Page:Mind (New Series) Volume 9.djvu/263

 JAMES WABD, Naturalism and Agnosticism. 249 as Prof. Ward argues, refutes itself the moment it is pushed to its logical consequences. In the very attempt to formulate its funda- mental conceptions we are driven to convert them all into a set of mathematical constants, eminently valuable for purposes of calcu- lation, but of no more avail than the xs and i/s of pure algebra as an account of real concrete processes. Thus, as Prof. Ward says, the application of the abstract kinetical scheme to the real facts of the phenomenal world is "throughout hypothetical, and absolute or unconditional mechanical statements concerning real world are therefore unwarrantable. There are no processes in the real world that are certainly entirely mechanical." Even the space, time, and motion of kinetic science are abstractions, and not the space, time, and motion of perceptual experience. The mathematician's space, unlike real space, has neither " here " nor " there," " up " nor " down," " right " nor " left " ; his time is the "absolute time " of Newton, unknown to any real experience, which " flows equably " ; the movements he calculates are those of mass-particles from one position relative to an imaginary set of axes to another, not movements of bodies from an " here " to a " there ". In a word, the full description of what " really goes on " would not be given even by a body of actual measurements, and abstract mechanics does not even measure, for you can only measure where there is something concrete and sensible to measure, and a concrete and sensible standard to measure it by ; it only calculates. Prof. Ward follows up this exposure of the essentially abstract and hypothetical character of the mechanical scheme by an incisive criticism of the attempts which have sometimes been made to translate its mathematical constants into concrete realities of an unseen order. These attempts, as he shows, for the most part rest on nothing better than baseless assumption. Thus against the dogmatic assertion that " atoms " of one element are all abso- lutely identical in quality, and all imperishable and unchangeable, an assertion which is in principle simply an identification of an " atom " in the chemist's sense of the word with the mass-particle of abstract kinematics, he argues irresistibly that every statement we can make about the weight or volume of an atom of one of the elements has to be made on the strength of measurements of a sensible mass in bulk. The atom itself not being accessible to direct measurement can only be reached by indirect methods ; sensible things may be measured or counted, but we can neither measure nor weigh the atom, nor yet count the atoms in a given mass of sensible dimensions ; all our theories about the weight or size of the individual atom rest not on measurement but on calculation. Hence, as the ablest specialists are not slow to admit, our assertions about e.g. the atomic weights of the ele- ments are exactly on a level with the statistics of economics or anthropology ; we may take them as valid statements of an aver- ci'/f, we must not treat them as necessarily exactly true in any single case. As Prof. Ward puts it, " Englishmen about to marry