structure for 'Formal Logic'    |     alphabetical list of themes    |     expand these ideas

4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / e. Axioms of PL

[statements treated as true without question]

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