MRBALFOURONCHANCE

Dominion, Volume 7, Issue 2010, 18 March 1914, Page 9

MRBALFOURONCHANCE

PROBABILITY IN THEORY AND PRACTICE. THE MATHEMATICAL CALCULUS Mr. Balfour began his seventh Gifford lecturo by.classifying beliefs into inevitablo and probable, and in tho interests of this classification he offered a criticism of the mathematical theory of probability. Traditional logical theory had confined itself to this particular kind of probability, and though tho mathematical statement of chances had yielded results of the first importance both for science and for practical life, it did not coyer the whole ground. It had not distinguished clearly different kinds of probabilities, and in particular it had failed to give any account of that large range of beliefs which were neither inevitable nor axiomatic, but which were yet conterminous with. our inevitable beliefs and wero part of tho necessary basis of all our knowledge. These beliefs Mr. Balfour called "probable," and it was in this sense that Butler(had used the term in his dictum that probability was the guide of life. Probability and Knowledge. Mr. Balfour's first task was to show precisely under what .conditions tho mathematical calculus was awjiicable. Ho began, to the delight of >.is audience, by expressing tho wish that ho wore a great mathematician, or even a mathematician at all, for the mathematician enjoyed unique advantages in method and in terminology so that no ambiguity could eccur in his expression or in his reasoning. But Mr. Balfour thought that mathematicians did not set forth their premises with the same rigour as. they deduced, their conclusions, and they did not appreciate the abstract character of their reasoning. He indicated the limits of the mathematical treatment of probability by considering an interesting excerpt from M. Poiiicare; to whose memory he paid a pious and graceful tribute.. M. Poincare had, argued that chance could not be, as previous logic had. taken it to be, merely the measure of .-our ignorance, for the statement of ■ chances was often the basis of useful knowledge. Mr. Balfour developed this thesis by considering some typical cases in which knowledge was furnished .by statement of | chances. There were, first of all, such cases as the tables of mortality or the laws of tho cxplosiveness of radium. Thero we wero dealing with croups of facts in a purely empirical fashion. A second set of cases was that in which tho statement of chances was based on "a priori" considerations. Though uxu'erionco confirmed the results of such theorising, it was possible to argue "a priori" that the chauces wero one in two that •he tossing of a penny would result in heads, and it was equally possible to say on purely "a priori" grounds that tlie chances wero. much against a visitor's leaving Monte Carlo with as mucn money in his pocket as he had had on entering. . . , . Probable Beliefs'. But Mr. Balfour argued that there was a definite limit \o this kind of reasoning. Thero was the difference in feeling,, if not in logic, between the argument from subjective ignorance. But those arguments were usually in tho same logical form, and logical theory did not distinguish them. The results of tho. confusion between 'thoso two became serious when tho attempt was made to ciury.. tie.argument from probability into "more "" fundamental spheres.. . . i . For example, an agnostic might .say that he could form no conclusion as to whether or not the world was createu uy an intelligent being. It might be replied to him that either it must have heen so created or it must not, and he might be forced by that argument to agree that tho chances of there being an intelligent Creator were even. To assert this, however, was to assert. a great deal about the world—indeed, as Mr, Balfour put it, it implied that the chancos of the existence of an intelligent Creator were rather able than tho chances of the black or red at Monte Carlo.

But this argument Mr. Balfour believed to be manifestly unfair. It was a case whjch the calculation of probability could not cover, and it plainly rested on an -imperfect analysis of the conditions under which i mathematical calculation was valid. Mathematical probability, he considered, had meaning only within a system already, determined, and tho knowledge of that. system must have been arrived at by other methods. For problems such as those ho belioved that another kind of probability was required different from that resting on the highly abstract mathematical calculation. So he was confirmed in his view that, in addition to inevitable beliefs, thero were probable beliefs to which wo were inclined, but not driven. They varied in degree of coercive power, but were capable of being detected throughout tho'wholo of scientific knowledge. These beliefs had not received sufficient treatment from philosophers, either of the critical school or of the empirical. Kant and Mill aliko had thought more of the grounds of belief than of- the actual content of belief, aiid Mr. Balfour pleaded for as impartial an investigation into what men of science- had actually believed as had beeu given 'to outworn philosophical creeds. He proposed to undertake, in bis next two lectures, a survey of some of these beliefs. They would go to support his ' general Theistic argument, but, -apart from that, they were of tho utmost significance for a sound philosophy of science. ;