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).
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:
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.
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.
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.
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?
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.
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.
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.
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.