Often the factors that determine a phenomenon don't determine it
uniquely. Sometimes this changes the phenomenon itself.
Take language. Plausibly, the meanings of our words are somehow determined by
patterns of use, but these patterns aren't specific enough to fix,
say, a unique extension or intension for our language. There is a
range of precise meaning assignments all of which fit our use equally
well. One might leave it at that and say that it is indeterminate
which of these precise languages we speak. But this misses
something. It misses the fact that we don't speak a precise
language. For example, in a precise language, "Mount Everest has sharp boundaries"
would be true, but in English it is false. The logic of a precise
language would (arguably) be classical, but the logic of English is
When we face a decision and work out what we should do, we gain information about what we will do. Taking into account this information can in turn affect what we should do. Here's an example.
Lewis, in "Causal Decision Theory" (1981, p.308):
Suppose we have a partition of propositions that distinguish worlds
where the agent acts differently ... Further, he can act at
will so as to make any one of these propositions hold, but he cannot
act at will so as to make any proposition hold that implies but is
not implied by (is properly included in) a proposition in the
partition. ... Then this is the partition of the agent's
That can't be right. Assume I "can act at will so as to make hold"
the proposition P that I raise my hand. Let Q be an arbitrary fact
over which I have no control, say, that Julius Caesar crossed the
Rubicon. Then I can also act at will so as to make P & Q true. (By
raising my hand, I make it true, by not raising it I make it false.)
So, by Lewis's definition, P is not an option, since I can act at will
so as to make a more specific proposition P & Q true (a
proposition that implies but is not implied by P). By the same
reasoning, all my options must entail Q. So they don't form a
partition: they don't cover regions of logical space where Q is
Consider a long list S1...Sn of sentences such that (a) each Si
is trivially equivalent to its predecessor and successor
(if any), and (b) S1 is not trivially equivalent to Sn.
For example, S1 might be a complicated mathematical or logical
statement, and S1...Sn a process of slowly transforming S1 into a
simpler expression. For another example, S1...Sn might be statements
in different languages, where each Si qualifies as a direct
translation of its neighbor(s) but S1 is not a direct translation
I recently accepted a Chancellor's Fellowship at the University of Edinburgh. So it looks like the next stop, after six years in Australia, will be Scotland. Woop!
Over the weekend I made a website that lets you search through the works of David Lewis. It's not perfect: a lot of the documents contain garbled words from OCR, the character encoding is messed up, and it doesn't show page numbers of matches. Maybe I'll fix that eventually. Also, three papers are currently missing from the index because I don't have them in PDF form: "Nachwort (1978)", "Lingue e Lingua", and "Review of Olson and Paul, Contemporary Philosophy in Scandanavia".
[Update: See the changelog for updates.]
In a large election, an individual vote is almost certain to make
no difference to the outcome. Given that voting is inconvenient and time-consuming,
this raises the question whether rational citizens should bother to
In her 2012 paper "Subjunctive
Credences and Semantic Humility" (2012), Sarah Moss presents an
interesting case due to John Hawthorne.
An amusing passage from a recent
paper by Erik and Martin Demaine on the hypar, a pleated hyperbolic
paraboloid origami structure:
Here is a coin. What would have happened if I had just tossed it?
It might have landed heads, and it might have landed tails. If the
coin is biased towards tails, it is more likely that it would have
landed heads. If it's a fair coin, both outcomes are equally
likely. That is, they are equally likely on the supposition that
the coin had been tossed. Let's write this as P(Heads // Toss) =
1/2, where the double slash indicates that the supposition in question
is "subjunctive" rather than "indicative".