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44 ideas

6. Mathematics / A. Nature of Mathematics / 2. Geometry
No perceptible object is truly straight or curved [Protagoras]
     Full Idea: No perceptible object is geometrically straight or curved; after all, a circle does not touch a ruler at a point, as Protagoras used to say, in arguing against the geometers.
     From: Protagoras (fragments/reports [c.441 BCE], B07), quoted by Aristotle - Metaphysics 998a1
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / k. Infinitesimals
Things get smaller without end [Anaxagoras]
     Full Idea: Of the small there is no smallest, but always a smaller.
     From: Anaxagoras (fragments/reports [c.460 BCE], B03), quoted by Gregory Vlastos - The Physical Theory of Anaxagoras II
     A reaction: Anaxagoras seems to be speaking of the physical world (and probably writing prior to the emergence of atomism, which could have been a rebellion against he current idea).
7. Existence / A. Nature of Existence / 1. Nature of Existence
Nothing is created or destroyed; there is only mixing and separation [Anaxagoras]
     Full Idea: No thing comes into being or passes away, but it is mixed together or separated from existing things. Thus it would be correct if coming into being was called 'mixing', and passing away 'separation-off''.
     From: Anaxagoras (fragments/reports [c.460 BCE], B17), quoted by Simplicius - On Aristotle's 'Physics' 163.20
7. Existence / A. Nature of Existence / 3. Being / f. Primary being
Anaxagoras's concept of supreme Mind has a simple First and a multiple One [Anaxagoras, by Plotinus]
     Full Idea: Anaxagoras, in his assertion of a Mind pure and unmixed, affirms a simplex First and a sundered One, though writing long ago he failed in precision.
     From: report of Anaxagoras (fragments/reports [c.460 BCE]) by Plotinus - The Enneads 5.1.09
     A reaction: The crunch question is whether the supreme One or Mind is part of Being, or is above and beyond Being. Plotinus claims that Anaxagoras was on his side (with Plato, against Parmenides).
7. Existence / C. Structure of Existence / 6. Fundamentals / a. Fundamental reality
Basic is the potentially perceptible, then comes the contrary qualities, and finally the 'elements' [Anaxagoras]
     Full Idea: We must recognise three 'originative sources': first that which is potentially perceptible body, secondly the contrarities (e.g hot and cold), and thirdly Fire, Water, and the like. Only thirdly, however, for these bodies change into one another.
     From: Anaxagoras (fragments/reports [c.460 BCE]), quoted by Aristotle - The History of Animals 529a34
     A reaction: The 'potentially perceptible' seems to be matter. The surprise here is that the contraries are more basic than the elements, rather than being properties of them. Reality is modes of matter, it seems.
11. Knowledge Aims / C. Knowing Reality / 2. Phenomenalism
Everything that exists consists in being perceived [Protagoras]
     Full Idea: Everything that exists consists in being perceived.
     From: Protagoras (fragments/reports [c.441 BCE]), quoted by Didymus the Blind - Commentary on the Psalms (frags)
     A reaction: A striking anticipation of Berkeley's "esse est percipi" (to be is to be perceived).
12. Knowledge Sources / B. Perception / 1. Perception
Snow is not white, and doesn't even appear white, because it is made of black water [Anaxagoras, by Cicero]
     Full Idea: Anaxagoras not only denied that snow was white, but because he knew that the water from which it was composed was black, even denied that it appeared white to himself.
     From: report of Anaxagoras (fragments/reports [c.460 BCE]) by M. Tullius Cicero - Academica II.100
     A reaction: Not ridiculous. Can you deny that red and yellow balls look orange from a distance? A failure of discrimination on your part. It sounds okay to say 'what I am really perceiving is red and yellow'. [see 'Anaxagoras' poem by D.H.Lawrence!]
12. Knowledge Sources / D. Empiricism / 5. Empiricism Critique
The senses are too feeble to determine the truth [Anaxagoras]
     Full Idea: Owing to the feebleness of the sense, we are not able to determine the truth.
