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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.

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.

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.

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

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:

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.

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".

Decision-making under determinism

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.

Review of Tyler Burge: Origins of Objectivity

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.

Some counterexamples to the Benchmark Theory

In "Gandalf's solution to the Newcomb problem" (2013), Ralph Wedgwood proposes a new form of decision theory, Benchmark Theory, that is supposed to combine the good parts of Causal and Evidential Decision Theory.

Like many formulations of Causal Decision Theory, Benchmark Theory (BT) assumes a privileged partition of states that are outside the agent's causal control. Like Evidential Decision Theory, BT only considers the probability of these states conditional on a given act A. However, what is weighted by the conditional probabilities P(S_i/A) is not the absolute utility of S_i & A, but the comparative utility of S_i & A, which is determined by the difference between the absolute utility U(S_i & A) and the average absolute utility U(S_i & A') for all options A'. (This average is the benchmark B(S_i).) So the degree of choiceworthiness of an act A is given by

The lure of free energy

There's an exciting new theory in cognitive science. The theory began as an account of message-passing in the visual cortex, but it quickly expanded into a unified explanation of perception, action, attention, learning, homeostasis, and the very possibility of life. In its most general and ambitious form, the theory was mainly developed by Karl Friston -- see e.g. Friston 2006, Friston and Stephan 2007, Friston 2009, Friston 2010, or the Wikipedia page on the free-energy principle.

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