The Axioms of Dialectic and of Syllogism, 29 BOOK I.
For I well know that axioms once rightly discovered will carry whole troops of works along with them, and produce them, not here and there one, but in clusters.
It is this which fills the plays of Shakespeare with practical axioms and domestic wisdom.
Lobachevskiy was one of the first thinkers to apply a critical treatment to the fundamental axioms of geometry, and he thus became a pioneer of the modern geometries which deal with space other than as treated by Euclid.
The public mind was divided between two classes of axioms and theories, each embodying sound reasoning and honest conviction, but resting at bottom upon divergent habits of life and forms of industry.
One of Mr. Gallatin's financial axioms was that the Treasury should be made to account specifically for every appropriation; a rule undoubtedly correct, but very difficult to apply.
Author of The Axioms of Geometry; Kant's Criticism; Logic; Psychological Researches on Reading (together with Prof.
Now all of these translucent axioms are true (are notaxioms always true?
If Kepler, or Herschel, or Fulton, or Ericcson had violated axioms and laws of mathematics and dynamics, their labors would have been as so much chaff and dust.
These dwellers in "flatland" could construct a plane geometry which would be exactly like ours in being based on the axiomsof Euclid.
Our edifice must have some support to rest upon, and we take these axioms as its foundation.
Thus, we are forced to ask ourselves, have we really a collection of ultimate moral principles which are analogous to the axioms of geometry?
What is the evidence of the axioms and definitions?
Euclid's axioms are useful because they are self-evident; and so long as people make mistakes in geometry, it will be necessary to expose their blundering by bringing out the contradictions involved.
As Hobbes observed, people would dispute even geometrical axioms if they had an interest in doing so; and, certainly, they are ready to dispute the plainest doctrines about money.
Such indemonstrable truths were called by the ancients axioms from their majesty and authority, as the assumptions which constitute demonstrative syllogisms derive all their force and efficacy from these.
And, in short, all the axioms of the theological science appear in perfection in this dialogue; and all the divine orders are exhibited subsisting in connection.
Hence it will follow that induction is no otherwise subservient to science, than as it produces credibility in axioms and petitions; and this by exciting the universal conception of these latent in the soul.
His pages are studded with axiomsof policy, and impress us by many an enduring truth.
The disciples of Pythagoras followed a similar precept, hence when the majority of them were destroyed in a fire the axioms of Pythagoras were largely lost.
Whatever may be the precise date of these axioms the ideas they express well repay careful consideration.
In mathematics, according to Euclid's treatment, the axioms alone are indemonstrable first principles, and all demonstrations are in gradation strictly subordinated to them.
But the axioms themselves have no more immediate evidence than any other geometrical problem, but only more simplicity on account of their smaller content.
Problems which had puzzled him to desperation suddenly became as obvious as the firstaxioms of geometry.
What if he demonstrated that even the axioms of Euclid could, under different conditions, be both true and false at the same time?
But of the axioms which they assume, in order to draw the conclusions which they desire, they think that two ought to be granted to them; for no one objects to them.
But there are other causes of certain axioms or notions, which it would be to the purpose to set forth by this method of ours; for it would thus appear what notions are more useful than others, and what notions have scarcely any use at all.
Again we should discern whence the notions called secondary derived their origin, and consequently the axioms on which they are founded, and other points of interest connected with these questions.
Young intellects, depraved by arguing for either side, now came into conflict with each other, and fearful axioms of the journalistic jurisprudence, then in its infancy, hurtled to and fro.
On the other hand, what are axioms to you are often problems to them.
The inferior race, the degraded and enslaved people, the small-minded individual, live in the details which to larger minds and more advanced tribes of men reduce themselves to axioms and laws.
Now let me give you some axioms I have arrived at, after seeing something of a great many kinds of good folks.
I had meant to make this note of our conversation a text for a few axioms on the matter of breeding.
And what is this king of all axioms and emperor of all fallacies?
Nietzsche harbored a fevered yearning to call all of these false prophets to book and to reduce their fine axioms to absurdity.
We are not speaking here of abstractions or wire-drawn corollaries, but of those plain ethical axioms which every man may apprehend, and which are so closely involved in the question now before the country for decision.
The above list will hopefully give you a few useful examples demonstrating the appropriate usage of "axioms" in a variety of sentences. We hope that you will now be able to make sentences using this word.
