Monday, August 29, 2005


The ECAP is now in full swing. It´s an event on an impressive scale, with long days comprising for the most part multiply parallel sessions. It´s also pretty warm in Lisbon right now, and many of the rooms have no air conditioning. This (together with the fact that the university is located under the flight path of the city´s airport) has been the main downer so far. Philosophically there has been plenty to entertain and to challenge. I´ll try and get comments on various papers up here eventually, but since I´m pushed for time now I´ll just briefly describe some material presented yesterday by David Papineau and this afternoon´s talk by Kit Fine.

Papineau was arguing that epistemologists and methodological philosophers of science once had a similar range of interests, but that recently (since Gettier, as far as I could tell) epistemologists have been moving away from methodological concerns, and focussing on other matters (the examples given were tracking, disjunctivism and contextualism). For a while I wondered whether Papineau was going to say that the methodologists were out of date, but it turned out the fault lay with the epistemologists, since Papineau could find little reason to be interested in the concept of knowledge except insofar as knowledge is a means to true beliefs, i.e. insofar as one is interested in the methodology of belief formation.

A few thoughts about this:
1. Even supposing there is a real difference of focus between epistemologists and methodological philosophers of science, I would prefer to think in terms of a division of labour than a competition as to whose project is more worthy.
2. Even if we are inclined to agree that we need a reason to be interested in knowledge which appeals to our prior interest in something else, there seem to be some which aren´t simply that our having knowledge is a means to our having true beliefs. For instance, there is Edward Craig´s idea that we are interested in knowledge because we are interested in the notion of a good informant. There´s still a focus on true belief here, in some sense, but for one thing the shift to the third-person perspective which is (at least sometimes) reasonable when we´re thinking about good informants seems to put issues like contextualism back on the menu. (When I spoke to Papineau after the talk he said he was already thinking about this, and also mentioned the Williamsonian idea of knowledge as the norm of assertion.)
3. It´s not even obvious to me that the only methodological reason for being interested in knowledge is that one is interested in securing true beliefs. Before we have a clear grasp of what knowledge is, gleaned from a thorough exploration of the concept of knowledge of the kind Papineau considers disreputable, how can we say whether methodologists should focus on finding out which belief-forming policies lead to true scientific beliefs, as opposed to saying that methodologists should focus on finding out which policies lead to scientific knowledge?

Kit Fine gave a very interesting paper (of which I´d heard an earlier version in St Andrews in June), in which he proposes a new approach to the notion of class. Rather than building a ZF-like hierarchy by starting with a grasp of the membership relation and using it to explain which sets there are (first the set with no members, then the set with the null set as its only member ... etc.), we would start off with all the classes and any urelemente as given, and then explain membership by saying which of those things the relation held between. He described this as a sort of Copernican Revolution.

In the question session I queried whether one could understand which classes there are without understanding what membership is. It´s not as if classes can be pointed out to us like boxes: to think about a particular class, we have to describe it, and presumably we will most often describe classes using descriptions of the form ´the class whose members are ...´. Fine initially proposed that we associate classes with certain conditions (e.g. the null class with the condition x is not identical to x) which, although they may contain a limited membership relation, do not contain the full notion. But since these are the conditions for membership of the class we are interested in, that doesn´t seem to help - understanding the relation between the condition and the class is understanding that the condition tells you which members the class has.

If something like this is right, then at most I think Fine might be able to claim that, instead of the traditional explanatory asymmetry between the membership relation and the notion of class, we have an interesting interdependence between the two. I don´t think he could say that the asymmetry was to be reversed in the way suggested by the phrase ´Copernican Revolution´.

Fine made a suggestion in reply, which was that we might associate conditions with the objects which would turn out to be the classes in some other way than by saying that the conditions specify the classes´ members. I´m still wondering what to think about this (comments welcome, obviously!), though an initial feeling is that we can´t really get an idea of which classes there are by this means. We would get the idea that there are these objects, but would we have enough information to understand that they were classes if we didn´t understand what membership was?


Carrie Jenkins said...

PS to this post: it occurred to me in conversation with Kit yesterday afternoon that my worry is something like a version of the Julius Caesar problem. Indeed, if Kit goes (as he seems keen to do) the way of abstraction in specifying the required relation between condition and class (abstracting on co-extensiveness of conditions), my worry will be identical to a version of the Julius Caesar problem.

Kenny said...

I don't know if I quite caught what you said Kit Fine's position is, but it strikes me as almost more reactionary than revolutionary. It seems like the model-theoretic way of understanding the universe of sets/classes. All the entities are specified and we try to understand the relation(s) among them. Maybe the model-theoretic way of seeing things wasn't so well-developed at the beginning of the 20th century, but I believe it was at least 1930 before the notion of the universe as built up in the cumulative hierarchy was established. This picture of the set-theoretic universe as being constructed from the empty set (or Urelemente) using the powerset operation seems to be the most often-cited evidence for the consistency of ZFC (or one's favorite class theory).

But perhaps Kit Fine is merely suggesting that the cumulative hierarchy is useful to show that ZFC is consistent, and we need a more model-theoretic view of things to give an explanation of what's actually going on, rather than what might be going on.