A Quote by James Clerk Maxwell
The true Logic for this world is the Calculus of Probabilities, which takes account of the magnitude of the probability.
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It has been pointed out already that no knowledge of probabilities, less in degree than certainty, helps us to know what conclusions are true, and that there is no direct relation between the truth of a proposition and its probability. Probability begins and ends with probability.
The theory of probabilities is at bottom nothing but common sense reduced to calculus; it enables us to appreciate with exactness that which accurate minds feel with a sort of instinct for which of times they are unable to account.
One influential philosophical position about the use of probability in science holds that probabilities are objective only if they are based on micro-physics; all other probabilities should be interpreted subjectively, as merely revealing our ignorance about physical details. I have argued against this position, contending that the objectivity of micro-physical probabilities entails the objectivity of macro-probabilities.
I am now about to set seriously to work upon preparing for the press an account of my theory of Logic and Probabilities which in its present state I look upon as the most valuable if not the only valuable contribution that I have made or am likely to make to Science and the thing by which I would desire if at all to be remembered hereafter.
If an event can be produced by a number n of different causes, the probabilities of the existence of these causes, given the event (prises de l'événement), are to each other as the probabilities of the event, given the causes: and the probability of each cause is equal to the probability of the event, given that cause, divided by the sum of all the probabilities of the event, given each of the causes.
It was our use of probability theory as logic that has enabled us to do so easily what was impossible for those who thought of probability as a physical phenomenon associated with "randomness". Quite the opposite; we have thought of probability distributions as carriers of information.
He who has heard the same thing told by 12,000 eye-witnesses has only 12,000 probabilities, which are equal to one strong probability, which is far from certain.
The calculus of probabilities, when confined within just limits, ought to interest, in an equal degree, the mathematician, the experimentalist, and the statesman.
But the indeterminate future is somehow one in which probability and statistics are the dominant modality for making sense of the world. Bell curves and random walks define what the future is going to look like. The standard pedagogical argument is that high schools should get rid of calculus and replace it with statistics, which is really important and actually useful. There has been a powerful shift toward the idea that statistical ways of thinking are going to drive the future.
The theory of ramification is one of pure colligation, for it takes no account of magnitude or position; geometrical lines are used, but these have no more real bearing on the matter than those employed in genealogical tables have in explaining the laws of procreation.
A man made for public life and authority never takes account of personalities; he only takes account of things, of their weight and their conseqences.
Without doubt, matter is unlimited in extent, and, in this sense, infinite; and the forces of Nature mould it into an innumerable number of worlds. Would it be at all astonishing if, from the universal dice-box, out of an innumberable number of throws, there should be thrown out one world infinitely perfect? Nay, does not the calculus of probabilities prove to us that one such world out of an infinite number, must be produced of necessity?
Geometric calculus consists in a system of operations analogous to those of algebraic calculus, but in which the entities on which the calculations are carried out, instead of being numbers, are geometric entities which we shall define.
But let us remember that we are dealing with infinities and indivisibles both of which transcend our finite understanding, the former on account of their magnitude, the latter because of their smallness.
The theory of probabilities is basically only common sense reduced to a calculus. It makes one estimate accurately what right-minded people feel by a sort of instinct, often without being able to give a reason for it.
The true power is in the imagination which dares to speculate upon that which is not yet. The imagination, backed by great expectations, can bring about almost any reality within the range of probabilities.
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