Philosophers sometimes also use 'reductionist' more strictly, to mean 'type-identities' between mental and physical categories, and to exclude 'non-reductive physicalisms' like metaphysical functionalism.
I'm not so sure that I am a reductionist in the strict type-identity sense. The issues here are messy. But I certainly a reductionist in the more general sense which is opposed to eliminativism and dualism.
Kripke says that physicalists like me can't explain the 'apparent contingency' of mind-brain identities. He maintains that, if I really believed that pains are C-fibres, then I ought no longer to have any room for the thought that 'they' might come apart. His argument is that, since pains aren't identified via some contingent description, but in terms of how they feel, I have no good way of constructing a possible world, so to speak, where C-fibres are present yet pains absent.
I say that there is nothing deficient about our current theoretical grasp of mind-brain identities. The problem is only that they are counter-intuitive.
Of course, there remains the question of why we should find mind-brain identities so persistently counter-intuitive, if they are true. But this is a simple psychological question, and there are a number of plausible explanations. Indeed this is a topic that is quite extensively discussed outside philosophy, by developmental psychologists and theorists of religion among others, under the heading of 'intuitive dualism'. It is rather shocking that so few of the many philosophers working on 'the explanatory gap' are familiar with this empirical literature.
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