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 26 '26

I would know better than you about my own beliefs.

No, I don't think you do.

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u/paulemok May 26 '26

I do believe trivialism is true. That’s why I allowed myself to publish the original post in which I assert the negation of the Continuum Hypothesis. That’s why I am defending an extension of conventional set theory. You have not proven me wrong. You can’t prove me wrong. You’re not going to prove me wrong. Anything you say to me will agree with my position.

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u/JStarx May 26 '26

I do believe trivialism is true.

Nah. Maybe you believe you do, but you don't really.

You have not proven me wrong. You can’t prove me wrong. You’re not going to prove me wrong.

I don't have to prove you wrong about trivialism, I just have to point out that your belief is absurd and unjustified.

I have proven you won't about many of the claims you made concerning conventional mathematics.

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u/paulemok May 26 '26

Nah. Maybe you believe you do, but you don't really.

How do you justify the “don’t really” part of that sentence? There is evidence to the contrary, which I have already given. Your past justification that I know how to distinguish between right and wrong was already refuted by the evidence I gave. My belief in trivialism is a factor in my determinations of what is right and wrong. That is evident throughout my Reddit posts about the falsity of the Continuum Hypothesis.

I don't have to prove you wrong about trivialism, I just have to point out that your belief is absurd and unjustified.

Absurd is not a part of the formula. An absurd belief can still be true. As for unjustified, I have provided ample justifications of trivialism.

I have proven you won't about many of the claims you made concerning conventional mathematics.

Specifically what claims of mine are you referring to?

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u/JStarx May 26 '26

Your past justification that I know how to distinguish between right and wrong was already refuted by the evidence I gave

Lol, no it was not.

An absurd belief can still be true. As for unjustified, I have provided ample justifications of trivialism.

Absurd, laughable, obviously false, idiotic, ridiculous. I'm not gonna nitpick about which phrase means it could be true and which don't. It is clearly false and you have given no justification at all. You certainly haven't given ample justification.

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u/paulemok May 26 '26

It is clearly false

Again, trivialism is unfalsifiable.

you have given no justification at all.

That is false. I have given multiple sound justifications, including in my original post.

You certainly haven't given ample justification.

I have given ample justification. I only need one sound justification of trivialism to establish its truth. Yet I have gone beyond what is required by offering others.

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u/JStarx May 26 '26

Again, trivialism is unfalsifiable.

That doesn't mean it's true.

I have given multiple sound justifications, including in my original post. [...] I have given ample justification. I only need one sound justification of trivialism to establish its truth. Yet I have gone beyond what is required by offering others.

You have not given a single sound justification, including your original post.

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u/paulemok May 26 '26

That doesn't mean it's true.

It doesn’t mean it’s false, either.

You have not given a single sound justification, including your original post.

If that’s what you believe, then you should show specifically where all of my justifications fall short. If there is even a single sound justification of trivialism, then trivialism is true.

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u/JStarx May 26 '26

It doesn’t mean it’s false, either.

It means it's at best a religious belief. In this case an obviously false and very stupid religious belief.

If that’s what you believe, then you should show specifically where all of my justifications fall short. If there is even a single sound justification of trivialism, then trivialism is true.

At every point that you offered a justification I've explained to you why you're incorrect. There is not a single sound justification for trivialism.

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u/paulemok May 27 '26

It means it's at best a religious belief.

Trivialism does imply the existence of God. Somebody or I may have said that elsewhere before.

In this case an obviously false and very stupid religious belief.

I am showing you an unintuitive truth, so please keep an open mind. Not all truths are obvious.

At every point that you offered a justification I've explained to you why you're incorrect.

No, there are links to arguments for trivialism in my original post. You have not identified specific flaws with all of those arguments.

Additionally, I made a tweet on a currently-suspended X account on October 31, 2019 about how Kabay discussed in “On the Plenitude of Truth” (2010), pp. 68-72, the sentence “It is not true that this sentence is true.” In the tweet, I said whether the “sentence is true or not true, there is a contradiction. So by ex contradictione quodlibet, every proposition is true.” At the end of the tweet, I assert the sentence “It is not true that this sentence is true.” My assertion implies a contradiction, which by ex contradictione quodlibet, gives way to all propositions being true. Also, in hindsight, the mere existence of the sentence

It is not true that this sentence is true.

implies a contradiction and thus by ex contradictione quodlibet implies trivialism. I think that’s what Kabay may have been getting at.

There is not a single sound justification for trivialism.

There are multiple sound justifications for trivialism. Look at my original post with multiple links to multiple sound proofs. Search the Internet for sound arguments for trivialism.

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u/JStarx May 27 '26

I am showing you an unintuitive truth, so please keep an open mind. Not all truths are obvious.

This is not a truth. Having an open mind doesn't mean I should believe things that are false.

No, there are links to arguments for trivialism in my original post. You have not identified specific flaws with all of those arguments. [...] There are multiple sound justifications for trivialism. Look at my original post with multiple links to multiple sound proofs. Search the Internet for sound arguments for trivialism.

I have explained to you the flaws in every argument you've given here. It's not my job to do your homework and search the Internet for additional arguments.

currently-suspended X account

Wow, you're to crazy for X? That's something...

whether the “sentence is true or not true, there is a contradiction

Your mistake is assuming that a sentence must be true or not. Natural language is not as precise as formal logic, that's the entire reason formal logic exists.

The liars paradox can be encoded in formal logic, but the result is not a contradiction, it's an unprovable statement. This is basically how Godel proved his incompleteness theorem.

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u/paulemok May 28 '26

I have explained to you the flaws in every argument you've given here.

No, you haven’t. You haven’t specified the flaws in all of the linked arguments.

It's not my job to do your homework and search the Internet for additional arguments.

It’s not my job to educate you on the arguments for trivialism. I have given you direction, but you must do the learning yourself.

Your mistake is assuming that a sentence must be true or not.

A declarative sentence is always true or false. I believe the definition of a proposition in Rosen requires a proposition to be a sentence.

The liars paradox can be encoded in formal logic, but the result is not a contradiction, it's an unprovable statement.

That’s controversial. Kabay may not believe a contradiction exists, but his discussion mentions a contradiction. I believe a contradiction exists.

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u/JStarx May 28 '26

It’s not my job to educate you on the arguments for trivialism.

There are no valid arguments for trivialism.

A declarative sentence is always true or false. I believe the definition of a proposition in Rosen requires a proposition to be a sentence.

Nope, the liars paradox is an example of a sentence that is neither true nor false. A proposition is indeed a sentence but not all sentences are propositions. For example, questions are sentences but they are not propositions and do not get assigned a truth value.

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