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Single Idea 20791

[filed under theme 4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / e. Axioms of PL ]

Full Idea

Chrysippus has five indemonstrables that do not need demonstration:1) If 1st the 2nd, but 1st, so 2nd; 2) If 1st the 2nd, but not 2nd, so not 1st; 3) Not 1st and 2nd, the 1st, so not 2nd; 4) 1st or 2nd, the 1st, so not 2nd; 5) 1st or 2nd, not 2nd, so 1st.

Gist of Idea

Chrysippus has five obvious 'indemonstrables' of reasoning

Source

report of Chrysippus (fragments/reports [c.240 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 07.80-81

Book Ref

'The Stoics Reader', ed/tr. Inwood,B/Gerson,L.P. [Hackett 2008], p.22

A Reaction

[from his lost text 'Dialectics'; squashed to fit into one quote] 1) is Modus Ponens, 2) is Modus Tollens. 4) and 5) are Disjunctive Syllogisms. 3) seems a bit complex to be an indemonstrable.

Related Ideas

Idea 8078 Modus ponens is one of five inference rules identified by the Stoics [Chrysippus, by Devlin]

Idea 1875 Dogs show reason in decisions made by elimination [Chrysippus, by Sext.Empiricus]

The 17 ideas with the same theme [statements treated as true without question]:

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]
20791 Chrysippus has five obvious 'indemonstrables' of reasoning [Chrysippus, by Diog. Laertius]
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 [Frege, by Burge]
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 [Russell/Whitehead, by Hughes/Cresswell]
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]