Combining Texts
Ideas for
'Defending the Axioms', 'The Evolution of Logic' and 'On the Introduction of Transfinite Numbers'
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12 ideas
5. Theory of Logic / C. Ontology of Logic / 3. If-Thenism
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17620
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Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy]
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5. Theory of Logic / G. Quantification / 3. Objectual Quantification
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13506
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The universal quantifier can't really mean 'all', because there is no universal set [Hart,WD]
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5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
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13512
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Modern model theory begins with the proof of Los's Conjecture in 1962 [Hart,WD]
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13505
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Model theory studies how set theory can model sets of sentences [Hart,WD]
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13511
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Model theory is mostly confined to first-order theories [Hart,WD]
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13513
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Models are ways the world might be from a first-order point of view [Hart,WD]
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5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
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17605
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Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy]
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17625
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If two mathematical themes coincide, that suggest a single deep truth [Maddy]
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5. Theory of Logic / K. Features of Logics / 6. Compactness
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13496
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First-order logic is 'compact': consequences of a set are consequences of a finite subset [Hart,WD]
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5. Theory of Logic / L. Paradox / 4. Paradoxes in Logic / c. Berry's paradox
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13484
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Berry's Paradox: we succeed in referring to a number, with a term which says we can't do that [Hart,WD]
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5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / c. Burali-Forti's paradox
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13482
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The Burali-Forti paradox is a crisis for Cantor's ordinals [Hart,WD]
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5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
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13507
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The machinery used to solve the Liar can be rejigged to produce a new Liar [Hart,WD]
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