On pages 148-155 of Naming and Necessity, Saul Kripke concludes his book by setting forth an argument against type-type identity theory (the view that that any given mental state is identical to a brain state). Kripke argues that a mental state (pain) cannot be identical to a brain state (C-fiber stimulation) because if the aforementioned states are identical, then they must be so necessarily; and since we can conceive of one state existing without the other, they cannot be identical. Below, I shall set forth a general argument (with explanatory comments) which demonstrates the basis of Kripke’s reasoning and then cite Krikpe’s example from the text (also with explanatory comments).

1. If X is a rigid designator and Y is a rigid designator, and if the statement “X is identical to Y” is true, then the statement “X is identical to Y” is necessarily true.

• An example of the above is “Mark Twain is identical to Samuel Clemens”. Since both of these names are rigid designators, then “Mark Twain is identical to Samuel Clemens” is true in every possible world in which these rigid designators pick out an individual. On the other hand, the statement “Mark Twain is identical to the author of The Adventures of Tom Sawyer” is composed of the rigid designator “Mark Twain” and the non-rigid designator “the author of The Adventures of Tom Sawyer”. While these two designators may be identical in the actual world, it is possible that someone else could have written The Adventures of Tom Sawyer. Thus, the latter example of identity is not necessary.

2. X is a rigid designator.

3. Y is a rigid designator.

4. However, “X is identical to Y” is not necessarily true.

5. Therefore, “X is identical to Y” is not true.

Below is a reconstruction of Kripke’s specific example involving “pain” and “C-fiber stimulation”:

1. If “pain” is a rigid designator and “C-fiber stimulation” is a rigid designator, then the statement “pain is identical to C-fiber stimulation” is necessarily true.

• Kripke anticipates that some people will object that the identity statement above cannot be necessary since it is known a posteriori. However, Kripke points out that the statement “pain is identical to C-fiber stimulation” is analogous to other necessary identity statements that are known a posteriori such as “water is identical to H2O” or “heat is identical to molecular motion”. Besides this, Kripke demonstrates early on (pp. 35-37) that some necessary truths are known a posteriori (like certain mathematical proofs that require a great deal of calculation).

2. “Pain” is a rigid designator.

• Once again Kripke anticipates objections to the above premise. He asserts that “pain” is a rigid designator because it picks out what it refers to by an essential property (the sensation of painfulness). It is impossible to conceive of pain existing without the property of “feeling painful”.

3. “C-fiber stimulation” is a rigid designator.

4. However, “pain is identical to C-fiber stimulation” is not necessarily true.

• It is possible to conceive of a world in which one can exist without the other.

5. Therefore, “pain is identical to C-fiber stimulation” is not true.

I must confess that the above argument appears to be a powerful refutation of identity theory. It seems to me that the only way out of the conclusion is to either deny Krikpe’s semantics or argue convincingly that either “pain” or “C-fiber stimulation” or both are not rigid designators.