Combining Texts

Ideas for 'Introduction to Russell's Theory of Types', 'Letters to Wagner' and 'Existence and Quantification'

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2 ideas

4. Formal Logic / D. Modal Logic ML / 1. Modal Logic
Quine says quantified modal logic creates nonsense, bad ontology, and false essentialism [Melia on Quine]
     Full Idea: Quine charges quantified modal systems of logic with giving rise to unintended sense or nonsense, committing us to an incomprehensible ontology, and entailing an implausible or unsustainable Aristotelian essentialism.
     From: comment on Willard Quine (Existence and Quantification [1966]) by Joseph Melia - Modality Ch.3
     A reaction: A nice summary. Personally I like essentialism in accounts of science (see Nature|Laws of Nature|Essentialism), so would like to save it in metaphysics. Possible worlds ontology may be very surprising, rather than 'incomprehensible'.
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility
The Axiom of Reducibility is self-effacing: if true, it isn't needed [Quine]
     Full Idea: The Axiom of Reducibility is self-effacing: if it is true, the ramification it is meant to cope with was pointless to begin with.
     From: Willard Quine (Introduction to Russell's Theory of Types [1967], p.152), quoted by Penelope Maddy - Naturalism in Mathematics I.1
     A reaction: Maddy says the rejection of Reducibility collapsed the ramified theory of types into the simple theory.