Ill] bF THE LAW OF ERROR 123 



in the vorld enables us to foretell no single unknown thing, not even 

 the turn of a card or the fall of a die. The theory of probabiUties 

 is a development of the theory of combinations, and only deals with 

 what occurs, or has occurred, in the long run, among large numbers 

 and many permutations thereof. Large numbers simplify many 

 things; a million men are easier to understand than one man out 

 of a million. As David Hume* said: "What depends on a few 

 persons is in a great measure to be ascribed to chance, or to secret 

 and unknown causes; what arises from a great many may often 

 be accounted for by determinate and known causes." Physics is, 

 or has become, a comparatively simple science, just because its laws 

 are based on the statistical averages of innumerable molecular or 

 primordial elements. In that invisible world we are sometimes told 

 that "chance" reigns, and "uncertainty" is the rule; but such 

 phrases as mere chance, or at random, have no meaning at all except 

 with reference to the knowledge of the observer, and a thing is a 

 "pure matter of chance" when it depends on laws which we do not 

 know, or are not considering f. Ever since its inception the merits 

 and significance of the theory of probabiUties have been variously 

 estimated. Some say it touches the very foundations of know- 

 ledge} ; and others remind us that "avec les chiffres on pent tout 

 demontrer." It is beyond doubt, it is a matter of common ex- 

 perience, that probability plays its part as a guide to reasoning. 

 It extends, so to speak, the theory of the syllogism, and has been 

 called the "logic of uncertain inference "§. 



In measuring a group of natural objects, our measurements are 

 uncertain on the one hand and the objects variable on the other; 

 and our first care is to measure in such a way, and to such a scale, 

 that our own errors are small compared with the natural variations. 

 Then, having made our careful measurements of. a group, we want 

 to know more of the distribution of the several magnitudes, and 



* Essay xiv. 



t So Leslie Ellis and G. B. Airy, in correspondence with Sir J. D. Forbes; see 

 his Life, p. 480. 



X Cf. Hans Reichenbach, Les fondements logiques du calcul des probabilit^s, 

 Annales de Vinst. Poincare, vii, pp. 267, 1937. 



§ Cf. J. M. Keynes, A Treatise on Probability, 1921; and A. C. Aitken's Statistical 

 Mathematics, 1939. 



