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All the ideas for 'Propositions', 'Which Logic is the Right Logic?' and 'Mathematical Methods in Philosophy'

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30 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
10775 The axiom of choice now seems acceptable and obvious (if it is meaningful) [Tharp]
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
10766 Logic is either for demonstration, or for characterizing structures [Tharp]
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
10767 Elementary logic is complete, but cannot capture mathematics [Tharp]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
10769 Second-order logic isn't provable, but will express set-theory and classic problems [Tharp]
5. Theory of Logic / A. Overview of Logic / 9. Philosophical Logic
18739 Three stages of philosophical logic: syntactic (1905-55), possible worlds (1963-85), widening (1990-) [Horsten/Pettigrew]
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
18741 Logical formalization makes concepts precise, and also shows their interrelation [Horsten/Pettigrew]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / b. Basic connectives
10762 In sentential logic there is a simple proof that all truth functions can be reduced to 'not' and 'and' [Tharp]
5. Theory of Logic / F. Referring in Logic / 1. Naming / b. Names as descriptive
9455 Maybe proper names have the content of fixing a thing's category [Bealer]
5. Theory of Logic / F. Referring in Logic / 2. Descriptions / b. Definite descriptions
9454 The four leading theories of definite descriptions are Frege's, Russell's, Evans's, and Prior's [Bealer]
5. Theory of Logic / G. Quantification / 2. Domain of Quantification
10776 The main quantifiers extend 'and' and 'or' to infinite domains [Tharp]
5. Theory of Logic / G. Quantification / 7. Unorthodox Quantification
10774 There are at least five unorthodox quantifiers that could be used [Tharp]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
18744 Models are sets with functions and relations, and truth built up from the components [Horsten/Pettigrew]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
10777 Skolem mistakenly inferred that Cantor's conceptions were illusory [Tharp]
10773 The Löwenheim-Skolem property is a limitation (e.g. can't say there are uncountably many reals) [Tharp]
5. Theory of Logic / K. Features of Logics / 3. Soundness
10765 Soundness would seem to be an essential requirement of a proof procedure [Tharp]
5. Theory of Logic / K. Features of Logics / 4. Completeness
10763 Completeness and compactness together give axiomatizability [Tharp]
5. Theory of Logic / K. Features of Logics / 5. Incompleteness
10770 If completeness fails there is no algorithm to list the valid formulas [Tharp]
5. Theory of Logic / K. Features of Logics / 6. Compactness
10771 Compactness is important for major theories which have infinitely many axioms [Tharp]
10772 Compactness blocks infinite expansion, and admits non-standard models [Tharp]
5. Theory of Logic / K. Features of Logics / 8. Enumerability
10764 A complete logic has an effective enumeration of the valid formulas [Tharp]
10768 Effective enumeration might be proved but not specified, so it won't guarantee knowledge [Tharp]
7. Existence / A. Nature of Existence / 1. Nature of Existence
18740 If 'exist' doesn't express a property, we can hardly ask for its essence [Horsten/Pettigrew]
10. Modality / E. Possible worlds / 1. Possible Worlds / a. Possible worlds
18745 A Tarskian model can be seen as a possible state of affairs [Horsten/Pettigrew]
18747 The 'spheres model' was added to possible worlds, to cope with counterfactuals [Horsten/Pettigrew]
10. Modality / E. Possible worlds / 1. Possible Worlds / b. Impossible worlds
18748 Epistemic logic introduced impossible worlds [Horsten/Pettigrew]
10. Modality / E. Possible worlds / 1. Possible Worlds / e. Against possible worlds
18746 Possible worlds models contain sets of possible worlds; this is a large metaphysical commitment [Horsten/Pettigrew]
18750 Using possible worlds for knowledge and morality may be a step too far [Horsten/Pettigrew]
19. Language / D. Propositions / 1. Propositions
9453 Sentences saying the same with the same rigid designators may still express different propositions [Bealer]
9452 Propositions might be reduced to functions (worlds to truth values), or ordered sets of properties and relations [Bealer]
19. Language / D. Propositions / 2. Abstract Propositions / a. Propositions as sense
9451 Modal logic and brain science have reaffirmed traditional belief in propositions [Bealer]