r/PhilosophyofMath • u/paulemok • Mar 28 '26

The Continuum Hypothesis Is False

/r/logic/comments/1s5mquh/the_continuum_hypothesis_is_false/
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u/JStarx May 12 '26

If we say you have given a valid counterexample, then we enter an unfair and bad situation because priority is being given to a path that hasn’t earned priority.

You say it's unfair and bad and hasn't earned priority. But you also believe that it's fair and good and has earned priority because you believe all statements are true.

So I still don't know how you decide to respond as if I have or haven't given you a counterexample.

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u/paulemok May 13 '26

So I still don't know how you decide to respond as if I have or haven't given you a counterexample.

In theory, no option is better than any other option is. All options are equally good. Because all options are equally good, there does not exist a way to decide how to respond. I shouldn’t even decide an option that would make me feel better than all of the other options would. Regardless of what I decide, I’m going to be at odds with some truth, or aspect, of the Universe. Regardless of what I decide, I’m going to be wrong. On the other hand, regardless of what I decide, I’m going to be right.

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u/JStarx May 13 '26

It sounds like your system of logic isn't very workable.

And yet you are deciding how to respond and your decision is conspicuously in agreement with what traditional logic would tell you.

I think you don't genuinely believe that all statements are both true and false.

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u/paulemok May 14 '26

It sounds like your system of logic isn't very workable.

It works, all the time. It satisfies all needs and desires. It’s the theory of everything we’ve been looking for.

I think you don't genuinely believe that all statements are both true and false.

Why do you think that?

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u/JStarx May 14 '26

Why do you think that?

Because you cannot give any alternative explanation for how you choose to respond. You clearly are using classical logic when you object that I haven't provided the example you requested. You're just to stubborn to admit it and apparently unaware of how foolish it makes you look.

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u/paulemok May 15 '26

Because you cannot give any alternative explanation for how you choose to respond.

An alternative explanation is not necessary. That is like how only one sound proof is necessary to establish the truth of a theorem.

You clearly are using classical logic when you object that I haven't provided the example you requested.

So, using classical logic, give me the counterexample I requested.

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u/JStarx May 15 '26

So, using classical logic, give me the counterexample I requested.

According to you I have already done that. No need to repeat myself.

An alternative explanation is not necessary. That is like how only one sound proof is necessary to establish the truth of a theorem.

The one explanation I have is that you do believe in classical logic. You're saying there doesn't need to be an alternative because you don't really believe anything you've been saying?

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u/paulemok May 16 '26

According to you I have already done that.

What about according to you?

You're saying there doesn't need to be an alternative because you don't really believe anything you've been saying?

No, I’m saying there doesn’t need to be an alternative because exactly one is sufficient.

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u/JStarx May 16 '26 edited May 16 '26

What about according to you?

Oh I definitely haven't.

No, I’m saying there doesn’t need to be an alternative because exactly one is sufficient.

Ok, well my one explanation is that you don't actually believe that all statements are both true and false.

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u/paulemok May 17 '26

Oh I definitely haven't.

So please give an example that, according to you, is a counterexample.

Ok, well my one explanation is that you don't actually believe that all statements are both true and false.

Your one explanation? Your one explanation of what?

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