Proving a Negative: Is it Really Impossible?

The Most Pervasive Fallacy in Modern Thought

It is a common misconception, even among logicians and scientists, to think that it is impossible to prove a negative. This is a fallacy of the first order. It is quite easy to prove a negative.

Mathematically, one can prove a negative statement through the most basic math: 2 - 3 = -1, for example. We can also look at proving a negative, in terms of the value of a statement, through a more tangible mathematic principle.

The essence of the operation of division is that to divide one number by another is the same as to multiply the first number by the reciprocal of the second. The same is true for non-numeric statements too: where 'proving a negative' might be quite burdensome in some circumstances, testing an equivalent positive statement, the reciprocal of a negative, is common practice.

Take, for example, the statement 'the world is not flat'. If we cannot prove a negative, how can we know that this statement is true? Obviously, we can test the positive form of this statement, 'the world is flat', and, finding it to be false, rule it out as a viable possibility. Alternately, we could test a related statement, 'the world is round', and, finding this to be true, the first statement is automatically disproven; the world cannot be both a flat plain and a sphere at the same time.

Whenever we find a positive statement to be true, an infinite number of negatives are also proven simultaneously. Determining that the sun is a ball of Hydrogen automatically rules out the possibility of the sun being made of Cheese Whiz or the souls of flushed gold fish. These things are 'proven false' when the one idea is proven true.

In point of fact, regardless of whether a person believes that a negative can be proven or not, this is the method by which science reaches every single one of its conclusions. We have already proven a countless number of negatives over the years: the Earth is not the center of the Solar System, the Milky Way is not the only galaxy, pizza does not grow on trees, and the Big Bang is not how the universe came to be. Saying that a negative cannot be proven is to deny the factual nature of all these things.