16
© Koninklijke Brill NV , Leiden, 2013 DOI: 10.1163/15685284-12341240 Phronesis 58 (2013) 17-31 brill.com/phro  Aristotle on the Impossibility of Anaximander’s apeiron: On Generation and Corruption, 332a20-25* Michael Wedin Philosophy Department, 1240 Social Sciences and Humanities University of California, Davis, One Shields Avenue, Davis, CA 95616. USA [email protected]  Abstract In On Generation and Corruption, Aristotle rejects the very possibility of such a thing as  Anaximander’s apeiron. Characterized as a kind of intermediate stu, the apeiron turns out to consist of contraries and as such is impossible. Commentators have rightly noted this point and some have also indicated that Aristotle oers an argument of sorts for his negative estimate. However, the argument has received scant attention, and it is fair to say that it remains unclear exactly why Aristotle rejects Anaximander’s intermediate stu. Indeed, it is unclear how Aristotle’s argument is supposed to run in the rst place. Tis paper oers a reconstruction of Aristotle’s argument for the impossibility of the apeiron, and on this basis oers to explain Aristotle’s grounds for rejecting Anaximander’s interme- diate stu. Tis is especially called for in light of the fact that Aristotle himself thinks that there can be intermediate stus. Finally, some attention is given to the parallel between the apeiron and Aristotle’s prime matter. Keywords  Aristotle, Anaximander, apeiron, prime matter, actuality, potentiality, elemental qualities, intermediate In Chapter 5 of Book II of On Generation and Corruption, Aristotle con- siders the view that the elements are the matter of which natural bodies * ) Te central idea of this paper emerged over a decade ago in the course of teaching Presocratic Philosophy at Davis. My thanks, and belated apologies, to several ights of students who cheerfully endured my fondness for logical reconstruction. I am additionally grateful to two readers for astute and useful remarks and to the editor for able assistance in the nal version.

Aristotle on the Impossibility of Anaximander’s apeiron

  • Upload
    qlchz

  • View
    214

  • Download
    0

Embed Size (px)

Citation preview

Page 1: Aristotle on the Impossibility  of Anaximander’s apeiron

7/27/2019 Aristotle on the Impossibility of Anaximander’s apeiron

http://slidepdf.com/reader/full/aristotle-on-the-impossibility-of-anaximanders-apeiron 1/15

© Koninklijke Brill NV, Leiden, 2013 DOI: 10.1163/15685284-12341240

Phronesis 58 (2013) 17-31 brill.com/phro

 Aristotle on the Impossibility of Anaximander’s apeiron:

On Generation and Corruption, 332a20-25*

Michael Wedin

Philosophy Department, 1240 Social Sciences and Humanities University of California, Davis, One Shields Avenue, Davis, CA 95616. USA

[email protected] 

 Abstract In On Generation and Corruption, Aristotle rejects the very possibility of such a thing as Anaximander’s apeiron. Characterized as a kind of intermediate stuff, the apeiron turnsout to consist of contraries and as such is impossible. Commentators have rightly noted

this point and some have also indicated that Aristotle offers an argument of sorts for hisnegative estimate. However, the argument has received scant attention, and it is fair tosay that it remains unclear exactly why Aristotle rejects Anaximander’s intermediate stuff.Indeed, it is unclear how Aristotle’s argument is supposed to run in the first place. Tispaper offers a reconstruction of Aristotle’s argument for the impossibility of the apeiron,and on this basis offers to explain Aristotle’s grounds for rejecting Anaximander’s interme-diate stuff. Tis is especially called for in light of the fact that Aristotle himself thinks thatthere can be intermediate stuffs. Finally, some attention is given to the parallel between theapeiron and Aristotle’s prime matter.

