Combining Philosophers

Ideas for Luitzen E.J. Brouwer, Henry Laycock and Charles Parsons

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5 ideas

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

15941	For intuitionists excluded middle is an outdated historical convention [Brouwer]
	Full Idea: From the intuitionist standpoint the dogma of the universal validity of the principle of excluded third in mathematics can only be considered as a phenomenon of history of civilization, like the rationality of pi or rotation of the sky about the earth.
	From: Luitzen E.J. Brouwer (works [1930]), quoted by Shaughan Lavine - Understanding the Infinite VI.2
	A reaction: [Brouwer 1952:510-11]

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

12797	If plural variables have 'some values', then non-count variables have 'some value' [Laycock]
	Full Idea: If a plural variable is said to have not a single value but some values (some clothes), then a non-count variable may have, more quirkier still, some value (some clothing, for instance) in ranging arbitrarily over the scattered stuff.
	From: Henry Laycock (Words without Objects [2006], 4.4)
	A reaction: We seem to need the notion of a sample, or an archetype, to fit the bill. I hereby name them 'sample variables'. Damn - Laycock got there first, on p.137.

5. Theory of Logic / G. Quantification / 4. Substitutional Quantification

9469	Substitutional existential quantifier may explain the existence of linguistic entities [Parsons,C]
	Full Idea: I argue (against Quine) that the existential quantifier substitutionally interpreted has a genuine claim to express a concept of existence, which may give the best account of linguistic abstract entities such as propositions, attributes, and classes.
	From: Charles Parsons (A Plea for Substitutional Quantification [1971], p.156)
	A reaction: Intuitively I have my doubts about this, since the whole thing sounds like a verbal and conventional game, rather than anything with a proper ontology. Ruth Marcus and Quine disagree over this one.

9468	On the substitutional interpretation, '(∃x) Fx' is true iff a closed term 't' makes Ft true [Parsons,C]
	Full Idea: For the substitutional interpretation of quantifiers, a sentence of the form '(∃x) Fx' is true iff there is some closed term 't' of the language such that 'Ft' is true. For the objectual interpretation some object x must exist such that Fx is true.
	From: Charles Parsons (A Plea for Substitutional Quantification [1971], p.156)
	A reaction: How could you decide if it was true for 't' if you didn't know what object 't' referred to?

5. Theory of Logic / G. Quantification / 6. Plural Quantification

12794	Plurals are semantical but not ontological [Laycock]
	Full Idea: Plurality is a semantical but not also an ontological construction.
	From: Henry Laycock (Words without Objects [2006], Intro 4)
	A reaction: I love it when philososphers make simple and illuminating remarks like this. You could read 500 pages of technical verbiage about plural reference without grasping that this is the underlying issue. Sounds right to me.