3 ms·
Your reasoning only works for valid statements. That is, statements that have a truth value. As you’ve demonstrated P does not have one. For no admissible sta
by skh 8y ago
Your reasoning only works for valid statements. That is, statements that have a truth value. As you’ve demonstrated P does not have one. For no admissible statement is P equal to not P.
- yters 8y ago1. Premise: P -> Q 2. Premise: ((P -> Q) -> P) -> P 3. (P -> Q) -> P, from 1 4. P, from 2 and 3 5. Q, from 1 and 4
- skh 8y agoThe P, in your original post, is not a valid formula since it does not have a truth value. You can construct all the proofs and whatnot you want but if P is not a logical statement (one that is either true or false but not both) then the arguments are not valid. Your Q was generic and could have been any statement. In particular one that has been provably shown to be false. If your arguments are correct then you have the ability to prove any false statement is true. Do you really think you have found a way to demonstrate that the standard two-valued logic used in mathematics leads to a contradiction?
- yters 8y agoJust repeating Curry's paradox from Wikipedia.
- skh 8y agoI see. The difference in our views comes from me being a mathematician. Curry’s Paradox is not a paradox in mathematical logic due to my objections. In mathematical logic we don’t allow statements that don’t have a well defined truth value. The premise in the start of Curry’s Paradox is a statement without a well defined truth value. Curry’s Paradox shows the limits if naive set theory. Thus mathematically we have to be OK with the idea that not all naive set constructions produce valid sets. In informal setttings we can argue that If this sentence is true then Santa Claus exists can’t be false. But then one usually assumes it must then be true. I would argue this isn’t the case. There are sentences that have no truth value. For instance, This sentence is false.
- yters 8y agoThanks, this clarifies things for me.