Keywords Aristotle, Anaximander, apeiron, prime matter, actuality, potentiality, elemental qualities,intermediate

In Chapter 5 of Book II of On Generation and Corruption, Aristotle con-siders the view that the elements are the matter of which natural bodies

*) Te central idea of this paper emerged over a decade ago in the course of teaching Presocratic Philosophy at Davis. My thanks, and belated apologies, to several flights of students who cheerfully endured my fondness for logical reconstruction. I am additionally grateful to two readers for astute and useful remarks and to the editor for able assistancein the final version.

Page 2: Aristotle on the Impossibility  of Anaximander’s apeiron

7/27/2019 Aristotle on the Impossibility of Anaximander’s apeiron

http://slidepdf.com/reader/full/aristotle-on-the-impossibility-of-anaximanders-apeiron 2/15

18  M. Wedin / Phronesis 58 (2013) 17-31

consist. Te elements must be one, two or more, but, says Aristotle, they cannot be one. For instance, the candidate singleton cannot be air because

for air to underlie fire would require that air be or become hot. But air iscold, so it would be both hot and cold. In short, as underlying matter air would be characterized by contraries. Tis is impossible, however, and soair cannot be the single underlying matter. Te same argument applies tothe other elements, and so Aristotle concludes, in Joachim’s phrase: ‘thereis no single one of them out of which they all originate.’1

Immediately, at 332a20-25, Aristotle extends this conclusion to Anaxi-mander’s singleton, to apeiron. Here is what he says, in the translation of 

Graham 2010, 53:

Nor indeed is there anything else besides them, for instance between air and water orair and fire which is denser than air and fire but finer than the others. For that will turnout to be air and fire with a contrary qualification. But one of the contraries is theprivation of the other. So it is never possible for the alleged source to exist by itself, assome claim the boundless and surrounding stuff does.

 Aristotle considers two candidates for the intermediate. Introduced in the

‘for instance’ clause, the candidates are explained in the immediately attached ‘which is’ clause. So the intermediate between air and water will be denser than air and finer than water and the intermediate betweenair and fire will be denser than fire but finer than air.2 Neither passesmuster.3 

1) Graham (2010) reads Aristotle’s Greek more strictly, and more generally, as: ‘Tere isnot one of these [elements] from which everything comes’ (322a19-20). Now, Aristotle’sargument implies that there cannot be a single element underlying anything that involvesanother element, for such a thing will be cold and dry, as air, and also hot or wet, depend-ing on which other element is involved. So, of course, Joachim would be correct to holdthat such an element could not underlie the other elements.2) Tis is made explicit in Joachim’s more expansive translation in vol. II of the Oxford Aristotle series: ‘But neither is there, beside these four, some other body from which they originate – a something intermediate, e.g. between Air and Water (coarser than Air, butfiner than Water), or between Air and Fire (coarser than Fire, but finer than Air). For thesupposed “intermediate” will be Air and Fire when a pair of contrasted qualities is added toit: but, since one of every two contrary qualities is a “privation”, the “intermediate” nevercan exist – as some thinkers assert the “Boundless” or the “Environing” exists – in isolation.’3) Because what is intermediate between air and water is different from what is intermedi-ate between air and fire, presumably the apeiron could not be both intermediates. But, while it is clear that for Aristotle his candidates cannot both obtain, it is not obvious that

Page 3: Aristotle on the Impossibility  of Anaximander’s apeiron

7/27/2019 Aristotle on the Impossibility of Anaximander’s apeiron

http://slidepdf.com/reader/full/aristotle-on-the-impossibility-of-anaximanders-apeiron 3/15

M. Wedin / Phronesis 58 (2013) 17-31 19

Tis is a puzzling passage. For why should it be impossible that there bea single thing intermediate between the elements? After all, precisely 

because such a thing would not be a standard element, an argumentexcluding an elemental singleton does not automatically apply to an inter-mediate singleton. Nonetheless, Aristotle appears to regard the extensionas unproblematic. But he may not regard it as entirely obvious, for he rec-ommends the extension on the basis of an argument. Unfortunately, thetext gives only a sketch of an argument, and it is not immediately clearhow to complete it. Indeed, some would roundly deny that the passagecontains an argument, citing for example one of its main claims, namely 

the claim that something intermediate between the elements will be airand fire together with contraries. So far from yielding an argument, it isnot even clear what this claim means. Nonetheless, it is the key to under-standing Aristotle’s objection to Anaximander’s apeiron.

