606 VIII. ON THE STRUCTURE OF MATHEMATICS
we are dealing here with an ingrained psycho-logical tendency which can be remedied only by a fundamental, structural, semantic investigation.
Let us analyse these quotations. In the second case, we hear, after a successful attack on plus tendencies, a statement that the 'individual represents heredity plus environment'. Is this statement true? Let us take examples, There are certain fishes which are heliotropic and swim toward the light, but if we change the temperature of the water they become negatively heliotropic and swim away from the light. Is this most complex activity of the organism-as-a-whole a 'plus environment' fact, or does the change of temperature produce some fundamental functional changes? When, for instance, a good mother rat, having been put on a different though still abundant diet, which is deprived of some minute amount of special vitamins, begins to eat her litters, is this again a 'plus' reaction, or is it a most" complex functional change of the organism-as-a-whole? Or when a human being, because he received in childhood an 'emotional' shock through outside events (action or language of parents, for instance) develops a functional disorder, or even a physical ailment, is this again a 'plus environment' problem? Or, when chickens fed on eggs laid by hens kept without sunlight or violet rays, or which have only received sunlight through a glass window, develop rickets and soon die, though they do not do so when the glass windows are removed and the sunlight is allowed to operate directly upon the hens. Is this again a 'plus environment' example?
One 'Smith' and one 'Smith' make two 'Smiths', as far as theatre or railway tickets are concerned, but in life, under proper conditions, they form a family and very often many more than two 'Smiths' come out of such 'addition'. How about their work? Is it a mere sum? In the case of inventors who may have been influenced by one or many men directly or indirectly, do their inventions produce a sum of the work of as many men? Surely the steam engine or the dynamo produces more work than not only the inventors, but the series of other men who have been indirectly responsible for the inspiration of the inventors, could ever have produced. So again it is not a 'plus' affair.
In the third case we see the author attacking the 'plus' tendency on one page, and planting another 'plus' a few pages further on, which implies at once some objectified additional entity. In this respect it must be noticed that this additive tendency represents a partial and important structural and semantic mechanism of identification, and to deal successfully with it, we must clear up the problem connected with the additive tendency.
The numberless and endless 'philosophical' volumes, for instance, which have been written about the 'body-soul' problems, show the tremendous structural and semantic importance of the clearing up of this 'plus' versus 'non-plus' issue. The reader may recall that the , the , and the systems have one underlying structural metaphysics. The systems deal with non-linear equations and with curved lines, of which the linear equation and the straight line, (one of zero curvature), are only particular cases. And the general theory of Einstein, which is the foundation of systems, also introduces non-linear equations. Ought we to be surprised to find that a -system must also solve