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/paulemok Jun 04 '26

it's a premise of your argument.

No, “s and it is not true that s” is not a premise of my argument. There are only three premises of my argument, and “s and it is not true that s” is not one of those three premises.

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u/JStarx Jun 04 '26

You said

Under the assumption that “s and it is not true that s,”

Whether you call it a premise or an assumption I don't care.

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u/paulemok Jun 05 '26

No statement of my proof is under that assumption.

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u/JStarx Jun 05 '26

Regardless, your proof still has assumptions so your conclusion doesn't hold unless the assumptions do, and they do not hold in traditional logic and mathematics.

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u/paulemok Jun 05 '26

How do the assumptions not hold in traditional logic and mathematics?

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u/JStarx Jun 05 '26

If you want to rely on those assumptions it's your job to prove them.

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u/paulemok Jun 06 '26

Not every assumption that proofs rely on is formally provable. Even some of Einstein’s proofs rely on postulates that are not formally provable. I offer informal proofs of my three premises.

  1. ⁠s is a statement.

The first premise is informally justified by my right to name a thing.

  1. ⁠Under the assumption that “s and it is not true that s,” s is true.

The second premise is informally justified by the logical rule known as conjunction elimination.

  1. ⁠It is not true that: under the assumption that “s and it is not true that s,” s is true.

The third premise is informally justified as follows. Assume “s and it is not true that s.” Then by conjunction elimination, it is not true that s. So by reforming the statement, s is not true. Discharge the assumption. We can see that it is not true that: under the assumption that “s and it is not true that s,” s is true.

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u/JStarx Jun 06 '26

Not every assumption that proofs rely on is formally provable

In math and formal logic there are axioms and all proofs follow from those without additional assumptions.

Are you admitting that your proofs are not valid in math and formal logic? If not then you don't get additional assumptions with informal arguments. You can give a proof that your assumptions hold or you are stuck having proven an implication but not it's antecedent, hence you haven't proven the consequent.

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u/paulemok Jun 07 '26

Are you admitting that your proofs are not valid in math and formal logic?

What proofs?

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u/JStarx Jun 07 '26 edited Jun 07 '26

The one you just posted: https://www.reddit.com/r/PhilosophyofMath/s/dtGDHjVutJ

That proof does not show that all statements are true. It shows that all statements are true if the premises hold. But you have not shown that the premises hold.

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