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Sunday, August 06, 2006

Kamp/Vlach Sentences Again

Consider the following sentences:

(1) One day, all persons alive now will be dead
(2) Once all persons alive then would be dead

Sentences like (1) and (2) can familiarly be translated using Hans Kamp's doubly indexed N operator, and Frank Vlach's doubly indexed K operator. Kamp's N operator shifts the time of evaluation for the sentence it embeds to the time of reference (which may or may not be the time of speech). Vlach's K operator is used in combination with the N operator. The K operator stores the time introduced by a past tense operator that embeds it, and the N operator is used to retrieve the stored time. (1) and (2) can be analyzed as follows (F is future, and P is past):

(1a) F(for all persons x: (N(Ax) --> Dx))
(2a) P K F (for all persons x: (N(Ax) --> Dx))

However, I think there is a simpler way to translate (1) and (2), for instance (where X is a plural variable):

(1b) For all persons X, F(the Xs do not exist).
(2b) It was the case that (for all persons X, F(the Xs do not exist)).

5 comments:

Jason Stanley said...

Brit,

If I'm not mistaken, there is a Phil Bricker paper from I think 1989 making these points, called "Quantified Modal Logic and the Plural De Re". I don't have the paper with me at the moment, so I can't check, but I will later...

Brit Brogaard said...

Thanks, Jason! I will see if I can find it.

Stephen Yablo said...

Also Bostock in a MIND article "Necessary Truth and Apriori Truth" (or something like that) does something similar. "Actually" becomes a scope indicator which with the help of plural quantification is supposed to do the same work as coindexed necessity and actuality operators.

Jason Stanley said...

Brit,

Also see pp. 93ff. of Graeme Forbes's *Languages of Possibility* (one of my favorite books!) where he also discussed this point (with "actually" rather than "now", but it's the same point). As he writes (p. 93):

"However, it is possible to get the effect of the simple 'actually' operator in ordinary modal language if we add plural quantification to the available non-modal means of expression. 'The Fs' is a plural quantifier, binding plural variables realized in English by '_ of them', and we can use this apparatus to express a characteristic sentence of (the relevant QML language with 'actually' operators) as follows:

18 The existents are such that possibly there is something distinct from all of them.

[This is 'There could have been things which do not actually exist'].

Brit Brogaard said...

Hi Stephen and Jason. Thanks a lot for the references! I will take a look at them.