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2009-09-27
Two-Dimensional Semantics
I am currently working on a small paper on Frank Jackson's From Metaphysics to Ethics, which has gotten me into the discussion of two-dimensional semantics.

According to this approach, there are two ways a term or a sentence can be said to apply or to be true at different possible worlds. The first way one can consider what some term applies to in a possible world, is by supposing that that possible world is the actual world. The second way one can consider what some term applies to in a possible world, is by treating the world as a counterfactual world. Jackson calls a term's extension, in the first sense, the term's A-extension; and in the second sense, the term's C-extension. Likewise, the intension of a term in a world considered as actual, is called the A-intension of the term; and the intension of a term in a world considered as counterfactual is called the C-intension of the term. David Chalmers has summarized (or, at least, mentioned someone else's summary) these two ways of thinking about possibilites in the following way: in the first case, one “considers a possibility as actual”, and in the second case, one “considers a possibility as counterfactual“.

To use Jackson's own example, consider the term “water” (we accept Kripke's view that terms like “water” are rigid designators). In a possible world considered as actual, the A-extension of water is whatever substance that plays the “watery role” in that world, be that H20, XYZ or whatever. In a possible world considered as counterfactual, what the term “water” denotes is H20 – its C-extension is only H20 – since “water” is a rigid designator.

My question is: Suppose w is the actual world, and that the substance that plays the watery role in w is XYZ. Then, of course, the A-extension of "water" in w is XYZ. But what about the C-extension of "water", under the supposition that w is the actual world? Do we take as a premise that w is the actual world, and that "water" in w denotes XYZ, and conclude that in every counterfactual world (that is, every other world than w), "water" denotes XYZ? I have a strong feeling I'm missing something here, but I'm not sure what it is.

2009-09-28
Two-Dimensional Semantics
That sounds right. Maybe the the scientists are wrong. Water isn't H2O, its actually some other substance (lets abbreviate its chemical make up as "XYZ"). Under such a supposition, any substance that is not XYZ does not count as water -- this includes very watery collections of H2O. A moral here is this: in order to make counterfactual assessments one must make antecedent assumptions about actuality. For a discussion of cases like this and the even trickier case of Dry Earth see Korman(2006).


2009-09-28
Two-Dimensional Semantics

For what it is worth, Scott Soames has written extensively on Two-Dimensionalism. He makes a strong case against it. See, in particular, his book: Reference and Description, Princeton University Press, 2005.

2009-11-19
Two-Dimensional Semantics
If w were the actual world, then the term "water" would rigidly designate XYZ.  So yes, when considering counterfactuals with w considered as actual, "water" denotes XYZ.