Combining Texts

Ideas for 'fragments/reports', 'Briefings on Existence' and 'The Concept of a Person'

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4 ideas

4. Formal Logic / B. Propositional Logic PL / 1. Propositional Logic

8077	Stoic propositional logic is like chemistry - how atoms make molecules, not the innards of atoms [Chrysippus, by Devlin]
	Full Idea: In Stoic logic propositions are treated the way atoms are treated in present-day chemistry, where the focus is on the way atoms fit together to form molecules, rather than on the internal structure of the atoms.
	From: report of Chrysippus (fragments/reports [c.240 BCE]) by Keith Devlin - Goodbye Descartes Ch.2
	A reaction: A nice analogy to explain the nature of Propositional Logic, which was invented by the Stoics (N.B. after Aristotle had invented predicate logic).

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

20791	Chrysippus has five obvious 'indemonstrables' of reasoning [Chrysippus, by Diog. Laertius]
	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.
	From: report of Chrysippus (fragments/reports [c.240 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 07.80-81
	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.

4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST

12337	There is 'transivity' iff membership ∈ also means inclusion ⊆ [Badiou]
	Full Idea: 'Transitivity' signifies that all of the elements of the set are also parts of the set. If you have α∈Β, you also have α⊆Β. This correlation of membership and inclusion gives a stability which is the sets' natural being.
	From: Alain Badiou (Briefings on Existence [1998], 11)

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX

12321	The axiom of choice must accept an indeterminate, indefinable, unconstructible set [Badiou]
	Full Idea: The axiom of choice actually amounts to admitting an absolutely indeterminate infinite set whose existence is asserted albeit remaining linguistically indefinable. On the other hand, as a process, it is unconstructible.
	From: Alain Badiou (Briefings on Existence [1998], 2)
	A reaction: If only constructible sets are admitted (see 'V = L') then there is a contradiction.