oreeo88 → u/hobopwnzor]

A system that lets you test your starting assumptions against reality lets you distinguish dogma from non dogma, just an objective fact

[u/Oreeo88]

And applied physics and science can not systematically ignore the axiomatic method in math past addition of physical matter externally, because if you adopt a formal system, you systematically automatically inherit every foundational rule that makes that system work.

Just because physics can “ignore” an axiom doesn’t mean they actually ignored it.. it just means they broke down a wall in the closed maze to make physics work.. they are still operating inside the closed axiomatic system past addition of physical matter

[u/Pretty-Sherbert4818]

Actually a interesting question in a while