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Some Thoughts on Kripke's Argument Against Identity Theory

In an excerpt from Naming and Necessity , Kripke argues that the type-type identity theory, which states that for every brain state there is corresponding mental state which is identical to that brain state, is rendered absurd using modal metaphysical notions, particularly the notion of rigid designation. Kripke explains that a rigid designator “designates the same object” “in every possible world” where that object exists (2). He then goes on to state that if there are two rigid designators, such as “‘ R 1 ’” and “‘ R 2 ’”, which are in fact identical to each other, as represented by “‘ R 1 = R 2 ’”, then, if it is true that “‘ R 1 = R 2 ’”, it is necessarily true that “‘ R 1 = R 2 ’” (9). This is because truths about identity are necessary truths. He then applies this to the type-type identity theory. He states that on this view, brain states are identical to mental states and so they necessarily share the same properties. Kripke uses the example of  “C-fiber stimulation” to illustra