Sometimes, when we say that someone can (or cannot, or must, or must not) do P, we really mean that they can (cannot, must, must not) do Q, where Q is logically stronger than P. By what linguistic mechanism does this strengthening come about?
Why maximize expected utility? One supporting consideration that is occasionally mentioned (although rarely spelled out or properly discussed) is that maximizing expected utility tends to produce desirable results in the long run. More specifically, the claim is something like this:
According to realist structuralism, mathematics is the study of structures. Structures are understood to be special kinds of complex properties that can be instantiated by particulars together with relations between these particulars. For example, the field of complex numbers is assumed to be instantiated by any suitably large collection of particulars in combination with four operations that satisfy certain logical constraints. (The four operations correspond to addition, subtraction, multiplication, and division.)
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.
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.
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.
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.
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.
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 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.
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