350 



SCIENCE 



[N. S. Vol. XL. No. 1027 



function and varieties of definition is given. 

 Every college, and especially every university, 

 ought to give a course of lectures on the sub- 

 ject of definition. There is scarcely any other 

 important scientific subject of universal inter- 

 est respecting ■which educated people know so 

 little, but they are not aware of it. How does 

 abstract logic get applied to reality and what 

 are the limits of such application? This very 

 difficult question is examined under many as- 

 pects and in many concrete connections : logical 

 representation and the postulate of knowl- 

 edge, substance (matter and energy), cause, 

 actual value of logical principles, the value of 

 logical principles, the objective reality of logic, 

 the problem of verification, the verification 

 of explicit hypotheses, the experience of a 

 finite number of objects, experience of the con- 

 tinuous, the postulate of continuity and the 

 psychological representation of cause (why 

 and how), the confirmation and verification of 

 implicit hypotheses, the present crisis in po- 

 litical economy, the vicious circle in science 

 and the physiological aspect of logic. 



There follows a chapter (59 pages) devoted 

 to geometry. Geometry is viewed, on the one 

 hand, as a part of physics, and, on the other 

 hand, as a purely abstract science. In the 

 latter sense it is a prolongation of logic. Per- 

 haps the most striking thesis in a thoroughly 

 up-to-date discussion, rich in suggestions and 

 insights, is found in that section which deals 

 with the parallel between the historical de- 

 velopment and the psycho-genetic development 

 of the postulates of geometry. The thesis is: 

 " The three groups of ideas thai are connected 

 with the concepts that serve as a hasis for the 

 theory of the continuum (Analysis situs), of 

 metrical, and of projective geometry, may he 

 connected, as to their psychological origin, 

 with three groups of sensations: with the gen- 

 eral tactile-muscular sensations, with those of 

 special touch, and with those of sight, respec- 

 tively." There be psychologists, and some edu- 

 cators, who think mathematics is so detached 

 from reality as to be an inferior discipline. 

 We should be much interested if these gentle- 

 men would favor us with an expert opinion 

 regarding that thesis of Professor Enriques. 



A chapter of 64 pages on mechanics re- 

 garded as an extension of geometry is followed 

 by a final chapter of 88 pages on physics in 

 which the leading question concerns the extent 

 in which physics may be regarded as an ex- 

 tension of mechanics. An admirable review 

 and critique of the conceptions and principles 

 of classical mechanics and classical physics in 

 their relation to the new more or less specula- 

 tive ideas lead to the general conclusion: 

 "Physics, instead of affording a more precise 

 verification of the classic mechanics, leads 

 rather to a correction of the latter science, 

 tahen apriori as rigid." The wide range of the 

 author's interest and thought is specially indi- 

 cated by the closing pages, which are devoted 

 to the mechanical hypothesis and the phenom- 

 ena of life. The conclusion is that, " in the 

 actual state of our knowledge, the mechanical 

 hypothesis does not appear to he incompatible 

 with the phenomena of life, hut it is unimpor- 

 tant for the study of these phenomena." The 

 student will find it instructive to compare the 

 conclusion and the temper of the related dis- 

 cussion with the temper and conclusion in Dr. 

 Crile's " A Mechanistic View of Psychology," 

 published in Science, August 29, 1913. In 

 this connection one should consider an article 

 by Professor W. B. Smith, entitled, " Are Mo- 

 tions Emotions ? " published in the Tulane 

 Graduates' Magazine for January, 1914. An 

 even more significant deliverance by the last- 

 named author dealing with the claims and lim- 

 itations of the mechanical hypothesis is an 

 article bearing the title " Push or Pull ? " pub- 

 lished in the Monist, January, 1913. 



In a review of moderate length it is not pos- 

 sible to give an adequate account of Enriques's 

 book. We know of no other work that gives 

 so keen a sense of the unity of all branches of 

 science. A final word as to its manner. The 

 section headings are too numerous, breaking 

 the continuity of the reader's attention; and 

 there are some obscure sentences and para- 

 graphs. These are external faults and are 

 trivial in relation to the inner excellencies of 

 the work. 



C. J. Keyser 



Columbia TJniveesitt 



