Combining Texts

All the ideas for 'Mathematical Methods in Philosophy', 'Continuity and Irrational Numbers' and 'Transworld Heir Lines'

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19 ideas

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 / C. Ontology of Logic / 1. Ontology of Logic
11970 Logicians like their entities to exhibit a maximum degree of purity [Kaplan]
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 / 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]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
17611 We want the essence of continuity, by showing its origin in arithmetic [Dedekind]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / i. Reals from cuts
10572 A cut between rational numbers creates and defines an irrational number [Dedekind]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / f. Arithmetic
17612 Arithmetic is just the consequence of counting, which is the successor operation [Dedekind]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / l. Limits
18087 If x changes by less and less, it must approach a limit [Dedekind]
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]
9. Objects / C. Structure of Objects / 7. Substratum
11969 Models nicely separate particulars from their clothing, and logicians often accept that metaphysically [Kaplan]
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]
10. Modality / E. Possible worlds / 3. Transworld Objects / a. Transworld identity
11971 The simplest solution to transworld identification is to adopt bare particulars [Kaplan]
10. Modality / E. Possible worlds / 3. Transworld Objects / c. Counterparts
11973 Unusual people may have no counterparts, or several [Kaplan]
11972 Essence is a transworld heir line, rather than a collection of properties [Kaplan]
19. Language / A. Nature of Meaning / 8. Synonymy
11967 Sentences might have the same sense when logically equivalent - or never have the same sense [Kaplan]