13 ideas
| 1813 | All reasoning endlessly leads to further reasoning (Mode 12) [Agrippa, by Diog. Laertius] |
| Full Idea: Twelfth mode: all reasoning leads on to further reasoning, and this process goes on forever. | |
| From: report of Agrippa (fragments/reports [c.60]) by Diogenes Laertius - Lives of Eminent Philosophers 09.Py.10 |
| 1811 | Proofs often presuppose the thing to be proved (Mode 15) [Agrippa, by Diog. Laertius] |
| Full Idea: Fifteenth mode: proofs often presuppose the thing to be proved. | |
| From: report of Agrippa (fragments/reports [c.60]) by Diogenes Laertius - Lives of Eminent Philosophers 09.Py.10 |
| 1815 | Reasoning needs arbitrary faith in preliminary hypotheses (Mode 14) [Agrippa, by Diog. Laertius] |
| Full Idea: Fourteenth mode: reasoning requires arbitrary faith in preliminary hypotheses. | |
| From: report of Agrippa (fragments/reports [c.60]) by Diogenes Laertius - Lives of Eminent Philosophers 09.Py.10 |
| 1812 | All discussion is full of uncertainty and contradiction (Mode 11) [Agrippa, by Diog. Laertius] |
| Full Idea: Eleventh mode: all topics of discussion are full of uncertainty and contradiction. | |
| From: report of Agrippa (fragments/reports [c.60]) by Diogenes Laertius - Lives of Eminent Philosophers 09.Py.10 |
| 13795 | Properties only have identity in the context of their contraries [Elder] |
| Full Idea: The very being, the identity, of any property consists at least in part in its contrasting as it does with its own proper contraries. | |
| From: Crawford L. Elder (Real Natures and Familiar Objects [2004], 2.4) | |
| A reaction: See Elder for the details of this, but the idea that properties can only be individuated contextually sounds promising. |
| 13798 | Maybe we should give up the statue [Elder] |
| Full Idea: Some contemporary metaphysicians infer that one of the objects must go, namely, the statue. | |
| From: Crawford L. Elder (Real Natures and Familiar Objects [2004], 7.2) | |
| A reaction: [He cites Zimmerman 1995] This looks like a recipe for creating a vast gulf between philosophers and the rest of the population. If it is right, it makes the true ontology completely useless in understanding our daily lives. |
| 13797 | The loss of an essential property means the end of an existence [Elder] |
| Full Idea: The loss of any essential property must amount to the end of an existence. | |
| From: Crawford L. Elder (Real Natures and Familiar Objects [2004], 3) | |
| A reaction: This is orthodoxy for essentialists, and I presume that Aristotle would agree, but I have a problem with the essence of a great athlete, who then grows old. Must we say that they lose their identity-as-an-athlete? |
| 13794 | Essential properties by nature occur in clusters or packages [Elder] |
| Full Idea: Essential properties by nature occur in clusters or packages. | |
| From: Crawford L. Elder (Real Natures and Familiar Objects [2004], 2.2) | |
| A reaction: Elder proposes this as his test for the essentialness of a property - his Test of Flanking Uniformities. A nice idea. |
| 13796 | Essential properties are bound together, and would be lost together [Elder] |
| Full Idea: The properties of any essential nature are bound together....[122] so any case in which one of our envisioned familiar objects loses one of its essential properties will be a case in which it loses several. | |
| From: Crawford L. Elder (Real Natures and Familiar Objects [2004], 3) | |
| A reaction: This sounds like a fairly good generalisation rather than a necessary truth. Is there a natural selection for properties, so that only the properties which are able to bind to others to form teams are able to survive and flourish? |
| 8850 | Agrippa's Trilemma: justification is infinite, or ends arbitrarily, or is circular [Agrippa, by Williams,M] |
| Full Idea: Agrippa's Trilemma offers three possible outcomes for a regress of justification: the chain goes on for ever (infinite); or the chain stops at an unjustified proposition (arbitrary); or the chain eventually includes the original proposition (circular). | |
| From: report of Agrippa (fragments/reports [c.60], §2) by Michael Williams - Without Immediate Justification §2 | |
| A reaction: This summarises Ideas 1911, 1913 and 1914. Agrippa's Trilemma is now a standard starting point for modern discussions of foundations. Personally I reject 2, and am torn between 1 (+ social consensus) and 3 (with a benign, coherent circle). |
| 1814 | Everything is perceived in relation to another thing (Mode 13) [Agrippa, by Diog. Laertius] |
| Full Idea: Thirteenth mode: everything is always perceived in relation to something else. | |
| From: report of Agrippa (fragments/reports [c.60]) by Diogenes Laertius - Lives of Eminent Philosophers 09.Py.10 |
| 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. |