Isn't the sentence 'You cannot prove a negative' a negative?

Question

So "you cannot prove a negaitive" is a paradox?

In other words, If indeed you cannot prove a negative, then you cannot prove that you cannot prove a negative.

Answer 1

No, the sentence is statement of logic, not fact.

Answer 2

The sentence is talking about proving an existential negative, in other words proving that X does not exist anywhere.


By the way, I don't buy the statement in its strongest form, since X might be self-contradictory (like most gods...), but in the end it's just a boring way of talking about the Invisible Pink Unicorn.


For a counterexample, I *can* prove something decidedly negative. For instance, I can prove that the set of real numbers is not countable. This is actually pretty easy to prove.

Answer 3

Consider the negative case. When it comes time to decide what to believe, if we did not assume such "unprovables" were false, we would either have to choose which unprovables to believe by some totally arbitrary means, which amounts to a ridiculous "belief by whim" method, or else we have to assume that all such statements are true. Of course, we only have to believe true those unprovables that do not contradict other proven statements or that do not contradict each other, but even in the latter case we have no grounds for choosing which of two contradictory unprovables we will believe, and this is the same "belief by whim" dilemma. But even with these provisions, this policy would result in a great number of absurd beliefs (like "there are big green Martians in the universe"). Thus, when finally deciding what to believe, it is clear that the best policy is to assume that all unprovables are false, until such time as they are proved. In other words, it is reasonable to disbelieve a proposition when there is no evidence. Even if it is less certainly false than propositions which are actually contradicted by evidence (although even that does not amount to a complete certainty), it is still reasonable to regard them as false so long as we've done some checking, and don't ignore new evidence that we come across.

Answer 4

you cant 'prove' a negative or a positive unless the statement is purely mathematically defined and all the axioms required for its proof have been defined. Proof does not refer to anything outside of mathematics.

I think you are a little confused over the concept of empirical evidence. If you can see a chair, then you have empirical evidence for its existence. However, you cant prove that chairs dont exist just because you happen to be sitting in a room with no chairs, they could be any place you might not be looking....ok this might be a little confusing, but if you try you can understand it, anyone can really. of course you cant provide empirical evidence for the nonexistence of god, or the nonexistence of anything, because nothing which can be observed, or measured, can proclaim that you have nothing left to observe or measure. Its important you understand this concept. Email me if you aren't understanding

Answer 5

A negative can be proven. Proof: Bush is an idiot. Very negative statement but easy to prove... just listen to him give a speech.

Answer 6

Paradoxically, your logic indicates that you cannot prove that you cannot prove that you cannot prove a negative.

Answer 7

That is sloppy language...you can not prove something does not exist.

~ Eric Putkonen

Answer 8

ofcourse you can prove a negative.

5 is not smaller than 7

proof :
suppose it is, then blah blah blah, boom contradiction thus 5 is smaller than 7.