wo's weblog

Quick logic question

2010-05-07T17:21:00+02:00

Suppose you add to the language of first-order logic a sentence operator L for which you stipulate that all instances of (L(p -> q) & Lp) -> Lq are valid and that validity is closed under prefixing L's: if p is valid, then so is Lp. For example, L could be the modal operator 'necessarily', or it could mean the same as ''. If it means the same as '', then is invalid, since it translates as . So the principle of Universal Instantiation ...

ANU

2010-04-20T17:58:00+02:00

Last week I accepted an offer for a post-doc at the ANU, starting in September. I will be working with Al Hajek on "the objects of probability". Should be great.

Extensionality and Leibniz' Law

2010-04-12T21:31:00+02:00

Extensional contexts are usually defined as positions in a sentence at which co-refering terms can be substituted without affecting the truth-value of the sentence. So 'Cicero' occupies an extensional position in 'Cicero denounced Catiline', but not in 'Philip said that Cicero denounced Catiline'. One might think that a term t occupies an extensional position in A(t) if and only if all instances of the following schema are true: (LL) x=y -> A(x) A(y). 'x=y' is true iff '...

"Norms of assertion"

2010-04-02T11:55:00+02:00

Two rather different things sometimes seem to go under the name "norms of assertion", and it might be useful to keep them apart. Often, e.g. by Williamson, norms of assertion are characterised as constitutive norms of a particular speech act. Roughly, a constitutive norm for an activity X is a norm you must obey, or try to obey, in order to partake in activity X. The rules of chess are a paradigm example: to play chess, you have to move the pieces in a particular way across the board...

Pre-fission possibilities

2010-03-26T19:22:00+01:00

Suppose tonight you will fission into two persons. One of your successors will wake up Mars and one on Venus. There are then two possibilities for how things might be for you tomorrow: you might wake up on Mars, and you might wake up on Venus. These are distinct centered possibilities that do not correspond to distinct uncentered possibilties. There is just one possibility for the world, but two possibilities for you. Indeed, the two possibilities are two actualities:...