### Some articles on *axiom systems, axioms, axiom, system*:

**Axiom Systems**

... Different modal logics can be derived from taking different subsets of these

**axioms**, and these logics are normally named after the important

**axioms**being employed ... In this case though, the knowledge

**axiom**no longer seems right—agents only sometimes believe the truth—so it is usually replaced with the Consistency

**Axiom**... When D replaces T in S5, the resulting

**system**is known as KD45 ...

... the "game" of Euclidean geometry (which is seen as consisting of some strings called "

**axioms**", and some "rules of inference" to generate new strings from given ones ... true statements are assigned to the

**axioms**and the rules of inference are truth-preserving), then you have to accept the theorem, or, rather, the interpretation you have ... Many formalists would say that in practice, the

**axiom systems**to be studied will be suggested by the demands of science or other areas of mathematics ...

### Famous quotes containing the words systems and/or axiom:

“We have done scant justice to the reasonableness of cannibalism. There are in fact so many and such excellent motives possible to it that mankind has never been able to fit all of them into one universal scheme, and has accordingly contrived various diverse and contradictory *systems* the better to display its virtues.”

—Ruth Benedict (1887–1948)

““You are bothered, I suppose, by the idea that you can’t possibly believe in miracles and mysteries, and therefore can’t make a good wife for Hazard. You might just as well make yourself unhappy by doubting whether you would make a good wife to me because you can’t believe the first *axiom* in Euclid. There is no science which does not begin by requiring you to believe the incredible.””

—Henry Brooks Adams (1838–1918)