Combining Philosophers

All the ideas for Protagoras, Marcus Rossberg and Richard Boyd

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29 ideas

5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
10757 Henkin semantics has a second domain of predicates and relations (in upper case) [Rossberg]
10751 Second-order logic needs the sets, and its consequence has epistemological problems [Rossberg]
10759 There are at least seven possible systems of semantics for second-order logic [Rossberg]
5. Theory of Logic / B. Logical Consequence / 2. Types of Consequence
10753 Logical consequence is intuitively semantic, and captured by model theory [Rossberg]
5. Theory of Logic / B. Logical Consequence / 3. Deductive Consequence |-
10752 Γ |- S says S can be deduced from Γ; Γ |= S says a good model for Γ makes S true [Rossberg]
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
10754 In proof-theory, logical form is shown by the logical constants [Rossberg]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
10756 A model is a domain, and an interpretation assigning objects, predicates, relations etc. [Rossberg]
5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms
10758 If models of a mathematical theory are all isomorphic, it is 'categorical', with essentially one model [Rossberg]
5. Theory of Logic / K. Features of Logics / 4. Completeness
10761 Completeness can always be achieved by cunning model-design [Rossberg]
5. Theory of Logic / K. Features of Logics / 5. Incompleteness
10755 A deductive system is only incomplete with respect to a formal semantics [Rossberg]
6. Mathematics / A. Nature of Mathematics / 2. Geometry
1553 No perceptible object is truly straight or curved [Protagoras]
11. Knowledge Aims / C. Knowing Reality / 2. Phenomenalism
1549 Everything that exists consists in being perceived [Protagoras]
13. Knowledge Criteria / D. Scepticism / 1. Scepticism
1545 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
1547 Man is the measure of all things - of things that are, and of things that are not [Protagoras]
3305 There is no more purely metaphysical doctrine than Protagorean relativism [Benardete,JA on Protagoras]
13. Knowledge Criteria / E. Relativism / 3. Subjectivism
3313 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]
3317 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
247 God is "the measure of all things", more than any man [Plato on Protagoras]
606 Protagoras absurdly thought that the knowing or perceiving man is 'the measure of all things' [Aristotle on Protagoras]
612 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
6016 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
1580 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
205 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
1659 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
532 Successful education must go deep into the soul [Protagoras]
25. Social Practice / E. Policies / 5. Education / b. Education principles
1552 He spent public money on education, as it benefits the individual and the state [Protagoras, by Diodorus of Sicily]
26. Natural Theory / B. Natural Kinds / 4. Source of Kinds
15150 The properties of an electron can't be explained just as 'clustering' [Chakravartty on Boyd]
15149 Properties cluster together, either because of intrinsic relations, or because of an underlying process [Boyd, by Chakravartty]
28. God / C. Attitudes to God / 5. Atheism
1551 He said he didn't know whether there are gods - but this is the same as atheism [Diogenes of Oen. on Protagoras]