Combining Texts

All the ideas for 'fragments/reports', 'Commentary on Euclid's 'Elements'' and 'Two Kinds of Possibility'

unexpand these ideas     |    start again     |     specify just one area for these texts

---

7 ideas

10. Modality / A. Necessity / 1. Types of Modality

12205	There are two families of modal notions, metaphysical and epistemic, of equal strength [Edgington]
	Full Idea: In my view, there are two independent families of modal notions, metaphysical and epistemic, neither stronger than the other.
	From: Dorothy Edgington (Two Kinds of Possibility [2004], Abs)
	A reaction: My immediate reaction is that epistemic necessity is not necessity at all. 'For all I know' 2 plus 2 might really be 95, and squares may also be circular.

10. Modality / A. Necessity / 5. Metaphysical Necessity

12207	Metaphysical possibility is discovered empirically, and is contrained by nature [Edgington]
	Full Idea: Metaphysical necessity derives from distinguishing things which can happen and things which can't, in virtue of their nature, which we discover empirically: the metaphysically possible, I claim, is constrained by the laws of nature.
	From: Dorothy Edgington (Two Kinds of Possibility [2004], §I)
	A reaction: She claims that Kripke is sympathetic to this. Personally I like the idea that natural necessity is metaphysically necessary (see 'Scientific Essentialism'), but the other way round comes as a bit of a surprise. I will think about it.

10. Modality / A. Necessity / 6. Logical Necessity

12206	Broadly logical necessity (i.e. not necessarily formal logical necessity) is an epistemic notion [Edgington]
	Full Idea: So-called broadly logical necessity (by which I mean, not necessarily formal logical necessity) is an epistemic notion.
	From: Dorothy Edgington (Two Kinds of Possibility [2004], §I)
	A reaction: This is controversial, and is criticised by McFetridge and Rumfitt. Fine argues that 'narrow' (formal) logical necessity is metaphysical. Between them they have got rid of logical necessity completely.

12208	An argument is only valid if it is epistemically (a priori) necessary [Edgington]
	Full Idea: Validity is governed by epistemic necessity, i.e. an argument is valid if and only if there is an a priori route from premises to conclusion.
	From: Dorothy Edgington (Two Kinds of Possibility [2004], §V)
	A reaction: Controversial, and criticised by McFetridge and Rumfitt. I don't think I agree with her. I don't see validity as depending on dim little human beings.

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.

21. Aesthetics / C. Artistic Issues / 7. Art and Morality

468	Musical performance can reveal a range of virtues [Damon of Ath.]
	Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice.
	From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where?