54 ideas
| 10170 | While true-in-a-model seems relative, true-in-all-models seems not to be [Reck/Price] |
| Full Idea: While truth can be defined in a relative way, as truth in one particular model, a non-relative notion of truth is implied, as truth in all models. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4) | |
| A reaction: [The article is actually discussing arithmetic] This idea strikes me as extremely important. True-in-all-models is usually taken to be tautological, but it does seem to give a more universal notion of truth. See semantic truth, Tarski, Davidson etc etc. |
| 10166 | ZFC set theory has only 'pure' sets, without 'urelements' [Reck/Price] |
| Full Idea: In standard ZFC ('Zermelo-Fraenkel with Choice') set theory we deal merely with pure sets, not with additional urelements. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §2) | |
| A reaction: The 'urelements' would the actual objects that are members of the sets, be they physical or abstract. This idea is crucial to understanding philosophy of mathematics, and especially logicism. Must the sets exist, just as the urelements do? |
| 10794 | The nominalist is tied by standard semantics to first-order, denying higher-order abstracta [Marcus (Barcan)] |
| Full Idea: The nominalist finds that standard semantics shackles him to first-order languages if, as nominalists are wont, he is to make do without abstract higher order objects. | |
| From: Ruth Barcan Marcus (Nominalism and Substitutional Quantifiers [1978], p.166) | |
| A reaction: Aha! Since I am pursuing a generally nominalist strategy in metaphysics, I suddenly see that I must adopt a hostile attitude to higher-order logic! Maybe plural quantification is the way to go, with just first-order objects. |
| 10786 | Anything which refers tends to be called a 'name', even if it isn't a noun [Marcus (Barcan)] |
| Full Idea: The tendency has been to call any expression a 'name', however distant from the grammatical category of nouns, provided it is seen as referring. | |
| From: Ruth Barcan Marcus (Nominalism and Substitutional Quantifiers [1978], p.162) |
| 10788 | Nominalists see proper names as a main vehicle of reference [Marcus (Barcan)] |
| Full Idea: For a nominalist with an ontology of empirically distinguishable objects, proper names are seen as a primary vehicle of reference. | |
| From: Ruth Barcan Marcus (Nominalism and Substitutional Quantifiers [1978], p.162) |
| 10799 | Nominalists should quantify existentially at first-order, and substitutionally when higher [Marcus (Barcan)] |
| Full Idea: For the nominalist, at level zero, where substituends are referring names, the quantifiers may be read existentially. Beyond level zero, the variables and quantifiers are read sustitutionally (though it is unclear whether this program is feasible). | |
| From: Ruth Barcan Marcus (Nominalism and Substitutional Quantifiers [1978], p.167) |
| 10790 | Quantifiers are needed to refer to infinitely many objects [Marcus (Barcan)] |
| Full Idea: An adequate language for referring to infinitely many objects would seem to require variables and quantifiers in addition to names. | |
| From: Ruth Barcan Marcus (Nominalism and Substitutional Quantifiers [1978], p.164) |
| 10791 | Substitutional semantics has no domain of objects, but place-markers for substitutions [Marcus (Barcan)] |
| Full Idea: On a substitutional semantics of a first-order language, a domain of objects is not specified. Variables do not range over objects. They are place markers for substituends (..and sentences are true-for-all-names, or true-for-at-least-one-name). | |
| From: Ruth Barcan Marcus (Nominalism and Substitutional Quantifiers [1978], p.165) |
| 10785 | Maybe a substitutional semantics for quantification lends itself to nominalism [Marcus (Barcan)] |
| Full Idea: It has been suggested that a substitutional semantics for quantification theory lends itself to nominalistic aims. | |
| From: Ruth Barcan Marcus (Nominalism and Substitutional Quantifiers [1978], p.161) |
| 10795 | Substitutional language has no ontology, and is just a way of speaking [Marcus (Barcan)] |
| Full Idea: Translation into a substitutional language does not force the ontology. It remains, literally, and until the case for reference can be made, a façon de parler. That is the way the nominalist would like to keep it. | |
| From: Ruth Barcan Marcus (Nominalism and Substitutional Quantifiers [1978], p.166) |
| 10798 | A true universal sentence might be substitutionally refuted, by an unnamed denumerable object [Marcus (Barcan)] |
| Full Idea: Critics say if there are nondenumerably many objects, then on the substitutional view there might be true universal sentences falsified by an unnamed object, and there must always be some such, for names are denumerable. | |
| From: Ruth Barcan Marcus (Nominalism and Substitutional Quantifiers [1978], p.167) | |
| A reaction: [See Quine 'Reply to Prof. Marcus' p.183] The problem seems to be that there would be names which are theoretically denumerable, but not nameable, and hence not available for substitution. Marcus rejects this, citing compactness. |
| 10175 | Three types of variable in second-order logic, for objects, functions, and predicates/sets [Reck/Price] |
| Full Idea: In second-order logic there are three kinds of variables, for objects, for functions, and for predicates or sets. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §5) | |
| A reaction: It is interesting that a predicate seems to be the same as a set, which begs rather a lot of questions. For those who dislike second-order logic, there seems nothing instrinsically wicked in having variables ranging over innumerable multi-order types. |
| 10165 | 'Analysis' is the theory of the real numbers [Reck/Price] |
| Full Idea: 'Analysis' is the theory of the real numbers. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §2) | |
