1. Suppose you have strong evidence that L are the true laws of nature, where L is
a system of deterministic laws. You also have strong evidence that the universe
started in the exact microstate P. Your have a choice of either affirming or
denying the conjunction of L and P. You want to speak truly. What should you do?
Intuitively, you should affirm. But what would happen if you denied?
Since L is deterministic, L & P either logically entails that you affirm, or it
logically entails that you don't affirm. Let's consider both possibilities.
Until recently, the Stanford Encyclopedia of Philosophy didn't have anything on
counterpart theory. The editors thought the topic isn't worth an entry of its
own, but at least it now has a section in the entry on "David Lewis's Metaphysics". This isn't ideal, since counterpart-theoretic approaches to
intensional constructions are best seen as metaphysically non-committal. But
it's better than nothing.
I also wrote an "appendix" to the entry with an overview over
counterpart-theoretic interpretations of quantified modal logic. It
explains some unusual features of counterpart-theoretic logics, how they arise,
and how they could be avoided.
By the way, here's another problem my prover can't solve (in reasonable time):
Show: ∀y∃z∀x(Fxz ↔ x=y) → ¬∃w∀x(Fxw ↔ ∀u(Fxu → ∃y(Fyu ∧ ¬∃z(Fzu ∧ Fzy))))
This is problem 54 in Pelletier 1986. It is a pure first-order adaptation of a
little theorem proved in Montague 1955. Montague gives a fairly simple proof.
His proof uses the Cut rule, which the tableau method doesn't have. I've tried
to construct a tableau proof by hand, but failed.
This might be a nice example of a relatively straightforward fact that can be
proved easily with Cut, but not without.
It's been quiet here. I haven't had much time or energy for philosophy since the
pandemic turned me into a stay-at-home dad on top of the regular job(s). At
least teaching has finally come to an end a few weeks ago. I've used my newly
found free time to build support for identity into the tree prover.
This is something I've wanted to do for a long time. Every five years or so I
look into it, but give up because it's too hard. Here I'll explain the
challenges, and the approach I chose.
Logic textbooks usually introduce two rules for handling identity: "Leibniz'
Law" (in both directions) and a rule that allows closing branches on which there
is a node of the form ¬t=t. These rules go back to Jeffrey 1967.
I've long been puzzled by the nature of quantities, but I've never really
followed the literature. Now I've read Jo Wolff's splendid monograph on the
topic. I'm still puzzled, but at least my puzzlement is a little better
The basic puzzle is simple and probably familiar. On the one hand, being 2m high
or having a mass of 2kg appear to be paradigm examples of simple, intrinsic
properties. On the other hand, these properties seem to stand in mysterious
relationships to other properties of the same kind. First, there's an exclusion
relationship: nothing can have a mass of both 2kg and 3kg. Second, there are
non-arbitrary orderings and numerical comparisons: one thing may be four times
as massive as another; the mass difference between x and y may be twice that
between z and w. If 2kg and 8kg are primitive properties, why couldn't an object
have both, and where does their quasi-numerical order and structure come from?
In my paper "Ability
and Possibility", I argued that ability statements should be analysed as
simple possibility modals: 'S can phi' is true iff S phis at some world
compatible with relevant circumstances.
This view is widely considered inadequate because it seems to violate two
(related) intuitions about ability.
One is that ability requires a kind of robustness: if you have the
ability to phi, then you reliably phi whenever the need arises, under a variety
I've been teaching a course on classical epistemology this term, so I've thought
a little about knowledge.
A common judgement in the literature seems to be that knowledge is incompatible
with a certain kind of luck -- the kind of luck we find in Gettier cases. This
is then cashed out in terms of safety: for a belief to constitute knowledge it
must be true in all nearby possible worlds.
While I share the initial judgement, the development in terms of safety doesn't
look plausible to me. It has the wrong kind of structure.
For example, any true belief that concerns a modally robust subject matter is
automatically safe. But such beliefs are not immune from Gettier cases. I'm sure
one can find examples where, say, Newton's laws are used to predict whether two
asteroids will collide, and the laws happen to give the correct answer ('no'),
but they don't predict the correct trajectories; the true reason why the
asteroids won't collide involves some feature of general relativity. Now if
someone in the mid 19th century asked whether the asteroids will collide, and
they used Newton's laws to figure out the answer, then their belief (that the
asteroids won't collide) is justified and true, but it isn't knowledge. And yet
it is arguably true in all nearby worlds.
A Sobel sequence is a sequence of conditionals with increasingly strong
antecedent. Lewis used Sobel sequences to motivate his "variably strict"
analysis of counterfactuals.
For example, intuitively (1) and (2) might both be
true, which seems to contradict a simple strict analysis:
(1) If the US had destroyed its nuclear weapons in 1965, there would have
(2) If every country destroyed its nuclear weapons in 1965, there would
have been peace.
A problem with this argument (pointed out in von Fintel 2001), is that the
intuition about (1) and (2) depends on the order in which the sentences are
considered. If we consider (2) first, and judge that it is true, then (1) looks
at best doubtful.
of Choice" paper has now appeared in Mind.
The paper asks how we should understand an agent's decision-theoretic options.
That is, what are the things whose expected utility we are supposed to maximize?
I think the question is a lot harder than often assumed. For example, I argue
that it won't do to say that the options are certain "willings" or "intentions",
as some authors have suggested.
In many respects, the problem of options mirrors the "input problem" for
Bayesianism: what are the propositions on which rational agents are supposed to
conditionalise (or Jeffrey-conditionalise)?
Friends of singular thought typically assume that in order to have a singular attitude towards an object, one must either stand in a special acquaintance relation to the object, or have a special kind of mental representation for it. Both of these views face a challenge from our practice of attitude reports: we can seemingly attribute attitudes with singular content even if neither condition is satisfied.
In a well-known example from Sosa 1970, the army generals decide that the shortest man should go first. The Sergeant tells Shorty: 'they want you to go first'. Here the generals need not be acquainted with Shorty, and it is doubtful that they must have a "mental file" for him.