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Ideas for 'fragments/reports', 'Aspects of Scientific Explanation' and 'Posterior Analytics'

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4 ideas

5. Theory of Logic / A. Overview of Logic / 6. Classical Logic

12376	Demonstrations by reductio assume excluded middle [Aristotle]
	Full Idea: Demonstrations by reduction to the impossible assume that everything is asserted or denied.
	From: Aristotle (Posterior Analytics [c.327 BCE], 77a23)
	A reaction: This sounds like the lynchpin of classical logic.

5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence

12373	Something holds universally when it is proved of an arbitrary and primitive case [Aristotle]
	Full Idea: Something holds universally when it is proved of an arbitrary and primitive case.
	From: Aristotle (Posterior Analytics [c.327 BCE], 73b33)
	A reaction: A key idea in mathematical logic, but it always puzzles me. If you snatch a random person in London, and they are extremely tall, does that prove that people of London are extremely tall? How do we know the arbitrary is representative?

5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle

12363	Everything is either asserted or denied truly [Aristotle]
	Full Idea: Of the fact that everything is either asserted or denied truly, we must believe that it is the case.
	From: Aristotle (Posterior Analytics [c.327 BCE], 71a14)
	A reaction: Presumably this means that every assertion which could possibly be asserted must come out as either true or false. This will have to include any assertions with vague objects or predicates, and any universal assertions, and negative assertions.

5. Theory of Logic / K. Features of Logics / 1. Axiomatisation

13004	Aristotle's axioms (unlike Euclid's) are assumptions awaiting proof [Aristotle, by Leibniz]
	Full Idea: Aristotle's way with axioms, rather than Euclid's, is as assumptions which we are willing to agree on while awaiting an opportunity to prove them
	From: report of Aristotle (Posterior Analytics [c.327 BCE], 76b23-) by Gottfried Leibniz - New Essays on Human Understanding 4.07
	A reaction: Euclid's are understood as basic self-evident truths which will be accepted by everyone, though the famous parallel line postulate undermined that. The modern view of axioms is a set of minimum theorems that imply the others. I like Aristotle.