Combining Philosophers

All the ideas for Herodotus, Richard Taylor and Leslie H. Tharp

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25 ideas

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]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / d. Ethical theory
5078 Kant and Mill both try to explain right and wrong, without a divine lawgiver [Taylor,R]
5067 Morality based on 'forbid', 'permit' and 'require' implies someone who does these things [Taylor,R]
22. Metaethics / C. The Good / 2. Happiness / a. Nature of happiness
5079 Pleasure can have a location, and be momentary, and come and go - but happiness can't [Taylor,R]
22. Metaethics / C. The Good / 2. Happiness / b. Eudaimonia
5068 'Eudaimonia' means 'having a good demon', implying supreme good fortune [Taylor,R]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / b. Basis of virtue
5076 To Greeks it seemed obvious that the virtue of anything is the perfection of its function [Taylor,R]
23. Ethics / D. Deontological Ethics / 1. Deontology
5077 The modern idea of obligation seems to have lost the idea of an obligation 'to' something [Taylor,R]
23. Ethics / D. Deontological Ethics / 2. Duty
5066 If we are made in God's image, pursuit of excellence is replaced by duty to obey God [Taylor,R]
5065 The ethics of duty requires a religious framework [Taylor,R]
29. Religion / D. Religious Issues / 2. Immortality / a. Immortality
1513 The Egyptians were the first to say the soul is immortal and reincarnated [Herodotus]