11 ideas
| 5831 | The new view is that "water" is a name, and has no definition [Schwartz,SP] |
| Full Idea: Perhaps the modern view is best expressed as saying that "water" has no definition at all, at least in the traditional sense, and is a proper name of a specific substance. | |
| From: Stephen P. Schwartz (Intro to Naming,Necessity and Natural Kinds [1977], §III) | |
| A reaction: This assumes that proper names have no definitions, though I am not clear how we can grasp the name 'Aristotle' without some association of properties (human, for example) to go with it. We need a definition of 'definition'. |
| 17833 | The first-order ZF axiomatisation is highly non-categorical [Hallett,M] |
| Full Idea: The first-order Sermelo-Fraenkel axiomatisation is highly non-categorical. | |
| From: Michael Hallett (Introduction to Zermelo's 1930 paper [1996], p.1213) |
| 17834 | Non-categoricity reveals a sort of incompleteness, with sets existing that the axioms don't reveal [Hallett,M] |
| Full Idea: The non-categoricity of the axioms which Zermelo demonstrates reveals an incompleteness of a sort, ....for this seems to show that there will always be a set (indeed, an unending sequence) that the basic axioms are incapable of revealing to be sets. | |
| From: Michael Hallett (Introduction to Zermelo's 1930 paper [1996], p.1215) | |
| A reaction: Hallett says the incompleteness concerning Zermelo was the (transfinitely) indefinite iterability of the power set operation (which is what drives the 'iterative conception' of sets). |
| 17837 | Zermelo allows ur-elements, to enable the widespread application of set-theory [Hallett,M] |
| Full Idea: Unlike earlier writers (such as Fraenkel), Zermelo clearly allows that there might be ur-elements (that is, objects other than the empty set, which have no members). Indeed he sees in this the possibility of widespread application of set-theory. | |
| From: Michael Hallett (Introduction to Zermelo's 1930 paper [1996], p.1217) |
| 5829 | We refer to Thales successfully by name, even if all descriptions of him are false [Schwartz,SP] |
| Full Idea: We can refer to Thales by using the name "Thales" even though perhaps the only description we can supply is false of him. | |
| From: Stephen P. Schwartz (Intro to Naming,Necessity and Natural Kinds [1977], §III) | |
| A reaction: It is not clear what we would be referring to if all of our descriptions (even 'Greek philosopher') were false. If an archaeologist finds just a scrap of stone with a name written on it, that is hardly a sufficient basis for successful reference. |
| 5830 | The traditional theory of names says some of the descriptions must be correct [Schwartz,SP] |
| Full Idea: The traditional theory of proper names entails that at least some combination of the things ordinarily believed of Aristotle are necessarily true of him. | |
| From: Stephen P. Schwartz (Intro to Naming,Necessity and Natural Kinds [1977], §III) | |
| A reaction: Searle endorses this traditional theory. Kripke and co. tried to dismiss it, but you can't. If all descriptions of Aristotle turned out to be false (it was actually the name of a Persian statue), our modern references would have been unsuccessful. |
| 17836 | The General Continuum Hypothesis and its negation are both consistent with ZF [Hallett,M] |
| Full Idea: In 1938, Gödel showed that ZF plus the General Continuum Hypothesis is consistent if ZF is. Cohen showed that ZF and not-GCH is also consistent if ZF is, which finally shows that neither GCH nor ¬GCH can be proved from ZF itself. | |
| From: Michael Hallett (Introduction to Zermelo's 1930 paper [1996], p.1217) |
| 5826 | The intension of "lemon" is the conjunction of properties associated with it [Schwartz,SP] |
| Full Idea: The conjunction of properties associated with a term such as "lemon" is often called the intension of the term "lemon". | |
| From: Stephen P. Schwartz (Intro to Naming,Necessity and Natural Kinds [1977], §II) | |
| A reaction: The extension of "lemon" is the set of all lemons. At last, a clear explanation of the word 'intension'! The debate becomes clear - over whether the terms of a language are used in reference to ideas of properties (and substances?), or to external items. |
| 20949 | Study the use of words, not their origins [Herder] |
| Full Idea: Not how an expression can be etymologically derived and determined analytically, but how it is used is the question. Origin and use are often very different. | |
| From: Johann Gottfried Herder (works [1784], p.153), quoted by Andrew Bowie - Introduction to German Philosophy 2 'Herder' | |
| A reaction: This doesn't quite say that meaning is use, and is basically an attack on the Etymological Fallacy (that origin gives meaning), but it is a strikingly modern view of language. |
| 7669 | We cannot attain all the ideals of every culture, so there cannot be a perfect life [Herder, by Berlin] |
| Full Idea: For Herder, we cannot attain to the highest ideals of all the centuries and all the places at once, and since we cannot do that, the whole notion of the perfect life collapses. | |
| From: report of Johann Gottfried Herder (works [1784]) by Isaiah Berlin - The Roots of Romanticism Ch.3 | |
| A reaction: Herder seems to be the father of modern cultural relativism. The idea is hard to challenge, but the ideals of some cultures should be ignored, if they diminish rather than enhance the good life for all. |
| 7668 | Herder invented the idea of being rooted in (or cut off from) a home or a group [Herder, by Berlin] |
| Full Idea: The whole notion of being at home, or being cut off from one's natural roots, the whole idea of roots, the whole idea of belonging to a group, a sect, a movement, was largely invented by Herder. | |
| From: report of Johann Gottfried Herder (works [1784], Ch.3) by Isaiah Berlin - The Roots of Romanticism | |
| A reaction: Hm. Broad generalisations are an awful temptation in the history of ideas. As a corrective to this, trying reading the two Anglo-Saxon poems 'The Wanderer' and 'The Seafarer'. Very Germanic, I suppose. Interesting, though. Leads to Hegel's politics. |