This led to someone else making a statement that is popular among atheist laymen. He wrote, "You can't prove a negative." I responded, "You can't? Why not? I can prove negatives. Who told you that you can't prove a negative?" Really, negatives are proven all day long and are very easy: you can prove that there is no full-sized elephant in your room right now. You can prove that, under normal conditions, if you drop a pencil, it will not fall up instead of down. These are perhaps silly examples, but proving negatives is one of the most common things

*to*prove. Here's a more realistic case. Many scientists and philosophers of science follow Popper in claiming that science cannot prove anything it can only falsify. Science cannot prove "if A --> B" because A and B may just be occuring together by coincidence. However science can falsify "if A --> B" by finding an example of A occurring without B. If we accept this account then not only is it possible to prove a negative, it means that science

*only*proves negatives.

Now I suspect the atheist who says you can't prove negatives is really thinking something else. Perhaps he's thinking that while you can prove negatives about observables you can't prove negatives about unobservables, like God. But of course this is false as well: you can prove that God did not just create a full-sized elephant in your room right now. The atheist may counter-respond that if we appeal to God we can make any absurd qualification we want. Maybe God just created a full-sized

*invisible*elephant in your room right now. If you object that part of your anti-elephant proof is that your room is not big enough for an elephant, you can maybe qualify it further. But these attempts are non-starters. Absent the specific qualification that the elephant is invisible (or any other

*ad hoc*qualification) the phrase "a full-sized elephant" by itself would mean that the elephant in question is visible (or lacks the

*ad hoc*qualification). I think the people who make this objection are thinking something along the lines of: the concept of God has been repeatedly qualified to render it immune to disproof. It used to refer to a physical person-like object, but then when that became philosophically and scientifically untenable it was upgraded to a non-physical person-like object, etc. This seems to presuppose a naive view of the origin and development of religion which was common in the second half of the 19th century. Certainly, the theistic concept of God has developed -- as it should -- but it is not clear to me that this has been a series of

*ad hoc*qualifications like, "Well, well, maybe he's just

*invisible!*" At any rate, atheism is guilty of the same thing, so it strikes me as a

*tu quoque*argument.

Or perhaps the atheist is thinking you can't prove a

*universal*negative. That's a more respectable claim: to say there are no X's would seem to require that one had searched all of reality and determined that no X's exist. Even more, it would seem to require that one had searched all of reality

*simultaneously:*otherwise, perhaps the X's were somewhere other than where you were looking at each particular moment; maybe they moved around so that they were always behind you or something. Unfortunately, this claim is still false. It assumes the only way you can prove something is via observation, that is, through scientific methods. This is scientism and scientism is a naive and foolish position. To make the most obvious point, you can prove things via logic -- specifically you can prove

*universal negatives*via logic. If something contradicts a law of logic then it is impossible and cannot exist anytime, anywhere. If the atheist challenges the laws of logic we can simply point out that science presupposes the laws of logic. Once you've abandoned logic you've abandoned science (not to mention knowledge and rationality). However, this has a limited application. That's why this objection is more respectable: in many cases you can't prove a universal negative. It's only when the universal negative contradicts a law of logic that it can be disproven.

A third possibility: perhaps the atheist is defining "prove" in the logical sense. You can give an argument for something, you can demonstrate that something is more likely true than false, you can even show that it is very probably true. But a logical proof is an

*absolute*proof. It cannot fail to be true (or, conversely, fail to be false). It holds of all possible worlds. But of course, this was already dealt with: to prove a universal negative via logic is to prove it absolutely.

Finally, I would just like to point out that the claim "You can't prove a negative"

*is a negative*. So by its own lights, it can't be proven. This doesn't necessarily render it invalid, since there are many things we can know that we can't prove. However, it does mean, at the very least, that the person who claims you can't prove a negative must give us a reason for thinking

*why*you can't prove a negative. This is likely to lead to one of the three possibilities above.

(Updated to add a point and clean up some awkward phrasings.)

**Update, 12 July:**Defining ignorance.

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*cross-posted at Quodlibeta*)