Wolfgang Schwarz

Imaginary Foundations

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.

Simplicity and indifference

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.

Strengthening the prejacent

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?

Long-run arguments for maximizing expected utility

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:

What i and -i could not be

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.)

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.

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.

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.

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.

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