5.2.8 Denying the consequent

There is a valid form of logical reasoning called “denying the consequent” (aka “modus tollens”) which can be used to show that induction is a valid and fully warranted methodology that we may rely upon. The form of the argument is:

If P, then Q.
Q is false.
Therefore P is false.

Following this logical form, the use of inference from real world experience is justified by the following sequence:

• If (P) induction from sense experience to make inferences about the world is invalid and unjustifiable, then (Q) science (which relies on inference) has no hope of working.


• However, (Q is false) science does work! There are countless examples of the progress that it has introduced, discoveries that it has made, and new technologies it has spawned. There are no counter examples to its success.


• Therefore, (P is false) our inferences from the real world ARE justified and valid.

Obviously if there was significant evidence in support of the claim that drawing conclusions through the scientific approach was invalid, then opponents would have a case. But such evidence is entirely absent, and there is overwhelming counter-evidence. Nor is there any competing theory as to why science tends to produce correct, useful, consistent, predictive, and informative results. Barring the existence of a competing explanation that accounts for its success (trickery by Satan to test our faith is one such untestable explanation, as is Solipsism), it’s plain, obvious, common sense to accept as fact that inference from the real world is valid. It would require agonizing logical contortions to explain away the falseness of statement “Q” above (i.e., “science has no hope of working”) using some other argument. The rule of Parsimony would indicate that the obvious explanation, above, is the correct one.

We should not become over excited by the fact that an established formal argument supports the use of induction. Language can be slippery, and we have seen earlier in this document a case where the cousin of modus tollens, modus ponens, was used to prove both that reality IS an illusion and later that reality IS NOT an illusion. So be careful with these simple techniques, they can be misused.