Combining Texts

All the ideas for 'Mereology', 'How there could be a private language' and 'Which Logic is the Right Logic?'

expand these ideas     |    start again     |     specify just one area for these texts

28 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
10653 Maybe set theory need not be well-founded [Varzi]
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]
4. Formal Logic / G. Formal Mereology / 1. Mereology
10648 Mereology need not be nominalist, though it is often taken to be so [Varzi]
10655 Are there mereological atoms, and are all objects made of them? [Varzi]
10659 There is something of which everything is part, but no null-thing which is part of everything [Varzi]
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 / 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 / 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 / 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]
9. Objects / C. Structure of Objects / 5. Composition of an Object
10661 'Composition is identity' says multitudes are the reality, loosely composing single things [Varzi]
9. Objects / C. Structure of Objects / 8. Parts of Objects / a. Parts of objects
10647 Parts may or may not be attached, demarcated, arbitrary, material, extended, spatial or temporal [Varzi]
10651 If 'part' is reflexive, then identity is a limit case of parthood [Varzi]
10649 'Part' stands for a reflexive, antisymmetric and transitive relation [Varzi]
10654 The parthood relation will help to define at least seven basic predicates [Varzi]
9. Objects / C. Structure of Objects / 8. Parts of Objects / c. Wholes from parts
10658 Sameness of parts won't guarantee identity if their arrangement matters [Varzi]
10. Modality / D. Knowledge of Modality / 4. Conceivable as Possible / b. Conceivable but impossible
10652 Conceivability may indicate possibility, but literary fantasy does not [Varzi]
18. Thought / B. Mechanics of Thought / 4. Language of Thought
2604 We must have expressive power BEFORE we learn language [Fodor]