Karl Pearson on Philosophy

"If any... work gives a description of phenomena that appeals to... imagination rather than to... reason, then it is bad science."

"andom spinning being assumed, the distribution of chance in the game depends upon the mechanical perfection of the teetotum; it must be equally likely to fall on all its thirty-seven sides, i.e. the frequency of all the numbers must in the long run be very nearly the same."

"rogress... enables me to define several... conceptions much more accurately than was possible in 1892, and to indicate, if only in vague outline, what a fascinating field is being here transferred from the synoptic to the precise division of science."

"While the moralists have boldly asserted that the service of the goddess Chance leads to a complete demoralisation of her worshippers... the mathematicians... start from the hypothesis that gambling is a game of chance—chance being defined in their own perfectly clear and definite sense. My object... is to show that chance in this sense... as it applies to the tossing of an unloaded coin, has no application to Monte Carlo."

"The next point to which I turned my attention was the frequency with which the several numbers themselves occurred. ...Each number might be expected to have occurred either 447 or 448 times. ... I found that they fitted to a standard deviation of 15.85 while the theoretical standard was 20.87 giving a difference of 5. ...What is a reasonable amount for the standard deviation of an experiment of this kind to differ from its theoretical value..? The mathematician answers... by finding the standard deviation of the standard deviation. It turned out... to be 2.43... the odds against a divergence as large or larger than 5...were ...21 to 1. In every two years I might expect such a deviation from the most probable results to occur once. ...I ...increased ...by counting the numbers for each week in the month instead of the total month. Here the experimental standard deviation 7.2, the theoretical being 10.34, a difference of 3.14, while the standard deviation between experiment and theory was only 0.60. The odds against a divergence so great as this are... about 2,000,000 to 1."

"Each one of us is... called upon to give a judgment upon an immense variety of problems, crucial for our social existence. If that judgment confirms measures and conduct tending to the increased welfare of society, then it may be termed a moral, or, better, a social judgment. It follows, then, that to ensure a judgement's being moral, method and knowledge are essential to its formation. ...he formation of a moral judgment—that is, one which the individual is reasonably certain will tend to social welfare—does not depend solely on the readiness to sacrifice individual gain or comfort, or on the impulse to act unselfishly: it depends in the first place on knowledge and method. The first demand of the state upon the individual is not for self-sacrifice but for self-development. ...he man who gives a vote... in the choice of a representative, after forming a judgement based upon knowledge, is... acting socially, and is fulfilling a higher standard of citizenship."

"Each metaphysician has his own system, which to a large extent excludes that of his predecessors and colleagues. Hence... metaphysics are built either on air or on quicksands—either they start from no foundation in facts at all, or the superstructure has been raised before a basis has been found in the accurate classification facts."

"To say that there are certain fields—for example, metaphysics—from which science is excluded, wherein its methods have no application, is merely to say that the rules of methodical observation and the laws of logical thought do not apply to the facts, if any, which lie within such fields. These fields, if indeed such exist, must lie outside any intelligible definition which can be given of the word knowledge."

"he philosophical method seems based upon an analysis which does not start with the classification of facts, but reaches its judgments by some obscure process of internal cogitation. It is therefore dangerously liable to the influence of individual bias; it results... in an endless number of competing and contradictory systems. It is because the so-called philosophical method does not, when different individuals approach the same range of facts, lead, like the scientific, to practical unanimity of judgment, that science, rather than philosophy, offers the better training for modern citizenship."