axioms


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Related to axioms: Euclid's axioms
See: premises
References in classic literature ?
It is an algebraic axiom, which makes us proceed from a known to an unknown quantity, and not from an unknown to a known; but sit down, sir, I beg of you."
"I have been nearly mad; and you know the axiom, -- non bis in idem.
A day will come, and perhaps quickly, wherein you will have occasion to remember that axiom: --
May it not be that Mother Nature may deliberately encourage decrease as well as increase--that it may be an axiom that what is gained in concentration is lost in size?
We shall not even take the trouble to demonstrate this, for it is an axiom in morals, as in physics.
In the jungle might is right, nor does it take long to inculcate this axiom in the mind of a jungle dweller, regardless of what his past training may have been.
Besides, we are safe for to-day; you know the axiom, `Non bis in idem.'"
This foundational theory, also called basis theory, is formalised in some fixed formal language and consists of a list of axioms, which are reasonable (self-evident) statements, in the fixed formal language, about the mathematical universe.
The theory is based on three assumptions: the logical closure of rational belief; the axioms of probability for rational degrees of belief; and the so-called Lockean thesis, in which the concepts of rational belief and rational degree of belief figure simultaneously.
One of the objections against the program was that it opened the floor for discussion on some well-established religious axioms. This is an acceptable argument, but the circle of these axioms was widened to contain many negotiable issues.
The axioms of ZFK are divided into two groups: G and [G.sub.k].
Mathematicians Ciesielski (West Virginia U.) and Pawlikowski (Wroclaw U.) present a new axiom of set theory they call the Covering Property Axiom, CPA, and show how it is consistent with the usual ZFC axioms, and is not only true in the iterated perfect set Sacks model but actually captures its combinatorial core.