 Aristotle’s commentators generally agree on his basic complaint, thatthe apeiron cannot be characterized as an intermediate entity because it would consist of contraries. More narrowly, of course, Aristotle says therecan be nothing at all that is intermediate between air and water or air andfire. A fortiori the apeiron could not be such a thing. What commentatorsremain silent about is exactly why there can be no such intermediate thing.4  After all, it surely seems that there might be such an intermediate thing,even if, as a matter of fact, there is none. Why can’t there be something intermediate between air and water or air and fire? As commentatorsrightly note, such a thing would be impossible by Aristotle’s lights. But why exactly is this impossible? Why, in short, must such a thing consistof contraries? Tis is the chief question I wish to address in this note,and I shall do so by offering a reconstruction of Aristotle’s argument in

332a20-25 for the claim in question.

one or the other must hold. After all, once standard Aristotelian elements are invoked as theflanking terms for Anaximander’s intermediate, another option emerges – namely, whatfalls between water and earth. So he may not be entertaining his two express candidates ascontradictory alternatives. It turns out, in any event, that the intermediate between waterand earth is excluded by the very argument that defeats the two candidates Aristotle does  introduce in 332a20-25. For how this works, see p. 26  below.4) Williams (1982, 164), for instance, comments that: ‘the argument at 332a20-27 repeats,rather less sketchily, that already given at II.1.329a10-13.’ He does not, however, state orexplain the argument at either place. Indeed, he rightly observes that the earlier argument‘needs completing’ – something I aim to provide in this note.

Page 4: Aristotle on the Impossibility  of Anaximander’s apeiron

7/27/2019 Aristotle on the Impossibility of Anaximander’s apeiron

http://slidepdf.com/reader/full/aristotle-on-the-impossibility-of-anaximanders-apeiron 4/15

20  M. Wedin / Phronesis 58 (2013) 17-31

 We may begin with an observation about the structure of the passage. Itconsists of an extended protasis fronting the conclusion that the apeiron 

cannot exist. Roughly, Aristotle maintains that if  there can be nothing intermediate in the way suggested, and if  the apeiron is construed as suchan intermediate, then the apeiron cannot exist. o make this precise willrequire some modest regimentation. Because the supposition that there isbut one element underlying everything leads to an incompatibility, wemay take Aristotle to hold that it is impossible that there be an elementalsingleton. Accordingly, the general principle backing this claim may beformulated as a modal thesis, namely:

(1) ¬◊(∃ x )( x consists of F and G  ∧ F is the contrary of G ).

 According to (1), then, it is not possible for there to exist something thatconsists of contraries. On the basis of (1), Aristotle already ruled out thepossibility that what underlies everything could be a standard elementsuch as air, for that would require that air itself have contrary properties. Accordingly, when Aristotle promises to deploy the same argument againstthe apeiron, we can expect him to appeal to (1). So I enter it as the first stepin the reconstruction.

Now Aristotle presumes, as ‘some assume’, that the apeiron is something intermediate. Tus, we add the fundamental presumption:

(2) x is apeiron ≡  x is intermediate,5

along with the rider that what is intermediate is intermediate between airand water or air and fire:

(3) x is intermediate →  x is between air and water ∨  x is between air and fire.6

5) A point of caution here. If taking (2) as fundamental suggests that Aristotle holds it as a general truth, then anything that is intermediate will count as the apeiron. Since he himself recognizes intermediates that do not fit this description, we might replace (2) in favor of itsleft-to-right entailment. Alternatively, we might restrict ‘fundamental’ to ‘fundamental inthe critique of Anaximander’. Te argument goes through on any of these construals.6) Tis note does not address whether Anaximander’s view is fairly captured by (2) and (3).Tis question is important, but at the moment I am concerned simply with making senseof what Aristotle says, given the presumptions in (2) and (3). For all I know they may behis invention.

