748 



SCIENCE 



[N. S. Vol. XL. No. 1038 



answer except one in terms of probability can 

 be offered; whilst to some there seems no pros- 

 pect of an answer even in these terms. Few 

 things are more pathetic than the assumption 

 which practically every philosopher makes 

 that his answer to such questions is the 

 unique possible answer; and few things are 

 funnier than the sight of a philosopher with 

 a theory about the real and the nature of per- 

 ception founded on numberless implicit as- 

 sumptions which, when made explicit, carry 

 no conviction whatever, telling the scientist 

 de haut en has that his atoms and ether are 

 mere economical hypotheses." This is a rather 

 long quotation, but it gives very vividly Mr. 

 Broad's philosophical standpoint. While it is 

 a good and safe attitude, one can not help 

 wondering what the value of a philosophical 

 determination of reality may be. Eeality 

 which depends at best on its prohable truth is 

 a doubtful reality and must continue to be a 

 question of dispute. Does it not become ulti- 

 mately a question of temperament; one either 

 is convinced of the reality of the external 

 world, or he is not, and logic will have but 

 little effect on his judgment? 



Mr. Eussell and his followers are able to 

 give a specious appearance of certainty to 

 their deductions by employing an esoteric sys- 

 tem of mathematical symbols and analysis. 

 He, himself, is both a mathematician and a 

 philosopher. As the former, he must know 

 that mathematical analysis will not give cor- 

 rect conclusions if the postulates contain an 

 error. He must also know that even if the 

 postulates be correct, the conclusion is with- 

 out meaning if the idea represented by a given 

 sjnnbol should change to an appreciable extent 

 during the transformations. For example, if 

 V represents a constant velocity and if, during 

 an experiment, the velocity should change by 

 a measurable amount, then no conclusion 

 could be drawn from our analysis unless V is 

 changed to V, and in addition we know the 

 exact relation between V and V. The reason 

 why mathematics can be applied to interpret 

 physical and astronomical phenomena so satis- 

 factorily is because the ideas represented by 

 the symbols in those sciences are simple and 



can be measured with great accuracy. Now 

 this is not the case, except to a much more 

 limited degree, even with the other sciences, 

 and it certainly does not obtain for the far 

 more complex questions of philosophy. 



While Mr. Broad employs the method of 

 Mr. EusseU more or less throughout his essay, 

 yet he rarely goes so far as to use the very 

 irritating symbolism of his teacher. He has 

 in fact only two specific examples, and of 

 these the one on page 318 applies to a com- 

 plicated problem of motion; the other ex- 

 ample, on page 165, is better suited as an 

 illustration for criticism. Here p is the prop- 

 osition, phenomenalism is true; and q is the 

 proposition that the objects of our perceptions 

 depend on the structure of our organs. Can 

 we prove p from this? By a manipulation of 

 p and q which is printed so as to resemble a 

 bastard kind of mathematics, he arrives at the 

 conclusion that we can not prove p from the 

 argument. We know that Berkeley was so 

 shocked when he arrived at the same conclu- 

 sion that he created God so that there might 

 be a reality which could always perceive our 

 organs of perception and thus give them a 

 kind of pseudo-reality when no one else was 

 near enough to perceive them. But that is not 

 the point. It is pretty certain that q stands 

 for so complex an idea or proposition that each 

 of Mr. Broad's n readers will have received 

 an idea differing sufficiently from the others 

 to make it advisable to represent the proposi- 

 tion in these varying aspects by the series 

 9i) Q'2> Qs> ■ • • In- And furthermore, during 

 an extended argument, each one's idea will, 

 I think, change sufficiently to require changes 

 in his q. The result is that q becomes the 

 highly complex series q^, q^, . . . g^; g/, 5/, 

 • ••?«'; 9i", 0.2'' • • ■ 1n'> etc. Not even the 

 mathematical laws of probability can cope 

 with such a problem. 



The fact is, no philosophical method has 

 been devised which can settle the questions 

 involved in realism and phenomenalism. But 

 much can be gained by a discussion of the 

 arguments for and against these ideas. And 

 it is in this discussion that the interest and 

 value of Mr. Broad's essay are displayed. 



