1188 | In the lower intellectual level assumptions are needed, but the higher level can move beyond them [PG on Plato] |
2145 | In mathematics certain things have to be accepted without further explanation [Plato] |
562 | Axioms are the underlying principles of everything, and who but the philosopher can assess their truth? [Aristotle] |
573 | The axioms of mathematics are part of philosophy [Aristotle] |
1668 | An axiom is a principle which must be understood if one is to learn anything [Aristotle] |
5620 | Philosophy has no axioms, as it is just rational cognition of concepts [Kant] |
9154 | Frege agreed with Euclid that the axioms of logic and mathematics are known through self-evidence [Burge on Frege] |
9585 | Since every definition is an equation, one cannot define equality itself [Frege] |
9542 | The best known axiomatization of PL is Whitehead/Russell, with four axioms and two rules [Hughes/Cresswell on Russell/Whitehead] |
9013 | We can eliminate 'or' from our basic theory, by paraphrasing 'p or q' as 'not(not-p and not-q)' [Quine] |
13610 | A logic with ¬ and → needs three axiom-schemas and one rule as foundation [Bostock] |
8086 | Predicate logic retains the axioms of propositional logic [Devlin] |
6299 | Axioms are often affirmed simply because they produce results which have been accepted [Resnik] |
8476 | Axiomatization simply picks from among the true sentences a few to play a special role [Orenstein] |
7797 | Axiom systems of logic contain axioms, inference rules, and definitions of proof and theorems [Girle] |
4632 | 'Natural' systems of deduction are based on normal rational practice, rather than on axioms [Baggini /Fosl] |
4631 | In ideal circumstances, an axiom should be such that no rational agent could possibly object to its use [Baggini /Fosl] |