12 ideas
| 23367 | Even pointing a finger should only be done for a reason [Epictetus] |
| Full Idea: Philosophy says it is not right even to stretch out a finger without some reason. | |
| From: Epictetus (fragments/reports [c.57], 15) | |
| A reaction: The key point here is that philosophy concerns action, an idea on which Epictetus is very keen. He rather despise theory. This idea perfectly sums up the concept of the wholly rational life (which no rational person would actually want to live!). |
| 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) |
| 18969 | How do you distinguish three beliefs from four beliefs or two beliefs? [Quine] |
| Full Idea: Suppose I say that I have given up precisely three beliefs since lunch. An over-coarse individuation could reduce the number to two, and an over-fine one could raise it to four. | |
| From: Willard Quine (Propositional Objects [1965], p.144) | |
| A reaction: Obviously if you ask how many beliefs I hold, it would be crazy to give a precise answer. But if I search for my cat, I give up my belief that it is in the kitchen, in the lounge and in the bathroom. That's precise enough to be three beliefs, I think. |
| 18967 | A 'proposition' is said to be the timeless cognitive part of the meaning of a sentence [Quine] |
| Full Idea: A 'proposition' is the meaning of a sentence. More precisely, since propositions are supposed to be true or false once and for all, it is the meaning of an eternal sentence. More precisely still, it is the 'cognitive' meaning, involving truth, not poetry. | |
| From: Willard Quine (Propositional Objects [1965], p.139) | |
| A reaction: Quine defines this in order to attack it. I equate a proposition with a thought, and take a sentence to be an attempt to express a proposition. I have no idea why they are supposed to be 'timeless'. Philosophers have some very odd ideas. |
| 18968 | The problem with propositions is their individuation. When do two sentences express one proposition? [Quine] |
| Full Idea: The trouble with propositions, as cognitive meanings of eternal sentences, is individuation. Given two eternal sentences, themselves visibly different linguistically, it is not sufficiently clear under when to say that they mean the same proposition. | |
| From: Willard Quine (Propositional Objects [1965], p.140) | |
| A reaction: If a group of people agree that two sentences mean the same thing, which happens all the time, I don't see what gives Quine the right to have a philosophical moan about some dubious activity called 'individuation'. |
| 18970 | The concept of a 'point' makes no sense without the idea of absolute position [Quine] |
| Full Idea: Unless we are prepared to believe that absolute position makes sense, the very idea of a point as an entity in its own right must be rejected as not merely mysterious but absurd. | |
| From: Willard Quine (Propositional Objects [1965], p.149) | |
| A reaction: The fact that without absolute position we can only think of 'points' as relative to a conceptual grid doesn't stop the grid from picking out actual locations in space, as shown by latitude and longitude. |