     From: Anaxagoras (fragments/reports [c.460 BCE], B21), quoted by Patricia Curd - Anaxagoras 5.1
     A reaction: Anaxagoras offers a corresponding elevation of the power of mind (Idea 13256), so I now realise that he is, along with Pythagoras and Parmenides, one of the fathers of rationalism in philosophy. They probably overrate reason.
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]
     Full Idea: Protagoras was the first to claim that there are two contradictory arguments about everything.
     From: report of Protagoras (fragments/reports [c.441 BCE], A01) by Diogenes Laertius - Lives of Eminent Philosophers 09.51
13. Knowledge Criteria / D. Scepticism / 2. Types of Scepticism
We reveal unreliability in the senses when we cannot discriminate a slow change of colour [Anaxagoras, by Sext.Empiricus]
     Full Idea: Our lack of sureness in the senses is shown if we take two colours, back and white, and pour one into the other drop by drop, we are unable to distinguish the gradual alterations although they subsist as actual facts.
     From: report of Anaxagoras (fragments/reports [c.460 BCE]) by Sextus Empiricus - Against the Logicians (two books) I.090
     A reaction: [Sextus calls Anaxagoras 'the greatest of the physicists'] I'm not sure what this proves. People with bad eyesight can distinguish very little, but that doesn't prove scepticism. And there are things too small for anyone to see.
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]
     Full Idea: He began one of his books as follows: 'Man is the measure of all things - of the things that are, that they are, and of the things that are not, that they are not'.
     From: Protagoras (fragments/reports [c.441 BCE], B01), quoted by Diogenes Laertius - Lives of Eminent Philosophers 09.51
There is no more purely metaphysical doctrine than Protagorean relativism [Benardete,JA on Protagoras]
     Full Idea: No purer metaphysical doctrine can possibly be found than the Protagorean thesis that to be (anything at all) is to be relative ( to something or other).
     From: comment on Protagoras (fragments/reports [c.441 BCE]) by José A. Benardete - Metaphysics: the logical approach Ch.3
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]
     Full Idea: Because the wind is cold to me but not you, Protagoras takes it to in itself neither cold nor not-cold. Accordingly, I very much doubt that he can allow the wind to be exactly as cold as itself.
     From: comment on Protagoras (fragments/reports [c.441 BCE]) by José A. Benardete - Metaphysics: the logical approach Ch.8
You can only state the problem of the relative warmth of an object by agreeing on the underlying object [Benardete,JA on Protagoras]
     Full Idea: Only if the thing that is cold to me is precisely identical with the thing that is not cold to you can Protagoras launch his argument, but then it is seen to be the thing in itself that exists absolutely speaking.
     From: comment on Protagoras (fragments/reports [c.441 BCE]) by José A. Benardete - Metaphysics: the logical approach Ch.8
13. Knowledge Criteria / E. Relativism / 6. Relativism Critique
God is "the measure of all things", more than any man [Plato on Protagoras]
     Full Idea: In our view it is God who is pre-eminently the "measure of all things", much more so than any "man", as they say.
     From: comment on Protagoras (fragments/reports [c.441 BCE]) by Plato - The Laws 716c
Protagoras absurdly thought that the knowing or perceiving man is 'the measure of all things' [Aristotle on Protagoras]
     Full Idea: When Protagoras quipped that man is the measure of all things, he had in mind, of course, the knowing or perceiving man. The grounds are that they have perception/knowledge, and these are said to be the measures of objects. Utter nonsense!
     From: comment on Protagoras (fragments/reports [c.441 BCE]) by Aristotle - Metaphysics 1053b
Relativists think if you poke your eye and see double, there must be two things [Aristotle on Protagoras]
     Full Idea: In fact there is no difference between Protagoreanism and saying this: if you stick your finger under your eyes and make single things seem two, then they are two, just because they seem to be two.
     From: comment on Protagoras (fragments/reports [c.441 BCE]) by Aristotle - Metaphysics 1063a06
15. Nature of Minds / A. Nature of Mind / 1. Mind / a. Mind
Nous is unlimited, self-ruling and pure; it is the finest thing, with great discernment and strength [Anaxagoras]
     Full Idea: Nous is unlimited and self-ruling and has been mixed with no thing, but is alone itself by itself. ...For it is the finest of all things and the purest, and indeed it maintains all discernment about everything and has the greatest strength.
