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Updated: May 19, 2025
The teacher, then, whom I speak of, will discourse thus in his secret heart:—He will begin, as many so far have done before him, by laying it down as if a position which approves itself to the reason, immediately that it is fairly examined,—which is of so axiomatic a character as to have a claim to be treated as a first principle, and is firm and steady enough to bear a large superstructure upon it,—that Religion is not the subject-matter of a science. “You may have opinions in religion, you may have theories, you may have arguments, you may have probabilities; you may have anything but demonstration, and therefore you cannot have science.
Thus the original, immediate relation between geometry and physical reality appears destroyed, and we feel impelled toward the following more general view, which characterizes Poincare's standpoint. Envisaged in this way, axiomatic geometry and the part of natural law which has been given a conventional status appear as epistemologically equivalent.
Even where it is not possible to secure in other nations the observance of the principles which we accept as axiomatic, it is necessary for us firmly to insist upon the rights of our own citizens without regard to their creed or race; without regard to whether they were born here or born abroad.
The standard theories of economic science have assumed the rights of property and contract as axiomatic premises and ultimate terms of analysis; and their theories are commonly drawn in such a form as would fit the circumstances of the handicraft industry and the petty trade, and such as can be extended to any other economic situation by shrewd interpretation.
In view of the diversity of human beliefs and the discredit which has historically fallen on the most axiomatic articles of faith, we must either admit scepticism to be the issue of the debate, or else, condemning our absolute view of truth, find some means of utilizing the relative truths which are all that humanity seems able to grasp.
But this is no answer at all, by his own showing, for has he not just admitted as a truism that "ability or inability to conceive is in no case to be received as a criterion of axiomatic truth."
With these conditions obtaining, its advantage rests upon the axiomatic principle that, other things being nearly equal, a place where commerce centres is a better strategic position than one which it neglects. The latter is the condition of the Chiriqui Lagoon.
This book began with the axiomatic statement that the symbol is the thing. From that it developed in great detail the fact that any part of a whole bearing similarity to the whole was also the whole; that each seven was the class of all sevens; and other details of the science of magical similarity followed quite logically from the single axiom.
As we ascend in numbers and in morals, the intuitive perceptions become less and less; and though the truths are there, and ought to be admitted as axiomatic, they are not at once seen and felt by ordinary minds. Now so far as the rights of blacks and the duties of whites are manifest to common and honest minds, so far would I admit the first and perform the second, though the heavens fall.
The average citizen of to-day is not conscious of the fact that he has ceased to be one. The man of three generations ago had certain ideas which he held to be axiomatic, such as that his house was his castle, and that property was property and that what was his was his. But these were to him things so obvious that he could not conceive any reasonable person doubting them.
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