Paradox II

[Dae314]

No pretty picture for this one (but if someone wants to make one feel free :3). I think this is an interesting paradox because the contradiction comes from the fact that you CAN logically prove the statement.

The key phrase goes like this: If this sentence is true, then Germany borders China.

Taking the formal logic approach to evaluating this statement, If turns into implies, and you're able to use a proof technique called "assuming the conjuncts of the antecedent" to prove the statement true. The conjuncts in this case is "this statement is true". By assuming that you can try to prove the entire statement, but in assuming that you've just proved the statement true .

In a more general form, anything that goes "If A, then B" is always true if A somehow relates the idea "this sentence is true". Therefore, the statement can be proven true regardless of B which can be any ludicrous idea in natural language.

Do you think you can crack this paradox?

source

[lemmingllama]

A problem should be proposed in the right writing so that it can be solved, or at least speculated on. It is just a circular argument, so that as soon as you assume it is true, then it must be true. Likewise, when you assume it is false then it is false. The problem that you gave can be solved in reverse by simply checking if Germany borders China. Heres another good one of this paradox that you can reverse

1.Tasmanian devils have strong jaws.

2.The second sentence on The List is circular.

3.If the third sentence on The List is true, then every sentence is true.

4.The List comprises exactly four sentences.

This paradox has been solved, but it requires some stupid math that I dont feel like explaining. So really just reverse engineer each problem to actually discover the truth of the statement.

[Dae314]

If you solve it that way then the statement becomes a false implies false which is still a valid logical statement. Like I said, the paradox isn't in the statement itself, but in the fact that you are able to prove the statement by assuming the conjuncts of the antecedent (you can't assume the coincident).

So really it's more asking "why can you prove this obviously false statement?"

[CaNzCo]

This is a very strange paradox, since it really is just a statement.

The part were this gets a little hazy for me is that the definition of truth does not really apply to a hypothetical. By it saying "If," the statement can be viewed as outside of reality, and only as a possible outcome, therefore it's truthfulness cannot be proven. (until the action has occurred)

One day, and this day may never come, China could take over all of the world except Germany, and on that day, this statement will be proven true. Until then, this is just a speculation.