  Like Lewis and Armstrong, functionalists define mental states and processes in terms of their causal relations to behaviour but stop short of identifying them with their neural realisations. Of course the term ‘functionalism’ has been used vaguely and in different ways, and it could be argued that even the theories of Place, Smart and Armstrong were at bottom functionalist. The word ‘functionalist’ has affinities with that of ‘function’ in mathematics and also with that of ‘function’ in biology. In mathematics a function is a set of ordered n-tuples. Similarly if mental processes are defined directly or indirectly by sets of stimulus-response pairs the definitions could be seen as ‘functional’ in the mathematical sense. However there is probably a closer connection with the term as it is used in biology, as one might define ‘eye’ by its function even though a fly's eye and a dog's eye are anatomically and physiologically very different. Functionalism identifies mental states and processes by means of their causal roles, and as noted above in connection with Lewis, we know that the functional roles are possessed by neural states and processes. (There are teleological and homuncular forms of functionalism, which I do not consider here.) Nevertheless an interactionist dualist such as the eminent neurophysiologist Sir John Eccles would (implausibly for most of us) deny that all functional roles are so possessed. One might think of folk psychology, and indeed much of cognitive science too, as analogous to a ‘block diagram’ in electronics. A box in the diagram might be labelled (say) ‘intermediate frequency amplifier’ while remaining) neutral as to the exact circuit and whether the amplification is carried out by a thermionic valve or by a transistor. Using terminology of F. Jackson and P. Pettit (1988, pp. 381–400) the ‘role state’ would be given by ‘amplifier’, the ‘realiser state’ would be given by ‘thermionic valve’, say. So we can think of functionalism as a ‘black box’ theory. This line of thought will be pursued in the next section.