Combining Philosophers

All the ideas for Archimedes, Robert Grosseteste and Robert Axelrod

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4 ideas

6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry

13007	Archimedes defined a straight line as the shortest distance between two points [Archimedes, by Leibniz]
	Full Idea: Archimedes gave a sort of definition of 'straight line' when he said it is the shortest line between two points.
	From: report of Archimedes (fragments/reports [c.240 BCE]) by Gottfried Leibniz - New Essays on Human Understanding 4.13
	A reaction: Commentators observe that this reduces the purity of the original Euclidean axioms, because it involves distance and measurement, which are absent from the purest geometry.

9. Objects / B. Unity of Objects / 2. Substance / b. Need for substance

16629	By comparing qualities and features, reason can gradually infer the nature of substance [Grosseteste]
	Full Idea: Awakened reason distinguishes color from size and shape from body and then shape and size from the substance of body, and so by drawing distinctions and abstracting, it arrives at a grasp of the substance of body, which supports size, shape and color.
	From: Robert Grosseteste (Commentary on 'Posterior Analytics' [1226], I.14), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 07.4
	A reaction: This optimistic view influenced Aquinas, and is called 'incrementalism' by Pasnau. It is the spirit of scientific essentialism, and a nice instance of inference to the best explanation (though 'substance' in itself explains virtually nothing).

23. Ethics / B. Contract Ethics / 8. Contract Strategies

22725	When players don't meet again, defection is the best strategy [Axelrod]
	Full Idea: When players will never meet again, the strategy of defection is the only stable strategy.
	From: Robert Axelrod (The Evolution of Co-Operation [1984], 5)
	A reaction: This gives good grounds for any community's mistrust of transient strangers, such as tourists. And yet any sensible tourist will want communities to trust tourists, and will therefore behave in a reliable way.

22724	Good strategies avoid conflict, respond to hostility, forgive, and are clear [Axelrod]
	Full Idea: Successful game strategies avoid unnecessary conflict, are provoked by an uncalled for defection, forgive after a provocation, and behave clearly so the other player can adapt.
	From: Robert Axelrod (The Evolution of Co-Operation [1984], 1)
	A reaction: [compressed] Exactly what you would expect from a nice but successful school teacher. The strategies for success in these games is the same as the rules for educating a person into cooperative behaviour. TIT FOR TAT does all these.