I've been reading about objective consequentialism lately. It's interesting how pervasive and natural the use of counterfactuals is in this context: what an agent ought to do, people say, is whichever available act would lead to the best outcome (if it were chosen). Nobody thinks that an agent ought to choose whichever act will lead to the best outcome (if it is chosen). The reason is clear: the indicative conditional is information-relative, but the 'ought' of objective consequentialism is not supposed to be information-relative. (That's the point of objective consequentialism.) The 'ought' of objective consequentialism is supposed to take into account all facts, known and unknown. But while it makes perfect sense to ask what would happen under condition C given the totality of facts @, even if @ does not imply C, it arguably makes no sense to ask what will happen under condition C given @, if @ does not imply C.
It has often been pointed out that the probability of an indicative conditional 'if A then B' seems to equal the corresponding conditional probability P(B/A). Similarly, the probability of a subjunctive conditional 'if A were the case then B would be the case' seems to equal the corresponding subjunctive conditional probability P(B//A). Trying to come up with a semantics of conditionals that validates these equalities proves tricky. Nonetheless, people keep trying, buying into all sorts of crazy ideas to make the equalities come out true.
Dutch Book arguments are often used to justify various epistemic norms – in particular, that credences should obey the probability axioms and that they should evolve by condionalization. Roughly speaking, the argument is that if someone were to violate these norms, then they would be prepared to accept bets which amount to a guaranteed loss, and that seems irrational.
My paper "Imaginary Foundations" has been accepted at Ergo (after rejections from Phil Review, Mind, Phil Studies, PPR, Nous, AJP, and Phil Imprint). The paper has been in the making since 2005, and I'm quite fond of it.
According to the Principle of Indifference, alternative propositions that are similar in a certain respect should be given equal prior probability. The tricky part is to explain what should count as similarity here.
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.
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