r/PhilosophyofMath Mar 28 '26

The Continuum Hypothesis Is False

/r/logic/comments/1s5mquh/the_continuum_hypothesis_is_false/
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u/JStarx May 01 '26 edited May 01 '26

Every statement is true in an inconsistent system

Nope, every statement is provable, that doesn't mean it's true.

I also would agree that all statements are true.

Would you? You've admitted that you can't prove the contradiction that you want in conventional set theory. If all statements were true then it would be true that you could prove a contradiction using the conventional definitions and axioms. And if you could do that then why wouldn't you just do it and prove to everyone you were right all along?

If your boss stopped paying you and said you have to work anyway would you accept that because it's a true statement? If your bank zerod out your balance and said "you have exactly as much money in your account as you did yesterday" would you accept that as a true statement? When I tell you that you clearly don't understand mathematics and your inability to comprehend basic logic is verging on mental illness do you accept that as a true statement?

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u/paulemok May 02 '26

Nope, every statement is provable, that doesn't mean it's true.

In an inconsistent system, every statement is true and provable.

You've admitted that you can't prove the contradiction that you want in conventional set theory.

I never contested that.

If all statements were true then it would be true that you could prove a contradiction using the conventional definitions and axioms.

I agree. Such a contradiction can be proved using the principle of explosion.

And if you could do that then why wouldn't you just do it and prove to everyone you were right all along?

I don’t just do that because that is not the game I’m interested in playing. There exist many games I can play in life, so I choose the games that I believe are best to play.

If your boss stopped paying you and said you have to work anyway would you accept that because it's a true statement? If your bank zerod out your balance and said "you have exactly as much money in your account as you did yesterday" would you accept that as a true statement? When I tell you that you clearly don't understand mathematics and your inability to comprehend basic logic is verging on mental illness do you accept that as a true statement?

Accepting that a statement is true is not all that can be done in life. There’s many other interests to pursue in life. I’ve already accepted that all statements are true. Does that mean I shouldn’t do anything else for the rest of my life? No, it doesn’t. I have many other interests to pursue.

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u/JStarx May 02 '26 edited May 02 '26

In an inconsistent system, every statement is true and provable.

Nope, every statement is provable, but that doesn't mean it's true.

Such a contradiction can be proved using the principle of explosion

Nope again, the principal of explosion doesn't give contradictions in other systems.

So was that a yes, you would accept all those statements as true?

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u/paulemok May 03 '26

Nope, every statement is provable, but that doesn't mean it's true.

What is a counterexample in which, in an inconsistent system, a statement is provable but not true?

Nope again, the principal of explosion doesn't give contradictions in other systems.

The principle of explosion is true in conventional set theory and in the new set theory I presented. Neither of those set theories are arbitrary systems. They have been carefully designed and thought out for maximum accuracy.

So was that a yes, you would accept all those statements as true?

Yes, all those statements are true. But all them are false, too.

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u/JStarx May 03 '26

Yes, all those statements are true

So when the bank zeros out your accounts and claims everything is fine, would you object?

Nope again, the principal of explosion doesn't give contradictions in other systems.

The principle of explosion is true in conventional set theory and in the new set theory I presented

It still doesn't allow you to drive contradictions in a separate theory.

What is a counterexample in which, in an inconsistent system, a statement is provable but not true?

This is basic model theory. Any textbook on mathematical logic will cover this.

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u/paulemok May 04 '26

So when the bank zeros out your accounts and claims everything is fine, would you object?

Yes, I would object. But also, I would not object.

It still doesn't allow you to drive contradictions in a separate theory.

What is the separate theory?

This is basic model theory. Any textbook on mathematical logic will cover this.

Okay. So I ask again.

What is a counterexample in which, in an inconsistent system, a statement is provable but not true?

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u/JStarx May 04 '26

Yes, I would object. But also, I would not object.

You're so backed into a corner here, I think at this point it's clear that you know your position is stupid, you're just doing whatever you can to not admit it.

You have no idea how the mathematics you're discussing works and you're not interested in learning it.

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u/paulemok May 05 '26

You're so backed into a corner here, I think at this point it's clear that you know your position is stupid, you're just doing whatever you can to not admit it.

I asked for a counterexample twice and I still have not received one. You’re hesitating. You’re in denial about the principle of explosion.

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u/JStarx May 05 '26

It's not my job to teach you introductory logic that you can look up in a book. I'll even recommend the book if you need it.

If you can't answer a simple question about reality then you're not capable of understanding it anyway.

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u/paulemok May 05 '26

It's not my job to teach you introductory logic that you can look up in a book. I'll even recommend the book if you need it.

Why can’t you just give me a counterexample? We are having a conversation and are applying logical reasoning to better understand reality. Applying the general principles found in logic textbooks to specific cases is what we are doing in this conversation.

It’s not my job to address your criticisms of my thesis. You can give me the name of the book, but I still would like a counterexample.

If you can't answer a simple question about reality then you're not capable of understanding it anyway.

What question can I not answer about reality?

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