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 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.
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".
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.
|< 595 older entries|