Ideas from 'fragments/reports' by Protagoras [441 BCE], by Theme Structure

[found in 'Early Greek Phil VIII: the Sophists, Socrates' by Socrates (ed/tr Laks,A/Most,G) [Harvard Loeb 2016,978-0-674-99709-7]].

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6. Mathematics / A. Nature of Mathematics / 2. Geometry
No perceptible object is truly straight or curved
11. Knowledge Aims / C. Knowing Reality / 2. Phenomenalism
Everything that exists consists in being perceived
13. Knowledge Criteria / D. Scepticism / 1. Scepticism
Protagoras was the first to claim that there are two contradictory arguments about everything [Diog. Laertius]
13. Knowledge Criteria / E. Relativism / 1. Relativism
There is no more purely metaphysical doctrine than Protagorean relativism [Benardete,JA]
13. Knowledge Criteria / E. Relativism / 3. Subjectivism
You can only state the problem of the relative warmth of an object by agreeing on the underlying object [Benardete,JA]
If my hot wind is your cold wind, then wind is neither hot nor cold, and so not as cold as itself [Benardete,JA]
13. Knowledge Criteria / E. Relativism / 6. Relativism Critique
Protagoras absurdly thought that the knowing or perceiving man is 'the measure of all things' [Aristotle]
God is "the measure of all things", more than any man [Plato]
Relativists think if you poke your eye and see double, there must be two things [Aristotle]
22. Metaethics / C. Ethics Foundations / 2. Source of Ethics / j. Ethics by convention
Early sophists thought convention improved nature; later they said nature was diminished by it [Miller,FD]
23. Ethics / B. Contract Ethics / 1. Contractarianism
For Protagoras the only bad behaviour is that which interferes with social harmony [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]
25. Society / C. Social Justice / 6. Right to Punish / b. Retribution for crime
Protagoras seems to have made the huge move of separating punishment from revenge [Vlastos]
25. Society / E. State Functions / 4. Education / a. Education principles
He spent public money on education, as it benefits the individual and the state [Diodorus of Sicily]
25. Society / E. State Functions / 4. Education / b. Aims of education
Successful education must go deep into the soul
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.]