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If you spin a wheel of fortune, the outcome -- red or black -- depends on the speed with which you spin. As you increase the speed, the outcome quickly cycles through the two possibilities red and black. As a consequence, any reasonably smooth probability distribution (or frequency distribution) over initial speed determines an approximately equal probability (frequency) for red and black. Here is an example of such a distribution, taken from Strevens.
I've been asked to review Michael Strevens's new book, Tychomancy. This motivated me to have another look at his earlier book Bigger than Chaos.
The aim of Bigger than Chaos is to explain how apparently chaotic interactions in highly complex systems often give rise to simple large-scale regularities, such as the laws of thermodynamics, the stability of predator/prey population levels, or the economic cycle. The basic explanatory strategy, which Strevens calls enion probability analysis (EPA), consists in aggregating the probabilistic dynamics for the individual components of a complex system into a probabilistic dynamics for macro-level features of the system.
Plausible moral theories should be agent-relative. They should permit us to care more about close friends than about distant strangers. They can prohibit killing ten innocent people even in circumstances where eleven innocent people would otherwise be killed by somebody else. They might say that it would be right for Alice to dance with Bob, but wrong for Bob to dance with Alice.
But how should we think about agent-relative values? It may seem that the state of affairs in which Alice dances with Bob is either right or not right. How could it be right relative to Alice but wrong relative to Bob? Or consider a case where I can prevent you from killing eleven by killing ten myself. If it is wrong that you kill the eleven, then surely I have a moral reason to see to it that you don't kill the eleven, just as I have a moral reason to see to it that I don't kill the ten. Moreover, presumably it is worse if you kill eleven than if I kill ten. So shouldn't my reason to prevent you from killing the eleven outweigh my reason to not kill the ten?
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 not.
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.
(I) In front of you are two opaque boxes, one black one white. You can open one of them and keep whatever is inside. Yesterday, a perfect (or almost perfect) predictor tried to predict what you would choose. If she predicted that you'd take the black box, she put a million dollars in the white box and two dollars in the black box. If she predicted that you'd take the white box, she put a thousand dollars in the black box and one dollar in the white box. Which box do you open?
Let's say that at the beginning of your deliberation, you are completely undecided, giving 50 percent credence to the hypothesis that you'll end up opening the black box. Standard formulations of causal decision theory then say that opening the white box has greater expected payoff: since there's a 50 percent probability that it contains a million, the expected payoff is 500000.50, which is a lot more than what you could possibly find in the black box. However, choosing to open the white box would provide you with highly relevant information: it would reveal that the predictor has (almost certainly) put only one dollar in the white box and a thousand in the black box. As a rational decision-maker you should take that information into account. Many putative "counterexamples" to causal decision theory, such as those in Richter 1985 and Egan 2007, are based on this observation.
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.
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