16 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 |
| 14249 | Boolos reinterprets second-order logic as plural logic [Boolos, by Oliver/Smiley] |
| Full Idea: Boolos's conception of plural logic is as a reinterpretation of second-order logic. | |
| From: report of George Boolos (On Second-Order Logic [1975]) by Oliver,A/Smiley,T - What are Sets and What are they For? n5 | |
| A reaction: Oliver and Smiley don't accept this view, and champion plural reference differently (as, I think, some kind of metalinguistic device?). |
| 10830 | Second-order logic metatheory is set-theoretic, and second-order validity has set-theoretic problems [Boolos] |
| Full Idea: The metatheory of second-order logic is hopelessly set-theoretic, and the notion of second-order validity possesses many if not all of the epistemic debilities of the notion of set-theoretic truth. | |
| From: George Boolos (On Second-Order Logic [1975], p.45) | |
| A reaction: Epistemic problems arise when a logic is incomplete, because some of the so-called truths cannot be proved, and hence may be unreachable. This idea indicates Boolos's motivation for developing a theory of plural quantification. |
| 10829 | A sentence can't be a truth of logic if it asserts the existence of certain sets [Boolos] |
| Full Idea: One may be of the opinion that no sentence ought to be considered as a truth of logic if, no matter how it is interpreted, it asserts that there are sets of certain sorts. | |
| From: George Boolos (On Second-Order Logic [1975], p.44) | |
| A reaction: My intuition is that in no way should any proper logic assert the existence of anything at all. Presumably interpretations can assert the existence of numbers or sets, but we should be able to identify something which is 'pure' logic. Natural deduction? |
| 10832 | '∀x x=x' only means 'everything is identical to itself' if the range of 'everything' is fixed [Boolos] |
| Full Idea: One may say that '∀x x=x' means 'everything is identical to itself', but one must realise that one's answer has a determinate sense only if the reference (range) of 'everything' is fixed. | |
| From: George Boolos (On Second-Order Logic [1975], p.46) | |
| A reaction: This is the problem now discussed in the recent book 'Absolute Generality', of whether one can quantify without specifying a fixed or limited domain. |
| 10834 | Weak completeness: if it is valid, it is provable. Strong: it is provable from a set of sentences [Boolos] |
| Full Idea: A weak completeness theorem shows that a sentence is provable whenever it is valid; a strong theorem, that a sentence is provable from a set of sentences whenever it is a logical consequence of the set. | |
| From: George Boolos (On Second-Order Logic [1975], p.52) | |
| A reaction: So the weak version says |- φ → |= φ, and the strong versions says Γ |- φ → Γ |= φ. Presumably it is stronger if it can specify the source of the inference. |
| 13841 | Why should compactness be definitive of logic? [Boolos, by Hacking] |
| Full Idea: Boolos asks why on earth compactness, whatever its virtues, should be definitive of logic itself. | |
| From: report of George Boolos (On Second-Order Logic [1975]) by Ian Hacking - What is Logic? §13 |
| 10833 | Many concepts can only be expressed by second-order logic [Boolos] |
| Full Idea: The notions of infinity and countability can be characterized by second-order sentences, though not by first-order sentences (as compactness and Skolem-Löwenheim theorems show), .. as well as well-ordering, progression, ancestral and identity. | |
| From: George Boolos (On Second-Order Logic [1975], p.48) |
| 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. |
| 23565 | Our obedience to the king erases any crimes we commit for him [Shakespeare] |
| Full Idea: We know enough if we know we are the king's men. Our obedience to the king wipes the crime of it out of us. | |
| From: William Shakespeare (Henry V [1599]), quoted by Michael Walzer - Just and Unjust Wars 03 | |
| A reaction: He is referring to the slaughter of the French servants behind the lines at Agincourt. A classic expression of 'I was just obeying orders', which was rejected at Nurnberg in 1946. Depends on the seriousness of the crime. |
| 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 |
| 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? |
| 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 |
| 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 |