Combining Texts

All the ideas for 'fragments/reports', 'Which Logic is the Right Logic?' and 'A Priori'

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

31 ideas

1. Philosophy / E. Nature of Metaphysics / 7. Against Metaphysics
17713 After 1903, Husserl avoids metaphysical commitments [Mares]
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 / 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
10773 The Löwenheim-Skolem property is a limitation (e.g. can't say there are uncountably many reals) [Tharp]
10777 Skolem mistakenly inferred that Cantor's conceptions were illusory [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]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
17715 The truth of the axioms doesn't matter for pure mathematics, but it does for applied [Mares]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
17716 Mathematics is relations between properties we abstract from experience [Mares]
10. Modality / D. Knowledge of Modality / 2. A Priori Contingent
17703 Light in straight lines is contingent a priori; stipulated as straight, because they happen to be so [Mares]
12. Knowledge Sources / A. A Priori Knowledge / 6. A Priori from Reason
17714 Aristotelians dislike the idea of a priori judgements from pure reason [Mares]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
17705 Empiricists say rationalists mistake imaginative powers for modal insights [Mares]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / a. Coherence as justification
17700 The most popular view is that coherent beliefs explain one another [Mares]
14. Science / B. Scientific Theories / 3. Instrumentalism
17704 Operationalism defines concepts by our ways of measuring them [Mares]
18. Thought / D. Concepts / 2. Origin of Concepts / b. Empirical concepts
17710 Aristotelian justification uses concepts abstracted from experience [Mares]
18. Thought / D. Concepts / 4. Structure of Concepts / c. Classical concepts
17706 The essence of a concept is either its definition or its conceptual relations? [Mares]
19. Language / C. Assigning Meanings / 8. Possible Worlds Semantics
17701 Possible worlds semantics has a nice compositional account of modal statements [Mares]
19. Language / D. Propositions / 3. Concrete Propositions
17702 Unstructured propositions are sets of possible worlds; structured ones have components [Mares]
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
1748 Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius]
27. Natural Reality / C. Space / 3. Points in Space
17708 Maybe space has points, but processes always need regions with a size [Mares]
27. Natural Reality / G. Biology / 3. Evolution
5989 Archelaus said life began in a primeval slime [Archelaus, by Schofield]