| A reaction: 'Analysis' began with the infinitesimal calculus, which later built on the concept of 'limit'. A continuum of numbers seems to be required to make that work. |
| 21382 | 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). |
| 10174 | Mereological arithmetic needs infinite objects, and function definitions [Reck/Price] |
| Full Idea: The difficulties for a nominalistic mereological approach to arithmetic is that an infinity of physical objects are needed (space-time points? strokes?), and it must define functions, such as 'successor'. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4) | |
| A reaction: Many ontologically austere accounts of arithmetic are faced with the problem of infinity. The obvious non-platonist response seems to be a modal or if-then approach. To postulate infinite abstract or physical entities so that we can add 3 and 2 is mad. |
| 10164 | Peano Arithmetic can have three second-order axioms, plus '1' and 'successor' [Reck/Price] |
| Full Idea: A common formulation of Peano Arithmetic uses 2nd-order logic, the constant '1', and a one-place function 's' ('successor'). Three axioms then give '1 is not a successor', 'different numbers have different successors', and induction. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §2) | |
| A reaction: This is 'second-order' Peano Arithmetic, though it is at least as common to formulate in first-order terms (only quantifying over objects, not over properties - as is done here in the induction axiom). I like the use of '1' as basic instead of '0'! |
| 10172 | Set-theory gives a unified and an explicit basis for mathematics [Reck/Price] |
| Full Idea: The merits of basing an account of mathematics on set theory are that it allows for a comprehensive unified treatment of many otherwise separate branches of mathematics, and that all assumption, including existence, are explicit in the axioms. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4) | |
| A reaction: I am forming the impression that set-theory provides one rather good model (maybe the best available) for mathematics, but that doesn't mean that mathematics is set-theory. The best map of a landscape isn't a landscape. |
| 10167 | Structuralism emerged from abstract algebra, axioms, and set theory and its structures [Reck/Price] |
| Full Idea: Structuralism has emerged from the development of abstract algebra (such as group theory), the creation of axiom systems, the introduction of set theory, and Bourbaki's encyclopaedic survey of set theoretic structures. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §2) | |
| A reaction: In other words, mathematics has gradually risen from one level of abstraction to the next, so that mathematical entities like points and numbers receive less and less attention, with relationships becoming more prominent. |
| 10169 | Relativist Structuralism just stipulates one successful model as its arithmetic [Reck/Price] |
| Full Idea: Relativist Structuralism simply picks one particular model of axiomatised arithmetic (i.e. one particular interpretation that satisfies the axioms), and then stipulates what the elements, functions and quantifiers refer to. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4) | |
| A reaction: The point is that a successful model can be offered, and it doesn't matter which one, like having any sort of aeroplane, as long as it flies. I don't find this approach congenial, though having a model is good. What is the essence of flight? |
| 10179 | There are 'particular' structures, and 'universal' structures (what the former have in common) [Reck/Price] |
| Full Idea: The term 'structure' has two uses in the literature, what can be called 'particular structures' (which are particular relational systems), but also what can be called 'universal structures' - what particular systems share, or what they instantiate. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §6) | |
| A reaction: This is a very helpful distinction, because it clarifies why (rather to my surprise) some structuralists turn out to be platonists in a new guise. Personal my interest in structuralism has been anti-platonist from the start. |
| 10181 | Pattern Structuralism studies what isomorphic arithmetic models have in common [Reck/Price] |
| Full Idea: According to 'pattern' structuralism, what we study are not the various particular isomorphic models of arithmetic, but something in addition to them: a corresponding pattern. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §7) | |
| A reaction: Put like that, we have to feel a temptation to wield Ockham's Razor. It's bad enough trying to give the structure of all the isomorphic models, without seeking an even more abstract account of underlying patterns. But patterns connect to minds.. |
| 10182 | There are Formalist, Relativist, Universalist and Pattern structuralism [Reck/Price] |
| Full Idea: There are four main variants of structuralism in the philosophy of mathematics - formalist structuralism, relativist structuralism, universalist structuralism (with modal variants), and pattern structuralism. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §9) | |
| A reaction: I'm not sure where Chihara's later book fits into this, though it is at the nominalist end of the spectrum. Shapiro and Resnik do patterns (the latter more loosely); Hellman does modal universalism; Quine does the relativist version. Dedekind? |
| 10168 | Formalist Structuralism says the ontology is vacuous, or formal, or inference relations [Reck/Price] |
| Full Idea: Formalist Structuralism endorses structural methodology in mathematics, but rejects semantic and metaphysical problems as either meaningless, or purely formal, or as inference relations. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §3) | |
| A reaction: [very compressed] I find the third option fairly congenial, certainly in preference to rather platonist accounts of structuralism. One still needs to distinguish the mathematical from the non-mathematical in the inference relations. |