Page 5: Aristotle on the Impossibility  of Anaximander’s apeiron

7/27/2019 Aristotle on the Impossibility of Anaximander’s apeiron

http://slidepdf.com/reader/full/aristotle-on-the-impossibility-of-anaximanders-apeiron 5/15

M. Wedin / Phronesis 58 (2013) 17-31 21

So the apeiron of interest is not any one of the four standard elements,but falls between pairs of such elements.7 Tis allows us to conclude, on

the basis of (2) and (3), that the apeiron falls between these same pairsof elements:

(4) x is apeiron →  x is between air and water ∨  x is between air and fire.

 While (4) may have characterized the apeiron in slightly more preciseterms, no grounds have been advanced that show how the apeiron, so char-acterized, runs afoul of (1). For this we must appeal to Aristotle’s more

detailed explanation of what (4) amounts to. He provides this at 332a21-22, where he asserts that the intermediate as characterized in (4) is ‘thickerthan air and fire but finer than the others (tōn de leptoteron)’. Te expres-sion ‘the others’ could refer to the elements other than air and fire, namely  water and earth. Tis is unlikely if only because earth is not mentioned inthe passage and so a claim about earth would not obviously advance anargument prosecuted in terms of fire, air, and water only. More likely, ‘theothers’ refers to the element that is paired with each of fire and air in (4).Tis gives us the following reading of 332a21-22:

(5) x is between air and water ∨  x is between air and fire →  x is thicker than air andfiner than water ∨  x is finer than air and thicker than fire.

Presumably, the first disjunct on the left of the arrow entails the lead dis- junct on the right side, and the second entails the remaining disjunct onthe right. Tus, whatever is between air and water is thicker than air andfiner than water, and whatever is between air and fire is finer than air

and thicker than fire.8

Armed with (5) Aristotle can make trouble for theapeiron, for the right side of (5) has an entailment that will prove to becrippling, namely:

7) Tis allows us to suppose that, for the sake of argument, Aristotle is construing Anaxi-mander’s intermediate as the only element, falling between items that are not proper ele-ments, namely the four Aristotelian elements, for no longer would these be the fundamental  elements.8) Although Aristotle does not include earth in claim (5), as we shall shortly see his argu-ment could be pressed against a corresponding claim that does mention earth.

Page 6: Aristotle on the Impossibility  of Anaximander’s apeiron

7/27/2019 Aristotle on the Impossibility of Anaximander’s apeiron

http://slidepdf.com/reader/full/aristotle-on-the-impossibility-of-anaximanders-apeiron 6/15

22  M. Wedin / Phronesis 58 (2013) 17-31

(6)  x  is thicker than air and finer than water ∨  x  is finer than air and thicker thanfire →  x is fire and air with something contrary.

 As it stands, (6) is a plain version of Aristotle’s words: ‘that will be air andfire together with a contrary.’ One might suppose that Aristotle is herecharacterizing the intermediate as a complex triple, consisting of air, fire,and a contrary. But since he begins in (3) by considering a pair of alterna-tives, he is more plausibly supposing that each alternative in the anteced-ent of (6), i.e. each element there mentioned, is to be paired with a contrary.Tis gives us:

(7)  x  is thicker than air and finer than water ∨  x  is finer than air and thicker thanfire →  x is fire with a contrary ∨  x is air with a contrary.

Tus, what is thicker than air and finer than water is fire with a contrary and what is finer than air and thicker than fire is air with a contrary. Now the consequent of (7) is problematic because it is reasonable to assume thatif something is F , say, and the contrary of F , then that thing consists of contraries. Tis amounts to:

(8) x is fire with a contrary ∨  x is air with a contrary →  x consists of contraries.

