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Those things that had been wont to be considered as axioms and irrefutable postulates in her daily acceptance were suddenly seen as the most ephemeral hypotheses.
That such a Bill as the Home Rule Bill should be treated as an invasion of Imperial rights is a proof of one, or perhaps of both, the following axioms that Bills are never read by their accusers, and that party spirit will distort the plainest facts.
That simple chemical reaction is like one of the axioms on which the edifice of geometry is reared. Matter and force are the everlasting mysteries, manifesting themselves in the twin mysteries of space and time. The manifestations are not mysteries only the stuff of the manifestations, matter and force; and the theater of the manifestations, space and time."
They have all pursued the method so emphatically condemned by Bacon, and the result has verified his prediction. “The usual method,” says he, “of discovery and proof by first establishing the most general propositions, then applying and proving the intermediate axioms according to these, is the parent of error and the calamity of every science.” They have set out with the universal law of causality or the principle of the sufficient reason, and thence have proceeded to ascertain and determine the actual nature and processes of things.
On the other hand, the self-evident propositions as to the relation of numbers, are certainly synthetical but not universal, like those of geometry, and for this reason cannot be called axioms, but numerical formulae. That 7 + 5 = 12 is not an analytical proposition. For neither in the representation of seven, nor of five, nor of the composition of the two numbers, do I cogitate the number twelve.
In this art of homemaking I have set down in my mind certain first principles, like the axioms of Euclid, and the first is, No home is possible without love. All business marriages and marriages of convenience, all mere culinary marriages and marriages of mere animal passion, make the creation of a true home impossible in the outset.
Not one of the boys believed that he would reap any benefit from repeating the names and dates of hated kings in their proper sequence, from learning dead languages, proving axioms, defining "a matter of course," and counting the anthers of plants and the joints on the hindlegs of insects, to knowing the end no more about them than their Latin names. How they scorned everything practical!
Normanton Hipperdon; more, perhaps: he would have been more in earnest. His store of political axioms was Tory; but he did remarkably well, and with no great difficulty, in confuting them to the wives of voters, to the voters themselves, and at public assemblies.
One would state with great confidence that he could convince any sane child that the simpler propositions of Euclid are true; but, nevertheless, he would fail, utterly, with one who should deny the definitions and axioms. The principles of Jefferson are the definitions and axioms of free society. And yet they are denied and evaded with no small show of success.
Everything depends on laws; therefore, there are final causes." Bouvard imagined that perhaps Spinoza would furnish him with some arguments, and he wrote to Dumouchel to get him Saisset's translation. Dumouchel sent him a copy belonging to his friend Professor Varelot, exiled on the 2nd of December. Ethics terrified them with its axioms, its corollaries.
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