Wolfgang Schwarz

Centering and self-ascription

One of the grave threats to the development of mankind in general, and philosophy in particular, is the assumption that the objects of propositional attitudes can be expressed by that-clauses. The assumption is often smuggled in via a definition, e.g. when propositions are defined as things that are 1) objects of attitudes and 2) expressed by that-clauses. No effort is made to show that anything satisfies both (1) and (2) -- let alone that the things that satisfy (1) coincide with the things that satisfy (2).

Semantic guilt

When reading technical material outside philosophy, I am often struck by the widespread use of non-rigid names and variables. A typical example goes like this. You introduce 'X' to stand for, say, the velocity of some object under investigation. When you want to say that at time t1, the velocity is 10 units, you put exactly this into symbols: 'at t1, X = 10'. If the velocity changes, we get a violation of the necessity of identity:

Preferring the less reliable method

Compare the following two ways of responding to the weather report's "probability of rain" announcement.

Good: Upon hearing that the probability of rain is x, you come to believe to degree x that it will rain.

Bad: Upon hearing that the probability of rain is x, you become certain that it will rain if x > 0.5, otherwise certain that it won't rain.

The Bad process seems bad, not just because it may lead to bad decisions. It seems epistemically bad to respond to a "70% probability of rain" announcement by becoming absolutely certain that it will rain. The resulting attitude would be unjustified and irrational.

Williamson on modal knowledge

Apropos Williamson. The following question came up last year when we discussed The Philosophy of Philosophy in Canberra. I thought it had a sensible answer that we just couldn't figure out, but then Dorothy Edgington raised the same question at the recent phloxshop workshop in Berlin, and even though there were quite a few Williamsonians present, there was no agreement on what the answer is, and the proposals didn't sound very convincing.

Intensions, extensions, and quantifiers

Suppose we want to follow Frege and distinguish an expression's denotation from its sense. Suppose also we take the denotation of a predicate to be its extension: the set of its instances. The following argument appears to show that this leads to trouble.

An argument against some causal decision theories

Here is an attempt at an argument against formulating causal decision theory in terms of counterfactuals (loosely following up on the discussion in the previous post). The point seems rather obvious, so it is probably old. Does anyone know?

Diodorus and actuality

Let [] and <> express alethic necessity and alethic possibility, let @ stand for 'actually', and L for 'it is unalterable that'. We are going to prove that if something happens, then it is unalterable that it happens.

The unity and disunity of epistemic values

Alvin Goldman has just been giving this year's summer school here in Cologne. When he put forward his view that what distinguishes good ways of belief formation from other ways is their truth-conduciveness, I found myself disagreeing and claiming that there is no general principle that distinguishes the good ways from others. This is somewhat surprising given that I've often claimed in recent times that the only epistemic criterion for evaluating belief-formation is truth-conduciveness. Here is how I think the two claims can go together.

Names and descriptions in modal logic

In the old days, it was common to exclude individual constants from quantified modal logic in favour of Russellian descriptions. I can see how this works if we have either fixed domains (the same individuals populating all worlds) or possibilist quantifiers. But in such systems individual constants don't cause much trouble anyway. Can one also make the description move in more liberal systems? I don't see how, but I guess I'm just missing something obvious.

Lewis on Counterfactuals, Similarity, and Morgenbesser's Coin

There is a mistake on page 49 of Lewis's "Counterfactual dependence and time's arrow" (1979). Since the mistake seems to be repeated all the time, it might be worth pointing it out.

Page 49 is where Lewis lists similarity standards for his analysis of counterfactuals. The analysis, recall, says that "if A were the case, then C" is true iff the closest A-worlds are C-worlds (or, more precisely, iff either there are no A-worlds or some A&C-worlds are closer to the actual world than any A&~C world). Closeness is a matter of similarity, and Lewis indicates what the relevant respects of similarity might be for certain ordinary counterfactuals in section 3.3 of his 1973 book, and again in the 1979 article on counterfactual dependence. Roughly, the closest A-worlds are those that perfectly match the actual world across as much of spacetime as possible without diverse and widespread violations of the actual laws. This won't do for indeterministic worlds, where generally no laws need to be violated at all in order to ensure perfect match of futures even after earlier divergence. So Lewis restricts his standards to deterministic worlds, returning to the indeterministic case in the 1986 postscript to the 1979 paper.