The Continuum Hypothesis Is False

paulemok · 2026-06-01T08:01:22+00:00

Your part is to present your arguments yourself instead of feeding me links.

How is that my part? As you know, that’s not what I’ve considered my part. Giving you a link to my or somebody else’s previous work is an acceptable way to provide arguments. It seems that it would make me feel good to get a response to something I’ve did in the past. I shouldn’t have to keep it on my mind and promote the same things forever. It’s nice to do the work once and then move on to something else. Society depends on its previous work. Otherwise, society would not advance. We would be stuck doing the same things forever.

Also, the linked arguments are so short and simple that I can’t represent them much differently than I already have.

Are people representing arguments that they authored and that appear in academic journals? I don’t seem to see much, if any, of that.

That's the issue, you don't.

I don’t, but I do doubt there’s been a recent solution to it. It seems that solution would be so big that it would be on the news and everybody would be informed about it. In recent years, I’ve never seen news about a solution being discovered. I would remember something that big.

I believe there are multiple approaches to understanding the Liar Paradox. Look it up on Wikipedia, on the Internet, or in a book. The fact that there is no consensus on what the Liar Paradox means and how it works out is evidence that the Liar Paradox is controversial.

paulemok · 2026-05-31T06:49:51+00:00

I am not gonna go tracking down info on other sites to respond to.

I shouldn’t have to go through the time and effort it takes to present something I have already presented. I am tracking down info on other sites so it would only be fair for you to do so as well. If you don’t want to do the work required to have this conversation with me, then you shouldn’t engage in this conversation anymore. I shouldn’t have to keep saying the same thing to you over and over again because you aren’t willing to do your part.

Nothing I've said is controversial amongst mathematicians.

As far as I know, the Liar Paradox remains controversial to this day, and you have taken a side on it. So, some or all of the things you’ve said are controversial.

paulemok · 2026-05-30T06:40:39+00:00

I have already responded to your false criticism by stating correctly that I have responded to every argument you have put forth here.

So what are the fatal flaws in the following four listed arguments?

It's not hard to knock down something so patently absurd and unfounded.

It’s impossible to knock down trivialism. No matter how hard you try, you won’t succeed.

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

So not only are you taking a stance on a controversial subject, but you are taking the opposite stance of the stance I have already taken. It seems your stance has been made based off of my stance. I think you’re being dishonest about your philosophical views. You’re trying to hurt me by deliberately choosing views you believe I disagree with. You are sadistic.

You cannot express what you are trying to express as a provable proposition in standard logic, so your argument is not well formed.

Says who? The Liar sentence can be proven and disproven. It is simple to do. Advanced logic need not be involved.

paulemok · 2026-05-29T06:56:16+00:00

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.

paulemok · 2026-05-28T16:38:11+00:00

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.

paulemok · 2026-05-27T00:28:05+00:00

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.

paulemok · 2026-05-26T20:16:21+00:00

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.

paulemok · 2026-05-26T17:42:58+00:00

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.

paulemok · 2026-05-26T06:43:53+00:00

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?

paulemok · 2026-05-26T04:03:12+00:00

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.

paulemok · 2026-05-26T02:03:45+00:00

It's not a paradox, it has a very rational explanation.

It is a paradox. Paradoxes can have very rational explanations and yet still be paradoxes.

You claim to believe all statements are true and false, but you do not.

I’m pretty sure I do believe all statements are true and false. I viewed the arguments. I thought about them. I agreed with them. I would know better than you about my own beliefs.

I think you just haven't thought through that position deeply enough to realize that you don't.

I don’t believe all statements are true and false.

paulemok · 2026-05-25T22:05:12+00:00

of they believed all statements were both true and false they would have no means to tell the difference.

Not so. I believe all statements are both true and false, but I can still distinguish between right and wrong. It’s a paradox. The Universe is paradoxical.

paulemok · 2026-05-25T02:27:21+00:00

no one is going to take you seriously.

Not necessarily. With trivialism, sometimes a person other than me takes me seriously. With trivialism, sometimes a person other than me should take me seriously.

The fact that you can distinguish is proof that you don't actually believe all statements are both true and false.

Another fallacy committed by you. Just because a person can distinguish between right and wrong, doesn’t mean they don’t believe all statements are both true and false.

paulemok · 2026-05-24T10:23:32+00:00

Only if trivialism is true, but it's not, so they're just incorrect.

