Last week I was doing some research for a presentation on accessibility relations for modal logic when I ran across a curious article by Vann McGee entitled A Counterexample to Modus Ponens (JoP 82). I discussed this article a bit over dinner last night, so imagine my surprise when I see that Brit Brogaard is blogging on the topic the next morning. Of course given how busy I've been I've really no business spending time on the article. Well, except for this, some people think that modus ponens is our most basic and common form of inference. So, if our most common form of inference is not truth preserving, then that is something to be concerned about. I ran one of McGee's counterexamples by a couple of colleagues and got mystified looks in return. Here is an example from McGee of a modus ponens that appears to be valid, and yet we shouldn't believe the conclusion.
Opinion polls taken just before the 1980 election showed the Republican Ronald Reagan decisively ahead of the Democrat Jimmy Carter, with the other Republican in the race, John Anderson, a distant third. Those apprised of the poll results believed, with good reason:I'll confess that I'm not to sure how to give an analysis of what's going on in the above passage. I initially thought we might be able to understand the conditionals as conditional assertions, but reading Lycan on the subject disabused me of that idea. Brogaard in her post favors a possible worlds analysis of McGee's proposed counterexample, but I suspect she doesn't feel a lot better about her answer than I do. I don't feel too terrible not having a response to the problem at this juncture, especially since the literature on the subject is still fresh 20 years on. Given that my philosophical superiors such as Lycan, Lowe, and Sinnott-Armstrong, have responded to the problem without quashing it makes me feel a little better in regards to my own mental abilities, though no better with regard to the problem. Fortunately I'll be doing an independent study on conditionals in the fall. I'll be reading at least Bennett's Guide to Conditionals, Lycan's Real Conditionals, and Gauker's Conditionals in Context. As always I welcome suggested readings. In the mean time, my biggest concern is that in another week or two I'm going to be standing in front of a room full of undergrads telling them that modus ponens is truth preserving, but now I'll have to extend my general caveat about some funny business with the truth-table.
- If a Republican wins the election, then if it's not Reagan who wins it will be Anderson.
- A Republican will win the election.
- If it's not Reagan who wins, it will be Anderson.
I hear 1 as a material conditional with an embedded material conditional and 3 as a counterfactual. I'm not sure why, but that's how it seems to me. When we read 3 as a counterfactual, it seems false. But as a material conditional it's true (since 2 is true).
Shouldn't that explain the puzzle?
I read (1) as shorthand for something like:
(1*) "If a Republican wins the election, then if Reagan isn't the Republican who wins then Anderson is."
i.e. the antecedent is, in a sense, "silently" carried over into the consequent. That would then explain why modus ponens fails -- the consequent alone is missing this embedded information.
On this view, it might be simplest to say that (1) is literally false. This is only counterintuitive because we are not inclined to read it literally. Instead, we naturally reinterpret it as a contraction of (1*).
I am a layman without training in logic and philosophy, so my comments may have fundamental problems and will not use correct terminology.
It seems to me that 2 is only true because the assumption is that the Republican Reagan will win. In other words, the real belief is "Reagan will win the election", and since Reagan is Republican, the substitute statement "A Republican will win the election" is made.
I confess that sometimes I'm tempted to an analysis of it like Douglas Walton's, which is the most plausible analysis I've seen arguing that MPP is not always valid.
My own view, though, is that McGee's apparent counterexample is not a counterexample at all; the argument is valid, and on the assumption that the premises are true, it is sound. The suggested paradox -- that the premises can be true even though the conclusion is false -- is due to equivocation in the interpretation of the conclusion. The interpretation of a conclusion is always conditioned by the meaning of the premises. Thus, for instance, in the old scholastic chestnut:
This ass is a mother.
This ass is yours.
Therefore this ass is your mother.
If the premises are true, the argument is sound; it's just that the conclusion is easily misinterpreted if its original context is not kept in mind, which requires interpreting 'your mother' as 'a mother that is yours' rather than in the ordinary sense. So it is here, I think, for slightly different, but similar, reasons. (I might be misunderstanding him, but Jeremy might have been proposing something that's a close cousin of this; in any case, I think he's on the right track.)
Bernard Katz has a reply to McGee's article (at least, I think it's a reply to McGee's piece--I haven't actually read it).
Katz, "On a Supposed Counterexample to Modus Ponens," JPhil (1999)
I was able to find the following opening sentences (but not much else) from Katz's paper online:
Vann McGee has set out several arresting examples which purport to show that modus ponens fails when applied to a conditional whose consequent is itself a conditional ("A Counterexample to Modus Ponens," The Journal of Philosophy 82 [1985] pp. 462-71). The present paper argues that McGee's examples rely for their plausibility not only on the assumption that the conditionals occurring in them, are not material conditionals but also on the assumption that they satisfy the law of exportation.
It looks like an interesting paper.
Thanks for the tips. The Walton paper is quite good. I haven't read the Katz yet but it is available via JSTOR. I'm going to try to get to the papers over the break next week, especially since I'll be introducing my students to MP when we get back from the break. Hopefully I'll have something new to say then.
A genuine counterexample would be an argument that has the form modus ponens, but is not truth-preserving. It's not clear to me that McGee's purported counterexample is genuine. Consider 2, which is true iff either Reagan will win the election, or Anderson will win the election. Suppose that Reagan will win the election. Then 2 is true, but intuitively, it no longer seems obvious that 1 is true: if a Republican wins the election, then if it's not Reagan who wins, God knows who will! On the other hand, suppose that Anderson will win the election. Then both 1 and 2 are fine, but so is 3.
I guess another move (which seems less appealing to me) would be to deny that McGee's argument really has the form modus ponens, by holding that although superficially, 1 seems to have the form "If A, then if B then C", it *really* has the form "If A and B, then C". (Perhaps, conditionals with conditional consequents literally make no sense.) A suggestion like this can be found in Edgington's commentary on Michael Woods's *Conditionals*, but I'm not sure whether she endorses it (1997, p. 121).