“I am persuaded that the world is made up of an immense number of bits, and that, so far as logic can show, each bit might be exactly as it is even if other bits did not exist.” (pp. 43-44)
"I began to develop a philosophy of my own during the year 1898, when, with encouragement from my friend G.E. Moore, I threw over the doctrines of Hegel. If you watch a bus approaching you during a bad London fog, you see first a vague blur of extra darkness, and you only gradually become aware of it as a vehicle with parts and passengers. According to Hegel, your first view as a vague blur is more correct than your later impression, which is inspired by the misleading impulses of the analytic intellect. This point of view was temperamentally unpleasing to me. Like the philosophers of ancient Greece, I prefer sharp outlines and definite separations such as the landscapes of Greece afford. When I first threw over Hegel, I was delighted to be able to believe in the bizarre multiplicity of the world. I thought to myself, ‘Hegel says there is only the One, but there really are twelve categories in Kant's philosophy’. It may seem queer that this was the example of plurality that specially impressed me, but I am concerned to report the facts without distortion.
"For some years after throwing over Hegel I had an optimistic riot of opposite beliefs. I thought that whatever Hegel had denied must be true. He had maintained that there is no absolute truth. The nearest approach (so he maintained) to absolute truth is truth about the Absolute; but even that is not quite true, because it unduly separates subject and object. Consequently I, in rebellion, maintained that there are innumerable absolute truths, more particularly in mathematics. Hegel had maintained that all separateness is illusory and that the universe is more like a pot of treacle that a heap of shot. I therefore said, 'the universe is exactly like a heap of shot.' Each separate shot, according to the creed I then held, had hard and precise boundaries and was as absolute as Hegel's Absolute. Hegel had professed to prove by logic that number, space, time and matter are illusions, but I developed a new logic which enabled me to think that these things were as real as any mathematician could wish. I read a paper to a philosophical conference in Paris in 1900 in which I argued that there really are points and instants. Broadly speaking, I took the view that, whenever Hegel's proof that some thing does not exist is invalid, one may assume that the something in question does exist - at any rate when that assumption is convenient to the mathematician. Pythagoras and Plato had let their views of the universe be shaped by mathematics, and I followed them gaily.
"It was Whitehead who was the serpent in this paradise of Mediterranean clarity. He said to me once: 'You think the world is what it looks like in fine weather at noon day; I think it is what it seems like in the early morning when one first wakes from deep sleep.' I thought his remark horrid, but could not see how to prove that my bias was any better than his. At last he showed me how to apply the technique of mathematical logic to his vague and higgledy- piggledy world, and dress it up in Sunday clothes that the mathematician could view without being shocked. This technique which I learned from him delighted me, and I no longer demanded that the naked truth should be as good as the truth in its mathematical Sunday best.
"Although I still think that this is scientifically the right way to deal with the world, I have come to think that the mathematical and logical wrappings in which the naked truth is dressed go to deeper layers than I had supposed, and that things which I had thought to be skin are only well-made garments. Take, for instance, numbers: when you count, you count 'things,' but 'things' have been invented by human beings for their own convenience. This is not obvious on the earth's surface because, owing to the low temperature, there is a certain degree of apparent stability. But it would be obvious if one could live on the sun where there is nothing but perpetually changing whirlwinds of gas. If you lived on the sun, you would never have thought of counting because there would be nothing to count. In such an environment, Hegel's philosophy would seem to be common sense, and what we consider common sense would appear as fantastic metaphysical speculation." (Bertrand Russell, "Beliefs: Discarded and Retained", in Portraits from Memory, pp. 40-42)
Here is Whitehead using the arithmetic proposition 'one and one makes two' to make this argument.
"So far, this lecture has proceeded in the form of dogmatic statement. What is the evidence to which it appeals?
"The only answer is the reaction of our own nature to the general aspect of life in the Universe.
"This answer involves complete disagreement with a widespread tradition of philosophic thought. This erroneous tradition presupposes independent existences; and this presupposition involves the possibility of an adequate description of finite fact. The result is the presupposition of adequate separate premises from which argument can proceed.
"For example, much philosophic thought is based upon the faked adequacy of some account of various modes of human experience. Thence we reach some simple conclusion as to the essential character of human knowledge, and of its essential limitation. Namely, we know what we cannot know.
"Understand that I am not denying the importance of the analysis of experience: far from it. The progress of human thought is derived from the progressive enlightenment produced thereby. What I am objecting to is the absurd trust in the adequacy of our knowledge. The self-confidence of learned people is the comic tragedy of civilization.
"There is not a sentence which adequately states its own meaning. There is always a background of presupposition which defies analysis by reason of its infinitude.
"Let us take the simplest case; for example, the sentence, 'One and one makes two.'
"Obviously this sentence omits a necessary limitation. For one thing and itself make one thing. So we ought to say, 'One thing and another thing make two things.' This must mean the togetherness of one thing with another thing issues in a group of two things.
"At this stage all sorts of difficulties arise. There must be the proper sort of things in the proper sort of togetherness. The togetherness of a spark and gunpowder produces an explosion, which is very unlike two things. Thus we should say, 'The proper sort of togetherness of one thing and another thing produces the sort of group which we call two things.' Common sense at once tells you what is meant. But unfortunately there is no adequate analysis of common sense, because it involves our relation to the infinity of the Universe.
"Also there is another difficulty. When anything is placed in another situation, it changes. Every hostess takes account of this truth when she invites suitable guests to a dinner party; and every cook presupposes it as she proceeds to cook the dinner. Of course, the statement, 'One and one make two' assumes that the changes in the shift of circumstances are unimportant. But it is impossible for us to analyse this notion of 'unimportant change.' We have to rely upon common sense.
"In fact, there is not a sentence, or a word, with a meaning which is independent of the circumstances under which it is uttered. The essence of unscholarly thought consists in a neglect of this truth. Also it is equally the essence of common sense to neglect these differences of background when they are irrelevant to the immediate purpose. My point is that we cannot rely upon any adequate explicit analysis.
"The conclusion is that Logic, conceived as an adequate analysis of the advance of thought, is a fake. It is a superb instrument, but it requires a background of common sense. …
"My point is that the final outlook of Philosophic thought cannot be based upon the exact statements which form the basis of special sciences.
"The exactness is a fake." (Whitehead "Immortality" in Essays in Science and Philosophy, pp. 72-4)
As Keynes points out, it is this "common sense" that "remorseless logicians" like Hayek lack.
Ted