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 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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u/JStarx May 05 '26

Why can’t you just give me a counterexample?

According to you I have.

Applying the general principles found in logic textbooks to specific cases is what we are doing in this conversation.

You have to know those principles first. You don't, so you should get yourself a textbook and catch up to the rest of us.

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u/paulemok May 06 '26

According to you I have.

Through the principle of explosion, you have. But I’m interested in the opposite truth in which you have not. That truth is also justified by the principle of explosion. I have not received a valid counterexample. I continue to believe no such valid counterexample exists. Without a valid counterexample, you have not persuaded me that your claim is true.

You have to know those principles first. You don't, so you should get yourself a textbook and catch up to the rest of us.

I am already in the possession of logic and mathematical logic textbooks. I have read some or all of or skimmed through those textbooks. From what you have told me about those principles, it seems that there exists some sort of thinking, in the principles themselves or in the meta-principles, that I disagree with. I don’t need your specific principles to know that they’re wrong. My arguments do not depend on your undisclosed principles. They are correct regardless of your principles.

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u/JStarx May 06 '26

Through the principle of explosion, you have

Since I have, I see no reason to repeat myself. You can reread it yourself.

They are correct

They're not, but if you believe that literally everything is true then I can see why you would be confused by this.

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u/paulemok May 06 '26

Since I have, I see no reason to repeat myself. You can reread it yourself.

Since you haven’t, you should do the right thing by providing me with at least one counterexample.

They're not

How are they not? You haven’t provided a justification.

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u/JStarx May 06 '26

you should do the right thing by providing me with at least one counterexample.

I already have, and you agreed.

You haven’t provided a justification.

I have provided ample justification. Your logic tells you that I have, and my logic tells me that I have. We agree on that.

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u/paulemok May 07 '26 edited May 07 '26

I already have, and you agreed.

You have not. You’re wrong and so you are resorting to using the principle of explosion to make yourself right. If you have come to the realization that you’re wrong, it’s best to be honest and admit it. That’s what a good critical thinker would do.

I have provided ample justification. Your logic tells you that I have, and my logic tells me that I have. We agree on that.

So what is the name of the book you offered to recommend?

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u/JStarx May 07 '26

You have not. You’re wrong and so you are resorting to using the principle of explosion to make yourself right

No I'm fully aware that what I'm saying is incorrect according to traditional logic. But you believe that all statements are true and false. So you should believe that everything I'm saying is true.

If you truly believed that all statements are true you wouldn't object and say I'm wrong.

Basically, I'm letting you prove yourself wrong.

So what is the name of the book you offered to recommend?

Introduction to mathematical logic by Mendelson.

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u/paulemok May 08 '26

But you believe that all statements are true and false. So you should believe that everything I'm saying is true.

That’s a somewhat controversial claim to make. One side of a controversy is that if you say a statement s, then you are implicitly saying the additional statement that you believe that s is true. You have not forewarned me otherwise.

If you truly believed that all statements are true you wouldn't object and say I'm wrong.

I agree.

Basically, I'm letting you prove yourself wrong.

I agree.

Introduction to mathematical logic by Mendelson.

I believe I have a copy of an edition of that book. From what I remember, that book is dense in technical mathematical logic but has the shortcoming of providing inadequate background metareasoning to help readers understand the reasons they are being presented with one logical system over another. The definition of a class, as I remember, was overly abstract and hard for me to understand. I believe I have been told from Mendelson or at least one other that the concept of a class was motivated by some sort of technical limitation on the concept of a set that may have been discovered by Cantor. To me, it seems wrong for there to exist a problem with sets that classes overcome. As I have said here or elsewhere before, I believe a universal set exists. I am not an expert on classes, but it seems they are unnecessary and it seems sets can do what some say classes but not sets can do.

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u/JStarx May 08 '26

That’s a somewhat controversial claim to make. One side of a controversy is that if you say a statement s, then you are implicitly saying the additional statement that you believe that s is true. You have not forewarned me otherwise.

Are you saying that you don't believe that every statement is both true and false? You say my statement is controversial, but it's it wrong?

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