Wolfgang Schwarz

Indeterminacy of representation and representation of indeterminacy

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.

Back to ratificationism?

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.

What are our options?

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.

A puzzle about belief reports

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.

Edinburgh

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!

Lewis search

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.]

Consequentialism and voting

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.

Subjunctive credence and statistical chance

In her 2012 paper "Subjunctive Credences and Semantic Humility" (2012), Sarah Moss presents an interesting case due to John Hawthorne.

Non-existent mathematical objects

An amusing passage from a recent paper by Erik and Martin Demaine on the hypar, a pleated hyperbolic paraboloid origami structure:

Supposing the truth

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".

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