Combining Texts

All the ideas for 'The Sign of Four', 'Things' and 'Plural Quantification Exposed'

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7 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / n. Axiom of Comprehension

10779	A comprehension axiom is 'predicative' if the formula has no bound second-order variables [Linnebo]
	Full Idea: If φ contains no bound second-order variables, the corresponding comprehension axiom is said to be 'predicative'; otherwise it is 'impredicative'.
	From: Øystein Linnebo (Plural Quantification Exposed [2003], §1)
	A reaction: ['Predicative' roughly means that a new predicate is created, and 'impredicative' means that it just uses existing predicates]

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 / G. Quantification / 6. Plural Quantification

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)

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)

9. Objects / A. Existence of Objects / 1. Physical Objects

10782	The modern concept of an object is rooted in quantificational logic [Linnebo]
	Full Idea: Our modern general concept of an object is given content only in connection with modern quantificational logic.
	From: Øystein Linnebo (Plural Quantification Exposed [2003], §2)
	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'.

9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta

7783	Bodies, properties, relations, events, numbers, sets and propositions are 'things' if they exist [Lowe]
	Full Idea: Not only material bodies but also properties, relations, events, numbers, sets, and propositions are—if they are acknowledged as existing—to be accounted ‘things’.
	From: E.J. Lowe (Things [1995])
	A reaction: There might be lots of borderline cases here. Is the sky a thing? Is air a thing? How is transparency a thing? Is minus-one a thing? Is an incomplete proposition a thing? Etc.

14. Science / C. Induction / 1. Induction

22200	If you eliminate the impossible, the truth will remain, even if it is weird [Conan Doyle]
	Full Idea: When you have eliminated the impossible, whatever remains, however improbable, must be the truth.
	From: Arthur Conan Doyle (The Sign of Four [1890], Ch. 6)
	A reaction: A beautiful statement, by Sherlock Holmes, of Eliminative Induction. It is obviously not true, of course. Many options may still face you after you have eliminated what is actually impossible.