“You can’t prove a negative!”

A lot of people seem to buy into the belief that “you can’t prove a negative!” and use it in order to deflect criticism or to keep themselves from fulfilling the burden of proof on their position. In fact, this never fails to annoy me, because it’s most definitely not true that “you can’t prove a negative.”

First of all, it’s important to remember that the actual saying is “you can’t prove a universal negative,” not “you can’t prove a negative.” A universal negative is a statement of the sort “there is no X such as…” (such as the famous “there are no teacups on the Moon” or “there are no black swans”). But people often use the “you can’t prove a negative” argument to prove that a statement of the sort “X is false” or “X is impossible” or “X cannot be proven” cannot be made. But a statement like “X is false” is not a universal negative.

Suppose I say “astrology is false.” You then reply with “you can’t possibly prove that astrology is false, you can’t prove a negative, all you can say is that you haven’t seen it work, it could work,” or some sort of reply like that. But it is very easy to prove that astrology is false: all you need to do is state what astrology predicts and test it. If it doesn’t happen, that shows that the prediction was based on false premises. An even simpler way to prove it is to demonstrate that planets and stars are so far away that other things around babies have more gravitational impact on them than astrology, thus defeating the whole premise of astrology.

It goes without saying that illogical or incoherent positions are false. If I say “I didn’t shoot John F. Kennedy,” simple logic tells us that, being born after the event, I could not possibly have committed it. It’s not “possible” for me to have shot John F. Kennedy, any more than it’s “possible” for horses to spout wings and fly, for a human being to walk on water or fly of his own power, or for the Earth to instantly stop spinning and start again.

The scientific process, in fact, works entirely by proving negatives. If one set out to prove astrology scientifically, one would try to find ways to disprove its premises. By testing those premises again and again and again, one would come to the conclusion that they are sound or unsound. If all of our negative statements are disproven, then our belief in astrology would be strengthened. If a negative statement is proven (such as “astrological predictions are no better than random chance”), then our belief must be wiped out.

What about universal negatives, the actual subject of the maxim? Is it true that you can’t prove a universal negative? Suppose I say “there is no Santa Claus.” I know this for a fact because I know that the concept of Santa Claus is a human invention. Even if there is a bearded guy with a red cloak living at the North Pole making toys for children, he’s not Santa Claus as defined by what we call the belief in Santa Claus: that belief is based on mythology.

Of course it is easy to refute a universal negative: all you have to do is find one instance of it. For example, people used to believe that there were no black swans. But then we found one, and that was the end of that. The error here was not to make a universal negative, but rather to make a universal negative without evidence: there is nothing in the nature of swans that makes it impossible for one to be black.

4 thoughts on ““You can’t prove a negative!”

  1. Scott August 8, 2009 at 20:03

    Great article!! Thank you.

  2. Kendall March 26, 2011 at 15:36

    You are right you can prove a universal negative, but your example is both wrong and weak. The issue of Santa Claus is based on observation; you can’t prove that at no point in time and space that such a being did not exist meeting all the criteria you attribute to Santa Claus. While Santa Claus remains implausible the argument doesn’t disprove him. A perfect example of this is the city of Troy, which was once thought to be a legend but was found in 1871 by Frank Calvert and archaeologist Heinrich Schliemann.
    A universal negative (No S is P) can be proven given that the subject and the condition each have mutually exclusive qualities. For example you could rightly say that no circle is a square because a circle has qualities that exempt it from being a square and a square has qualities that exempt it from being a circle, to change one into the other would negate its previous form. It is only under the specific circumstances that a universal negative can be proven.

    • Francois Tremblay March 26, 2011 at 15:53

      “you can’t prove that at no point in time and space that such a being did not exist meeting all the criteria you attribute to Santa Claus.”

      Don’t be a troll.

  3. Samuli December 5, 2011 at 07:18

    Here’s a couple of quick thoughts on subject. First of all, if you can’t prove universal negative, you cannot prove universal affirmative. The claims,

    “No swan is black” is equivalent to “All swans are non-black” via simple obversion. Or more generally “No S are P” –> “All S are non-P”. Obversion is truth-preserving.

    Second, most people do not understand what universal claim means in logic. Universal simply means “all of S” instead of the particular “some of S”. Subject “the S” can be as well-defined as you want, and, in fact, the claim, “Santa Claus is not real”, is a universal affirmative claim (practically) about a singular (There is only one possible Santa Claus that fits the definition). Like-wise your statement,”I did not shoot Kennedy”, is a universal affirmative claim, where S is singular. Predicate can be as well-defined as we want as well. For example “No mice are in my closet”.

    So to try to keep it short: Negative and affirmative claims are obversed trivially between each other, and the scope of the argument does not need to be high for a “universal” claim. When people say “universal negatives cannot be proved”, they are thinking of claims where the field of knowledge required for the claim to be proven true or false is absurdly high. This is of course trivially true akin to a tautology: “A claim that cannot (practically, given the amount of work needed) be proved, cannot (practically) be proved”. Claims like, “No bearded, jolly, fat man who owns flying reindeers exist anywhere in the universe.”

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