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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
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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
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In mathematics certain things have to be accepted without further explanation
[Plato]
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562
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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
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An axiom is a principle which must be understood if one is to learn anything
[Aristotle]
|
20791
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Chrysippus has five obvious 'indemonstrables' of reasoning
[Chrysippus, by Diog. Laertius]
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5620
|
Philosophy has no axioms, as it is just rational cognition of concepts
[Kant]
|
9154
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Frege agreed with Euclid that the axioms of logic and mathematics are known through self-evidence
[Frege, by Burge]
|
9585
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Since every definition is an equation, one cannot define equality itself
[Frege]
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9542
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The best known axiomatization of PL is Whitehead/Russell, with four axioms and two rules
[Russell/Whitehead, by Hughes/Cresswell]
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9013
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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
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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
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In ideal circumstances, an axiom should be such that no rational agent could possibly object to its use
[Baggini /Fosl]
|