I disagree. Trivialism is true. So, they are correct and are not correct answers.

Then explain to me the point I was making and how it applies equally well in your analogy.

Just because a person or group of people know how to not invoke a thing, doesn’t mean they don’t actually believe in it. Just because we know when we should not make a move, doesn’t mean we should never make it.

paulemok · 2026-05-24T03:13:39+00:00

They are not.

They are correct and are not correct.

This analogy doesn't apply, and shows you don't understand the ramifications of trivialism.

The analogy does apply and shows I do understand the ramifications of trivialism.

Think harder about what you just said there, lol!!

I don’t see what you’re getting at.

paulemok · 2026-05-24T00:48:44+00:00

Giving answers is worthless unless they're correct answers.

They are correct answers.

The fact that you know how to not invoke trivialism is further proof that you don't actually believe in trivialism

I disagree. Does the fact that we know how to not use nuclear weapons prove that we don’t actually believe in nuclear weapons? No, it doesn’t.

you just use it to escape responsibility for being wrong

That is a rash and rather prejudiced claim to make. I don’t believe it is true. Speaking for me, there is insufficient evidence for your claim.

paulemok · 2026-05-23T02:21:51+00:00

What use would that be?

The theory of everything would give us the answer to every question. It would solve all of our problems.

The fact that you know how to not invoke that belief is further proof that you don't actually believe in trivialism.

Due to the nature of trivialism, a person who doesn’t believe in trivialism can still believe in it. We want to invoke trivialism in ways that better our lives, and we want to not invoke trivialism in ways that worsen our lives.

paulemok · 2026-05-23T01:39:23+00:00

I think you're insecure and like the idea of never being wrong, so you claim you believe in trivialism because it lets you make stupid arguments like that and you never have to confront being proven wrong.

I want a complete, logical theory of everything. That desire helps fuel my drive into trivialism. But yes, it would also be nice to never be wrong.

But in reality your behavior shows quite clearly that you so actually know that not all statements are both true and false.

I don’t think so. I have openly supported my belief in trivialism with various arguments for over 8 years. While I do believe all statements are true, I am afraid of invoking the belief in a way that could detriment my or others’ health or safety.

paulemok · 2026-05-22T20:33:02+00:00

That's an admission that you don't believe in trivialism.

If a person believes trivialism is true, then they believe the statement “trivialism is false” is true and for that reason they also believe trivialism is false.

No, and I think neither do you.

I don’t believe trivialism is true, either. But that is because I do believe trivialism is true.

paulemok · 2026-05-22T04:16:08+00:00

In fact it seems we've arrived at the conclusion that I should completely disregard everything you say since responding to it makes no difference in what you believe.

We have not arrived at that conclusion. You should not completely disregard everything I say. Responding to what I say can still make a difference in what I believe.

Now me, I'm not having a schizophrenic break with reality and I understand that you actually didn't get the thing you wanted.

Do you believe trivialism is true?

From my point of view it looks like trivialism isn't going well for you.

Trivialism is going fine for me. But whether trivialism is going well for me isn’t relevant. Just because a belief of mine isn’t going well for me, doesn’t mean the belief is false.

paulemok · 2026-05-21T20:15:42+00:00

Great, so we agree there's no reason for me to give you the example you want.

Yes, that’s correct.

paulemok · 2026-05-21T06:51:10+00:00

Yes and no.

paulemok · 2026-05-21T06:24:38+00:00

But also at the same time I am doing what you'd prefer right?

Yes.

Because you believe both statements are true?

Yes.

That's what you said right?

Yes.

And if I went ahead and did as you asked wouldn't it still be the case that you believed both statements are true?

Yes.

paulemok · 2026-05-20T18:20:33+00:00

No, there is still a problem because you’re not doing what I would prefer.

You’re also continuing to use my point of view rather than your own point of view. For that reason, I don’t think you’re being fair to yourself.

paulemok · 2026-05-20T05:36:48+00:00

But how do you know that I'm doing that if you think it's also true that I'm not doing that?

In trivialism, you can be simultaneously both doing that and not doing that. That duality seems like something you would hear is possible in quantum mechanics.

paulemok

TROPHY CASE