18 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. |
| 7719 | European philosophy consists of a series of footnotes to Plato [Whitehead] |
| Full Idea: The safest general characterization of the European philosophical tradition is that it consists of a series of footnotes to Plato. | |
| From: Alfred North Whitehead (Process and Reality [1929], p.39) | |
| A reaction: Outsiders think this is a ridiculous remark, but readers of Plato can only be struck by what a wonderful tribute Whitehead has come up with. I would say that at least 80% of this database deals with problems which were discussed at length by Plato. |
| 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 |
| 17879 | Axiomatising set theory makes it all relative [Skolem] |
| Full Idea: Axiomatising set theory leads to a relativity of set-theoretic notions, and this relativity is inseparably bound up with every thoroughgoing axiomatisation. | |
| From: Thoralf Skolem (Remarks on axiomatised set theory [1922], p.296) |
| 13536 | Skolem did not believe in the existence of uncountable sets [Skolem] |
| Full Idea: Skolem did not believe in the existence of uncountable sets. | |
| From: Thoralf Skolem (works [1920], 5.3) | |
| A reaction: Kit Fine refers somewhere to 'unrepentent Skolemites' who still hold this view. |
| 10656 | With 'extensive connection', boundary elements are not included in domains [Whitehead, by Varzi] |
| Full Idea: In Whitehead's theory of extensive connection, no boundary elements are included in the domain of quantification. ...His conception of space contains no parts of lower dimensions, such as points or boundary elements. | |
| From: report of Alfred North Whitehead (Process and Reality [1929]) by Achille Varzi - Mereology 3.1 | |
| A reaction: [Varzi says we should see B.L.Clarke 1981 for a rigorous formulation. Second half of the Idea is Varzi p.21] |
| 17878 | If a 1st-order proposition is satisfied, it is satisfied in a denumerably infinite domain [Skolem] |
| Full Idea: Löwenheim's theorem reads as follows: If a first-order proposition is satisfied in any domain at all, it is already satisfied in a denumerably infinite domain. | |
| From: Thoralf Skolem (Remarks on axiomatised set theory [1922], p.293) |
| 17880 | Integers and induction are clear as foundations, but set-theory axioms certainly aren't [Skolem] |
| Full Idea: The initial foundations should be immediately clear, natural and not open to question. This is satisfied by the notion of integer and by inductive inference, by it is not satisfied by the axioms of Zermelo, or anything else of that kind. | |
| From: Thoralf Skolem (Remarks on axiomatised set theory [1922], p.299) | |
| A reaction: This is a plea (endorsed by Almog) that the integers themselves should be taken as primitive and foundational. I would say that the idea of successor is more primitive than the integers. |
| 17881 | Mathematician want performable operations, not propositions about objects [Skolem] |
| Full Idea: Most mathematicians want mathematics to deal, ultimately, with performable computing operations, and not to consist of formal propositions about objects called this or that. | |
| From: Thoralf Skolem (Remarks on axiomatised set theory [1922], p.300) |
| 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. |
| 15389 | In Whitehead 'processes' consist of events beginning and ending [Whitehead, by Simons] |
| Full Idea: There are no items in Whitehead's ontology called 'processes'. Rather, the term 'process' refers to the way in which the basic things - which are still events - come into existence and cease to exist. Whitehead called this 'becoming'. | |
| From: report of Alfred North Whitehead (Process and Reality [1929]) by Peter Simons - Whitehead: process and cosmology 'The mature' |
| 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 |
| 15247 | Whitehead held that perception was a necessary feature of all causation [Whitehead, by Harré/Madden] |
| Full Idea: On Whitehead's view, not only is a volitional sense of 'causal power' projected on to physical events, but 'perception in the causal mode' is literally ascribed to them. | |
| From: report of Alfred North Whitehead (Process and Reality [1929]) by Harré,R./Madden,E.H. - Causal Powers 3.II | |
| A reaction: This seems to be a close relative of Leibniz's monads. 'Perception' is a daft word for it, but in some way everything is 'responsive' to the things adjacent to it. |
| 16962 | Whitehead replaced points with extended regions [Whitehead, by Quine] |
| Full Idea: Whitehead tried to avoid points, and make do with extended regions and sets of regions. | |
| From: report of Alfred North Whitehead (Process and Reality [1929]) by Willard Quine - Existence and Quantification p.93 |
| 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 |