14 ideas
| 5988 | Anaximander produced the first philosophy book (and maybe the first book) [Anaximander, by Bodnár] |
| Full Idea: Anaximander was the first to produce a philosophical book (later conventionally titled 'On Nature'), if not the first to produce a book at all. | |
| From: report of Anaximander (fragments/reports [c.570 BCE]) by István Bodnár - Anaximander | |
| A reaction: Wow! Presumably there were Egyptian 'books', but this still sounds like a stupendous claim to fame. |
| 1496 | The earth is stationary, because it is in the centre, and has no more reason to move one way than another [Anaximander, by Aristotle] |
| Full Idea: Something which is established in the centre and has equality in relation to the extremes has no more reason to move up than it has down or to the sides (so the earth is stationary) | |
| From: report of Anaximander (fragments/reports [c.570 BCE], A26) by Aristotle - On the Heavens 295b11 |
| 11022 | Gentzen introduced a natural deduction calculus (NK) in 1934 [Gentzen, by Read] |
| Full Idea: Gentzen introduced a natural deduction calculus (NK) in 1934. | |
| From: report of Gerhard Gentzen (works [1938]) by Stephen Read - Thinking About Logic Ch.8 |
| 11065 | The inferential role of a logical constant constitutes its meaning [Gentzen, by Hanna] |
| Full Idea: Gentzen argued that the inferential role of a logical constant constitutes its meaning. | |
| From: report of Gerhard Gentzen (works [1938]) by Robert Hanna - Rationality and Logic 5.3 | |
| A reaction: Possibly inspired by Wittgenstein's theory of meaning as use? This idea was the target of Prior's famous connective 'tonk', which has the role of implying anything you like, proving sentences which are not logical consequences. |
| 11023 | The logical connectives are 'defined' by their introduction rules [Gentzen] |
| Full Idea: The introduction rules represent, as it were, the 'definitions' of the symbols concerned, and the elimination rules are no more, in the final analysis, than the consequences of these definitions. | |
| From: Gerhard Gentzen (works [1938]), quoted by Stephen Read - Thinking About Logic Ch.8 | |
| A reaction: If an introduction-rule (or a truth table) were taken as fixed and beyond dispute, then it would have the status of a definition, since there would be nothing else to appeal to. So is there anything else to appeal to here? |
| 11213 | Each logical symbol has an 'introduction' rule to define it, and hence an 'elimination' rule [Gentzen] |
| Full Idea: To every logical symbol there belongs precisely one inference figure which 'introduces' the symbol ..and one which 'eliminates' it. The introductions represent the 'definitions' of the symbols concerned, and eliminations are consequences of these. | |
| From: Gerhard Gentzen (works [1938], II.5.13), quoted by Ian Rumfitt - "Yes" and "No" III | |
| A reaction: [1935 paper] This passage is famous, in laying down the basics of natural deduction systems of logic (ones using only rules, and avoiding axioms). Rumfitt questions whether Gentzen's account gives the sense of the connectives. |
| 10067 | Gentzen proved the consistency of arithmetic from assumptions beyond arithmetic [Gentzen, by Musgrave] |
| Full Idea: Gentzen proved the consistency of arithmetic from assumptions which transcend arithmetic. | |
| From: report of Gerhard Gentzen (works [1938]) by Alan Musgrave - Logicism Revisited §5 | |
| A reaction: This does not contradict Gödel's famous result, but reinforces it. The interesting question is what assumptions Gentzen felt he had to make. |
| 14874 | Anaximander saw the contradiction in the world - that its own qualities destroy it [Anaximander, by Nietzsche] |
| Full Idea: Anaximander discovers the contradictory character of our world: it perishes from its own qualities. | |
| From: report of Anaximander (fragments/reports [c.570 BCE]) by Friedrich Nietzsche - Unpublished Notebooks 1872-74 19 [239] | |
| A reaction: A lovely gloss on Anaximander, though I am not sure that I understand what Nietzsche means. |
| 1495 | Anaximander introduced the idea that the first principle and element of things was the Boundless [Anaximander, by Simplicius] |
| Full Idea: Anaximander said that the first principle and element of existing things was the boundless; it was he who originally introduced this name for the first principle. | |
| From: report of Anaximander (fragments/reports [c.570 BCE], A09) by Simplicius - On Aristotle's 'Physics' 9.24.14- | |
| A reaction: Simplicius is quoting Theophrastus |
| 405 | The essential nature, whatever it is, of the non-limited is everlasting and ageless [Anaximander] |
| Full Idea: The essential nature, whatever it is, of the non-limited is everlasting and ageless. | |
| From: Anaximander (fragments/reports [c.570 BCE], B2), quoted by (who?) - where? |
| 13222 | The Boundless cannot exist on its own, and must have something contrary to it [Aristotle on Anaximander] |
| Full Idea: Those thinkers are in error who postulate ...a single matter, for this cannot exist without some 'perceptible contrariety': this Boundless, which they identify with the 'original real', must be either light or heavy, either hot or cold. | |
| From: comment on Anaximander (fragments/reports [c.570 BCE]) by Aristotle - Coming-to-be and Passing-away (Gen/Corr) 329a10 | |
| A reaction: A dubious objection, I would say. If there has to be a contrasting cold thing to any hot thing, what happens when the cold thing is removed? |
| 404 | Things begin and end in the Unlimited, and are balanced over time according to justice [Anaximander] |
| Full Idea: The non-limited is the original material of existing things; their source is also that to which they return after destruction, according to necessity; they give justice and make reparation to each other for injustice, according to the arrangement of Time. | |
| From: Anaximander (fragments/reports [c.570 BCE], B1), quoted by Simplicius - On Aristotle's 'Physics' 24.13- | |
| A reaction: Simplicius is quoting Theophrastus |
| 1746 | The parts of all things are susceptible to change, but the whole is unchangeable [Anaximander, by Diog. Laertius] |
| Full Idea: The parts of all things are susceptible to change, but the whole is unchangeable. | |
| From: report of Anaximander (fragments/reports [c.570 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.An.2 |
| 5957 | Absurd superstitions make people atheist, not disharmony in nature [Plutarch] |
| Full Idea: Men have never thought the universe godless on the ground of detecting some fault in stars or seasons; ..it is the ridiculous things that superstition does that makes people say it would be better if there were no gods at all. | |
| From: Plutarch (14: Superstition [c.85], §12) | |
| A reaction: Not true, I would say. Absurd superstitions do discredit belief in the supernatural, but earthquakes are a disharmony in nature, and a nasty one at that. Nowadays we have other explanations to rival those of religion. |