Combining Philosophers

All the ideas for Engelbretsen,G/Sayward,C, Alan Musgrave and Cian Dorr

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19 ideas

4. Formal Logic / A. Syllogistic Logic / 1. Aristotelian Logic
13913 The four 'perfect syllogisms' are called Barbara, Celarent, Darii and Ferio [Engelbretsen/Sayward]
13914 Syllogistic logic has one rule: what is affirmed/denied of wholes is affirmed/denied of their parts [Engelbretsen/Sayward]
4. Formal Logic / A. Syllogistic Logic / 2. Syllogistic Logic
13915 Syllogistic can't handle sentences with singular terms, or relational terms, or compound sentences [Engelbretsen/Sayward]
4. Formal Logic / A. Syllogistic Logic / 3. Term Logic
13916 Term logic uses expression letters and brackets, and '-' for negative terms, and '+' for compound terms [Engelbretsen/Sayward]
5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
13850 In modern logic all formal validity can be characterised syntactically [Engelbretsen/Sayward]
5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
13849 Classical logic rests on truth and models, where constructivist logic rests on defence and refutation [Engelbretsen/Sayward]
5. Theory of Logic / C. Ontology of Logic / 3. If-Thenism
10065 Perhaps If-thenism survives in mathematics if we stick to first-order logic [Musgrave]
10061 The If-thenist view only seems to work for the axiomatised portions of mathematics [Musgrave]
5. Theory of Logic / D. Assumptions for Logic / 4. Identity in Logic
13851 Unlike most other signs, = cannot be eliminated [Engelbretsen/Sayward]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
10049 Logical truths may contain non-logical notions, as in 'all men are men' [Musgrave]
10050 A statement is logically true if it comes out true in all interpretations in all (non-empty) domains [Musgrave]
5. Theory of Logic / K. Features of Logics / 5. Incompleteness
13852 Axioms are ω-incomplete if the instances are all derivable, but the universal quantification isn't [Engelbretsen/Sayward]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
10058 No two numbers having the same successor relies on the Axiom of Infinity [Musgrave]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
10063 Formalism is a bulwark of logical positivism [Musgrave]
10062 Formalism seems to exclude all creative, growing mathematics [Musgrave]
8. Modes of Existence / E. Nominalism / 1. Nominalism / c. Nominalism about abstracta
14596 Call 'nominalism' the denial of numbers, properties, relations and sets [Dorr]
8. Modes of Existence / E. Nominalism / 5. Class Nominalism
14597 Natural Class Nominalism says there are primitive classes of things resembling in one respect [Dorr]
10. Modality / A. Necessity / 11. Denial of Necessity
14598 Abstracta imply non-logical brute necessities, so only nominalists can deny such things [Dorr]
19. Language / A. Nature of Meaning / 5. Meaning as Verification
10060 Logical positivists adopted an If-thenist version of logicism about numbers [Musgrave]