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Anaxagoras' Theory of Matter—I

  • F. M. Cornford (a1)
Extract

Anaxagoras’ theory of matter offers a problem which, in bald outline, may be stated as follows. The theory rests on two propositions which seem flatly to contradict one another. One is the principle of Homoeomereity: A natural substance such as a piece of gold, consists solely of parts which are like the whole and like one another—every one of them gold and nothing else. The other is: ‘There is a portion of everything in everything’, understood to mean that a piece of gold (or any other substance), so far from containing nothing but gold, contains portions of every other substance in the world. Unless Anaxagoras was extremely muddleheaded, he cannot have propounded a theory which simply consists of this contradiction. One or the other proposition must be reinterpreted so as to bring them into harmony. Some critics attack one, some the other; some try to modify both. Mr. C. Bailey has recently published a fresh attempt to reconstruct the theory in a form consistent with itself. But the result, as he admits, is arbitrary and (above all) uneconomical. These defects, like all the contradictions and obscurities found in other accounts of the system, can be traced to the second proposition: ‘There is a portion of everything in everything’, or rather to the construction put upon it. The language is crude, vague, and ambiguous. What does ‘everything’ mean? Has the first ‘everything’ the same sense as the second ? If taken to mean that there is a portion of every material substance in every material substance, the proposition leads to a result for which ‘uneconomical’ is an indulgent epithet.

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page 14 note 1 Greek Atomists (Oxford), 1928, pp. 34 sqq. App. I.

page 15 note 1 I use the word ‘germ’ (not ‘seed’) to avoid confusion with Anaxagoras' use of σπÉρμα to denote a particle of any homoeomerous substance, organic or inorganic.

page 15 note 2 This fragment, quoted only here, probably comes from some authority who knew Anaxagoras' book and was not merely copying from Aristotle and the doxographers.

page 15 note 3 The inchoate Atomism of Zeno's Pythagorean contemporaries. See Cornford, F. M., Mysticism and Science in the Pythagorean Tradition, C.Q. XVI. 137 sqq., XVII. 1 sqq.

page 15 note 4 Cf. Aristotle's objections to Empedocles' theory, de gen. et corr. 334a 26 sqq.

page 16 note 1 оτε γáρ τοÛ σμικoÛ ἐστιτό γε ἐλόϰιστoѵ, ἐλλ' λασσoѵ ἀεί. τὸ γὰρ ἐὸѵ oὐκ ἔστι τὸ μὴ (τoμ,ῇ, Zeller) oὐκ εἷѵαι. Zeller's emendation does not substantially alter the sense.

page 16 note 2 Cf. Simplic. Phys. 167, 23 σάρκας καί ὀστᾶ καὶ ᾄøθαρτα κατ’ ‘Aѵαξ. ἐστίѵ. ὥστε oὐκ ἂѵ ὑπoμέѵoι τὴѵ μεϰρὶ øθoρᾶς τoÛ oἰκείoυ εἴδoυ διαίρεσιѵ. Frag. 6 probably asserts the same principle.

page 16 note 3 Ar. de gen. et corr. 314a 18 ὁ μὲѵ γὰκ (’ Aѵαξ.) τὰ ὁμoιoμερῆ στoιϰεῖα τίθμσιѵ oἷoѵ ὀστoῖα τίθησιѵ oἷoν ὀστoῦν και σάρκα καὶ μνελὸν καὶ τῶν άλλων ὠν ἐκ἗στῳ συνώνυμoν τἐμέρoς ἐρτίν. Cf 647b 17.

page 16 note 4 Protagoras 329D. The word ὁμoιoμερ, if in use, would be too technical for a literary dialogue; but gold is the favourite instance of a homoeomeror substance in the testimonies about Anaxagoras, and Plato may have taken the conception and the illustration from him. The suggestion in Aet. I.3.5 àπò τοȖ οὐν Ŏμοια τὰ μὲναι ὲν τῆτροϕῆ τοȋσ γεννωμὲοις ὁμοςομε ρείας αὐτὰς ἐκάλεσ is the irresponsible conjecture of a doxographer. Anaxagoras, if he called flesh and the other tissues ‘things having like parts’, could not have meant ‘having parts like the parts of the food which nourishes them’; and gold is not nourished by food at all.

