Combining Philosophers

All the ideas for Douglas Lackey, Francesco Orsi and Leslie H. Tharp

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32 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]
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / b. Cantor's paradox
21554 Sets always exceed terms, so all the sets must exceed all the sets [Lackey]
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / c. Burali-Forti's paradox
21553 It seems that the ordinal number of all the ordinals must be bigger than itself [Lackey]
7. Existence / C. Structure of Existence / 5. Supervenience / a. Nature of supervenience
18680 To avoid misunderstandings supervenience is often expressed negatively: no A-change without B-change [Orsi]
20. Action / C. Motives for Action / 3. Acting on Reason / c. Reasons as causes
18684 Rather than requiring an action, a reason may 'entice' us, or be 'eligible', or 'justify' it [Orsi]
22. Metaethics / B. Value / 1. Nature of Value / a. Nature of value
18666 Value-maker concepts (such as courageous or elegant) simultaneously describe and evaluate [Orsi]
18667 The '-able' concepts (like enviable) say this thing deserves a particular response [Orsi]
18685 Final value is favoured for its own sake, and personal value for someone's sake [Orsi]
18679 Things are only valuable if something makes it valuable, and we can ask for the reason [Orsi]
18682 A complex value is not just the sum of the values of the parts [Orsi]
18683 Trichotomy Thesis: comparable values must be better, worse or the same [Orsi]
18686 The Fitting Attitude view says values are fitting or reasonable, and values are just byproducts [Orsi]
22. Metaethics / B. Value / 1. Nature of Value / c. Objective value
18672 Values from reasons has the 'wrong kind of reason' problem - admiration arising from fear [Orsi]
22. Metaethics / B. Value / 1. Nature of Value / f. Ultimate value
18677 A thing may have final value, which is still derived from other values, or from relations [Orsi]
22. Metaethics / B. Value / 2. Values / a. Normativity
18668 Truths about value entail normative truths about actions or attitudes [Orsi]
18670 The Buck-Passing view of normative values says other properties are reasons for the value [Orsi]
18669 Values can be normative in the Fitting Attitude account, where 'good' means fitting favouring [Orsi]