The Possibility of Proving the Non-Existence of Something

In a recent blog entry, theistic philosopher William Vallicella criticizes a statement made by psychologist Paul Vitz, in which Vitz asserted that it is “intrinsically impossible” to “prove the non-existence of anything.” As Vallicelli correctly points out:

“But surely there are things whose nonexistence can be proven. The nonexistence of a round square can be proven a priori by simply noting that something that is both round and nonround cannot exist.”

What Vallicelli writes is consistent with my own essay on the subject, where I made the following observation.

Indeed, there are actually two ways to prove the nonexistence of something. One way is to prove that it cannot exist because it leads to contradictions (e.g., square circles, married bachelors, etc.). …

The other way to prove the nonexistence of something is, in the words of Keith Parsons, “by carefully looking and seeing.”

I could not agree with Vallicelli more when he concludes that Vitz’s assertion is “plainly false.”

Swinburne’s Argument from Religious Experience – Part 2
Swinburne’s Argument from Religious Experience – Part 3
Evolution vs. The Argument from Providence
Swinburne’s Argument from Religious Experience – Part 5
About Jeffery Jay Lowder

Jeffery Jay Lowder is President Emeritus of Internet Infidels, Inc., which he co-founded in 1995. He is also co-editor of the book, The Empty Tomb: Jesus Beyond the Grave.

  • shargash

    A proof is a formal construct of logic and mathematics. It really has no place in the natural world. For example, I can prove the Pythagorean theorem in Euclid’s geometry. What I cannot “prove” is the applicability of Euclidean geometry to the natural world.

    The gets to the heart of the difference between a theorem (of mathematics) and a theory (of science). A theorem can potentially be proved or disproved. A theory cannot, by definition. It can only be supported (or contradicted) by observations.

    To try to apply Pythagoras’ theorem to the natural world, we would first need to convert it into a hypothesis. Then we would test it against existing observations and make predictions for the outcome of experiments not yet conducted.

    When we did that, we would find that observations in a curved space-time continuum do not agree as well with the Pythagorean hypothesis as other geometries. This would lead us to reject the hypothesis, or at least send it back to its maker for modification.

    It is important to emphasize the meaning of this: the Pythaorean theorem has been proved to be true and yet observations demonstrate that, while it is a reasonable approximation, it is not true in the natural world.

    I can construct any number of other geometries by altering postulates other than the “paralell line” postulate. Many of those will bear little relationship to the natural world, and yet I can “prove” theorems in those geometries as well.

    So, back to the top of the original post, “the Possibility of Proving the Non-Existence of Something” — with a suitable choice of axioms, you can “prove” or “disprove” just about anything you care to. However, the expression “non-existence of something” implies a correspondence to the natural world, which can never be established with the certainty of a proof. A natural hypothesis can only be shown to be in agreement, or not in agreement, with observations. There can be no certainty that future observations, or observations made with greater precision, will not falsify the hypothesis. Falsification is at the core of naturalism (something the proponents of ID don’t get), whereas falsification of something that has been proved is an oxymoron.

    In short, you can’t “prove” anything in the real world.