Page:Mind (New Series) Volume 9.djvu/506

492 W. E. BOYCE GIBSON : The subordination of the fundamental principle of Con- tinuity to the principle of Economy, implied in these last words, and indeed in Mach's statements generally, seems to me to be psychologically incorrect. That Knowledge should proceed gradually from the known to the unknown is surely a more primary consideration of the man of science than that the mentality and feeling of himself or others should be spared. Economy seems here to be rather the happy effect of Continuity not its final Cause. The systematic activity of the Scientific Consciousness is again, to my mind, dominated by the principle of Continuity. This is shown in the deductive form all such systematisation takes. The mechanics of Lagrange which Mach refers to as a stupendous contribution to the Economy of thought l is the classical instance of the deduction of a science through the continuous application of a single principle. Mach him- self points out the fundamental importance of this principle in the deductive development of the system of mechanics, but here again he subordinates the principle to that of Economy. ' Mathematics,' he says, ' may be defined as the Economy of counting,' 3 and adds : ' It is the method of replacing in the most comprehensive and economical manner possible new numerical operations by old ones done already with known results.' 3 Perhaps his most explicit recognition of Con- tinuity and the cumulative factor it involves is given when he tells us that ' the object of all arithmetical operations is to save direct numeration by utilising the results of our old operations of counting '. 4 But though the deductive instinct seems to me to be a more fundamental instinct of the scientific consciousness than the instinct for economy, it is undoubtedly true that the scientific consciousness does deliberately set itself to economise labour by such devices as that of abbreviation. This is due to obvious considerations of time and memory. Mach, indeed, lays the very greatest stress on this fact. ' Within the short span of a human life, and with man's limited powers of memory, any stock of Knowledge worthy of the name is unattainable except by the greatest mental economy ; science itself, therefore, may be regarded as a minimal problem, consisting of the completest possible presentment of facts with the least possible expenditure of thought ; ' and Mach further points out how, in mathemati- cal science, the whole system of symbols, semimechanical 1 Mach, id., p. 467. 2 Ibid., id., p. 486. r - Ibid., id., p. 195. 4 Ibid., id., p. 486. * Ibid,, id., p. 490.