8 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!). |
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 |
15938 | Platonists ruin infinity, which is precisely a growing structure which is never completed [Dummett] |
Full Idea: The platonist destroys the whole essence of infinity, which lies in the conception of a structure which is always in growth, precisely because the process of construction is never completed. | |
From: Michael Dummett (Elements of Intuitionism [1977], p.57), quoted by Thomas J. McKay - Plural Predication | |
A reaction: I don't warm to intuitionism, but I warm to this conception of infinity. Completed infinities are convenient reifications for mathematicians. |
15939 | For intuitionists it is constructed proofs (which take time) which make statements true [Dummett] |
Full Idea: For an intuitionist a mathematical statement is rendered true or false by a proof or disproof, that is, by a construction, and constructions are effected in time. | |
From: Michael Dummett (Elements of Intuitionism [1977], p.336), quoted by Shaughan Lavine - Understanding the Infinite VI.2 | |
A reaction: Lavine is quoting this to draw attention to the difficulties of thinking of it as all taking place 'in time', especially when dealing with infinities. |
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. |