11 ideas
| 21757 | Philosophy is the conceptual essence of the shape of history [Hegel] |
| Full Idea: Philosophy is the supreme blossom - the concept - of the entire shape of history, the consciousness and the spiritual essence of the whole situation, the spirit of the age as the spirit present and aware of itself in thought. | |
| From: Georg W.F.Hegel (Lectures on the History of Philosophy [1830], p.25), quoted by Stephen Houlgate - An Introduction to Hegel 01 | |
| A reaction: This sees philosophy as intrinsically historical, which is a founding idea for 'continental' philosophy. Analysis is tied to science, in which the history of the subject is seen as irrelevant to its truth. Does this mean we can't go back to Aristotle? |
| 21552 | Common speech is vague; its vocabulary and syntax must be modified, for precision [Russell] |
| Full Idea: I am persuaded that common speech is full of vagueness and inaccuracy, and that any attempt to be precise and accurate requires modification of common speech both as regards vocabulary and as regards syntax. | |
| From: Bertrand Russell (Mr Strawson on Referring [1957], p.123) | |
| A reaction: It is interesting that he cites the syntax of ordinary language, as well as the vocabulary. The implication is that vagueness can also be a feature of syntax (and hence his pursuit of logical form), which is not normally mentioned |
| 21551 | Empirical words need ostensive definition, which makes them egocentric [Russell] |
| Full Idea: The meanings of all empirical words depend ultimately upon ostensive definitions, ostensive definitions depend upon experience, and that experience is egocentric. | |
| From: Bertrand Russell (Mr Strawson on Referring [1957], p.122) | |
| A reaction: He seems to imply that this makes them partly subjective, but I don't see why an objective consensus can't be reached when making an ostensive definition. We just need to clearly agree what 'that' refers to. |
| 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) |
| 21550 | Science reduces indexicals to a minimum, but they can never be eliminated from empirical matters [Russell] |
| Full Idea: It is of the essence of a scientific account of the world to reduce to a minimum the egocentric element in assertion, but success in this attempt is a matter of degree, and is never complete where empirical matter is concerned. | |
| From: Bertrand Russell (Mr Strawson on Referring [1957], p.121) | |
| A reaction: He cites ostensive definitions. The key issue is whether they can be wholly eliminated when we try to be objective. Russell here endorses Perry's claim that they never go away. Personally I just think that (if so) we should try harder. |