Safalra's Website Philosophy Logical Fallacies Negative Proof

Negative Proof

Negative Proof refers to the fallacy of using an argument, about a phenomenon P, of the form:

  1. P has not been observed
  2. Therefore P does not exist

An argument of this form is most convincing when the existence of P seems implausible.

Relation to Denying The Antecedent

Negative Proof is a special case of the fallacy of Denying The Antecedent if we accept the additional premise that observing a phenomenon implies that it exists. With this additional premise, the above argument can be rewritten:

  1. If P has been observed then P exists
  2. P has not been observed
  3. Therefore P does not exist

Example

This fallacy is often employed in the criticism of a new scientific theory, by arguing that the theory is false because a phenomenon it predicts has not yet been observed. More formally:

  1. P has not been observed
  2. Therefore P does not exist
  3. Therefore the theory predicting P is false

For example, black holes were predicted decades before astronomers found reliable evidence of their existence.

The argument becomes valid if P has not been observed in an experiment in which the theory predicts that P must occur.

A note on parsimony the scientific method

An countably infinite number of possible scientific theories exist, but only a finite number of experiments will ever be performed. As a result, a principle is needed to choose between competing theories that predict all observed phenomena and don't predict any phenomena shown not to exist. The principle used is known as parsimony, and states that the simplest theory should be chosen (this principle is also known as Occam's Razor). In general this means rejecting theories that predict many phenomena that have not been observed or shown not to exist.

The justification for using Negative Proof in this context is that no other method exists for chosing between the theories. The use of Negative Proof in place of performing experiments is not justified - it should only be used once all currently possible relevant experiments have been performed and all relevant data have been collected.

Further reading

For a comprehensive reference on logical fallacies and the principles of good argument, see Attacking Faulty Reasoning: A Practical Guide To Fallacy-Free Arguments: