Ad Geachem

Peter Geach has argued that :

[A] "Ad hominem arguments. …you start from something he believes as a premise, and infer a conclusion he won't admit to be true. If you have not been cheating in your reasoning, you will have shown that your opponent's body of beliefs is inconsistent, and it's up to him to modify it somewhere. ...But an ad hominem argument may be perfectly fair play. ...A logically sound ad hominem argument does a service, even if an unwelcome one, to its victim - it shows him that his present position is untenable and must be modified. Peter Geach (Reason and Argument: pp. 26 - 27)

[B] Because men are fallible, overall consistency is probably never achieved; and even large scale consistency is difficult to achieve. (Reason and Argument: pp. 6)

Given these two premisses, we have good reason not to believe Geach when he asserts that the ad hominem is an acceptable form of argument.

The Rejoinder

People’s beliefs are either consistent or not consistent. (with all proper restrictions to those capable of having beliefs etc.)

Probably, no individual man ever achieves complete consistency in his beliefs.

So

Probably: For all x, if x is a man, then x has inconsistent beliefs. (that is, given his beliefs, a contradiction can be derived from them by accepted rules of inference)

For all x, if x is a man, then x either has consistent or onconsistent beliefs.

So:

Probably: No x is such that x is a man and x has consistent beliefs.

So, in the individual case, then:

Probably: Peter Geach is not immune from contradictory beliefs.

So, probably, Geach believes both P and ~ P; where P is the thesis that ad hominem arguments are instances of valid forms of argumentation.

(maybe at this point we could add a stipulation that probably means more likely than not.)

Given this, then by his own criteria , [A] and [B]; we ought not to accept Geach’s story about ad hominem arguments.