Combining Texts

All the ideas for 'Necessary Existents', 'Assertion' and 'Commentary on Euclid's 'Elements''

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5 ideas

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 / D. Propositions / 3. Concrete Propositions

19216	Propositions (such as 'that dog is barking') only exist if their items exist [Williamson]
	Full Idea: A proposition about an item exists only if that item exists... how could something be the proposition that that dog is barking in circumstances in which that dog does not exist?
	From: Timothy Williamson (Necessary Existents [2002], p.240), quoted by Trenton Merricks - Propositions
	A reaction: This is a view of propositions I can't make sense of. If I'm under an illusion that there is a dog barking nearby, when there isn't one, can I not say 'that dog is barking'? If I haven't expressed a proposition, what have I done?

19. Language / F. Communication / 2. Assertion

18052	An assertion aims to add to the content of a context [Stalnaker, by Magidor]
	Full Idea: Stalnaker starts with the general thesis that the role of a successful assertion of s is to update the context by adding to it the content of s.
	From: report of Robert C. Stalnaker (Assertion [1978]) by Ofra Magidor - Category Mistakes 5.3.2
	A reaction: This is to be compared with criteria of meaningfulness, such as verificationism, and with Grice's rules of conversational implicature. Presumably if you assert what the context presupposes, you fail to assert, without being meaningless.

19. Language / F. Communication / 5. Pragmatics / b. Implicature

14718	An assertion is an attempt to rule out certain possibilities, narrowing things down for good planning [Stalnaker, by Schroeter]
	Full Idea: Stalnaker's guiding idea is that in making an assertion the speaker is trying to get the audience to rule out certain possibilities. ....If all goes well, further planning will proceed on the basis of a smaller and more accurate range of possibilities.
	From: report of Robert C. Stalnaker (Assertion [1978]) by Laura Schroeter - Two-Dimensional Semantics
	A reaction: This sounds intuitively rather plausible, and is a nice original thought. This is what we pay clever chaps like Stalnaker to come up with. It seems to imply some notion of verisimilitude (qv. under 'truth'), depending on how much narrowing happens.