     From: Anaxagoras (fragments/reports [c.460 BCE], B12), quoted by Patricia Curd - Anaxagoras 3.3
     A reaction: Anaxagoras seems to have been a pioneer in elevating the status of the mind, which is a prop to the rationalist view, and encourages dualism. More naturalistic accounts are, in my view, much healthier.
15. Nature of Minds / A. Nature of Mind / 1. Mind / c. Features of mind
Mind is self-ruling, pure, ordering and ubiquitous [Anaxagoras, by Plato]
     Full Idea: Anaxagoras says that mind is self-ruling, mixes with nothing else, orders the things that are, and travels through everything.
     From: report of Anaxagoras (fragments/reports [c.460 BCE]) by Plato - Cratylus 413c
     A reaction: This elevation of the mind in the natural scheme of things by Anaxagoras looks increasingly significant in western culture to me. Without this line of thought, Descartes and Kant are inconceivable.
16. Persons / F. Free Will / 1. Nature of Free Will
Anaxagoras says mind remains pure, and so is not affected by what it changes [Anaxagoras, by Aristotle]
     Full Idea: Anaxagoras says that intellect (which is a cause of change) is not affected by or mixed in with anything else; for this is the only way in which it can cause change, while being itself changeless, and control things without mixing with them.
     From: report of Anaxagoras (fragments/reports [c.460 BCE]) by Aristotle - Physics 256b24
     A reaction: I suggest that this is the germ of the original concept of freewill - of the mind as somehow outside the causal processes of the world, so that it can initiate change without itself being affected by other causes. Aristotle says he's right; I disagree.
19. Language / F. Communication / 3. Denial
Contradiction is impossible, since only one side of the argument refers to the true facts [Prodicus, by Didymus the Blind]
     Full Idea: Prodicus insists that contradiction is impossible, since if two people are contradicting each other, they cannot both be speaking of the same fact. Only the one who is speaking the truth is speaking of facts as they are; the other does not speak facts.
     From: report of Prodicus (fragments/reports [c.423 BCE]) by Didymus the Blind - Commentary on Ecclesiastes (frags)
     A reaction: cf. Kant's 100 thalers example
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]
     Full Idea: Protagoras and Hippias evidently believed that convention was an improvement on nature, whereas later sophists such as Antiphon, Thrasymachus and Callicles seemed to contend that conventional morality was undermined because it was 'against nature'.
     From: report of Protagoras (fragments/reports [c.441 BCE]) by Fred D. Miller jr - Classical Political Thought
     A reaction: This gets to the heart of a much more interesting aspect of the nomos-physis (convention-nature) debate, rather than just a slanging match between relativists and the rest. The debate still goes on, over issues about the free market and intervention.
23. Ethics / B. Contract Ethics / 1. Contractarianism
For Protagoras the only bad behaviour is that which interferes with social harmony [Protagoras, by Roochnik]
     Full Idea: For Protagoras the only constraint on human behaviour is that it not interfere with social harmony, the essential condition for human survival.
     From: report of Protagoras (fragments/reports [c.441 BCE]) by David Roochnik - The Tragedy of Reason p.63
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]
     Full Idea: Protagoras claimed that virtue was teachable, but now tries to show it is not knowledge, which makes it less likely to be teachable.
     From: comment on Protagoras (fragments/reports [c.441 BCE]) by Plato - Protagoras 361b
23. Ethics / C. Virtue Theory / 3. Virtues / g. Contemplation
Anaxagoras said a person would choose to be born to contemplate the ordered heavens [Anaxagoras]
     Full Idea: When Anaxagoras was asked what it was for which a person would choose to be born rather than not, he said it would be to apprehend the heavens and the order in the whole universe.
     From: Anaxagoras (fragments/reports [c.460 BCE], 1216), quoted by Aristotle - Eudemian Ethics 8 'Finality'
     A reaction: [Anaxagoras, quoted by Aristotle, quoted by Korsgaard, quoted by me, and then quoted by you, perhaps]
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]
     Full Idea: The distinction of punishment from revenge must be regarded as one of the most momentous of the conceptual discoveries ever made by humanity in the course of its slow, tortuous, precarious, emergence from barbaric tribalism. Protagoras originated it.