| 10178 | Maybe we should talk of an infinity of 'possible' objects, to avoid arithmetic being vacuous [Reck/Price] |
| Full Idea: It is tempting to take a modal turn, and quantify over all possible objects, because if there are only a finite number of actual objects, then there are no models (of the right sort) for Peano Arithmetic, and arithmetic is vacuously true. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §5) | |
| A reaction: [compressed; Geoffrey Hellman is the chief champion of this view] The article asks whether we are not still left with the puzzle of whether infinitely many objects are possible, instead of existent. |
| 10176 | Universalist Structuralism is based on generalised if-then claims, not one particular model [Reck/Price] |
| Full Idea: Universalist Structuralism is a semantic thesis, that an arithmetical statement asserts a universal if-then statement. We build an if-then statement (using quantifiers) into the structure, and we generalise away from any one particular model. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §5) | |
| A reaction: There remains the question of what is distinctively mathematical about the highly generalised network of inferences that is being described. Presumable the axioms capture that, but why those particular axioms? Russell is cited as an originator. |
| 10177 | Universalist Structuralism eliminates the base element, as a variable, which is then quantified out [Reck/Price] |
| Full Idea: Universalist Structuralism is eliminativist about abstract objects, in a distinctive form. Instead of treating the base element (say '1') as an ambiguous referring expression (the Relativist approach), it is a variable which is quantified out. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §5) | |
| A reaction: I am a temperamental eliminativist on this front (and most others) so this is tempting. I am also in love with the concept of a 'variable', which I take to be utterly fundamental to all conceptual thought, even in animals, and not just a trick of algebra. |
| 10171 | The existence of an infinite set is assumed by Relativist Structuralism [Reck/Price] |
| Full Idea: Relativist Structuralism must first assume the existence of an infinite set, otherwise there would be no model to pick, and arithmetical terms would have no reference. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4) | |
| A reaction: See Idea 10169 for Relativist Structuralism. They point out that ZFC has an Axiom of Infinity. |
| 481 | 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 |
| 21822 | 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). |
| 10787 | Is being just referent of the verb 'to be'? [Marcus (Barcan)] |
| Full Idea: Being itself has been viewed as referent of the verb 'to be'. | |
| From: Ruth Barcan Marcus (Nominalism and Substitutional Quantifiers [1978], p.162) |
| 17995 | 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. |
| 10789 | Nominalists say predication is relations between individuals, or deny that it refers [Marcus (Barcan)] |
| Full Idea: Nominalists have the major task of explaining how predicates work. They usually construct it as a relation between individuals, or deny the referential function of predicates. | |
| From: Ruth Barcan Marcus (Nominalism and Substitutional Quantifiers [1978], p.163) |
| 10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
| Full Idea: One way for a nominalist to reject appeal to all abstract objects, including sets, is to only appeal to nominalistically acceptable objects, including mereological sums. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4) | |
| A reaction: I'm suddenly thinking that this looks very interesting and might be the way to go. The issue seems to be whether mereological sums should be seen as constrained by nature, or whether they are unrestricted. See Mereology in Ontology...|Intrinsic Identity. |
| 10796 | If objects are thoughts, aren't we back to psychologism? [Marcus (Barcan)] |
| Full Idea: If objects are thoughts, aren't we back to psychologism? | |
| From: Ruth Barcan Marcus (Nominalism and Substitutional Quantifiers [1978], p.166) | |
| A reaction: Personally I don't think that would be the end of the world, but Fregeans go into paroxyms at the mention of 'psychology', because they fear that it destroys objectivity. That may be because they haven't understood thought properly. |
| 10797 | Substitutivity won't fix identity, because expressions may be substitutable, but not refer at all [Marcus (Barcan)] |
| Full Idea: Substitutivity 'salve veritate' cannot define identity since two expressions may be everywhere intersubstitutable and not refer at all. | |
| From: Ruth Barcan Marcus (Nominalism and Substitutional Quantifiers [1978], p.167) |
| 20802 | 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!] |
| 13257 | 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. |
| 22761 | 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. |
| 13256 | 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. |
| 13784 | 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. |
| 5118 | 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. |
| 18231 | 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] |
| 631 | 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 |
| 22727 | 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. |
| 550 | 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 |
| 21383 | 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. |
| 13208 | 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. |
| 367 | 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 |
| 21381 | 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? |
| 22726 | 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. |
| 2629 | 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 |
| 480 | 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 |
| 5956 | 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. |
| 7488 | 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. |