Ideas from 'Plural Quantification Exposed' by Øystein Linnebo [2003], by Theme Structure
[found in 'Nous' (ed/tr -) [- ,]].
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / n. Axiom of Comprehension
10779
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A comprehension axiom is 'predicative' if the formula has no bound second-order variables
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Full Idea:
If φ contains no bound second-order variables, the corresponding comprehension axiom is said to be 'predicative'; otherwise it is 'impredicative'.
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From:
Øystein Linnebo (Plural Quantification Exposed [2003], §1)
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A reaction:
['Predicative' roughly means that a new predicate is created, and 'impredicative' means that it just uses existing predicates]
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5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
10781
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A 'pure logic' must be ontologically innocent, universal, and without presuppositions
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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).
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From:
Øystein Linnebo (Plural Quantification Exposed [2003], §1)
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5. Theory of Logic / G. Quantification / 6. Plural Quantification
10783
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Plural quantification depends too heavily on combinatorial and set-theoretic considerations
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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.
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From:
Øystein Linnebo (Plural Quantification Exposed [2003], §4)
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10778
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Can second-order logic be ontologically first-order, with all the benefits of second-order?
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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.
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From:
Øystein Linnebo (Plural Quantification Exposed [2003], §0)
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9. Objects / A. Existence of Objects / 1. Physical Objects
10782
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The modern concept of an object is rooted in quantificational logic
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Full Idea:
Our modern general concept of an object is given content only in connection with modern quantificational logic.
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From:
Øystein Linnebo (Plural Quantification Exposed [2003], §2)
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A reaction:
[He mentions Frege, Carnap, Quine and Dummett] This is the first thing to tell beginners in modern analytical metaphysics. The word 'object' is very confusing. I think I prefer 'entity'.
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