THE FIELD OF LOGIC 



BY FREDERICK J. E. WOODBRIDGE 



[Frederick J. E. Woodbridge, Johnsonian Professor of Philosophy in Columbia 

 University, New York, N. Y., since 1902. b. Windsor, Ontario, Canada, 

 March 26, 1867. A.B. Amherst College, 1889; Union Theological Seminary, 

 1892; A.M. 1898, LL.D. 1903, Amherst College. Post-grad. Berlin Univers- 

 ity. Instructor in Philosophy, University of Minnesota, 1894-95; Professor 

 of Philosophy and head of department, 1895-1902. Member of American 

 Association for the Advancement of Science, American Philosophical Associ- 

 ation, American Pyschological Association. Editor of the Journal of Philo- 

 sophy, Psychology and Scientific Methods.] 



CURRENT tendencies in logical theory make a determination of the 

 field of logic fundamental to any statement of the general problems 

 of the science. In view of this fact, I propose in this paper to attempt 

 such a determination by a general discussion of the relation of logic 

 to mathematics, psychology, and biology, especially noting in con- 

 nection with biology the tendency known as pragmatism. In con- 

 clusion, I shall indicate what the resulting general problems appear 

 to be. 



I 



There may appear, at first, little to distinguish mathematics in its 

 most abstract, formal, and symbolic type from logic. Indeed, math- 

 ematics as the universal method of all knowledge has been the ideal 

 of many philosophers, and its right to be such has been claimed of 

 late with renewed force. The recent notable advances in the science 

 have done much to make this claim plausible. A logician, a non- 

 mathematical one, might be tempted to say that, in so far as mathe- 

 matics is the method of thought in general, it has ceased to be 

 mathematics; but, I suppose, one ought not to quarrel too much 

 with a definition, but should let mathematics mean knowledge 

 simply, if the mathematicians wish it. I shall not, therefore, enter 

 the controversy regarding the proper limits of mathematical inquiry. 

 I wish to note, however, a tendency in the identification of logic and 

 mathematics which seems to me to be inconsistent with the real 

 significance of knowledge. I refer to the exaltation of the freedom 

 of thought in the construction of conceptions, definitions, and hypo- 

 theses. 



The assertion that mathematics is a "pure" science is often taken 

 to mean that it is in no way dependent on experience in the construc- 

 tion of its basal concepts. The space with which geometry deals 

 may be Euclidean or not, as we please; it may be the real space of 



