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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
Reply to Robin Robin
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
Reply to Robin Robin

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
Reply to Robin Robin
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.