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For earth-measuring has to do with the possibilities of the disposition of certain natural objects with respect to one another, namely, with parts of the earth, measuring-lines, measuring-wands, etc. It is clear that the system of concepts of axiomatic geometry alone cannot make any assertions as to the relations of real objects of this kind, which we will call practically-rigid bodies.
Every word of it was written, every sentence had been tested; but the speaker delivered it without manuscript or notes. It was not an ordinary oration, but, in the main, an argument, as sententious and axiomatic as if made to a bench of jurists.
This hardly seems to give us a "sure and connected knowledge of the duties of man" deduced from axiomatic principles. On what authority shall we suspend for the time being this axiomatic principle or that? Is there some deeper principle which lends to each of them its authority, and which may, for cause, withdraw it?
Though he had consistently guarded himself against the obvious suggestions arising out of his intercourse with the Warricombe family, though he still emphasised every discouraging fact, and strove to regard it as axiomatic that nothing could be more perilous to his future than a hint of presumption or self-interest in word or deed beneath that friendly roof, it was coming to pass that he thought of Sidwell not only as the type of woman pursued by his imagination, but as herself the object of his converging desires.
It has always been regarded as axiomatic that the subjects or citizens of Western countries, when they travel or reside in Oriental territories, should be exempted from the penalties and processes of the latter's criminal laws. In other words, there is reserved to a Christian the privilege, when within the territories of a pagan State, of being tried for penal offences by Christian judges.
These two phantoms must of course do all that their wizard wants of them and so their united productions are a matter of complete indifference to the rest of the world. Now let us follow Herr Duehring's axiomatic utterances a little further. These two men cannot make positive demands upon each other.
It is true that the various schools of Hindu philosophy agree in regarding a few fundamental ideas as axiomatic, but philosophy is not religion. The Mohammedans are one because they have a common religion and a common law. The Christians are one, because at least one point of faith is common. But the Hindus have neither faith, nor practice, nor law to distinguish them from others.
Our judgment may indeed be said in this case to rest on the experience we have of the laws governing the frequency of occurrence of the different cases; but such experience is universal and axiomatic, and not specific experience about a particular event. Except, however, in games of chance, the purpose of which requires ignorance, such specific experience can generally be, and should be gained.
The mathematical method, "Everything must be decided on simple axiomatic foundation principles, just as if it were concerned with the simple principles of mathematics," this method is for the first time here applied. "The all-embracing existence is sole."
As soon as human thought, instead of condensing itself, as it was formerly forced to do to remain in communicable form, took on a multitude of garments and became, as it were, the people itself, instead of remaining a sort of axiomatic divinity, there were two multitudes to combat, the multitude of ideas, and the multitude of men.
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