Thursday, March 15, 2007

Notes on Ludlow: Ch. 3

**WARNING: Technical Post **
In chapter 3, Ludlow supports the idea that the character or role of indexicals ought to find their way into the semantics for such terms. For an example, consider this quote of his (p59):

In a house of mirrors, someone might point at a man who is about to be attacked by a dog, saying 'He is being attacked by a dog', and I may assent to this judgement, not realizing that I am about to be attacked. Intuitively, someone who says 'You are about to be attacked by a dog' is saying something more than the first speaker. To say that this extra information lies outside the province of semantics seems to be surrendering all too quickly.

But "saying something more" in what sense? Is that "something more" really something semantic and if so what is that "something more"? Perhaps it is just something more in the sense that it is of a different form and admits of a different cognitive, practical, or functional role. But that need not mean that this something more must show up in the truth conditions of a sentence unless we are liberal in what we ascribe to the sense of a sentence. If we don't do this, then it is not clear, without further information, whether Ludlow really disagrees with his opponents here since they are just forming truth conditions for differing purposes. After all, it's not clear to me that the "something more" is really "extra information" at all rather than old information in a different, more useful (or differently useful) form. Even if there is extra information carried by the different sentences, why think that this is semantically rather than pragmatically conveyed. Why think that just because a sentence carries information that this must fall into its semantics? Every spoken sentence, for instance, carries the information that it is spoken at a specific time by a specific person who is in certain brain states, etc. But clearly if we allow all the information carried by an utterance into the semantics, that would not be a good idea - the whole notion of semantics would be stretched to the breaking point.

Let's say that the extra information for a word like "you" is that it refers to the person being addressed, so that "you are the person I'm addressing with this utterance" is true iff the person I'm addressing with this utterance is the person I'm addressing with this utterance. But if we want to such truth-conditions to capture as much as possible, as Ludlow seems to want, then is clearly not acceptable - the sentence on the right hand side clearly does not have the same sense (in the widest sense) as the sentence mentioned on the left. For one thing, they have differing cognitive significance. I can, for instance, know that the former is true without having any clear idea whether the latter is true. And the former is contingently true whereas the latter is necessarily, and trivially, true.

Ludlow's proposed fix here is not persuasive in the least. He proposes that a sentence like (25) "It could have been the case that you are not the person I'm addressing with this utterance" is to be analyzed (? - it's not clear whether he's saying it's synonymous or that this really what the sentence is like at the level of logical form or what) as (26) "It could have been that the person I'm addressing with this utterance is not the person I'm addressing with this utterance". That sentence seems ambiguous between de re and de dicto readings and Ludlow seems to think that we should treat the original sentence as the de re version of its analysis. But it's not clear why it should be the de re reading rather than the de dicto. Or why we should take the alleged fact that 26 gives us the truth conditions for 25 as reason to think that 25 has a similar structure.

Consider the following exchange between Paul Teller and me on this sort of account for the word "now", where "e is now" is true iff e is the time of this utterance:

Paul: If there is a model then there are questions about scope Consider (1) "E might have occurred now" We could read this as
(a) Possibly [te is the time at which e occurs, tu is the time at which the utterance occurs, and te = tu]
I don't think this reading can be given to (1), but we'll have to consult with the experts whether this is just bad ear on my part. It seems to me that the natural reading is
(b) tu is the time at which the utterance occurse, (viz, in the real world) and possibly [te is the time at which e occurs and te = tu that is there is some possible world in which e occurs at the time in which the utterance occurs in the real world.

Me: The trouble here is that in (1) we have a possibility operator applied to a single sentence - "e occurs now" - which does not apparently have the internal structure specified in the above truth conditions. I'm not quite sure how the logical form of a sentence using "occurs" would get written out (since sentences about events are tricky like that), so let's use a simpler example:
(2) e is now
Again, applying a possibility operator to (2) does not seem to produce a sentence that has the internal structure of the truth conditions provided by either of the examples above. This is because (2) seems, grammatically, to be an atomic sentence and hence lacks the structure to support the scope ambiguity you mention above. (2), in logical notation, seems to come out as
(3) Ne
and applying a possibility operator to this we get
(4) Pos (Ne)
There seems to be only one scope possible for the possibility operator here - that is, to operate over the entire sentence, which means that to evaluate the truth of (4) we must look in every possible world and see if there is one where (3) is true. To find a possible world where (3) is true is just to find one where the truth conditions for (3) are met. And since the token reflexive theory requires that the truth conditions for (3) require a token of the sentence to exist, (4) requires there to be some possible world where a token exists - so something like (a) would be the correct truth conditions, not (b). That the statement of the truth conditions for any of these sentences is complex and can have varying scope for possibility operators is besides the point since the fact that the statement of a sentence's truth conditions has a certain structure does not entail anything about the structure of the sentence itself. Consider the following statement of truth conditions for "Jerry is a bachelor":
(5) "Jerry is a bachelor" is true iff Jerry is unmarried, marriagable, and male. Now consider the following sentence:
(6) Jerry is necessarily a bachelor.
If we treat (6) in the same way (4) is treated by (b) above then we can get the following incorrect truth conditions for (6):
(7) (6) is true iff Jerry is unmarried and necessarily (Jerry is marriagable and male)
But clearly (7) is not correct - where a modal operator applies to an atomic sentence, there is no way to move the operator further inside the sentence - the operator clearly applies to the entire sentence. EVEN IF the statement of the truth conditions for the atomic sentence is not itself atomic.

So one of Ludlow's proposals, to give a kind of token-reflexivy analysis of the truth-conditions for indexical sentences, is not going to be very promising unless all we are after is extensional equivalence (which Ludlow is clearly not - he wants to load up sense as much as possible and stick it all in the truth-conditions or have it "displayed" there if he can). Of course, if all we are after is extensional equivalence, anyone - opponents included - could be happy with these sorts of truth conditions.

Ludlow's other proposal is to take it that (28a) 'I walk' is true iff I walk. The trouble is applying this sort of T-schema to other people's utterances of the same thing. One way to take care of this is to say that the truth conditions we use are different when others are speaking. But that seems rather ad hoc, especially if the truth conditions are supposed to display the sense of such a sentence. But since I use 28a for 'I walk' it should not matter whether I say it or not since the sense seems to be the same no matter who uses it. But then that's not very plausible since when someone else says 'I walk' they are not saying that I walk. Clearly, then, if we are to use differing truth conditions in our evaluations of sentences when they come from us or from someone else, that must mean that we display different aspects of the sentence in each case. And if that's so then it seems that we can't be too liberal about what must be included in the sense of a sentence if both truth conditions for myself and those for others are both supposed to display senses. It can't be required to capture the full cognitive significance of such a sentence, which calls into question Ludlow's program a bit.

Perhaps, though, the truth conditions are supposed to represent just the facts a person knows and just the way they know them. So maybe it is true that I use things like 28a in interpreting what I am saying since I must represent the truth conditions in such a way in order to use them. But that doesn't mean (to anticipate my objections to later chapters) that in representing things in the way 28a does that I am representing some fact over and above the fact that (28b) 'I walk' is true iff Ian Spencer walks - even though I have to represent it like 28a rather than like 28b.

More later.

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