94 II. GENERAL ON STRUCTURE
I accept the propositional function of Russell.
I accept the doctrinal function of Keyser, and generalize the system function of Sheffer.
I introduce the four-dimensional theory of propositions and language.
I establish the multiordinality of terms.
I introduce and apply psychophysiological considerations of non-el orders of abstractions.
I expand the two-term 'cause-effect' relation into an oo-valued causality.
I accept the oo-valued determinism of maximum probability instead of the less general two-valued one.
I base the-system on extensional methods, which necessitates the introduction of a new punctuation indicating the 'etc' in a great many statements.
I define 'man' in nan-el and functional terms.
This list is also not complete and is given for orientation and justification of the name of a non-aristotelian system.
In the rough, all science is developing in the A direction. The more it succeeds in overcoming the old structural implications of speech, and the more successful it is in building new vocabularies, the further and more rapidly it will progress.
Our human relations at present are still mostly based on the /4-system-function. The issues are definite. Either we shall have a science of man, and, therefore, have to part company with the structural implications of our old language and corresponding s.rand this means we shall have to build up a new terminology, which is A in structure, and use different methods;or we shall remain in A semantic clutches, use A language and methods, involving older s.r, and have no science of man. As I am engaged in building up a science of man, all departures I am forced to make from accepted methods are necessary semantic preliminaries to the building of my system and need no apology.
It is no exaggeration to say that the A, E, and N systems have one most interesting structural and semantic characteristic in common; namely, that they have a few unjustified 'infinities' too many. The modern E, N, and, finally, A systems, after analysis, eliminate these unjustified notions. New systems arise, quite different from the old ones, which again have this structural characteristic in common, that they have a few 'infinities' lessan important semantic factor, especially in the ^-system, as it helps to eliminate our older delusional mythologies. In the mathematical reconstruction of Brouwer, Weyl, and the Polish School, a similar