Affirming the consequent

Suppose in an argument one were to affirm the "then" part of a conditional (the consequent) first, and conclude with the "if" part (the antecedent).

If P, then Q.

Q.

Therefore, P.

This argument form has the name affirming the consequent, because in arguing this way one does indeed affirm the consequent in the second premise ("Q" is the consequent of the conditional claim, "If P, then Q"). This is a logical fallacy. If we argue this way, we make a mistake. One can see this with an example:

There is oxygen here. Therefore, there is fire here.

This fallacy is best countered by analogously stating a different example of affirming the consequent, correcting it, then comparatively correcting the arguer's fallacy in this way:

"That is like saying that 'Where there is clay there is pottery,' when clearly pottery is not dug out of the ground, but clay is, then pottery is formed from the clay. Likewise fire is not all around us, but oxygen is, then fire is achieved by putting a sufficient heat source to any gas, such as oxygen, to ignite it."

Another, more simple, solution is to politely consider the absurdity of the statement with another conditional statement:

"If there were fire everywhere there is oxygen, then we would be burning right now, for oxygen is all around us."

Broken down, this appears this way:

Where there is oxygen there is fire.

Oxygen is all around us.

Therefore, fire would be all around us

We would burn.

See also: modus ponens, modus tollens, denying the antecedent.

Referenced By