A.— MATHEMATICAL AND PHYSICAL SCIENCES 39 



der Bewegung ; als ihre Aufgabe bezeichnen wir : die in der Natur vor 

 sich gehenden Bewegung vollstdndig und auf die einfachste Weise zu 

 beschrieben,' touches very nearly the root of the matter. 



We live, in fact, amid a mass of perceptions ; and it is the business of 

 physical science to correlate, in as simple a fashion as may be, a certain 

 section of these facts. To this end the physicist devises a conceptual 

 world of atoms and molecules, from which he builds up a system — a 

 world- picture — of molar masses whose motions correspond to the routine 

 of our sense impressions. Given a frame of reference, we can formulate 

 laws of motion for two isolated particles in a conceptual world which may 

 be summed up in the statement that whatever be the positions and 

 velocities of the particles the ratio of their accelerations is always constant ; 

 this ratio is defined as the inverse mass-ratio of the particles ; and in virtue 

 of this we have the relation that — 



Mass of A x acceleration of A = Mass of B x acceleration of B. 



We give the name force to this product, and hence obtain the law that 

 action and reaction are equal and opposite. On the basis of such de- 

 finitions we can build up a structure of bodies in the conceptual world 

 the motions of which, predictable under the descriptive laws formulated, 

 will agree with the routine of our world of sense perceptions. We have 

 in fact explained certain phenomena. 



There is, of course, no logical reason why, in this description, we 

 should stop short at the second derivative — acceleration — or go forward 

 to it for that matter. We are concerned to find the simplest and most 

 consistent explanation, and this procedure provides it. Indeed something 

 of assthetics may also influence our choice. 



The atom, whatever its complexity, whether the concept remains sharp 

 as that of a billiard ball or a miniature solar system, or whether its outlines 

 disappear in a probability-smear, remains a concept outside the realm of 

 perceptual happenings which it is the business of the concept to correlate. 

 It may or may not emerge into the perceptual world ; unless and until it 

 does discussion of its reality is beside the mark. 



Planck, defining the causal condition in the statement that an event 

 is causally conditioned if it can be predicted with certainty, goes on to 

 remark that the possibility of making a correct prediction has not to be 

 interpreted as anything more than a criterion for a causal correction, but 

 not that the two mean one and the same thing. Day is not the cause of 

 night, although we may be able to predict the advent of night in the day- 

 time. Day is therefore a causally conditioned event. 4 



Taking the definition as it stands, we find that in the realm of quanti- 

 tative physical events we cannot, purely as a matter of measurement, 

 predict accurately in advance any one physical event — this, without 

 introducing quantum considerations. Prof. Planck escapes from the 

 indeterminist position by transferring the definition to a conceptual 



4 This definition should be carefully examined in the light of the arguments 

 of Hume (Enquiry concerning Human Understanding, Section VII) and of Mill 

 (Logic, Book III, Chap. V). 