However, the consequent of (8) is impossible according to (1), the generalprinciple governing Aristotle’s argument. For if the free variables in (8)have values then there will be something that consists of contraries, con-trary to the decree of (1).

So we must reject the antecedent of (8) – there cannot be something 

that is fire with a contrary or air with a contrary. But the antecedent of (8)is the consequence of (7). Because it is false, we must reject the antecedentof (7) and so enter

(9) ¬◊(∃ x )( x is thicker than air and finer than water ∨  x is finer than air and thickerthan fire)

as the next step of the proof. Because (9) denies the consequent of (5), wemay reject (5)’s antecedent and so assert:

(10) ¬◊(∃ x )( x is between air and water ∨  x is between air and fire).

Page 7: Aristotle on the Impossibility  of Anaximander’s apeiron

7/27/2019 Aristotle on the Impossibility of Anaximander’s apeiron

http://slidepdf.com/reader/full/aristotle-on-the-impossibility-of-anaximanders-apeiron 7/15

M. Wedin / Phronesis 58 (2013) 17-31 23

 What (10) denies is just what (3) asserts is a necessary condition for some-thing’s being an intermediate. So no such intermediate entity can be the

underlying stuff of anything; nor, a fortiori , can it be the underlying stuff of everything.9 In short, we may enter:

(11) ¬◊(∃ x )( x is intermediate).

Ten, given the equivalence asserted in (2), (11) allows us to conclude:

(12) ¬◊(∃ x )( x is apeiron).

 Anaximander’s apeiron is, in a word, impossible.Te above reconstruction appears to give Aristotle a valid argument

against the very possibility of the apeiron. As far as it goes, the argument iscomplete, at least insofar as it captures Aristotle’s reasoning in 332a20-25.Nonetheless, there is something unsettling about the argument. Te trou-ble lies in step (7). It is crucial for the claim that the intermediate consistsof contraries, but it stands in need of explanation, if not argument. Nei-ther is provided in the passage. Without some account of (7), Aristotle’sbold claim about Anaximander’s apeiron remains mysterious.

 What explains Aristotle’s confidence in (7)? Or, less ambitiously, how is(7) to be explained, quite apart from its plausibility or truth? Well, onemight appeal to passages such as 331a1-3, where Aristotle speaks of theelements themselves as contraries, suggesting that at 332a20-25 what it isto be fire or air with a contrary is just to be fire plus another element, or airplus another element. But this suggestion fails to do justice to the claimthat the apeiron is held to be something besides the four standard elements,

something intermediate between them. Arguably, combining canonicalelements does not yield something besides the elements. A different expla-nation would be welcome.

9) Note that, as a matter of logic, one could deny that something was the underlying stuff of everything and still hold that it is the underlying stuff of something. By denying that theintermediate can be the underlying stuff of anything, Aristotle blocks this move. Of course,this allows that something could be said to underlie itself, so long as it does not consist of contraries. But this is a harmless case as far as the argument goes because the apeiron just isan intermediate and so consists of contraries.

Page 8: Aristotle on the Impossibility  of Anaximander’s apeiron

7/27/2019 Aristotle on the Impossibility of Anaximander’s apeiron

http://slidepdf.com/reader/full/aristotle-on-the-impossibility-of-anaximanders-apeiron 8/15

24  M. Wedin / Phronesis 58 (2013) 17-31

I shall suggest, then, that in frames such as (7) Aristotle in effect replacesoccurrences of elements with occurrences of the property-pairs that consti-

tute the elements.10 Tus, air gives way to hot and wet, fire to hot and dry,and water to cold and wet. Tis gives Aristotle a richer set of items from which to construct the alleged intermediate entity he identifies with theapeiron. So the antecedent of (7) may be rewritten as:

(7*) x is thicker than hot + wet [air] and finer than cold + wet [water] ∨  x is finer thanhot + wet [air] and thicker than hot + dry [fire] →  x is fire with a contrary ∨  x is air with a contrary.

