Combining Philosophers

All the ideas for Proclus, Leucippus and Paul M. Pietroski

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4 ideas

10. Modality / A. Necessity / 8. Transcendental Necessity

490	Everything happens by reason and necessity [Leucippus]
	Full Idea: Nothing happens at random; everything happens out of reason and by necessity.
	From: Leucippus (fragments/reports [c.435 BCE], B002), quoted by (who?) - where?

14. Science / D. Explanation / 2. Types of Explanation / g. Causal explanations

13165	Geometrical proofs do not show causes, as when we prove a triangle contains two right angles [Proclus]
	Full Idea: Geometry does not ask 'why?' ..When from the exterior angle equalling two opposite interior angles it is shown that the interior angles make two right angles, this is not a causal demonstration. With no exterior angle they still equal two right angles.
	From: Proclus (Commentary on Euclid's 'Elements' [c.452], p.161-2), quoted by Paolo Mancosu - Explanation in Mathematics §5
	A reaction: A very nice example. It is hard to imagine how one might demonstrate the cause of the angles making two right angles. If you walk, turn left x°, then turn left y°, then turn left z°, and x+y+z=180°, you end up going in the original direction.

18. Thought / E. Abstraction / 1. Abstract Thought

9569	The origin of geometry started in sensation, then moved to calculation, and then to reason [Proclus]
	Full Idea: It is unsurprising that geometry was discovered in the necessity of Nile land measurement, since everything in the world of generation goes from imperfection to perfection. They would naturally pass from sense-perception to calculation, and so to reason.
	From: Proclus (Commentary on Euclid's 'Elements' [c.452]), quoted by Charles Chihara - A Structural Account of Mathematics 9.12 n55
	A reaction: The last sentence is the core of my view on abstraction, that it proceeds by moving through levels of abstraction, approaching more and more general truths.

19. Language / B. Reference / 5. Speaker's Reference

21650	No language is semantically referential; it all occurs at the level of thought or utterance [Pietroski, by Hofweber]
	Full Idea: For Paul Pietroski no expression in natural language is semantically referential. ....Reference to objects occurs not at the level of semantics, but at the level of thought or utterance.
	From: report of Paul M. Pietroski (Events and Semantic Architecture [2004]) by Thomas Hofweber - Ontology and the Ambitions of Metaphysics 07.2
	A reaction: Love this. It has always struck me that reference is what speakers do. Try taking any supposedly referential description and sticking 'so-called' in front of it. That seems to leave you with the reference even though you have denied the description.