E.G.

Here’s an interesting post from Dworkin over at Left2Right.  In the course of the post, Dworkin considers the claim that "argument is only useful if there are common premises that both parties share."  (Obviously, the two "parties" here are the person giving the argument, and the person hearing the argument.)  Let’s call this the "principle of shared premises."  Dworkin says:

This [i.e., the "principle of shared premises"] might seem to be a truism; actually it is false. It is possible to argue ad hominem, i.e. showing an opponent that from premises he accepts, although I do not, one gets a contradiction. Thus he must give up at least one of his views. This, of course, does not show the view he abandons is false. Just that he has no grounds for holding it.

I think Dworkin means to refer to reductio-style arguments here, not ad hominem ones (though I’m not completely sure of this; see the usage note in the second link).  Reductio-style arguments do seem to be a counterexample to the principle of shared premises, but I’m not sure they really are.  Here I’ll show why, but first it will be worthwhile to say a few very basic things about deductive propositional logic. 

In deductive arguments, not all assumptions are created equal.  Let’s distinguish "regular assumptions" from "working assumptions."  Regular assumptions are those assumptions upon which my conclusion depends.  Consider this argument:

1. P
2. If P, then Q
3. If Q, then R
4. Q (from 1 and 2)
5. R (from 3 and 4)
6. Thus, if P then R

This argument is of a form sometimes called "conditional proof."  It should be obvious that my conclusion in 6 depends on the assumptions in lines 2 and 3, but not on the assumption in 1.  That is: As long as 2 and 3 are true, it does not matter whether 1 is true or false; 6 has to be true.  Thus 2 and 3 are regular assumptions, while 1 is a working assumption.

Now here’s a reductio-style argument:

1. P
2. If P, then Q
3. If P, then not Q
4. Q (from 1 and 2)
5. not Q (from 1 and 3)
6. Q and not Q (from 4 and 5)
7. Thus, not P

Again: To compel assent to my conclusion in 7, 2 and 3 must be true, but premise 1 obviously does not need to be true.  Thus 1 is a working assumption, while 2 and 3 are regular assumptions.

Now again consider the principle of shared premises, which says that "argument is only useful if there are common premises that both parties share."  "Premises" here presumably refers to what I’ve been calling "assumptions."  If the principle is supposed to say something about assumptions in general, then the principle is obviously false, as Dworkin says; we’ve already seen two argument-forms which are indisputably useful even though they do not require anyone, let alone "both parties," to believe all the assumptions involved.  But if the principle is supposed to be talking about just regular assumptions, not working assumptions, then I think the principle is defensible.  In that case, the principle would say that arguments are only useful when both parties assent to all the regular assumptions.  It’s not clear whether this is the case or not.  We know that arguments are not useful when the person hearing the argument doesn’t assent to all the regular assumptions; the question, then, is whether arguments can be useful when the person giving the argument doesn’t assent to all the regular assumptions, i.e. "begs the question against herself," as I have called it previously.

………………………..

After writing this post, I e-mailed Dworkin to ask whether he meant something other than "ad hominem."  He said:

No, I mean ad hominem.  Not in the sense of arguing about the caracter of the opponent, but in the sense of arguing that HE cannot accept all the views he holds.  This leaves open the question of the truth or falsity of what he gives up. 

Here is a source which uses the term as I intended to use it.

The second form of the ad hominem was identified by John Locke <link> in his Essay Concerning Human Understanding <link>, when he wrote that it was

to press a man with consequences drawn from his own principles or concessions.  This is already known under the name of argumentum ad hominem.