Standard decision theory studies one-shot decisions, where an agent faces a single choice. Real decision problems, one might think, are more complex. To find the way out of a maze, or to win a game of chess, the agent needs to make a series of choices, each dependent on the others. Dynamic decision theory (aka sequential decision theory) studies such problems.
There are two ways to model a dynamic decision problem. On one approach, the agent realizes some utility at each stage of the problem. Think of the chess example. A chess player may get a large amount of utility at the point when she wins the game, but she plausibly also prefers some plays to others, even if they both lead to victory. Perhaps she enjoys a novel situation in move 23, or having surprised her opponent in move 38. We can model this by assuming that the agent receives some utility for each stage of the game. The total utility of a play is the sum of the utilities of its stages.
Suppose there are no objective moral facts. It's tempting to think that this calls for a special semantics for moral language. Perhaps moral statements somehow express moral attitudes rather than describe the world. The trouble is that moral statements seem to behave like ordinary descriptive statements. Not only can we freely conjoin moral and descriptive statements. We can even use the same words – say, 'you ought to leave' – to express a moral attitude but also to report the implications of some contextually salient norms. It would be nice if we could use a standard descriptivist semantics for 'ought' statements even if we don't believe in objective normative facts.
A common worry about mathematical platonism is how we could know about an independent realm of mathematical facts. The same kind of worry arises for moral realism: if there are irreducible moral facts, how could we have access to them?
Benacerraf (1973) put the problem in terms of causation. Knowledge of maths, he suggested, would require some kind of causal connection between the mathematical facts and our mathematical beliefs, but modern platonists typically don't believe in such a connection.
Ability modals have a "specific" and a "general" reading. If a pianist is locked in a piano-free cell, they can play the piano in the general sense, but not in the specific sense. Roughly, an agent has the "general ability" to φ if they have the internal constitution required to φ. They have the "specific ability" to φ if, in addition, the external circumstances make it possible for them to φ.
What is the connection between the two notions? Some, e.g. Mandelkern, Schultheis, and Boylan (2017), hold that 'S can φ' expresses specific ability, and that the general reading results from the application of a tacit genericity operator 'Gen'. This is a natural idea, given that general abilities are often called 'general'. (Mandelkern, Schultheis, and Boylan (2017) even call them 'generic'!) The proposal is also tempting for accounts of ability that only directly capture the specific reading. (The locked-in pianist, for example, clearly wouldn't succeed to play the piano if they tried.)
Remember the miners problem. Ten miners are trapped in a mine and threatened by rising water. You don't know if they are in shaft A or shaft B, and you can only block off one of the shafts. Let's not ask about what you ought to do, but about what you can do. Specifically, can you save the ten miners?
According to the simple conditional analysis, you can save the miners iff you would succeed if you tried. So what would happen if you tried to save the miners?
I assume you don't actually try to save the ten miners. You keep both shafts open, knowingly causing the shortest miner to drown. Let's assume that (unbeknown to you) the miners are in shaft A. If you tried to rescue the ten miners, you would arbitrarily choose one of the shafts to block. Let's say you would choose shaft A, simply because you like the letter 'A'. You don't think this is relevant: you don't think the miners are any more likely to be in shaft A than in shaft B. But you have to make your choice somehow. Might as well make it based on your irrelevant preference for the letter 'A'.
Humean accounts of physical laws seem to have an advantage when it comes to explaining our epistemic access to the laws: if the laws are nothing over and above the Humean mosaic, it's no big mystery how observing the mosaic can provide information about the laws. If, by contrast, the laws are non-Humean whatnots, it's unclear how we could get from observations of the mosaic to knowledge of the laws. This line of thought is developed, for example, in Earman and Roberts (2005). Chen (2023) (as well as Chen (2024)) argues that it rests on a mistake. Eddy suggests that Primitivists about physical laws have no more trouble explaining our epistemic access than friends of the Best-System Analysis.
A common assumption in discussions of abilities is that phobias restrict an agent's abilities. Arachnophobics, for example, can't pick up spiders. I wonder if this is true, if we're talking about the pure 'can' of ability.
The problem is that 'can' judgements (and 'ability' judgements) are often sensitive to relevant preferences or norms: I might say that I can't come to a meeting (or that I'm not able to come) because I have to pick up my kids from school. This is what I'd call an impure use of 'can'. I don't actually lack the ability to come to the meeting. It's just that doing so would come at too high a cost. Perhaps arachnophobia similarly associates a high cost with picking up spiders.
A new paper (draft) on counterfactuals with unspecific antecedents, to appear in a festschrift for Al Hájek. The paper discusses a range of phenomena related to the "Simplification of Disjunctive Antecedents". I argue that they can't be explained by a chance-based account of counterfactuals, as Hájek has suggested. Instead, I hint at an RSA-type explanation. I also suggest that this explanation might somewhat weaken the case for counterfactual skepticism.
I regret how much time I have spent on this topic. I first noticed it in 2006, and thought I had a nice explanation. When I posted it on the blog, Kai von Fintel kindly pointed me towards some literature. A little later, Paolo Santorio suggested that my explanation resembles the one in Klinedinst (2007). This seemed right, but I had in mind a more pragmatic implementation. I eventually wrote up my proposal in Schwarz (2021). Although my original interest was sparked by conditionals, that paper focuses on possibility modals, and only briefly mentions how the account might be extended to conditionals. When I got the invitation to write something for Al's festschrift, I thought I could spell out the application to conditionals, and compare it with Al's account. But I couldn't really make it work. So I ended up defending a more orthodox derivation based on Kratzer and Shimoyama (2002).
It would be nice if my papers and lecture notes were available in HTML, I thought. Let's start with my lecture notes on modal logic (PDF) I thought. I'll need to convert them from LaTeX to HTML, but surely there are tools for that. I thought.
I was right. But ah, LaTeX! There are, of course, multiple options. You can use pandoc. Or tex4ht. Or lwarp. Or LaTeXML. All of them sort of work, after some fiddling and consulting their thousand-page manuals. But none of them support all the packages I use. And shouldn't those gather lists have more line-spacing, etc.?
According to a popular view about counterfactuals, a counterfactual hypothesis 'if A had happened…' shifts the world of evaluation to worlds that are much like the actual world until shortly before the time of A, at which point they start to deviate from the actual world in a minimal way that allows A to happen. 'If A had happened, C would have happened' is true iff all such worlds are C worlds. The time "shortly before A" when the worlds start to deviate is the fork time.
Now remember the case of Pollock's coat (introduced in Nute (1980)). John Pollock considered 'if my coat had been stolen last night…'. He stipulates that there were two occasions on which the coat could have been stolen. By the standards of Lewis (1979), worlds where it was stolen on the second occasion are more similar to the actual world than worlds where it was stolen on the first occasion. Lewis's similarity semantics therefore predicts that if the coat had been stolen, it would have been stolen on the second occasion. This doesn't seem right.