     From: report of Protagoras (fragments/reports [c.441 BCE]) by Gregory Vlastos - Socrates: Ironist and Moral Philosopher p.187
25. Social Practice / E. Policies / 5. Education / a. Aims of education
Successful education must go deep into the soul [Protagoras]
     Full Idea: Education does not take root in the soul unless one goes deep.
     From: Protagoras (fragments/reports [c.441 BCE], B11), quoted by Plutarch - On Practice 178.25
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]
     Full Idea: He used legislation to improve the condition of illiterate people, on the grounds that they lack one of life's great goods, and thought literacy should be a matter of public concern and expense.
     From: report of Protagoras (fragments/reports [c.441 BCE]) by Diodorus of Sicily - Universal History 12.13.3.3
26. Natural Theory / A. Speculations on Nature / 2. Natural Purpose / a. Final purpose
For Anaxagoras the Good Mind has no opposite, and causes all movement, for a higher reason [Anaxagoras, by Aristotle]
     Full Idea: Anaxagoras says the good is a principle as the source of movement, in the form of Mind. However it does it for the sake of something else, which is a further factor. And he allows no opposite to the good Mind.
     From: report of Anaxagoras (fragments/reports [c.460 BCE]) by Aristotle - Metaphysics 1075b
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / a. Greek matter
Mind creates the world from a mixture of pure substances [Anaxagoras, by ]
     Full Idea: Anaxagoras assumed that Mind, which is God, is the efficient principle, and the multi-mixture of homoeomeries is the material principle.
     From: report of Anaxagoras (fragments/reports [c.460 BCE]) by - I.6
     A reaction: The choice of homoeomeries as basic is a good one. They are much better candidates than materials which are made of parts of a quite different kind, where the parts are a better candidate than the whole.
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / c. Ultimate substances
Anaxagoras said that the number of principles was infinite [Anaxagoras, by Aristotle]
     Full Idea: Anaxagoras said that the number of principles was infinite.
     From: report of Anaxagoras (fragments/reports [c.460 BCE]) by Aristotle - Metaphysics 984a
The ultimate constituents of reality are the homoeomeries [Anaxagoras, by Vlastos]
     Full Idea: Anaxagoras contrasts with other thinkers in the formula that his 'elements' were not the air of Anaximenes or the fire of Heraclitus or the roots of Empedocles or the atoms of Leucippus, but the infinite variety of homoiomereia.
     From: report of Anaxagoras (fragments/reports [c.460 BCE]) by Gregory Vlastos - The Physical Theory of Anaxagoras III
     A reaction: Not sure about the 'roots' of Empedocles. Anaxagoras is particularly thinking of the basic stuffs that make up the body, such as hair, bone and blood. It is plausible to reduce everything to stuffs that seem to have no further structure.
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / f. Ancient elements
Anaxagoreans regard the homoeomeries as elements, which compose earth, air, fire and water [Anaxagoras, by Aristotle]
     Full Idea: The followers of Anaxagoras regard the 'homoeomeries' as 'simple' and elements, whilst they affirm that Earth, Fire, Water and Air are composite; for each of these is (according to them) a 'common seminary' of all the homoeomeries.
     From: report of Anaxagoras (fragments/reports [c.460 BCE]) by Aristotle - Coming-to-be and Passing-away (Gen/Corr) 314a28
     A reaction: Compare Idea 13207. Aristotle is amused that the followers of Empedocles and of Anaxagoras have precisely opposite views on this subject.
26. Natural Theory / C. Causation / 1. Causation
Anaxagoras says mind produces order and causes everything [Anaxagoras, by Plato]
     Full Idea: Anaxagoras asserted that it is mind that produces order and is the cause of everything.
     From: report of Anaxagoras (fragments/reports [c.460 BCE]) by Plato - Phaedo 097d
27. Natural Reality / G. Biology / 1. Biology
Germs contain microscopic organs, which become visible as they grow [Anaxagoras]
     Full Idea: In the germ there are hair, nails, arteries, sinews, bones, which are not manifest because of the smallness of their parts, but become distinct little by little as they grow. For how could hair come from not-hair, or flesh from non-flesh.