page 16 note 5 cf. the classification in Plato's Soph. 265c sqq.: the creations of divine art are ζῷα (animals) and ϕυτά. Φυτὰ are subdivided into (a) plants, (b) metals and minerals (ὅσα ᾰψυχα ἐν γῆξυίσταται σώματα τηκτὰ καὶ ᾰτηκτα Finally there are the elements ἐξ ῶν τὰ πɛθυκὁτ’ ἐστί, πȖρ καὶ ὓδωρ καὶ τὰ τούτων ἀδελθά. Cf. also Simplic. de caelo, 3.

page 17 note 1 De caelo 302a 28, Anaxagoras’ view of the elements is the opposite of Empedocles’. Empedocles says that Fire and Earth and the things of the same class as these are elements of bodies and all things are composed of them, ‘Aναξ. δὲτοὐναντίον τὰ γὰρ ὁμοιομερ στοιχεȋα (λέγω δε οȋονσάρκα καὶ ὀστοȖν καὶ τῶν τοιοὐτσν ἕκαστον), ἀἐρα δκαὶ πȖρ μείγματα τοὑτων καὶ τκαῶν ᾰλλων σπερμάτων πάντων. εȋναι γὰρ ἑκάτερον αὐτῶν ἐξ ἀοράτυν ὁμοιομερῶν πάντων ἠθροισμένον. διò καὶ γίγνεσͥαι πཱντ’ ἐκ τούτων τὸ γὰρ πȖρ καὶ τὸν αἰθέρα προσαγορεύει ταὐτό. Here Air and Fire (Aether) are specially mentioned because of their prominence in Anaxagoras’ scheme of evolution, as the first great masses that become distinguishable. But there is no reason to infer that Water and Earth (which become distinct later) are not also masses of Seeds of all kinds. And Aristotle expressly states that they are at de gen. et corr. 314a 28 οἱ δὲ (περὶ αναξ.) ταȖτα μὲν (flesh, bone and other such ὀμοιομερῆ) ἁπλᾶ καὶ στοιχεȋα, γῆν δὲ καὶ πȖρ καὶ ὓδωρ καὶ ἀέρα σὐνθετα πανσπερμίαν γὰρ εȋνι τυύτων. Frag. 4 (as will appear later) is not inconsistent with this account of the nature of Earth (and Water), which is accepted e.g. by Simplicius on Phys. 188a 17 and else where. See Ross on Ar. Met. 984a 14.

page 17 note 2 E.g. Simplicius at Phys. 27, 5, where (though he knew better) Simplicius is writing with a doxography before him (he presently quotes Theophrastus) and unthinkingly transcribes the phrase οȋον ὓδωρ ω πȖρ, which I take to be derived from Aristotle's καθcάπερ ὓδωρ ῆ πȖρ.

page 17 note 3 This passage will be discussed later, p. 27.

page 17 note 4 ‘Simple’ because, like Aristotle's ‘simple bodies’, they cannot be actually divided into any substances of a prior order, but are themselves ‘elements.’.

Page 18 note 1 This general remark brings in one version of the proposition ‘a portion of everything in everything’, which we have determined to exclude until we find a need for it. I ignore it because, as I am showing, there is no need for it in the solution of this germ problem. I shall later show how I think it came to be imported (first by Aristotle) into the explanation of this and other cases of apparent becoming or change, where it has no place.

page 18 note 2 Aristotle it gen. anim, 723a 7 compares the medical theory that the resemblance of offspring to parents is to be explained by the semen coming from all parts of the body (Hippocr. π ἀἑρων 14 ὸ γὰρ γόνος πανταχόθεν ἕρχεται τοȖ σώματος: π. γονῆς 3 τὴν δὲ γονήν θημι ἀποκρνεσθαι ἀπὸ παντὸς τοȖ σώματος), remarking that it seems to be the same as Anaxagoras1 theory that ‘none of the ὁμοιομερῆ comes into being’ (but all are represented already in the germ), except that A. applied this to all things and not only to the generation ofanimals. Cf, 769a 28, the theory that the semen is a πανσπερμία πογγῶν.

