Combining Texts

All the ideas for 'The Advancement of Learning', 'Introduction to German Philosophy' and 'Which Logic is the Right Logic?'

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30 ideas

1. Philosophy / E. Nature of Metaphysics / 1. Nature of Metaphysics
12124 Metaphysics is the best knowledge, because it is the simplest [Bacon]
1. Philosophy / E. Nature of Metaphysics / 4. Metaphysics as Science
12123 Natural history supports physical knowledge, which supports metaphysical knowledge [Bacon]
1. Philosophy / E. Nature of Metaphysics / 5. Metaphysics beyond Science
12119 Physics studies transitory matter; metaphysics what is abstracted and necessary [Bacon]
12120 Physics is of material and efficient causes, metaphysics of formal and final causes [Bacon]
2. Reason / A. Nature of Reason / 1. On Reason
20955 Art can make reason more all-inclusive, by articulating what seemed inexpressible [Bowie]
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
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]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / d. Absolute idealism
20950 German Idealism says our thinking and nature have the same rational structure [Bowie]
12. Knowledge Sources / D. Empiricism / 1. Empiricism
12121 We don't assume there is no land, because we can only see sea [Bacon]
14. Science / A. Basis of Science / 3. Experiment
12117 Science moves up and down between inventions of causes, and experiments [Bacon]
14. Science / B. Scientific Theories / 5. Commensurability
12127 Many different theories will fit the observed facts [Bacon]
15. Nature of Minds / C. Capacities of Minds / 5. Generalisation by mind
12126 People love (unfortunately) extreme generality, rather than particular knowledge [Bacon]
16. Persons / E. Rejecting the Self / 2. Self as Social Construct
20942 Nazis think race predetermines the self [Bowie]
19. Language / F. Communication / 1. Rhetoric
20946 Rhetoric is built into language, so it cannot be stripped from philosophy [Bowie]
26. Natural Theory / A. Speculations on Nature / 2. Natural Purpose / c. Purpose denied
12125 Teleological accounts are fine in metaphysics, but they stop us from searching for the causes [Bacon]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / a. Scientific essentialism
12118 Essences are part of first philosophy, but as part of nature, not part of logic [Bacon]