“The fallacy behind fallacies”
My response to Gerald J. Massey
Gerald J. Massey argues in “The fallacy behind fallacies” that logicians lack a consistent theory of fallacies. He makes an example of the fallacy of the converse (or affirming the consequent) in order to prove that it is not a formal fallacy. His argument is fascinating but wrong, and his errors confirm the widespread miscomprehension of the logical structure of sense.
The fallacy of the converse is a derivative of Modus Ponens, and can be formalised as follows:
P implies Q;
Q;
therefore P.
Nothing follows from Q about P, hence the reasons are insufficient to draw the conclusion P. To accept validity without sufficient reasons allows the opposite of any conclusion to be also validly concluded, therefore contradiction, therefore non-sense.
Massey purports to present a logically valid counter-example that fits the form of the fallacy. He is mistaken, misidentifying the form of his own example, which is in fact different to the form of the fallacy.
His example assumes that 'everything' implies 'something', or else his "valid" conclusion would not follow, but if 'everything implies something' then we are no longer dealing with one-directional implication that the fallacy of the converse requires, but with bi-implication (equivalence), to which the fallacy does not apply. His first premise may thus be extended to include what is taken for granted by the conclusion:
If something has been created by God, then everything has been created by God; AND If everything has been created by God, then something has been created by God.
This statement of bi-implication can be condensed like this:
If and only if something has been created by God, then everything has been created by God.
The necessity-condition only if (in addition to if standing alone, which is the sufficiency-condition) ensures bi-directionality: 'everything only if something' implies 'if everything then (necessarily) something'. This is no longer the form he purports to refute, therefore a case of equivocation (violation of the law of identity) which implies contradiction.
I agree with Massey that formulas and fallacy descriptions are an inadequate standard of judgment because people fail to understand the underlying principle that makes the formula invalid, and Massey confirms this with his own failure of interpretation.