< 653 older entriesHome117 newer entries >

Might counterfactuals

A might counterfactual is a statement of the form 'if so-and-so were the case then such-and-such might be the case'. I used to think that there are different kinds of might counterfactuals: that sometimes the 'might' takes scope over the entire conditional, and other times it does not.

For example, suppose we have an indeterministic coin that we don't toss. In this context, I'd say (1) is true and (2) is false.

(1) If I had tossed the coin it might have landed heads.
(2) If I had tossed the coin it would have landed heads.

These intuitions are controversial. But if they are correct, then the might counterfactual (1) can't express that the corresponding would counterfactual is epistemically possible. For we know that the would counterfactual is false. That is, the 'might' here doesn't scope over the conditional. Rather, the might counterfactual (1) seems to express the dual of the would counterfactual (2), as Lewis suggested in Counterfactuals: 'if A then might B' seems to be equivalent to 'not: if A then would not-B'.

A few links

I stumbled across a few interesting free books in the last few days.

1. Tony Roy has a 1051 page introduction to logic on his homepage, which slowly and evenly proceeds from formalising ordinary-language arguments all the way to proving Gödel's second incompleteness theorem. All entirely mainstream and classical, but it looks nicely presented, with lots of exercises.

2. Ariel Rubinstein has made his six books available online (in exchange for some personal information): Bargaining and Markets, A Course in Game Theory, Modeling Bounded Rationality, Lecture Notes in Microeconomics, Economic Fables, and the intriguing Economics and Language, which applies tools from economics to the study of meaning.

Ifs and cans

Is 'can' information-sensitive in an interesting way, like 'ought'?

An example of uninteresting information-sensitivity is (1):

(1) If you can lift this backpack, then you can also lift that bag.

Informally speaking, the if-clause takes wide scope in (1). The truth-value of the consequent 'you can lift that bag' varies from world to world, and the if-clause directs us to evaluate the statement at worlds where the antecedent is true.

Should you rescue the miners?

Many accounts of deontic modals that have been developed in response to the miners puzzle have a flaw that I think hasn't been pointed out yet: they falsely predict that you ought to rescue all the miners.

The miners puzzle goes as follows.

Ten miners are trapped in a shaft and threatened by rising water. You don't know whether the miners are in shaft A or in shaft B. You can block the water from entering one shaft, but you can't block both. If you block the correct shaft, all ten will survive. If you block the wrong shaft, all of them will die. If you do nothing, one miner will die.

Let's assume that the right choice in your state of uncertainty is to do nothing. In that sense, then, (1) is true.

Iterated prisoner dilemmas

There's something odd about how people usually discuss iterated prisoner dilemmas (and other such games).

Let's say you and I each have two options: "cooperate" and "defect". If we both cooperate, we get $10 each; if we both defect, we get $5 each; if only one of us cooperates, the cooperator gets $0 and the defector $15.

This game might be called a monetary prisoner dilemma, because it has the structure of a prisoner dilemma if utility is measured by monetary payoff. But that's not how utility is usually understood.

Time consistency and stationarity

Suppose you prefer $105 today to $100 tomorrow. You also prefer $105 in 11 days to $100 in 10 days. During the next 10 days, your basic preferences don't change, so that at the end of that period (on day 10), you still prefer $105 now (on day 10) to $100 the next day. Your future self then disagrees with your earlier self about whether it's better to get $105 on day 10 or $100 on day 11.

In economics jargon, your preferences are called time inconsistent. Time inconsistency is supposed to be a failure of ideal rationality.

Decision theory notes

In the last four months I wrote a draft of a possible textbook on decision theory. Here it is.

I've used these notes as basis for my honours/MSc course "Belief, Desire, and Rational Choice". They're tailored to my usage, but they might be useful to others as well.

The main difference to other textbooks is that I talk at length about the structure and interpretation of subjective probabilities and utilities. In part, this is because it makes a great difference to the plausibility of the expected utility norm whether, say, utilities are defined in terms of individual welfare, in terms of choice dispositions, or taken as primitive. But I also think these are independently interesting philosophical topics.

Three kinds of preference

The decision-theoretic concept of preference is linked to the concepts of subjective probability and utility by the expected utility principle:

(EUP) A rational agent prefers X to Y iff the expected utility of X exceeds the expected utility of Y.

Economists usually take preference to be the more basic concept and interpret the EUP as an implicit definition of the agent's utilities (and sometimes also her probabilities).

Justification at a distance

According to a popular picture, some beliefs are justified by "seemings": under certain conditions, if it seems to you that P, then you are justified to believe that P, without the assistance of other beliefs. So seemings provide a kind of foundation for belief, albeit a fallible kind of foundation.

But most of our beliefs are not justified by seemings (or by beliefs which are justified by seemings, etc.). I once learned that Luanda is the capital of Angola and I've retained this belief for many years, although I rarely think about Angola and thus rarely experience any relevant seemings that could justify the belief.

Lewis on possible worlds and the grounds of modality

Friends of primitive powers and dispositions often contrast their view with an alternative view, usually attributed to Lewis, on which modal facts about powers, dispositions, laws, counterfactuals etc. are grounded in facts about other possible worlds. But Lewis never held that alternative view – nor did anyone else, as far as I know. The allegedly mainstream alternative is entirely made of straw. The real alternative that should be addressed is the reductionist view that powers and dispositions are reducible to ultimately non-modal elements of the actual world.

< 653 older entriesHome117 newer entries >