Combining Philosophers

All the ideas for Engelbretsen,G/Sayward,C, Protagoras and Leslie H. Tharp

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41 ideas

4. Formal Logic / A. Syllogistic Logic / 1. Aristotelian Logic
The four 'perfect syllogisms' are called Barbara, Celarent, Darii and Ferio [Engelbretsen/Sayward]
Syllogistic logic has one rule: what is affirmed/denied of wholes is affirmed/denied of their parts [Engelbretsen/Sayward]
4. Formal Logic / A. Syllogistic Logic / 2. Syllogistic Logic
Syllogistic can't handle sentences with singular terms, or relational terms, or compound sentences [Engelbretsen/Sayward]
4. Formal Logic / A. Syllogistic Logic / 3. Term Logic
Term logic uses expression letters and brackets, and '-' for negative terms, and '+' for compound terms [Engelbretsen/Sayward]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
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
Logic is either for demonstration, or for characterizing structures [Tharp]
5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
In modern logic all formal validity can be characterised syntactically [Engelbretsen/Sayward]
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
Elementary logic is complete, but cannot capture mathematics [Tharp]
5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
Classical logic rests on truth and models, where constructivist logic rests on defence and refutation [Engelbretsen/Sayward]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
Second-order logic isn't provable, but will express set-theory and classic problems [Tharp]
5. Theory of Logic / D. Assumptions for Logic / 4. Identity in Logic
Unlike most other signs, = cannot be eliminated [Engelbretsen/Sayward]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / b. Basic connectives
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
The main quantifiers extend 'and' and 'or' to infinite domains [Tharp]
5. Theory of Logic / G. Quantification / 7. Unorthodox Quantification
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
The Löwenheim-Skolem property is a limitation (e.g. can't say there are uncountably many reals) [Tharp]
Skolem mistakenly inferred that Cantor's conceptions were illusory [Tharp]
5. Theory of Logic / K. Features of Logics / 3. Soundness
Soundness would seem to be an essential requirement of a proof procedure [Tharp]
5. Theory of Logic / K. Features of Logics / 4. Completeness
Completeness and compactness together give axiomatizability [Tharp]
5. Theory of Logic / K. Features of Logics / 5. Incompleteness
If completeness fails there is no algorithm to list the valid formulas [Tharp]
Axioms are ω-incomplete if the instances are all derivable, but the universal quantification isn't [Engelbretsen/Sayward]
5. Theory of Logic / K. Features of Logics / 6. Compactness
Compactness is important for major theories which have infinitely many axioms [Tharp]
Compactness blocks infinite expansion, and admits non-standard models [Tharp]
5. Theory of Logic / K. Features of Logics / 8. Enumerability
A complete logic has an effective enumeration of the valid formulas [Tharp]
Effective enumeration might be proved but not specified, so it won't guarantee knowledge [Tharp]
6. Mathematics / A. Nature of Mathematics / 2. Geometry
No perceptible object is truly straight or curved [Protagoras]
11. Knowledge Aims / C. Knowing Reality / 2. Phenomenalism
Everything that exists consists in being perceived [Protagoras]
13. Knowledge Criteria / D. Scepticism / 1. Scepticism
Protagoras was the first to claim that there are two contradictory arguments about everything [Protagoras, by Diog. Laertius]
13. Knowledge Criteria / E. Relativism / 1. Relativism
Man is the measure of all things - of things that are, and of things that are not [Protagoras]
There is no more purely metaphysical doctrine than Protagorean relativism [Benardete,JA on Protagoras]
13. Knowledge Criteria / E. Relativism / 3. Subjectivism
If my hot wind is your cold wind, then wind is neither hot nor cold, and so not as cold as itself [Benardete,JA on Protagoras]
You can only state the problem of the relative warmth of an object by agreeing on the underlying object [Benardete,JA on Protagoras]
13. Knowledge Criteria / E. Relativism / 6. Relativism Critique
God is "the measure of all things", more than any man [Plato on Protagoras]
Protagoras absurdly thought that the knowing or perceiving man is 'the measure of all things' [Aristotle on Protagoras]
Relativists think if you poke your eye and see double, there must be two things [Aristotle on Protagoras]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / j. Ethics by convention
Early sophists thought convention improved nature; later they said nature was diminished by it [Protagoras, by Miller,FD]
23. Ethics / B. Contract Ethics / 1. Contractarianism
For Protagoras the only bad behaviour is that which interferes with social harmony [Protagoras, by Roochnik]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / d. Teaching virtue
Protagoras contradicts himself by saying virtue is teachable, but then that it is not knowledge [Plato on Protagoras]
25. Social Practice / D. Justice / 3. Punishment / b. Retribution for crime
Protagoras seems to have made the huge move of separating punishment from revenge [Protagoras, by Vlastos]
25. Social Practice / E. Policies / 5. Education / a. Aims of education
Successful education must go deep into the soul [Protagoras]
25. Social Practice / E. Policies / 5. Education / b. Education principles
He spent public money on education, as it benefits the individual and the state [Protagoras, by Diodorus of Sicily]
28. God / C. Attitudes to God / 5. Atheism
He said he didn't know whether there are gods - but this is the same as atheism [Diogenes of Oen. on Protagoras]