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If someone uses the premise that: 1=1 and then arrives at the conclusion that: 1=2 this means that the conclusion has proven the premise wrong; and if the premise is wrong, then the conclusion is wrong; and if it is wrong, then the premise is not proven wrong

This phenomenon (let's call it cctpp; short for "conclusion-contradicts-the-premise phenomenon") can be used to solve the radical skepticism paradox, but I know before I start the skeptic will ask, "How do you know that this phenomenon [is] right?"

So, as we see, cctpp is correct reason which follows logic. So the skeptic asks, "How do you know logic or correct reasoning is right? Maybe they are wrong and we are not justified in using them."

Ok, good. So where is the solution now? The thing is, the radical skeptic argument itself relies on correct reasoning and logic. But the thing here is the skeptic is using the premise that he is justified to use correct reasoning. So if he concludes that we are not justified in using correct reasoning because we cant know if it's right or wrong, then he has proven the premise wrong and the cctpp occurs here; which means he has proven the premise wrong; which means that the conclusion is wrong; which means that the premise is not wrong.

And from here we can know that we are justified in using correct reasoning

What do you think about this, guys, and will [you] want to know: does the cctpp lead to an infinite loop or to concluding the premise is right and not proven wrong?

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  • so in "logic calculus" false -> X always evaluates to true, which means saved calculation time (at least in computing science ...if you are "clever time bound being", you can also save reading/evaluation (=life) time of X....)
    – xerx593
    Commented Jan 13 at 22:16
  • accordingly we can skip evaluation(=save time) of X in X -> true
    – xerx593
    Commented Jan 13 at 22:21
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    There really isn't a radical skeptic paradox, except from the point of view of someone who insists that absolute certainty is neccessary, a thing the RS does not concede.
    – philosodad
    Commented Jan 13 at 23:52
  • If I understand what you are saying, I think you are correct. see here: philosophy.stackexchange.com/questions/103103/…
    – Olivier5
    Commented Jan 14 at 9:09
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    "if someone uses the premise that: 1=1 and then arrive at the conclusion that: 1=2 this means that" there is a mistake in the argument producinf the purported conclusion. Commented Jan 15 at 7:55

3 Answers 3

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Unfortunately, there is a mistake in your first section:

Consider the implication "A => B".

If the premiss A is false, then the implication is always true, independent from the truth value of B. As a consequence, you cannot conclude that the falseness of the premiss implies the falseness of the conclusion:

If "A => B" then not necessarily "non A => non B".

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  • i dont really get it can you explain it more with a different example Commented Jan 13 at 20:16
  • @NeoGranicen It is the logical rule "ex falso quodlibet (= from a false premiss you can conclude every statement), for an introduction see en.wikipedia.org/wiki/Principle_of_explosion
    – Jo Wehler
    Commented Jan 13 at 20:44
  • if the presime is false doesn't this mean that the conclusion will be false Commented Jan 14 at 12:32
  • @NeoGranicen No. The falseness of the premiss does not imply the falseness of the conclusion: "(1=2) => (1+1=2)". The premiss "1=2" is false, the conclusion "1+1=2" is true. The implication is valid. - One can understand this by resolving "A => B" according to its definition as "not (A and not B)". Now: If A is false, then also "A and not B" is false, independently from B. Hence "not (A and not B)" is true, the implication is valid.
    – Jo Wehler
    Commented Jan 14 at 13:28
  • I always wondered if there was some logic operation that works the way everyone naively expects implication to work, and why we don't use that instead?
    – Scott Rowe
    Commented Feb 14 at 2:19
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Felicitations, yep, that is a classic refutation of skepticism you stumbled upon there. Skepticism is what we call a peritrope (refutes itself): If it's right, it's wrong. The problem is if it's right, dogmatists, sworn enemies of skeptics, are wrong as well. To take the matter to its logical conclusion, if skeptics are right, I'm wrong as well. We're all wrong!! 😀

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  • It would be best if we all, from the first, simply admit that we are wrong about everything. We can then work on being less wrong. Woe betide those who are not even wrong, they are beyond redemption.
    – Scott Rowe
    Commented Feb 14 at 2:15
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    @ScottRowe, 🤣. I don't have the tools to parse what you said, but I can tell you this ... Pauli would probably be happy to see his dismissal become an internet meme.
    – Hudjefa
    Commented Feb 14 at 13:43
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You're correct that (p -> ~p) -> ~p. And you're correct that there are propositions like "no statement is true" that imply their falsity and thus are false. However, it is difficult for me to perceive, how "belief in no statement is justified" is self-contradictory in this way. It implies that the statement "belief in no statement is justified" isn't justified, which doesn't mean it's false.

Although under many theories of evidence this is simply a ridiculous claim to make.

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