6 August 1959: α. Cogitations

The waking unconscious thinking. Does this have the function I attribute to α, or does α carry out the transformation of sense impressions which makes these storable in such a form that they are available for waking unconscious thinking? When Y winces at each word said, it seems clear that the words are not, outwardly at least, being transformed by α into a form, ‘notation’, that makes the experience of the analysis available to him.

But the transformation by α is not all by symbol formation. For example, it is clearly of consequence to know from a particular transaction in which the individual possessor of two apples, when given two more, ends up having four apples, that this peculiarity applies always, namely that if two things of any kind whatever are added to two others of the same kind, the result will be a total of four such objects.

That 2 + 2 = 4 is sometimes said to be self-evident, an axiom. But it is by no means clear that this is or always has been so, any more than it has always been obvious that if I want something in my room which is out of reach I shall have to leave my chair, walk over to it and fetch it. At some point even the process of walking required thought, probably conscious thought. My suggestion is that it still requires thought, but that it is now waking unconscious thought which has been made possible by α. And it is similarly thanks to the operation of α that it seems obvious that 2 + 2 = 4. If α has not operated, it is probable that it would not be ‘obvious’ at all.

At first sight it seems that the mathematical capacities of the individual must depend on an α-operation which effects abstraction or generalization, but as usual these convenient simplifications are, by their nature, only approximations, and in some instances the approximation is found not to be sufficiently close. It is probably more true to say that concretization, pictorial or otherwise, may be inseparable from the faculty of abstraction or generalization. Let us then cons