Combining Philosophers
Ideas for Anaxarchus, Mark Colyvan and ystein Linnebo
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15 ideas
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 [Linnebo]
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10638
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A pure logic is wholly general, purely formal, and directly known [Linnebo]
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5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
17924
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Excluded middle says P or not-P; bivalence says P is either true or false [Colyvan]
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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 [Linnebo]
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10635
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Second-order quantification and plural quantification are different [Linnebo]
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10641
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Traditionally we eliminate plurals by quantifying over sets [Linnebo]
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10778
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Can second-order logic be ontologically first-order, with all the benefits of second-order? [Linnebo]
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10640
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Instead of complex objects like tables, plurally quantify over mereological atoms tablewise [Linnebo]
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10636
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Plural plurals are unnatural and need a first-level ontology [Linnebo]
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10639
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Plural quantification may allow a monadic second-order theory with first-order ontology [Linnebo]
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5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
23447
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In classical semantics singular terms refer, and quantifiers range over domains [Linnebo]
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5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
17929
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Löwenheim proved his result for a first-order sentence, and Skolem generalised it [Colyvan]
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5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
23443
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The axioms of group theory are not assertions, but a definition of a structure [Linnebo]
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23444
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To investigate axiomatic theories, mathematics needs its own foundational axioms [Linnebo]
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17930
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Axioms are 'categorical' if all of their models are isomorphic [Colyvan]
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