Combining Texts

Ideas for 'Thinking About Mathematics', 'Material Beings' and 'Two Dogmas of Empiricism'

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5 ideas

5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle

17587	The 'Law' of Excluded Middle needs all propositions to be definitely true or definitely false [Inwagen]
	Full Idea: I think the validity of the 'Law' of Excluded Middle depends on the assumption that every proposition is definitely true or definitely false.
	From: Peter van Inwagen (Material Beings [1990], 18)
	A reaction: I think this is confused. He cites vagueness as the problem, but that is a problem for Bivalence. If excluded middle is read as 'true or not-true', that leaves the meaning of 'not-true' open, and never mentions the bivalent 'false'.

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.

5. Theory of Logic / E. Structures of Logic / 4. Variables in Logic

17558	Variables are just like pronouns; syntactic explanations get muddled over dummy letters [Inwagen]
	Full Idea: Explanations in terms of syntax do not satisfactorily distinguish true variables from dummy or schematic letters. Identifying variables with pronouns, however, provides a genuine explanation of what variables are.
	From: Peter van Inwagen (Material Beings [1990], 02)
	A reaction: I like this because it shows that our ordinary thought and speech use variables all the time ('I've forgotten something - what was it?'). He says syntax is fine for maths, but not for ordinary understanding.

5. Theory of Logic / F. Referring in Logic / 1. Naming / f. Names eliminated

9204	Quine's arguments fail because he naively conflates names with descriptions [Fine,K on Quine]
	Full Idea: Quine's logical argument against modality presupposes a naïve view of singular terms under which no significant distinction is to be drawn between the use of names and descriptions.
	From: comment on Willard Quine (Two Dogmas of Empiricism [1953]) by Kit Fine - Intro to 'Modality and Tense' p. 6
	A reaction: See Idea 9201 for Quine's argument. The question is whether '9' and 'the number of planets' are names or descriptions. The 'number of planets' is not remotely descriptive of 9, so it must be referential. So '9' is a name? Hm.

5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / b. The Heap paradox ('Sorites')

17583	There are no heaps [Inwagen]
	Full Idea: Fortunately ....there are no heaps.
	From: Peter van Inwagen (Material Beings [1990], 18)
	A reaction: This is the nihilist view of (inorganic) physical objects. If a wild view solves all sorts of problems, one should take it serious. It is why I take reductive physicalism about the mind seriously. (Well, it's true, actually)