Combining Texts

All the ideas for 'fragments/reports', 'Sources of the Self' and 'Which Logic is the Right Logic?'

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27 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]
16. Persons / A. Concept of a Person / 4. Persons as Agents
4020 The modern self has disengaged reason, self-exploration, and personal commitment [Taylor,C]
16. Persons / B. Nature of the Self / 2. Ethical Self
4002 My aim is to map the connections between our sense of self and our moral understanding [Taylor,C]
16. Persons / E. Rejecting the Self / 3. Narrative Self
4006 I can only be aware of myself as a person who changes by means of my personal history [Taylor,C]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / b. Defining ethics
4003 Selfhood and moral values are inextricably intertwined [Taylor,C]
23. Ethics / C. Virtue Theory / 3. Virtues / e. Honour
4021 Willingness to risk life was the constitutive quality of the man of honour [Taylor,C]
23. Ethics / C. Virtue Theory / 3. Virtues / h. Respect
4005 To have respect for people, you must feel their claims, or their injustices, or hold them in awe [Taylor,C]
23. Ethics / D. Deontological Ethics / 4. Categorical Imperative
4004 Consistency presupposes intrinsic description [Taylor,C]
23. Ethics / E. Utilitarianism / 1. Utilitarianism
4010 In later utilitarianism the modern stress on freedom leads to the rejection of paternalism [Taylor,C]
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 / G. Biology / 3. Evolution
5989 Archelaus said life began in a primeval slime [Archelaus, by Schofield]
28. God / A. Divine Nature / 6. Divine Morality / d. God decrees morality
4009 Nominalists defended the sovereignty of God against the idea of natural existing good and evil [Taylor,C]