Wolfgang Schwarz

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".

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.

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.

Indefinites and implicatures

Suppose I say (*), with respect to a particular gambling occasion.

(*) A gambler lost some of her savings. Another lost all of hers.

There is an implicature here that the first gambler, unlike the second, didn't lose all her savings. How does this implicature arise?

Against countable additivity

Imagine the universe has a centre that regularly produces new stars which then drift away at a constant speed. This has been going on forever, so there are infinitely many stars. We can label them by age, or equivalently by their distance from the centre: star 1 is the youngest, then comes star 2, then star 3, and so on, without end. The stars in turn produce planets at regular intervals. So the older a star, the more planets surround it. Today, something happened to one (and only one) of the planets. Let's say it exploded. Given all this, what is your credence that the unfortunate planet belonged to the first 100 stars? What about the second 100? It would be odd to think that the event is more likely to have happened at one of the first 100 stars than at one of the next 100, since the latter have far more planets. Similarly if we compare the first 1000 stars with the next 1000, or the first million with the next million, and so on. But there is no countably additive (real-valued) probability measure that satisfies this constraint.

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