Talk:Paradox of entailment

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[edit] If it is raining, water exists

Is water only able to produce rain? Can other substances rain? If yes, this premise is incorrect and since the logic is based on this premise, this statement is then incorrect. Food for thought, Daimanta 16:47, 5 January 2007 (UTC)


It's a perfectly valid and sound argument.

if

2 + 2 = 4

and

2 + 2 = 5

then

2 = 1

Therefore, since Elvis and the Pope are two people, Elvis and the Pope are one person.

Grahamsw

This makes no sense at all and it is completely idiotic. 2 plus 2 does not equal 5, end of story. To base an argument on something like this is stupid. This isn't a paradox, it's just stupid.

  • To expand on the above in a more logical manner. You can not use an untrue math formula to prove the Paradox of entailment, as the basis for the paradox is using two statements that can be true by themselves, but NOT true in conjunction with each other . Since 2+2 can never equal 5, your second premise is never true, and your conclusion can be disproved based on that. See also the Heisenberg uncertainty principle Cstella23 16:40, 12 March 2007 (UTC)
Clearly, it's stupid to base an argument on any set of inconsistent premises. Since they're inconsistent, the argument can never be sound, and thus will not mean anything of value. Boycottfood (talk) 01:18, 9 December 2007 (UTC)

This is an old joke. Recently someone added something similar, but with the added line:

Similarly, any arithmeticaly inconsistent premises can be used to construct the statement "1=2". Then the same argument shows that P = Q, for any two satements P and Q.

There is a little bit of truth to this last bit, but not much. Not enough for the article, even in the state it is currently in. 192.75.48.150 20:15, 25 August 2006 (UTC)

"...inconsistent premises imply all conclusions are true." - shouldn't that be changed into "... inconsistent premises imply that even wrong conclusions make the implication as a whole a true statement."?

No, I don't think so. If I take as my premises A and \lnot A, then I can prove that anything is true. I write down the implication (A \land \lnot A) \rightarrow I am a fish, which is a tautology. Then, since I know A and I know \lnot A, as they were my premises, I know (A \land \lnot A). Then, using that, Modus Ponens brings us to the conclusion that I am a fish. Obviously, you could substitute any conclusion you want in the place I put I am a fish. Boycottfood (talk) 01:18, 9 December 2007 (UTC)

[edit] "George Washington is the Pope" vs. "Water exists"

Is there a specific reason why this diff changes the conclusion? — metaprimer (talk) 04:52, 15 September 2007 (UTC)

I imagine it has something to do with the "pope" reference, perhaps? I'm inclined to put a different phrase there. I think "Water exists" is a poor conclusion to demonstrate the the paradox, first because it is related to the premises and second because it's true. Boycottfood (talk) 06:57, 9 December 2007 (UTC)


[edit] Inconsistent Premise

Could a better example for the inconsistent premise be:

   * If it is raining, water exists (1st premise; always true)
   * Water exists (2nd premise)
   * It is raining (Conclusion)

The conclusion is not certain (since it may not be raining, you may just be sat in a bath tub full of water) sorry if I totally misunderstood the topic —Preceding unsigned comment added by 213.249.229.58 (talk) 12:46, 7 February 2008 (UTC)

Those premises are not inconsistent.  :) Djk3 (talk) 08:13, 8 February 2008 (UTC)