Thursday, April 10, 2008

Conjunctive analyses

Sometimes we try to analyze a concept as a conjunction of two or more concepts. Thus, we might say that x knows p provided p is true and x justifiably believes p. Frequently, such proposed analyses founder on counterexamples—Gettier examples in this case.

I want to highlight one kind of failure. Sometimes analyzing x's being an F in terms of x's being a G and x's being an H, fails because to be an F, not only does x have to be a G and an H, but x's Gness and Hness have to be appropriately connected. While Gness and Hness are ingredients in Fness, their interconnection matters, just as one doesn't simply specify an organic compound by listing the number of atoms of each type in the compound, but one must also specify their interconnection.

I suspect this kind of connection-failure of conjunctive definitions is common. One way to see what is wrong with the justified true belief analysis of knowledge is to note that there has to be a connection between the justification and the truth and the belief. Specifying what the connection has to be like is hard (that is my understatement of the week).

Here's another case of the same sort. Suppose we say that an action is a murder provided it is a killing and morally wrong. Then we have a counterexample. Igor, who used to be a KGB assassin, has turned over a new leaf. As part of his turning over a new leaf, he has promised his wife that, no matter what, he will never kill again, no matter what. Maybe in ordinary cases that promise would be inappropriate. But given Igor's life history, it is quite appropriate. Now, Tatyana has just mugged Igor and is about to stab him to death so as not to leave any witnesses. Igor picks up a rock and kills her in self-defense. What he has done was a killing and it was morally wrong—it was the breaking of a promise. But it wasn't a murder because the connection between the fact that the action was a killing and the fact that the action was morally wrong wasn't of the right sort. (One might try to say that it was a killing and immoral, but wasn't immoral qua killing.)

When we hear a conjunctive analysis being given in philosophy, I think it's time to look for a connection-counterexample, a case where each conjunct is satisfied, but the satisfaction of the conjuncts lacks the right kind of interconnection. Sometimes, I think, one can intuitively tell that a proposed analysis is unsatisfactory for lack of such interconnection even without coming up with a counterexample. Here is a case in point. Consider the notion of "causal necessitation". A natural-sounding definition is this: an event E causally necessitates an event F provided that (i) it is nomically necessary that if E holds, then F holds; and (ii) E causes F. But even if it turns out that this is a correct characterization—that necessarily E causally necessitates F if and only if (i) and (ii) hold—I don't think it's a good definition. For it misses out the fact that one wants a connection between the necessitating and the causing—the co-presence of the two factors shouldn't be merely coincidental. But it's really hard to come up with an uncontroversial case where we have a difference between the two. (Interestingly, it may be possible to do so if Molinism is true.)

We are rightly suspicious of disjunctive analyses. I think we should have a similar, though weaker, suspicion of conjunctive ones.

There is a structural connection between the points in this post and Aristotle's Metaphysics H6. The point is also similar to Geach's discussion of the good. We cannot define a "good basketball player" as someone who is (i) good and (ii) a basketball player.


Alexander R Pruss said...

In certain kinds of experiments, it is important to record the methodology ahead of time, lest one change the methodology to fit the data. I am going to check how common the interconnection problem is. Specifically, my plan is to go to the library, and look at the last three issues of the three top H-index ('97-07) general philosophy journals (JPhil, Mind, Phil Studies) and of the top ethics journal (Ethics). Then I will look at all the articles which I can understand (i.e., which aren't in fields so abstruse that they're beyond me) and which offer an analysis of something in conjunctive terms or at least which offer a conjunctive necessary and sufficient condition. I will then see whether the method of this post can be used to generate a plausible counterexample, and, failing that, a per impossibile counterexample.

If I don't find at least five analyses/nec-suff cond sets in papers I can understand in the last three issues of the journals, I will increase the number of issues examined (of all the four journals) to the set to be examined until I get my count up to at least five. (So, for instance, if examining the last four issues of the four journals yields 4 items, I will look at the last five issues of the four journals, hoping to get at least 5.)

Maybe this experiment is kind of silly. But at least I'll have fun trying to generate counterexamples, which is one of the most pleasurable non-supernatural activities there are. :-)

Alexander R Pruss said...

Progress report:

I've gone through half of the issues I was sampling (I had to skip an issue and use an earlier one in one case, as the library was missing it). I've found six non-stipulative conjunctive nec/suff condition sets defended by the author. Of these, I generated interaction-counterexamples to four. One of these counterexamples also was a counterexample to the fifth (but wasn't an interaction-counterexample to it). The remaining nec/suff condition set was clearly flawed, and after fixing it, became subject to an interaction-counterexample.

I have to confess, though, that in one case I wasn't explicitly thinking via the method when coming up with the counterexample, though the resultant counterexample could be seen as fitting into the pattern.

Anonymous said...

Thanks for this work, Alex.

I have felt the-lack-of-a-connection-problem with many analyses for a long time, but I never formulated it. We cut the concepts into pieces, but then we, exhausted by the chopping, don't have the energy to cobble them so that a correct analyses and insight is reached.

1. It's not clear to me that: Igor's promise was appropriate, even given his history (is it OK to give up killing a human in self-defense no matter what?), or his killing his wife was morally wrong (do not promises commonly have implicit conditions?, maybe some pertinent, implicit condition was not satisfied).

2. What's the specific problem with disjunctive analyses?



Alexander R Pruss said...

It wouldn't seem wrong for a religious order to include a vow of non-violence along with vows of poverty, celibacy and obedience.

At least the following seems fine: a vow of not resorting to violence except in defense of someone innocent who hasn't taken this vow. And that's all I need for the argument. (I can see how one might object to a vow of not engaging in the defense of innocent others.)

Natural concepts have a certain unity, and hence are not likely to be disjunctive.

All this stuff reminds me of Aristotle's discussion of the unity of a definition, and how a definition is different from the Iliad.

One can think of the Iliad as a conjunctive definition of a state of affairs: The state of affairs of its being the case that
(i) the goddess should sing the anger of Achilles son of Peleus, that brought countless ills upon the Achaeans, and that many a brave soul did it send hurrying down to Hades, and many a hero did it yield a prey to dogs and vultures, for so were the counsels of Jove fulfilled from the day on which the son of Atreus, king of men, and great Achilles, first fell out with one another, and that
(ii) the god that set them on to quarrel was the son of Jove and Leto; for he was angry with the king and sent a pestilence upon the host to plague the people, because the son of Atreus had dishonoured Chryses his priest, and that
(iii) Chryses had come to the ships of the Achaeans to free his daughter, and had brought with him a great ransom: moreover he bore in his hand the sceptre of Apollo wreathed with a suppliant's wreath and he besought the Achaeans, but most of all the two sons of Atreus, who were their chiefs, and that ...