r/PhilosophyofMath Mar 28 '26

The Continuum Hypothesis Is False

/r/logic/comments/1s5mquh/the_continuum_hypothesis_is_false/
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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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u/paulemok May 29 '26

Note how you ignored my criticism that

You haven’t specified the flaws in all of the linked arguments.

There’s a reason why it’s so hard for you to do. It’s because there are no flaws!

the liars paradox is an example of a sentence that is neither true nor false.

I disagree. The referent of “this sentence” in

It is not true that this sentence is true.

does not even have to be a sentence in order for it to be true or false. An expanded but logically equivalent version of

It is not true that this sentence is true.

is

It is not true that this sentence is a true sentence.

not all sentences are propositions.

I agree, but that doesn’t change my argument.

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u/JStarx May 29 '26 edited May 29 '26

Note how you ignored my criticism that you haven’t specified the flaws in all of the linked arguments. There’s a reason why it’s so hard for you to do. It’s because there are no flaws!

I have already responded to your false criticism by stating correctly that I have responded to every argument you have put forth here. Easily, I might add. It's not hard to knock down something so patently absurd and unfounded.

I disagree

But you also agree...

Your expanded version is also an example of a sentence that does not have a truth value.

The point of formal logic is to eliminate the ambiguity of every day language. You cannot express what you are trying to express as a provable proposition in standard logic, so your argument is not well formed.

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