Friday, February 01, 2008

The Logic of Indeterminacy

Alex's comment to my previous post reminded me that I need to say a bit more about my treatment of indeterminacy. He wonders how the following claims of mine could be consistent:
(1) It is indeterminate whether 'Bob' denotes Bob1 or Bob2.
(2) It is likewise indeterminate whether 'Mirror-Bob' denotes Bob1 or Bob2.
(3) But it is determinate that 'Bob' and 'Mirror-Bob' do not co-refer.

After all, if you took 1 and 2 to be the fundamental semantic facts in this scenario, then there is nothing to rule out their being coreferential -- it would simply appear to be indeterminate whether that's actually the case. To supervaluate: there are four ways* to resolve the indeterminacy, and on two of them the names co-refer, and on the other two they don't. So we cannot settle the question whether the terms co-refer.
* = Those four ways are:
(a) 'Bob' denotes Bob1, 'Mirror-Bob' denotes Bob1 [co-refer]
(b) 'Bob' denotes Bob1, 'Mirror-Bob' denotes Bob2
(c) 'Bob' denotes Bob2, 'Mirror-Bob' denotes Bob1
(d) 'Bob' denotes Bob2, 'Mirror-Bob' denotes Bob2 [co-refer]

But that's the wrong way to go about things. While 1 and 2 offer a partial description of the semantic situation, such an atomistic approach cannot capture everything that's going on. It is whole scenarios that are instead fundamental. Compare 1 and 2 with:
# (4) It is indeterminate which of the four semantic scenarios, a-d, obtains.

This is the situation as Alex took it to be. But it is not what I had in mind. And this way of presenting things brings out some alternative possibilities, such as:
# (5) It is indeterminate whether semantic scenario a or d obtains.
(6) It is indeterminate whether semantic scenario b or c obtains.

This is my claim. Crucially, it is 6, not 1 and 2, which provides the fundamental account of the situation I had in mind. (1 and 2 are consistent with any of 4, 5, or 6. That is why they are merely partial descriptions.) To derive more particular claims -- e.g. my 1, 2, and 3 -- from the fundamental account (6), we simply supervaluate. That is, a claim is:
(I) determinately true if it is true in all allowed scenarios;
(II) determinately false if it is false in all allowed scenarios; and
(III) indeterminate if it is true in some allowed scenarios and false in others.

Since my allowed scenarios are b and c only, we obtain the following results:
My claim 1 is true because 'Bob' denotes different people in scenarios b and c.
Likewise for claim 2 and 'Mirror-Bob'.
3 is true because in both b and c, 'Bob' and 'Mirror-Bob' denote different people.

Does that all make sense?


  1. (Again, I might be missing something, but..)

    It makes sense, but I don't see the justification for thinking that (6) is more justified than the weaker (4). Why think that the only "allowed" scenarious are (b) and (c)?

  2. It's the same reason for thinking that the names refer to people rather than pumpkins: I just stipulate that as a condition on the terms as I mean to use them. That is, it's analytic that Bob and Mirror-Bob are different people (if they exist at all).

  3. Something worries me about basing an argument against a semantic theory based on arbitrarily stipulated meanings.

    If that were allowable, couldn't you simply stipulate the meaning of a term so as ensure that compositionality was false without the need for the intermediate argument? "I define 'blah' as meaning X when embedded in sentences of kind Y, and meaning F when embedded in sentences of kind G. Therefore strict compositionality is false."

    But I fear I'm misunderstanding here, so I'll give it some more thought.

  4. That seems more suspicious, insofar as it involves introducing two distinct meanings (and so, arguably, two distinct words). My example of 'Bob' seems to hold the same meaning throughout, and the stipulation distinguishing it from 'Mirror-Bob' seems more natural/intuitive, and less gerrymandered/ad hoc. (The condition really seems to capture how we would use those names. I can't imagine any natural language term behaving as you describe, by contrast.)

  5. To clarify: I take it that compositionality fails not because the semantic value of 'Bob' changes from one sentence to the next (I may have mistakenly written that in my first post), but because the semantic value of the whole sentence cannot be reduced to the SVs of its atomic parts.


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