12 ideas
| 1597 | Thales was the first western thinker to believe the arché was intelligible [Roochnik on Thales] |
| Full Idea: Thales was the first thinker in the west to believe that the arché (the basis of things) was intelligible. | |
| From: comment on Thales (fragments/reports [c.585 BCE]) by David Roochnik - The Tragedy of Reason p.138 |
| 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 |
| 18189 | ZFC could contain a contradiction, and it can never prove its own consistency [MacLane] |
| Full Idea: We have at hand no proof that the axioms of ZFC for set theory will never yield a contradiction, while Gödel's second theorem tells us that such a consistency proof cannot be conducted within ZFC. | |
| From: Saunders MacLane (Mathematics: Form and Function [1986], p.406), quoted by Penelope Maddy - Naturalism in Mathematics | |
| A reaction: Maddy quotes this, while defending set theory as the foundation of mathematics, but it clearly isn't the most secure foundation that could be devised. She says the benefits of set theory do not need guaranteed consistency (p.30). |
| 3013 | Nothing is stronger than necessity, which rules everything [Thales, by Diog. Laertius] |
| Full Idea: Necessity is the strongest of things, for it rules everything. | |
| From: report of Thales (fragments/reports [c.585 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 01.2.9 |
| 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 |
| 1494 | Thales said water is the first principle, perhaps from observing that food is moist [Thales, by Aristotle] |
| Full Idea: Thales says water is the first principle (which is why he declared the earth is on water); perhaps he concluded this from seeing that all food is moist. | |
| From: report of Thales (fragments/reports [c.585 BCE], A12) by Aristotle - Metaphysics 983b12 |
| 1713 | Thales must have thought soul causes movement, since he thought magnets have soul [Thales, by Aristotle] |
| Full Idea: Thales seems, from what is recorded of him, to have supposed that the soul is something productive of movement, if he really said that the magnet has soul because it produces movement in iron. | |
| From: report of Thales (fragments/reports [c.585 BCE]) by Aristotle - De Anima 405a20 |
| 1742 | Thales said the gods know our wrong thoughts as well as our evil actions [Thales, by Diog. Laertius] |
| Full Idea: When asked whether a man who did wrong could escape the notice of the gods, Thales is said to have replied: 'No, not even if he thinks wrong.' | |
| From: report of Thales (fragments/reports [c.585 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 01.Th.9 |