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This may suffice to show how realistic are the mathematical concepts which we have here tried to build up. We were thereby led to realize that man's general capacity for thinking mathematically is the outcome of early experiences of this kind. It is evident that geometrical concepts arising in man's mind in this way must be those of Euclidean geometry.
Modern philosophers, after collecting and classifying their annals, have been led by the nature of their labors to deal also with history: then it was that they saw, not without surprise, that the HISTORY OF PHILOSOPHY was the same thing at bottom as the PHILOSOPHY OF HISTORY; further, that these two branches of speculation, so different in appearance, the history of philosophy and the philosophy of history, were also only the stage representation of the concepts of metaphysics, which is philosophy entire.
I want to show that without any extraordinary difficulty we can illustrate the theory of a finite universe by means of a mental image to which, with some practice, we shall soon grow accustomed. First of all, an observation of epistemological nature. A geometrical-physical theory as such is incapable of being directly pictured, being merely a system of concepts.
The rightful interpretation of those ancient and obscured truths, erroneously classified as "myths" and "superstitions," will reveal a universal truth, and will also show their relation to modern concepts.
While it is clear that "system of systems" and other alternative military concepts are under consideration, for the time being, these have not replaced the current platform and force-on-force attrition orientation. It should be noted, there will be no doctrinal alternatives unless ample effort is made to provide a comprehensive and detailed examination of possible alternatives.
This intuitional coinage in fixed standard concepts, this creation of an easily handled intellectual cash, is no doubt of evident practical utility.
These are the languages that cut most to the bone of linguistic expression. B. Such as express concepts of groups I, II, and IV; in other words, languages that keep the syntactic relations pure and that also possess the power to modify the significance of their radical elements by means of affixes or internal changes.
The concepts and principles of theology are valid only as descriptions and presentations of feelings, not as cognitions; by their unavoidable anthropomorphic character alone they are completely unfitted for science. The dogmatic system is an envelopment which religion accepts with a smile. He who treats religious doctrines as science falls into empty mythology.
The psychology of the crowd, and the psychology of war, cannot be contained in the psychology of the herd, however attractive the simplicity of these concepts may be.
It is no wonder that earlier thinkers, forgetting that concepts are only man-made extracts from the temporal flux, should have ended by treating them as a superior type of being, bright, changeless, true, divine, and utterly opposed in nature to the turbid, restless lower world. The latter then appears as but their corruption and falsification.
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