Once upon a time there was a tough-minded philosopher who said, ‘What is all this talk about “minds”, “ideas”, and “sensations”? Really – and I mean really in the real world – there is nothing to these so-called “mental” events and entities but certain processes in our all-too-material heads.’

And once upon a time there was a philosopher who retorted, ‘What a masterpiece of confusion! Even if, say, pain were perfectly correlated with any particular event in my brain (which I doubt) that event would obviously have certain properties – say, a certain numerical intensity measured in volts – which it would be senseless to ascribe to the feeling of pain. Thus, it is two things that are correlated, not one – and to call two things one thing is worse than being mistaken; it is utter contradiction.’

For a long time dualism and materialism appeared to exhaust the alternatives. Compromises were attempted (‘double aspect’ theories), but they never won many converts and practically no one found them intelligible. Then, in the mid-1930s, a seeming third possibility was discovered. This third possibility has been called logical behaviorism. To state the nature of this third possibility briefly, it is necessary to recall the treatment of the natural numbers (i.e. zero, one, two, three…) in modern logic. Numbers are identified with sets, in various ways, depending on which authority one follows.