Combining Texts

All the ideas for 'Reason, Emotions and Good Life', 'The Origin of Forms and Qualities' and 'Which Logic is the Right Logic?'

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27 ideas

2. Reason / D. Definition / 4. Real Definition
15957 Essential definitions show the differences that discriminate things, and make them what they are [Boyle]
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]
8. Modes of Existence / C. Powers and Dispositions / 1. Powers
15965 Boyle attacked a contemporary belief that powers were occult things [Boyle, by Alexander,P]
8. Modes of Existence / C. Powers and Dispositions / 6. Dispositions / a. Dispositions
16735 In the 17th century, 'disposition' usually just means the spatial arrangement of parts [Boyle, by Pasnau]
9. Objects / C. Structure of Objects / 2. Hylomorphism / a. Hylomorphism
16034 Form is not a separate substance, but just the manner, modification or 'stamp' of matter [Boyle]
15953 To cite a substantial form tells us what produced the effect, but not how it did it [Boyle]
12. Knowledge Sources / B. Perception / 2. Qualities in Perception / d. Secondary qualities
15962 Boyle's term 'texture' is not something you feel, but is unobservable structures of particles [Boyle, by Alexander,P]
15964 Boyle's secondary qualities are not illusory, or 'in the mind' [Boyle, by Alexander,P]
14. Science / D. Explanation / 2. Types of Explanation / i. Explanations by mechanism
15960 Explanation is deducing a phenomenon from some nature better known to us [Boyle]
20. Action / C. Motives for Action / 3. Acting on Reason / a. Practical reason
4316 Either all action is rational, or reason dominates, or reason is only concerned with means [Cottingham]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / g. Atomism
15952 The corpuscles just have shape, size and motion, which explains things without 'sympathies' or 'forces' [Boyle, by Alexander,P]
26. Natural Theory / A. Speculations on Nature / 7. Later Matter Theories / b. Corpuscles
15972 The corpuscular theory allows motion, but does not include forces between the particles [Boyle, by Alexander,P]