Wednesday, April 9, 2008

Analyses: a hypothesis

In philosophy journals, one occasionally sees things like this:

Necessarily, x is an F if and only if x satisfies each of the following n conditions:
(i) ...
(ii) ...
(iii) ...
(iv) ...
I hypothesize that every philosophical claim of this form that has ever been made in print by a Western philosopher with the number of conditions n greater than or equal to 4 is:
  1. false, and/or
  2. stipulative, and/or
  3. circular, and/or
  4. redundant.
By "circular" I mean that Fness is implicitly or explicitly found in the conditions. By "redundant" I mean that one of the conditions is entailed by the others.

My evidence for the hypothesis is inductive. I have never seen a correct, non-stipulative, non-circular and non-redundant set of necessary and sufficient conditions for anything philosophical where there are more than three conditions.

It could be that the hypothesis is false. Is there a counterexample?


Mike Almeida said...

Where's the surprise in that? Most of the things philosophers are keen to analyze are very difficult. I'm not surprised at all that we do not have an analysis of, say, causation that is certainly correct. And I do not think it bodes ill for the method of analysis, as some have suggested. The fact that none has been certainly correct does not entail that we have not learned a great deal from these efforts. Further, when we are in the "philosophy room" the standards for a correct analysis of anything go through the roof. If we lowered the standards to typical scientific ones, we'd be claiming success all over the place.

Alexander R Pruss said...

Yes, we have learned a great deal from these efforts. The point about standards is also important.

But I wasn't actually claiming that no analysis has succeeded. I was claiming that no giving of necessary and sufficient conditions in terms of four or more conjuncts has succeeded.

Are there some concepts for which an giving necessary and sufficient conditions in terms of fewer than four conjuncts has succeeded?

I think so. For instance, the at-at account of change: "Necessarily, x changes in respect of property P iff (a) there is a t1 such that x has P at t1 and (b) there is a t2 such that x has not-P at t2." Some folks think there is something left out of the at-at analysis, something like "objective change" or "the flow of time". But even these people will, I think, agree that if (a) and (b) are true, then x changes in respect of P (how can it not if it has P at one time and lacks it at another), and conversely. They will think that the at-at theory is not a good analysis but they will admit that the necessary and sufficient conditions it offers are correct.

So I wasn't making a pessimistic point. Rather, it seems to me unlikely that an ordinary, non-gerrymandered concept should have conjunctive form with four or more conjuncts. (As tomorrow's post will make clear, I think we have reason to be suspicious of conjunctive analyses in general, though there probably are some that do work.)

Anonymous said...

Hi Alex, could you please elaborate on why you chose 4 as a (sharp) lower bound on failure of analyses? (Or perhaps you intended to do that tomorrow...) Thanks!

Alexander R Pruss said...

Well, I have a potential counterexample to my claim with 3.

Necessarily, x is a bachelor iff:
(i) x is a man
(ii) x is never married
(iii) x is marriageable.

(Accept no substitutes for this definition. Occasionally one hears that a bachelor is an unmarried man. But widowers are not bachelors. Nor is a bachelor the same as a never married man, because the Pope is not a bachelor.)

I wouldn't be surprised if some philosophy paper said this. Mind you, maybe "bachelor" is gerrymandered.

Alexander R Pruss said...

The account of change I gave is actually incorrect. Suppose there are island universes U1 and U2 which have separate time lines, and suppose x exists in both U1 and U2. Then x might have P in U1 at time t1, and not-P in U2 at time t2, but this wouldn't be change. Change is not just having a property at one time and lacking it at another. The two times have to be connected.

The following is a better necessary and sufficient characterization of change: x has P at t1 and has not-P at t2 and t1 is earlier than t2 or t2 is earlier than t1.

But perhaps even that doesn't work if multilocation is possible. Suppose x is multilocated at positions p1 and p2, and x at location p1 always has P and x at location p2 always has not-P. Suppose, moreover, that x's presence at p1 starts at t1, and then some time later x's presence at p2 starts, and then some time later x's presence at p1 ends, and then at t2 x's presence at p2 also ends. Then, at t1, x has P simpliciter, and at t2, x has not-P simpliciter. But I am not sure it's right to say x has changed from having P to having not-P. But that's such a weird case that my intuitions aren't reliable.