Charitably, you take a false proposition p. You extend that by building a true proposition ¬p from it. I'm not sure your interpretation is charibable — InPitzotl
p: <- the false proposition.Notice that in your example: q = ~p , you used q (~p is true) and not p (p is false). — TheMadFool
p is true here, right?p→Kp — TheMadFool
Notice that in your example: q = ~p , you used q (~p is true) and not p (p is false).
— TheMadFool
p: <- the false proposition.
q: <- the true proposition.
q = ~p <- makes true proposition q out of false proposition p.
Does your proof need a true proposition? Use q.
What's the problem?
p→Kp
— TheMadFool
p is true here, right?
Let's change labels from p to q. q→Kq. Now q must be true (because we changed labels), right?
So let's take the case where q = ~p, where p is false. q is still true, right? What did q have to be? True? Okay, well it is true. What did p have to be to extend to falsehoods? False? Okay, well, it's false.
Now, we can talk about p's that are false. And when you do your proof, you use q's for where you used to use p's. What's wrong?
We can do the same thing in reverse. Just take p, where p is true, and that's your typical application. To do falsehoods, take p where p is false. But we can't do the typical, we have to convert that to a true proposition. No problem; add a complement; if p is false, ~p. But the proof only works when p is a true proposition. Okay, no problem; relabel p's in the proof as q's, and say q=~p. Now we have a false p, and a proof that uses the fact that q is true. What's wrong? — InPitzotl
What does it mean to say that falsehoods are or are not in the scope of Fitch's paradox? What does being "in the scope" of a paradox exactly mean in this context? — TonesInDeepFreeze
Suppose p is a sentence that is an unknown truth; that is, the sentence p is true, but it is not known that p is true. — Wikipedia
¬p→K¬p = all false propositions are known propositions — Olivier5
No one believes that as a generalization for all q. — TonesInDeepFreeze
Well, maybe you'll get it one day, if you decide to apply your mind to it. — Olivier5
It is not the case that for all sentences p, we have p -> LKp — TonesInDeepFreeze
Everything is not known. But every existing proposition has been proposed by someone or another, by definition of what a proposition is. Thus every proposition in existence will be known at least by he or she who originally made the proposition.It is an extraordinarily outlandish view that everything is known. — TonesInDeepFreeze
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