7 ideas
| 4037 | Ockham's Razor is the principle that we need reasons to believe in entities [Mellor/Oliver] |
| Full Idea: Ockham's Razor is the principle that we need reasons to believe in entities. | |
| From: DH Mellor / A Oliver (Introduction to 'Properties' [1997], §9) | |
| A reaction: This presumably follows from an assumption that all beliefs need reasons, but is that the case? The Principle of Sufficient Reason precedes Ockham's Razor. |
| 4027 | Properties are respects in which particular objects may be alike or differ [Mellor/Oliver] |
| Full Idea: Properties are respects in which particular objects may be alike or differ. | |
| From: DH Mellor / A Oliver (Introduction to 'Properties' [1997], §1) | |
| A reaction: Note that this definition does not mention a causal role for properties. |
| 4029 | Nominalists ask why we should postulate properties at all [Mellor/Oliver] |
| Full Idea: Nominalists ask why we should postulate properties at all. | |
| From: DH Mellor / A Oliver (Introduction to 'Properties' [1997], §3) | |
| A reaction: Objects might be grasped without language, but events cannot be understood, and explanations of events seem inconceivable without properties (implying that they are essentially causal). |
| 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. |
| 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. |
| 4039 | Abstractions lack causes, effects and spatio-temporal locations [Mellor/Oliver] |
| Full Idea: Abstract entities (such as sets) are usually understood as lacking causes, effects, and spatio-temporal location. | |
| From: DH Mellor / A Oliver (Introduction to 'Properties' [1997], §10) | |
| A reaction: This seems to beg some questions. Has the ideal of 'honour' never caused anything? Young men dream of pure velocity. |
| 7492 | Early societies are based on community, and modern societies on association [Tönnies, by Watson] |
| Full Idea: Pre-modern societies are based on community (Gemeinschaft), whereas modern societies are based on association (Gesellschaft). | |
| From: report of Ferdinand Tönnies (Community and Association [1887]) by Peter Watson - Ideas Ch.32 | |
| A reaction: A very interesting distinction. The modern term implies contracts, and it strikes me as an extremely accurate description of modern liberal democracies. There is very little sense of community, but a strong sense of innumerable contracts that bind us. |