page 18 note 3 Diels, Vors. 46 A 113, 117, 42.

page 18 note 4 Frag, li ἐν παντὶ παντòς μοȋρα ενεστι πλὴν νοȖ, ἕστιν οȋσι δὲ καὶ νοȖς ἒνι. Frag. 12 καὶ ὄσα γε ψυχὴν ἔχει καὶ καὶ, πxάντων νοȖς κρατεȋ. On the action of Notts MrPeck, (C.Q. XX. 57 sqq.) makes some interesting observations, though I cannot accept his conclusions.

page 19 note 1 διὸ ταȖτα ἐν τῇ τροθῇ ὐπέλαβεν εȋναι is the MSS. reading. In his edition of Simplicius Phys. (1882) Diels apparently meant to read σιὰ with the Aldine (for σιὰ), as he does in Vors. 4 A 45. There seem to be misprints in both texts (in Vors. 4 386, 36, the full stop after ὁμοίψ should probably be a colon, as at Phys. 460, 17; 1. 38 omits καἰ ϕύλλα after ϕύαν; at Phys. 460, 14 the bracket after πxȖρ should probably be deleted as in Vors.), and the construction of Simplicius’ sentence is anyhow irregular. But our point is unaffected. Whetherδιὸ or διὸ be read, Sim plicius meant that the tissues he has just named were in the food that nourishes us, just as the plant tissues he proceeds to name must be in the water that nourishes trees.

page 20 note 1 Aristotle, de gen. anim. 723a 10 ‘αναξ. μὲν γὰρ εὐλόγως ϕησἰ σάρκας ἐκ τῆς τροϕῆς προσιέναι ταȋς σαρξὶν. Cf. Plato, Phaedo 96c διὰ τί ἅνθρωπος αὐξάνεται… ἐπειδὰν γὰρ ἐκ τῷȋς μὲν σαρξὶ σαρκες προσγένωνται, τοȋς δὲ ὀστοȋς ὐστᾶ, καὶ οὔτω κατὰ τὸν αὐτόν λόγον καὶ τοȋς ἄλλοις τὰ αὐτῶν οικεα εκάσνοις προσγένηταιτούτων δὲ οὔτω διακρι;νμένων, ἐννῆ τροϕῇ τῇ προσϕεκομένῃ χρῂ δοκεȋν πάντα ἐνεȋναι καὶ ξ ἐόντων χρημάτωτ πάττα αὔξεσθαι. ‘Since these things (the tissues) become distinct (in the grow ing animal) we must think that they are all present in the food we take, and that all things grow from things that are.’ Simplicius would correctly represent the first πάντα; while Aetius’ authority took it to mean πάντα χρήματα and substituted πάντα τὰ ὄντα. Contrast FRAG. 3, fin.ἐν τῷ σύμπαντι χρῂ δοκεȋν ἐνεȋναι πάντα χρῄματα which does mean that ‘all things’ (generally) must be in the ‘sum of things’ (not in each thing).

page 20 note 4 Plut.Epit. 1. 3 (Dox. 279) τροϕῂν γοȖν προσϕερόμεθα ἀπλῆν καὶ μονοειδῆ οȋον τὸν δημῄτρειον ἄρτον, τὸ ὔδωρ πίνοντες. Dicendu m fuisse τὸν δημῄτριον καρπὀν ἐσθίοντες καὶ’ (Diels). Burnet (E.G.P. 3 262) accepts Usener's καρπὸν.

page 21 note 1 If we understand ‘partly composed’, the statement is accurate.

page 21 note 2 Since animals feed on leaves and other parts of plants as well as on their fruit (‘germ’), those other parts which serve as food must containan admixture of animal tissue with the homoeomerous plant-tissues proper to them. This animal tissue would come out of the germ and be distributed among the parts of the grown plant, though there may be little of it in the less eatable parts, none in the uneatable. The planttissues proper (‘bark’, ‘wood’, etc.) will none the less be homoeomerous in substance.

