- #1
lolgarithms
- 120
- 0
Curry's paradox can be used to (dis)prove the riemann hypothesis and string theory, and even prove the (non)existence of God... no, actually, Curry's paradox IS God.
Just kidding... I am now (speaking somewhat hyperbolically) freaked out. Does Curry's paradox go like this (try "1 = 0" or anything you like for P): I don't think you need the whole contraction (A->(A->B) = A->B) thing for this paradox to appear. Contraction is just substituted by properties of OR, and I use the definition of the material conditional.
1. Let S := "If (material conditional) S is true, then P" = "S -> P"
2. Which also means: "P, or S is false" = "P or not-S"
3. S implies itself: S -> S
4. substitute: "If S is true, then (P, or S is false)" = S -> (P or not-S)
5. the material conditional means: (P or not-S) or not-S
6. OR (logical disjunction) is associative: P or (not-S or not-S)
7. x OR x = x: P or not-S
8. Hey, that's... S. Both the conditional and the condition (S is true) are now proven.
9. Therefore, P.
[tex]\mathcal{Q.E.D.}[/tex]
" *evil laugh* now all your common sense is (not) destroyed... muhahahaha... "
Contraction? Some logics explicitly allow it. but I think it only depends on the definition of material conditional, associativity and idempotence (X or X = X) of OR, and S->S, which are more fundamental in ways.
P.S. Simpler presentation for laymen:
consider the sentence: "If this sentence is true, then the Flying Spaghetti Monster exists"
Alright. suppose the sentence is true. then:
*If the sentence is true, then the Flying Spaghetti Monster exists.
*the sentence is true.
*Therefore, the Flying Spaghetti Monster exists.
So if the sentence is true, then the Flying Spaghetti Monster exists.
But that's what the sentence says, so the sentence is true.
Therefore, the Flying Spaghetti Monster exists.
Just kidding... I am now (speaking somewhat hyperbolically) freaked out. Does Curry's paradox go like this (try "1 = 0" or anything you like for P): I don't think you need the whole contraction (A->(A->B) = A->B) thing for this paradox to appear. Contraction is just substituted by properties of OR, and I use the definition of the material conditional.
1. Let S := "If (material conditional) S is true, then P" = "S -> P"
2. Which also means: "P, or S is false" = "P or not-S"
3. S implies itself: S -> S
4. substitute: "If S is true, then (P, or S is false)" = S -> (P or not-S)
5. the material conditional means: (P or not-S) or not-S
6. OR (logical disjunction) is associative: P or (not-S or not-S)
7. x OR x = x: P or not-S
8. Hey, that's... S. Both the conditional and the condition (S is true) are now proven.
9. Therefore, P.
[tex]\mathcal{Q.E.D.}[/tex]
" *evil laugh* now all your common sense is (not) destroyed... muhahahaha... "
Contraction? Some logics explicitly allow it. but I think it only depends on the definition of material conditional, associativity and idempotence (X or X = X) of OR, and S->S, which are more fundamental in ways.
P.S. Simpler presentation for laymen:
consider the sentence: "If this sentence is true, then the Flying Spaghetti Monster exists"
Alright. suppose the sentence is true. then:
*If the sentence is true, then the Flying Spaghetti Monster exists.
*the sentence is true.
*Therefore, the Flying Spaghetti Monster exists.
So if the sentence is true, then the Flying Spaghetti Monster exists.
But that's what the sentence says, so the sentence is true.
Therefore, the Flying Spaghetti Monster exists.
Last edited: