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3 ideas
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. |
8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
Full Idea: Intuitionists in mathematics deny excluded middle, because it is symptomatic of faith in the transcendent existence of mathematical objects and/or the truth of mathematical statements. | |
From: Stewart Shapiro (Thinking About Mathematics [2000], 1.2) | |
A reaction: There are other problems with excluded middle, such as vagueness, but on the whole I, as a card-carrying 'realist', am committed to the law of excluded middle. |
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 |