page 22 note 1 Ar. de cailo 392a 31 (quoted above, p. 17) and 302b 14, all the ὁμοιομερῆ are στοιχεȋα. Simplic. ad loc. 603, 26 ὁδὲ’ αναξ. καὶ ταȖτα (Empedocles’ 4 ‘elements’) καὶ τά ᾰλλα πάντα ἀπὀ τῶν ὁμο οομερῶν συνίστησι. Cf. Phys. 167, 9 οὐδὲν γὰρ τοὑτων (τῶν ὁμοιοερῶν) ἀνωτἑρω κατ’ αὐτόν.

page 22 note 2 Ar. (de gen. et corr. 324b 17, Phys. 203a 19)couples Anax. and Democritus as both having ἄπειρα.

page 22 note 3 Ar. Met. 984a 13.

page 22 note 4 FRAG. 5. Simpl. Phys. 156, 9.

page 22 note 5 Ar. (Phys. 187b 13) attempts to refute the fiepelas. view he ascribes to Anax., that it is possible for flesh, bone, etc., to be of any size ἐπὶ τὀ μεȋζον ἠἐπὶ τὀ ἔλατοu;τν. Simplic. ad loc. 166, 15 cites FRAG. 3 οῠτε τοȖσμικρȖ ἐστι τοὐλἁχιστον ἀλἀ ἔλασσον ἀεἱ.

page 22 note 6 Ar. (de gen. et corr. 314b 15) remarks that for the pluralists the πἀθη concerned in ἀλλοίωσις (hot, cold, etc.) constitute the differences which characterize their elements, and so no change of these qualities can occur.

page 22 note 7 Simplic. de caelo, 229, 32 ὡς 'αναξ. ἐδόκεο μερείας.

page 23 note 1 Ar. Phys. 203a 19 δσοι δἐ ἄπειρα τἀ στοιχεȋα, καθάπερ'αναξ. καὶ δημόκριτος, ὁ μἐν ἐκ τῶν ὁμοιομερῶν ὀ δὲ ἐκ τῆς πανσπερμίας τῶν σχημάτων, τῇ ἁϕῇ συνεχὲς τὸ ἄπειρον εȋναί ϕασιν. Simplic. Phys. 154, 10 τὸ μȋγμα, δ ῆν κατἀ μἐν’ αναξ. ἐκ τῶν ομοιομερῶν ἀπείρων τῷ πλῄθει μεμιγμένον.

page 23 note 2 E.g. Mr. Peck, C.Q. XX. 59; Mr. Bailey, Greek Atomists, App. I.; Mr. Joachim on de gen. et corr. 314a 24.

page 23 note 3 Ar. Phys. 250b 24 ὁμοȖ πάντων ὄντων καὶ ἠρεμούντων τὸν ἄπειρον χρὁνον, κίνησιν ἐμποιῆσαι τὸν νοȖν καὶ This implies that our world was not preceded by any other world. De caelo 301a 12 ἐξ ἀκινῄτων γἀρ ἄρχεται κοσμοποιεȋν.

page 23 note 4 FRAG. 12.

page 23 note 5 Aet. II. 1, 2 ‘αναξ… ἔνα τὸν κόσμον. Ar.Phys.187a 22 ὥσπερ ‘αμρεδοκλῆς καὶ’ αναξαγὁρας ἐκ τοȖ μίγματος γἀρ καὶ οτοι ἐκκρίνουσι τλλα. διαϕέρουσι δὲ τῷ μὲν περὶοδον τὰ τούτων, τὸν δ ἅπαξ. Simplic. ad loc. 154, 30 τὸν ‘νναξ. λγειν ἅπαξ γενόμενον τὀν κόσμον ἐκ τοȖ μίγματος διαμένεν λοιπὸν ὑπὀ τοȖ νοȖ ἐϕεστῶτος διοικούμενόν τε καὶ διακρονόμενον. Simplic. Phys. 178, 25 contrasts Anaxagoras and Empedocles, who have only one world at a time (ἔνα τὸν κόσμονϕασίν) with Democritus who has innumerable contemporary worlds. So does Aristotle(Phys. 250b 18 sqq.). This testimony is not outweighed FRAG. 4 (Burnet, E.G.P.3, 270).