     From: Anaxagoras (fragments/reports [c.460 BCE], B10), quoted by Gregory Vlastos - The Physical Theory of Anaxagoras I
     A reaction: Compare Aristotle's apparent view that the physical world has no microscopic structure, and Democritus's view that hair can come from not-hair by the organisation of atoms. Is this the first suggestion that we need to know what is microscopic?
28. God / A. Divine Nature / 1. God
When things were unified, Mind set them in order [Anaxagoras]
     Full Idea: All things were together, and Mind came and set them in order.
     From: Anaxagoras (fragments/reports [c.460 BCE])
     A reaction: This is presumably the source for the passionate belief of Plato in the importance of order. Existence seems like chaos, with order residing beneath it, but we can wonder whether if we go even deeper it is chaos again.
Anaxagoras was the first to say that the universe is directed by an intelligence [Anaxagoras, by Cicero]
     Full Idea: Anaxagoras, pupil of Anaximenes, was the first to maintain that the form and motion of the universe was determined and directed by the power and purpose of an infinite intelligence.
     From: report of Anaxagoras (fragments/reports [c.460 BCE]) by M. Tullius Cicero - On the Nature of the Gods ('De natura deorum') I.26
28. God / B. Proving God / 3. Proofs of Evidence / b. Teleological Proof
Past, present and future, and the movements of the heavens, were arranged by Mind [Anaxagoras]
     Full Idea: Whatever was then in existence which is not now, and all things that now exist, and whatever shall exist - all were arranged by Mind, as also the revolution followed now by the stars, the sun and the moon.
     From: Anaxagoras (fragments/reports [c.460 BCE], B12), quoted by Simplicius - On Aristotle's 'Physics' 164.24
28. God / B. Proving God / 3. Proofs of Evidence / c. Teleological Proof critique
People used to think anything helpful to life was a god, as the Egyptians think the Nile a god [Prodicus]
     Full Idea: In the old days people regarded the sun, the moon, rivers, springs, and everything else which is helpful for life as gods, because we are helped by them, just as the Egyptians regard the Nile as a god.
     From: Prodicus (fragments/reports [c.423 BCE], B05), quoted by Sextus Empiricus - Against the Professors (six books) 9.18
28. God / C. Attitudes to God / 5. Atheism
Anaxagoras was the first recorded atheist [Anaxagoras, by Watson]
     Full Idea: Anaxagoras was the first recorded atheist.
     From: report of Anaxagoras (fragments/reports [c.460 BCE]) by Peter Watson - Ideas Ch.25
     A reaction: He was a very lively character, right in the middle of the Athenian golden age.
He denied the existence of the gods, saying they are just exaltations of things useful for life [Prodicus]
     Full Idea: He says that the gods worshipped by men neither exist nor have knowledge, but that the ancients exalted crops and everything else which is useful for life.
     From: Prodicus (fragments/reports [c.423 BCE]), quoted by Anon (Herc) - fragments 1428 19.12
He said he didn't know whether there are gods - but this is the same as atheism [Diogenes of Oen. on Protagoras]
     Full Idea: He said that he did not know whether there were gods - but this is the same as saying that he knew there were no gods.
     From: comment on Protagoras (fragments/reports [c.441 BCE], A23) by Diogenes (Oen) - Wall inscription 11 Chil 2
The gods are just personified human benefits [Prodicus]
     Full Idea: Things from which benefits to human life have been derived have come to be considered deities, such as Demeter and Dionysus.
     From: Prodicus (fragments/reports [c.423 BCE], B5), quoted by (who?) - where?
Anaxagoras was charged with impiety for calling the sun a lump of stone [Anaxagoras, by Plutarch]
     Full Idea: Anaxagoras was charged with impiety because he called the sun a lump of stone.
     From: report of Anaxagoras (fragments/reports [c.460 BCE]) by Plutarch - 14: Superstition §9
     A reaction: The point is that he was supposed to say that the sun is a god.