Combining Texts

All the ideas for 'works', 'Foundations of Geometry' and 'Plural Quantification Exposed'

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11 ideas

1. Philosophy / G. Scientific Philosophy / 1. Aims of Science
6782 Realism is the only philosophy of science that doesn't make the success of science a miracle [Putnam]
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]
5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
10781 A 'pure logic' must be ontologically innocent, universal, and without presuppositions [Linnebo]
5. Theory of Logic / G. Quantification / 6. Plural Quantification
10783 Plural quantification depends too heavily on combinatorial and set-theoretic considerations [Linnebo]
10778 Can second-order logic be ontologically first-order, with all the benefits of second-order? [Linnebo]
6. Mathematics / A. Nature of Mathematics / 2. Geometry
13472 Hilbert aimed to eliminate number from geometry [Hilbert, by Hart,WD]
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
9546 Euclid axioms concerns possibilities of construction, but Hilbert's assert the existence of objects [Hilbert, by Chihara]
18742 Hilbert's formalisation revealed implicit congruence axioms in Euclid [Hilbert, by Horsten/Pettigrew]
18217 Hilbert's geometry is interesting because it captures Euclid without using real numbers [Hilbert, by Field,H]
7. Existence / D. Theories of Reality / 4. Anti-realism
22181 Putnam says anti-realism is a bad explanation of accurate predictions [Putnam, by Okasha]
9. Objects / A. Existence of Objects / 1. Physical Objects
10782 The modern concept of an object is rooted in quantificational logic [Linnebo]