7 ideas
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. |
12219 | Whether a modal claim is true depends on how the object is described [Quine, by Fine,K] |
Full Idea: Quine says if ∃x□(x>7) makes sense, then for which object x is the condition rendered true? Specify it as '9' and it is apparently rendered true, specify it as 'the number of planets' and it is apparently rendered false. | |
From: report of Willard Quine (Three Grades of Modal Involvement [1953]) by Kit Fine - Quine on Quantifying In p.105 | |
A reaction: This is normally characterised as Quine saying that only de dicto involvement is possible, and not de re involvement. Or that that all essences are nominal, and cannot be real. |
10922 | Objects are the values of variables, so a referentially opaque context cannot be quantified into [Quine] |
Full Idea: The objects of a theory are not properly describable as the things named by the singular terms; they are the values, rather, of the variables of quantification. ..So a referentially opaque context is one that cannot properly be quantified into. | |
From: Willard Quine (Three Grades of Modal Involvement [1953], p.174) | |
A reaction: The point being that you cannot accurately pick out the objects in the domain |
10923 | Aristotelian essentialism says a thing has some necessary and some non-necessary properties [Quine] |
Full Idea: What Aristotelian essentialism says is that you can have open sentences Fx and Gx, such that ∃x(nec Fx.Gx.Źnec Gx). For example, ∃x(nec(x>5). there are just x planets. Źnec(there are just x planets)). | |
From: Willard Quine (Three Grades of Modal Involvement [1953], p.176) | |
A reaction: This is a denial of 'maximal essentialism', that all of a things properties might be essential. Quine is thus denying necessity, except under a description. He may be equivocating over the reference of 'there are just 9 planets'. |
10921 | Necessity can attach to statement-names, to statements, and to open sentences [Quine] |
Full Idea: Three degrees necessity in logic or semantics: first and least is attaching a semantical predicate to the names of statements (as Nec '9>5'); second and more drastic attaches to statements themselves; third and gravest attaches to open sentences. | |
From: Willard Quine (Three Grades of Modal Involvement [1953], p.158) |
10924 | Necessity is in the way in which we say things, and not things themselves [Quine] |
Full Idea: Necessity resides in the way in which we say things, and not in the things we talk about. | |
From: Willard Quine (Three Grades of Modal Involvement [1953], p.176) | |
A reaction: This is a culminating idea of Quine's thoroughgoing empiricism, as filtered through logical positivism. I would hardly dare to accuse Quine of a use/mention confusion (his own bęte noir), but one seems to me to be lurking here. |
468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice. | |
From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where? |