**tl;dr version: every truth claim has a burden of proof. it doesn't matter whether or not the claim contains a negation.**

I feel like I'm derailing the UA vs. gravity thread, so I'm starting a new one. This isn't strictly about FET, but it comes up a lot.

It's often claimed in various threads by members of both sides that one cannot proves a negative claim like, "There is no *x*." This is a popular belief, and it's completely false. Deductive reasoning is *valid* if and only if it is impossible for its premises to be true and its conclusion false. Deductive reasoning is *sound* if and only if it is valid *and* its premises are true. That's all. It makes no difference if the premises or conclusions contain negations.

First, all truth claims carry a burden of proof. Consider the following statement: Barack Obama does not exist. The statement is not relieved of a burden of proof simply because it contains a negation. Anyone making this claim would be required to offer evidence supporting the truth of its claim. This is because all truth claims, negative or positive, carry a burden of proof.

Negative claims can also be proven deductively. Consider the following argument:

1. If A, then B. (*If A exists, then B exists*)

2. Not B. (*B does not exist*)

3. Therefore: not A. (*A does not exist*)

This argument uses a basic rule of inference called modus tollens, and we just used it to prove a negative: not A. It's logically *valid* because if the premises are true, then the conclusion cannot be false. Whether or not it's *sound* depends on the truth of the premises.

Let's consider a less abstract example:

If Barack Obama exists, then a birth certificate for Barack Obama exists.

A birth certificate for Barack Obama does not exist.

Therefore, Barack Obama does not exist.

This is a good example because it illustrates a point that is often missed in these discussions. Notice that we can still argue and debate the truth of premises. A proof can be both valid and not sound. Obviously the argument I just made is very unsound (the premises are untrue), but if the premises were true, then it would be a logically valid proof of the conclusion (if the premises are true, then the conclusion must be true).

There are obviously a host of other issues that would have to be resolved with the premises (What do we mean by Barack Obama? Anyone with that name? The person who is the president? Does the argument require that the person who is the president be named Barack Obama?). And, in practice, some conclusions and their associated premises might be too complex in reality for us to resolve; but, the fact that our reasoning includes statements with negatives doesn't make them necessarily irresolvable.

And, we can't just assume that every negative claim is true until proven otherwise. There's at least one good reason for this: every positive truth claim can be reformulated into a negative one. It's called double negation. '*x* exists' can be rewritten as '*x* does not not exist,' or, 'it is not the case that *x* does not exist.' If every negative claim is assumed true until proven false, then all claims must be assumed true until proven false. That is the opposite of skepticism.