Axioms

However, one of my main axioms is this: "All religions are nut magnets." ❋ Gkingsley (2004)

These are structural laws, or what he calls axioms in his Erkenntnislehre, that govern relations between elementary psychical formations. ❋ Unknown (2009)

Amongst his axioms is the following verse, which he sings with great expression. ❋ Frances Erskine Inglis (1843)

It is not necessary to show that the truths which we call axioms are originally _suggested_ by observation, and that we should never have known that two straight lines cannot inclose a space if we had never seen a straight line: thus much being admitted by Dr. Whewell, and by all, in recent times, who have taken his view of the subject. ❋ John Stuart Mill (1839)

It is not necessary to show that the truths which we call axioms are originally _suggested_ by observation, and that we should never have known that two straight lines can not inclose a space if we had never seen a straight line: thus much being admitted by Dr. Whewell, and by all, in recent times, who have taken his view of the subject. ❋ John Stuart Mill (1839)

Apparently, one of Rand's basic axioms is "Existence exists." ❋ M_francis (2009)

Samuelson's revealed preference axioms or, perhaps less aptly, Savage's axioms, is a premise that most of us economists are loath to give up, even though we recognize that there may be contexts in which we would do well to depart from it. ❋ Unknown (2007)

It is well understood that a computer can be constructed so as to operate with certain axioms and formalized rules of logic, deriving in this way any number of 'proved declarative sentences'. ❋ Unknown (1972)

You then make the economic argument that the optimisation problem is usefully analogous to the problem of valuing a firm, the axioms are a reasonable description of how a company generates cash flows and the invariant parameter is analogous to "leverage". ❋ Unknown (2009)

But all that is really implied in the name [axiom] is that truths when called axioms are used for the deductive proof of other truths, and that their own proof is not involved in the process. ❋ De Groot, Jean (2009)

For a reader who is already familiar with ZF set theory, we now briefly recall the axioms of the systems CZF and IZF. ❋ Crosilla, Laura (2009)

Mathematics also proceeds by taking self-evident truths called axioms about properties of numbers and geometry and then by applying basic rules of logic you proceed to move mathematics from its starting point to deduce new statements about numbers and geometry. ❋ Jan (2008)

Taft described as axioms might more accurately be seen as postulates. ❋ Papabear (2008)

Large cardinal axioms (also referred to as axioms of strong infinity) form a hierarchy whereby a stronger axiom not only implies a weaker axiom but also proves its consistency. ❋ Jech, Thomas (2002)

For indeed every demonstrative science has three elements: (1) that which it posits, the subject genus whose essential attributes it examines; (2) the so-called axioms, which are primary premisses of its demonstration; (3) the attributes, the meaning of which it assumes. ❋ Aristotle (2002)

We must state whether it belongs to one or to different sciences to inquire into the truths which are in mathematics called axioms, and into substance. ❋ Aristotle (2002)

And Bossuet de - clares: “Those propositions which are clear and intelli - gible by themselves are called axioms or first princi - ples” (Connaissance de Dieu I, 13). ❋ ROBERT BLANCH (1968)

And thus it is rare that mathematicians are intuitive and that men of intuition are mathematicians, because mathematicians wish to treat matters of intuition mathematically and make themselves ridiculous, wishing to begin with definitions and then with axioms, which is not the way to proceed in this kind of reasoning. ❋ 1623-1662 (1944)

Pure mathematics is a collection of hypothetical, deductive theories, each consisting of a definite system of primitive, undefined, concepts or symbols and primitive, unproved, but self-consistent assumptions (commonly called axioms) together with their logically deducible consequences following by rigidly deductive processes without appeal to intuition. ❋ Unknown (1910)

The first of these axioms, which is the third axiom of congruence, is that if ABC is a triangle of rects in any moment and D is the middle event-particle of the base ❋ Alfred North Whitehead (1904)