And the above principles are as true of mathematical concepts as of chemical. Everywhere it is "capacity of adaptation to facts" that is the criterion of a branch of mathematics, except, of course, that in mathematics the facts are not always physical facts. Mathematics has successfully accomplished a generalization whereby its own methods furnish the material for higher generalizations. The imaginary number and the hyper-dimensional or non-Euclidian geometries may be absurd if measured by the standard of physical reality, but they nevertheless have something real about them in relation to certain mathematical processes on a lower level. There is no philosophic paradox about modern arithmetic or geometry, once it is recognized that they are merely abstractions of genuine features of simpler and more obviously practical manipulations that are clearly derived from the dealing of a human being with genuine realities. In the light of these considerations, I cannot help feeling that the frequent attempts of mathematicians with a philosophical turn of mind, and philosophers who are dipping into mathematics, to derive geometrical entities from psychological considerations are quite mistaken, and are but another example of those traditional presuppositions of psychology which, Professor Dewey has pointed out (_Jour. of Phil., Psy., and Sci. Meth._, XI, No. 19, p. 508), were "bequeathed by seventeenth-century philosophy to psychology, instead of originating within psychology" ... that "were wished upon it by philosophy when it was as yet too immature to defend itself."