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
alternative options.
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
false.
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
of Sn.
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
vote.
It obviously depends on the citizen's values. For a completely
selfish person, the answer may well be 'no'. Different election
outcomes typically don't matter too much for an ordinary citizen's
selfish interests; and a miniscule chance of a medium-sized gain does
not offset the cost in time and inconvenience.
In her 2012 paper "Subjunctive
Credences and Semantic Humility" (2012), Sarah Moss presents an
interesting case due to John Hawthorne.
Suppose that it is unlikely that you perform a certain physical
movement M tomorrow, though in the unlikely event that you
contract a rare disease D, the chance of your performing M is
high. Suppose also that the combination of contracting D and
performing M causes death. Then many judge that the objective
chance of 'if you were to perform M tomorrow, you would die' is low,
but the conditional objective chance of this subjunctive given that
you perform M is high.
The intuitive judgments Moss reports are
An amusing passage from a recent
paper by Erik and Martin Demaine on the hypar, a pleated hyperbolic
paraboloid origami structure:
Recently we discovered two surprising facts about the
hypar origami model. First, the first appearance of the model is much
older than we thought, appearing at the Bauhaus in the late
1920s. Second, together with Vi Hart, Greg Price, and Tomohiro Tachi,
we proved that the hypar does not actually exist: it is impossible to
fold a piece of paper using exactly the crease pattern of concentric
squares plus diagonals (without stretching the paper). This discovery
was particularly surprising given our extensive experience actually
folding hypars. We had noticed that the paper tends to wrinkle
slightly, but we assumed that was from imprecise folding, not a
fundamental limitation of mathematical paper. It had also been
unresolved mathematically whether a hypar really approximates a
hyperbolic paraboloid (as its name suggests). Our result shows one
reason why the shape was difficult to analyze for so long: it does not
even exist!
So the hypar joins the ranks of phlogiston,
the planet Vulcan,
the largest
prime, or the quintic
formula: objects of inquiry that turned out not to exist.
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".
Suppose you have a choice between two options, say, raising your
arm and lowering your arm. To evaluate these options, we should
compare their outcomes: what would happen if you raise your arm, what
if you don't? But we don't want to be misled by merely evidential
correlations. Your raising your arm might be evidence that your twin
raised their arm in a similar decision problem yesterday, but since
you have no causal control over other people's past actions, we should
hold them fixed when evaluating your options. Similarly, your choice
might be evidentially relevant to hypotheses about the laws of nature,
but you have no causal control over the laws, so we should hold them
fixed. But now we have a problem. The class of facts outside your
causal control is not closed under logical consequence. On the
contrary, if the laws are deterministic then facts about the distant
past together with the laws logically settle what you will do. We
can't hold fixed both the past and the laws and vary your choice.
Earlier this year, I read Tyler Burge's Origins of
Objectivity. It's a very long book. Here is an abridged version. A few comments below.
Origins of Objectivity
Representation is a basic explanatory kind in psychology that should
be distinguished from mere information-carrying. The most fundamental
type of representational state is perception. In perception, an
organism attributes properties to objects in its environment. To do
this, the organism does not need linguistic capacities, nor does it
need to know (or otherwise represent) necessary and sufficient
conditions for being the relevant object. Instead, the science of
perception reveals that it is sufficient that the organism stands in a
suitable causal relation to the object and that its perceptual state
involves certain constancies (for shape or colour or distance or
whatever) which characterize the object "objectively", abstracting
away from contingencies of the present stimulus.
I like the starting point — to think of intentional states as
explanatory scientific kinds. Burge doesn't say
what exactly he means by this. I would put it as a kind of
functionalism: intentional states are characterized (at least
in part) by their functional inter-connections and their relationship
to environmental causes, behaviour and other psychologically relevant
facts.