You're basically just baking in an ex falso quodlibet into the premise. — Pfhorrest
This sentence is false or I am a woman.
I think that assuming P1 to be true is to assume that I am a woman. Is that really a paradox? — Michael
Formal proof:
The main statement is: If this sentence is true, then P2
Let P1 = if this sentence is true then P2
Further translation yields P1 = P1 > P2
1. P1 = (P1 > P2)....assume
2. P1 > P1......Id
3. P1 > (P1 > P2)....1 Id
4. (P1 & P1) > P2....3 Exp
5. P1 > P2............4 Taut
6.P1....from 1, 5
7. P2....5, 6 MP
Informal proof:
The statement P1 = If P1 then P2. Assuming P1 means both P1 and if P1 then P2 are true. Apply modus ponens and P2 is true which means if P1 then P2 is true. We know then that P1 is true because P1 = P1 > P2. Use modus ponens one more time and we get P2.
The paradox is that P2 can be any imaginable proposition.
As another way of proving anything, distinct from the more familiar ex falso quodlibet, I'd like some opinions on this paradox. — TheMadFool
Where is the contradiction? — TheMadFool
P1 is equivalent to “this sentence is false or P2”, so I think assuming P1 is to assume P2, not to prove it. — Michael
Where is the contradiction? — TheMadFool
"This sentence is false."
If P1 is "not P1", assuming P1 assumes a contradiction.
So if P1 is "not-P1 or P2", assuming P1 assumes either a contradiction or P2.
And "If P1 then P2" is logically equivalent to "not-P1 or P2", so if P1 is "if P1 then P2", same situation.
P1 is equivalent to “this sentence is false or P2”, so I think assuming P1 is to assume P2, not to prove it. — Michael
:100:
A loose more idiomatic way of phrasing P1 would be "If I'm right, P2" or "Unless I'm wrong, P2." That's basically just a way of asserting P2. — Pfhorrest
P1 is equivalent to “this sentence is false or P2”, so I think assuming P1 is to assume P2, not to prove it. — Michael
This is what happens when you play with words without meaning or logic...you end up with nonsense. — A Seagull
I don't think anyone is saying that the proof is invalid, just that it's conclusion is trivial. All conclusions of valid arguments are baked into their premises, that's how truth preservation works, but the conclusion of this argument is so transparently baked into the premise that it's not really surprising or a paradox that it can be proven. Or that "anything can be proven this way", because consider for comparison an argument that "From 'If TRUE then P' we can prove P, for any P". That's correct, but it's hardly surprising, because 'if TRUE then P" is pretty much just asserting P. — Pfhorrest
This is what happens when you play with words without meaning or logic...you end up with nonsense. — A Seagull
Would you like to read the above replies. — TheMadFool
I would prefer you to admit that you can't answer my questions nor respond sensibly to my comments. — A Seagull
I would prefer you to admit that you can't answer my questions nor respond sensibly to my comments. — A Seagull
Perhaps you'd like to hear it straight from the horse's mouth...Curry's paradox — TheMadFool
The main statement is: If this sentence is true, then P2 — TheMadFool
The problem with the Curry sentence is that it's not evaluable and thus not truth-apt. The truth value of the antecedent depends on the truth value of the sentence. But the truth value of the sentence depends on the truth value of the antecedent (and consequent). So the sentence has a circular dependency. — Andrew M
The sentence can be either true or false.
If it's false then it's antecedent is false and that means the entire sentence evaluates to true.
If it is true, well, then it's true — TheMadFool
You're just plugging in values to see what happens. That's not the same as evaluating the sentence — Andrew M
So yeah, you can use this to "prove" any P2, but that's just because you're transparently baking P2, whatever it is, into the single premise of the argument. — Pfhorrest
This isn't a paradox, it's just a really useless trivially valid argument — Pfhorrest
The problem is that there is no well-defined or logical process for determining whether a statement is 'true' or 'false'. — A Seagull
The problem is that there is no well-defined or logical process for determining whether a statement is 'true' or 'false'. — A Seagull
Truth tables can be used to explore all possibilities. — TheMadFool
How would you evaluate a conditional sentence in a way different to the way I did the Curry's sentence? — TheMadFool
bool result = theCurrySentence() is true bool theCurrySentence() { if (theCurrySentence() is true) then { if (germanyBordersChina() is true) then return true else return false } else return true }
Truth tables can be used to explore all possibilities. — TheMadFool
Sure, but that doesn't mean that they are 'true'. — A Seagull
It doesn't prove every P2 simultaneously — Pfhorrest
if (germanyBordersChina() is true) — Andrew M
The step 6 doesn't make sense. — BlueBanana
if (germanyBordersChina() is true)
— Andrew M
There shouldn't be "if" in the above statement. — TheMadFool
bool result = theCurrySentence() is true bool theCurrySentence() { if (theCurrySentence() is true) then return (germanyBordersChina() is true) else return true }
P1 = (P1 > P2) — TheMadFool
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