page 23 note 6 FRAG. 2 ἀῄρ τε καὶ αἰθῄρ ἀποπίνονται ἀπὀ τοȖ πολλοȖ τοȖ περοȖ. Ar. Phys. 187a 23 (see last note). Simplic. Phys. 460, 20 τxῂν γἑνεσιν κατὰ ἔκκισιν γίνεσθαι.

page 24 note 7 Theophr. ap. Simplic. Phys. 27, 12 ἐν τῇ διακρίσɛι τοȖ ἀπείρου τὰ συγγενῆ ϕέρεσθαι πρὸς ἄλληλα. Hippol. Ref. I, 8, 2 συνελθεȋν τε τὰ ὄμοια.

page 24 note 1 The relation of the Opposites to the Seeds and to Air and Aether will be discussed later.

page 24 note 2 FRAG. 16.

page 24 note 3 According to Aet. II. 13, 3 (Dox. 341) it was the rotation of the Aether (not of the Earth) that tore these rocks from the Earth : τὸν περικείμενον αἰθέρα πύρινον μἐν εȋναι κατὰ τῂν οὐσίαν, τῇ δ’ εὐτονία τῆς περιδινῄσεως ναρπὰσανταπὲτρους απὀ τῆς γῆς καὶ καταϕλὲξαντα τούτους ἠστηρικὲναι. Hippol. Ref. 1, 8, 6 ἤλιον δὲ καὶ πὰντα τὰ στρα λίθους εȋναι ἐμπύρους συμπεριληϕέντας ὑπ τῆς αἰθέρος περιϕορᾶς. But FRAG. 16 οτοι ἐ (λίθοι) ἐκχωρέουσι μᾶλλον τοȖ ὔδατος (if it refers these rocks) suggests a centrifugal flinging off.

page 24 note 4 ὀμοȖ πάντα χρῄματα ν, πειρα καὶ πλῆθος καὶ σμικρτητα καὶ γάρ τὸ σμικρν πειρον ν καὶ πάντων μαȖ ἐὁντων οὐδν ἕνδηλον ν ὑπὸ σμικρότητος πάντα γὰρ ἀῄρ τε καὶ αἰθῂρ κατεȋχεν, ἀμϕότερα πειρα ἑὁντα ταȖτα γὰρ μέγιστα νεστιν ἐν τοȋς σὑμπασι καὶ πλῄθει καὶ μεγέθει.

page 24 note 5 Hippol. Ref. 1. 7. 2.

page 25 note 1 The nature of these Opposites will be discussed later.

page 25 note 2 Theophr. de sens. 59 οῑον ὅτι τὸ μέν μανὀν καὶ ^lamda;επτὸν θερμόν,τό δὲ πυκνὸν καὶ παχὺ ψυχρόν, ὥσπερ 'αναξ. διαιρεῖ τὸν ἐὲρα καὶ τὸν αιθέρα.

page 25 note 3 Theophr. (ap. Simplic. Phys. 27. 13) πησὶν … ὅτι μὲν ἐν τῷ παντὶ χρυσὸς ἠγίνεσθαι χρυσόν, ὅτι δὲ γῆ, γῆν.

page 26 note 1 Diels inserts ‘andere’ (in italics) in his translation.

page 26 note 2 ‘Stones’ would include both the homoeomerous minerals, which are finally separated off from all foreign substances, and conglomerates of several minerals. These are the densest and coldest substances of all.

page 26 note 3 For this proposition cannot merely mean that Fire, Air, Water, Earth, and any intermediate forms contain (as they do) Seeds of all kinds, and hence can be ‘separated off’ from one another.

