Ideas from 'works (all lost)' by Protagoras [441 BCE], by Theme Structure

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6. Mathematics / A. Nature of Mathematics / 5. 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
13. Knowledge Criteria / E. Relativism / 1. Relativism
There is no more purely metaphysical doctrine than Protagorean relativism
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
If my hot wind is your cold wind, then wind is neither hot nor cold, and so not as cold as itself
13. Knowledge Criteria / E. Relativism / 6. Relativism Critique
God is "the measure of all things", more than any man
Protagoras absurdly thought that the knowing or perceiving man is 'the measure of all things'
Relativists think if you poke your eye and see double, there must be two things
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
23. Ethics / B. Contract Ethics / 1. Contractarianism
For Protagoras the only bad behaviour is that which interferes with social harmony
25. Society / C. Social Justice / 5. Right to Punish / b. Retribution for crime
Protagoras seems to have made the huge move of separating punishment from revenge
25. Society / E. State Functions / 4. Education / a. Education principles
He spent public money on education, as it benefits the individual and the state
25. Society / E. State Functions / 4. Education / b. Aims of education
Successful education must go deep into the soul
28. God / E. Attitudes to God / 4. Atheism
He said he didn't know whether there are gods - but this is the same as atheism