Combining Texts

All the ideas for 'fragments/reports', 'Commentary on Euclid's 'Elements'' and 'Sentences'

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

---

6 ideas

8. Modes of Existence / A. Relations / 1. Nature of Relations

18528	The single imagined 'interval' between things only exists in the intellect [Auriol]
	Full Idea: It appears that a single thing, which must be imagined as some sort of interval [intervallum] existing between two things, cannot exist in extramental reality, but only in the intellect.
	From: Peter Auriol (Sentences [1316], I fols318 v a-b), quoted by John Heil - The Universe as We Find It 7
	A reaction: This is the standard medieval denial of the existence of real relations. It contrasts with post-Russell ontology, which seems to admit relations as entities. Heil and Auriol and right.

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?

26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / b. Prime matter

16589	Prime matter lacks essence, but is only potentially and indeterminately a physical thing [Auriol]
	Full Idea: Prime matter has no essence, nor a nature that is determinate, distinct, and actual. Instead, it is pure potential, and determinable, so that it is indeterminately and indistinctly a material thing.
	From: Peter Auriol (Sentences [1316], II.12.1.1), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 03.1
	A reaction: Pasnau thinks Auriol has the best shot at explaining the vague idea of 'prime matter', with the thought that it exists, but indeterminateness is what gives it a lesser mode of existence. It strikes me as best to treat 'exist' as univocal.

28. God / A. Divine Nature / 4. Divine Contradictions

16651	God can do anything non-contradictory, as making straightness with no line, or lightness with no parts [Auriol]
	Full Idea: If someone says 'God could make straightness without a line, and roughness and lightness in weight without parts', …then show me the reason why God can do whatever does not imply a contradiction, yet cannot do these things.
	From: Peter Auriol (Sentences [1316], IV.12.2.2), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 11.4
	A reaction: How engagingly bonkers. The key idea preceding this is that God can do all sorts of things that are beyond our understanding. He is then obliged to offer some examples.