Combining Texts

Ideas for 'Essays on Intellectual Powers: Conception', 'Plural Quantification Exposed' and 'Mr Strawson on Logical Theory'

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5 ideas

5. Theory of Logic / A. Overview of Logic / 4. Pure Logic

10781	A 'pure logic' must be ontologically innocent, universal, and without presuppositions [Linnebo]
	Full Idea: I offer these three claims as a partial analysis of 'pure logic': ontological innocence (no new entities are introduced), universal applicability (to any realm of discourse), and cognitive primacy (no extra-logical ideas are presupposed).
	From: Øystein Linnebo (Plural Quantification Exposed [2003], §1)

5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic

22437	Logical languages are rooted in ordinary language, and that connection must be kept [Quine]
	Full Idea: A logical language is not independent of ordinary language. It has its roots in ordinary language, and these roots are not to be severed.
	From: Willard Quine (Mr Strawson on Logical Theory [1953], V)
	A reaction: Music to my ears. When you study logic, no one has to teach you what the words 'or' and 'if-then' mean, but they are disambiguated by the symbolism. The roots of logic are in ordinary talk of 'and', 'or' and 'not', which is the real world.

5. Theory of Logic / E. Structures of Logic / 1. Logical Form

22434	Reduction to logical forms first simplifies idioms and grammar, then finds a single reading of it [Quine]
	Full Idea: Ordinary language is reduced to logical form in two ways: reduction of the variety of idioms and grammatical constructions, and reduction of each surviving idiom to one fixed and convenient interpretation.
	From: Willard Quine (Mr Strawson on Logical Theory [1953], V)
	A reaction: Is there a conflict between a 'fixed' and a 'convenient' result? By 'fixed' I suppose he means it is a commitment (to not waver). What is the logical form of a sentence which is deliberately ambiguous?

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

10778	Can second-order logic be ontologically first-order, with all the benefits of second-order? [Linnebo]
	Full Idea: According to its supporters, second-order logic allow us to pay the ontological price of a mere first-order theory and get the corresponding monadic second-order theory for free.
	From: Øystein Linnebo (Plural Quantification Exposed [2003], §0)

10783	Plural quantification depends too heavily on combinatorial and set-theoretic considerations [Linnebo]
	Full Idea: If my arguments are correct, the theory of plural quantification has no right to the title 'logic'. ...The impredicative plural comprehension axioms depend too heavily on combinatorial and set-theoretic considerations.
	From: Øystein Linnebo (Plural Quantification Exposed [2003], §4)