page 27 note 1 I understand σχεδόν as qualifying the whole statement: ‘Practically he says…’ Cf. 990b 4 σχεδόν γάρ ῐσα ἢ οὐκ ἐλάττω ἐστὶ τὰ εἴδσχεδὸν does not go only with ἴσα but means ‘Roughly you may say the Ideas are at least as numerous.’

page 27 note 2 Taking οὔτω as the antecedent of καθάπερ (= ὥσπερ cf. 353b 14 καθάπερ… τὸν αὐτὸν τρὸπον Bonitz, Index, 354a 18). If this is the construction, Aristotle is not here guilty of implying that Fire and Water are ὁμοιομερῆ in Anaxagoras' system. See above, p. 17.

page 27 note 2 The previous context of this seems to me to belong to Simplicius, not Theophrastus.

page 28 note 1 Phys. 177, 20 'αναξ…δνλός στι τήν γένεσιν ἑκάστου τῶ συνθέτων κατἀ τήν τ῰ν ὁμοίωσὑνθεσιν ἐπιτελεῖσθαι βουλόμενος, διότι καἰ διαιροὑμενα εἰς τὰ ὅμοια ἑρα (σάρκα γὰρ εἰς σάρκας καὶ ὀστοῦν εἰσ ὀστᾶ), δοκεῖ δὲ ἕκαστον εἰς ἐκεῖνα διαιρεῖσθαι ἐξ ὠν σὑγκειται. 165, 1 και τοῦτο δἐ ὁ 'αναξ. ἀξιοῖ τὀ ἔκαστον τῶν αἰσθητῶν ὁμοιομερῶν κατἀ τήν τῶν ὁμοίων σὑνθεσσιν γίνεσθαί τε καὶ χαρακτρίζεσθαι.

page 28 note 2 ἀπεκώλυε γὰρ ἡ σὑμμιξς πάντων χρὴματων, τοῦ τε διεροῦ καὶ τοῦ ξηροῦ καὶ τοῦ θερμοῦ καὶ τοῦ ψυχροῦ καὶ τοῦ λαμπροῦ καὶ τοῦ ζοφεροῦ, καὶ γῆς πολλῆς ἐνεοὑσης καὶ σπερμάτων ἀπείρων πλὴθους οὐδὲν ἐοικότων ἀλλὴλοις. In both places where Simplicius quotes this (Phys. 34, 24; 156, 8) the MSS. read πλὴθους. Diels retains πλὴθους. in Simplicius (ed. of 1882), but prints the conjeeture πλὴθος. in Vors., though his translation seems to render πλὴθους. (sc. ἐνεόντος). Burnet (E.G.P.3 258) translates πλὴθους, but takes both genitives γῆς and πλὴθους. to be governed by ἡ σὑμμιξις. πλὴθους can be retained, with either of the two constructions above translated.

page 28 note 3 οὐδὲ γὰρ τῶν ἄλλων οὐδὲν ἔοικε το ἓτερον' τῷ ἑτέρῳ. At Simpl. Phys. 34, 25 this clause does not appear. At 156, 8 it stands at the end of the quotation, the following sentence being omitted. It is possible that it does not belong to Anaxagoras, but to Simplicius, who might be paraphrasing FRAG. 12 fin.ἔτερον δὲ οὐδέν ἐστιν ὅμοιον οὐδενί. (There ἕτερον means ‘other than Nous’, which has just been declared to be ‘all alike.’ The things other than Nous are called τὰ ἄλλα at the beginning of FRAG. 12.) This hypothesis would explain the ἄλλων in our clause, which taken as part of the fragment is obscure: other than what ? To a Platonist τὰ ἄλλα is a familiar term for what is contrasted with ‘the One’ (whether the One be identified with νοῶς or with the μῖγμα). It is possible, however, to retain the clause and to explain τῶν ἄλλων (see below).

page 29 note 1 Cf. Simplic, . de caelo 543, 3 τήν γῆν μεμιγμένην τέως τοῖς ἄλλοις, εῑτα διακρινομένην, ὡς 'αναξαγόρας ἐδόκει λέγειν…καὶ περομένην ὲπὶ το μέσον.

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