Definition of Axioms

plural of axiom

- Reality is to be set forth in theorems derived from fundamental
**axioms**and definitions. - For us it still lies beyond reason, but is beginning to be clearer than the
**axioms**of reason. - The entire books of Euclid are after all but the outcome of a few
**axioms**and accepted definitions. - The process of proof is purely Deductive (the
**axioms**and definitions being granted). - First, there are Axioms or Principles, that is real, universal, self-evident propositions.
- The consistency of the axiom of choice and of the generalized continuum-hypothesis with the
**axioms**of set theory. - Why may not even our sense of the validity of inference and of the truth of the
**axioms**of geometry be a pure hallucination? - Congruence is extended in any space beyond parallel rects to all rects by two
**axioms**depending on perpendicularity. - In modern expositions of the
**axioms**of geometry certain conditions are laid down which the relation of congruence between segments is to satisfy. - By the aid of these two
**axioms**the theory of congruence can be extended so as to compare lengths of segments on any two rects. - Ethics have their
**axioms**like other sciences; and these**axioms**are rightly called in all languages moral truths. - The reader will of course understand the precise amount of seasoning which must be added to it before he adopts it as one of the
**axioms**of his life. - It is very evident that there are no mathematics without
**axioms**and definitions, that is to say, without absolute principles. - We cannot prove all our
**axioms**by the study of errors and, indeed, are by no means solely dependent on this material. - We must know how to write longhand before we can write shorthand; we must know the
**axioms**before we can propound original geometric theories. - These two high art
**axioms**may be given as a safe foundation for the choice of colors, in following which no one can greatly err. - There was a well-dressed bald-headed individual laying down the
**axioms**of that very Socialism of which Geisner and he had been talking. - The essential logical characteristics of this relation from which all the properties of space spring are expressed by mathematicians in the
**axioms**of geometry. - The Mathematical Axioms would then never be applicable to space or time, or to the objects or processes that fill them.
- A man who was continuously firing off adages and
**axioms**would be as terrible an infliction as the inveterate anecdotist or the everlasting pun-producer. - By means of these
**axioms**formulae for the transformation of measurements made in one time-system to measurements of the same facts of nature made in another time-system can be deduced. - Men and women of the younger generation, whatever their views, find no support in him, because he appeals to
**axioms**and postulates which to them seem unreal. - From such remarks proceeded that great number of sententious distichs, which have passed into conversation, and are added as proverbial
**axioms**to the general stock of practical knowledge. - Being an attempt to get rid of
**axioms**altogether; and to establish the theory of parallel lines, without the introduction of any principle not common to other parts of the elements. - His opinions undoubtedly shifted with the veering of his moods, but on the whole these
**axioms**of suspense mark the central point to which they constantly tended to return, and at which they rested longest. - Such are what some people have called the laws of thought, the conceptions of space and of time, and
**axioms**or first principles, which need no proof and cannot be proved or denied.

- All
**axioms**are verbal propositions. - But neither of these
**axioms**is universally correct. - Spinoza believed his definitions and
**axioms**expressed. - The details of these
**axioms**do not now concern us. - These
**axioms**help us to build up certain propositions. - By Machiavelian
**axioms**taught? - Into the ground of these
**axioms**the geometrician does not enquire. - On the other hand, what are
**axioms**to you are often problems to them. - This disposition to cavil at received
**axioms**has beset me through life. - The principles of ethics are immutable
**axioms**like those of geometry. - To these
**axioms**agreed the press, the pulpit and the politician. - If the
**axioms**mean anything for men, they mean something for women. - The principles of Jefferson are the definitions and
**axioms**of free society. - It is not this which is denied by the
**axioms**of Montaigne and Bacon.