Combining Philosophers

Ideas for Anaxarchus, C. Anthony Anderson and Timothy Williamson

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5 ideas

5. Theory of Logic / G. Quantification / 1. Quantification

18492	Not all quantification is either objectual or substitutional [Williamson]
	Full Idea: We should not assume that all quantification is either objectual or substitutional.
	From: Timothy Williamson (Truthmakers and Converse Barcan Formula [1999], p.262)
	A reaction: [see Prior 1971:31-4] He talks of quantifying into sentence position.

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

15136	Substitutional quantification is metaphysical neutral, and equivalent to a disjunction of instances [Williamson]
	Full Idea: If quantification into sentence position is substitutional, then it is metaphysically neutral. A substitutionally interpreted 'existential' quantification is semantically equivalent to the disjunction (possibly infinite) of its substitution instances.
	From: Timothy Williamson (Truthmakers and Converse Barcan Formula [1999], §2)
	A reaction: Is it not committed to the disjunction, just as the objectual reading commits to objects? Something must make the disjunction true. Or is it too verbal to be about reality?

5. Theory of Logic / G. Quantification / 5. Second-Order Quantification

18763	Basic variables in second-order logic are taken to range over subsets of the individuals [Anderson,CA]
	Full Idea: Under its now standard principal interpretation, the monadic predicate variables in second-order logic range over subsets of the domain on individuals.
	From: C. Anthony Anderson (Identity and Existence in Logic [2014], 1.5)
	A reaction: This is an interpretation in which properties are just sets of things, which is fine if you are a logician, but not if you want to talk about anything important. Still, we must play the game. Boolos introduced plural quantification at this point.

5. Theory of Logic / G. Quantification / 7. Unorthodox Quantification

15138	Not all quantification is objectual or substitutional [Williamson]
	Full Idea: We should not assume that all quantification is objectual or substitutional.
	From: Timothy Williamson (Truthmakers and Converse Barcan Formula [1999], §2)

18771	Stop calling ∃ the 'existential' quantifier, read it as 'there is...', and range over all entities [Anderson,CA]
	Full Idea: Ontological quantifiers might just as well range over all the entities needed for the semantics. ...The minimal way would be to just stop calling '∃' an 'existential quantifier', and always read it as 'there is...' rather than 'there exists...'.
	From: C. Anthony Anderson (Identity and Existence in Logic [2014], 2.6)
	A reaction: There is no right answer here, but it seems to be the strategy adopted by most logicians, and the majority of modern metaphysicians. They just allow abstracta, and even fictions, to 'exist', while not being fussy what it means. Big mistake!