November 4, 1904.] 



SCIENCE. 



587 



If there were not other evidence to the 

 contrary, the existence of this general 

 principle, which is also applicable to many 

 other properties, would almost warrant the 

 conclusion that the salts are completely 

 ionized up to the concentration in ques- 

 tion, and that the decrease in conductivity 

 is due merely to a change in migration 

 velocity. But, in view of the apparently 

 conclusive evidence against such a hypoth- 

 esis, we can only conclude that the form of 

 union represented by the un-ionized mole- 

 cules of salts ditfers essentially from ordi- 

 nary chemical combination, it being so 

 much less intimate that the ions still ex- 

 hibit their characteristic properties, in so 

 far as these are not dependent upon their 

 existence as separate aggregates. 



These then are the empirical principles 

 to which a critical analysis of the experi- 

 mental data leads. Upon these principles 

 must be based the rational, theoretical ex- 

 planation of the phenomena in question. 

 The discovery of that explanation consti- 

 tutes one of the most important of the 

 present problems of physical chemistry. 

 Arthur A. Notes. 



THE FIELD OF LOGIC* 

 Current tendencies in logical theory 

 make a determination of the field of logic 

 fundamental to any statement of the gen- 

 eral problems of the science. In view of 

 this fact, I propose in this paper to attempt 

 such a determination by a general discus- 

 sion of the relation of logic to mathematics, 

 psychology and biology, especially noting 

 in connection with biology the tendency 

 known as pragmatism. In conclusion, I 

 shall indicate what the resulting general 

 problems appear to be. 



* Address before the Section of Logic, Inter- 

 national Congress of Arts and Science, Universal 

 Exposition, St. Louis. 



There may appear, at first, little to dis- 

 tinguish mathematics in its most abstract, 

 formal and symbolic type from logic. In- 

 deed, mathematics 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 plaus- 

 ible. A logician, a non-mathematical one, 

 might be tempted to say, that in so far as 

 mathematics 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 i-egarding 

 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, defini- 

 tions and hypotheses. 



The assertion ^ that mathematics is a 

 'pure' science is often taken to mean that 

 it is in no way dependent on experience in 

 the construction 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 experience or not; the 

 properties of it and the conclusions reached 

 about it may hold in the real world or they 

 may not; for the mind is free to construct 

 its conception and definition of space in 

 accordance with its own aims. Whether 

 geometry is to be ultimately a science of 

 this type must be left, I suppose, for the 

 mathematicians to decide. A logician may 

 suggest, however, that the propriety of call- 

 ing all these conceptions 'space' is not as 

 clear as it ought to be. Still further, there 