Te transformation encoded in (7*) enables us to see how something inter-mediate between elements consists of contraries and so is impossible. How,exactly? Well, consider the first case mentioned in (7*). If something isthicker than hot + wet and finer than cold + wet, then it will have an addi-tional determinant. By definition of the case, this must come from eitherair or water. Te additional determinant cannot be the property wet,because where x is air, we would be adding a determinant to something that already is wet, so that the addition of wet could not make x thicker.

Moreover, because x is between air and water, the additional determinantmust come from water. Since it cannot be wet, it must be in virtue of hav-ing cold that x is thicker than hot + wet. Terefore, what is between air and water must be (hot + wet) + cold. But cold is the contrary of hot and so thealleged intermediate is nothing but air (i.e. hot + wet) plus a contrary (i.e.cold). So the intermediate, x , will, after all, consist of contraries. Since thisis impossible, so is the intermediate.

 Alternatively, and this is the second option Aristotle considers, one

might begin with air and fire, which is hot + dry. If there is to be some-thing intermediate between air and fire, then fire must have an additionaldeterminant. Tis cannot be hot, because fire already is hot and so addi-tion of this would not yield anything different. What must be added, of course, is the other determinant of fire, namely, dry. But now what isintermediate between fire and air will consist of (hot + wet) + dry. Te

10) In support of this suggestion, note that Aristotle pursues a similar strategy in the passagethat immediately precedes the argument of 332a20-25. For an outline of the earlier argu-ment, see our opening paragraph.

Page 9: Aristotle on the Impossibility  of Anaximander’s apeiron

7/27/2019 Aristotle on the Impossibility of Anaximander’s apeiron

http://slidepdf.com/reader/full/aristotle-on-the-impossibility-of-anaximanders-apeiron 9/15

M. Wedin / Phronesis 58 (2013) 17-31 25

intermediate so characterized will be air plus a contrary and, as before, it will consist of contraries and so will be an impossible object.

Slightly regimented the above alternatives can be represented as:

(7a) x is between air and water →  x is (hot + wet) + cold

and:

(7b) x is between air and fire →  x is (hot + wet) + dry.

Tese, in turn, entail corresponding contraries, namely:

(7a*) x is hot + cold

and:

(7b*) x is wet + dry.

But the terms in (7a*) and (7b*) are each other’s privations. Hence, therecan be nothing that satisfies the open sentences of either formula. Alterna-tively, we can give ‘+’ conjunctive force. Ten (7a*) and (7b*) entail,respectively, that x is hot and x is cold, and that x is wet and x is dry. Teseexpress logically incompatible formulae in the sense that for any value of  x a pair of incompatible propositions results. So where this value is theintermediate, as in Aristotle’s proof, we are left with an impossible object.Tis gives full force to Aristotle’s claim that the intermediate, and so theapeiron, will, in Graham’s lean translation, ‘turn out to be air and fire with

a contrary qualification.’ Tere can be no such thing, just as advertised.11

Tere is, of course, more to the story. I begin with two comments about Aristotle’s strategy of argumentation, and then press a pair of more sub-stantive points. Regarding strategy, note, first, that the argument is robustin two ways. Just as what is between air and water is air with a contrary, so

11) It is worth mentioning that, as reconstructed, Aristotle’s argument requires, somewhatimplausibly in my view, that wet, dry and the like are what might be called non-additiveproperties. Tat is, addition of wet to wet does not result in something different, i.e. some-thing yet wetter; and addition of wet to dry yields something with contrary componentsrather than something different that is neither as wet nor as dry as its components.

Page 10: Aristotle on the Impossibility  of Anaximander’s apeiron

7/27/2019 Aristotle on the Impossibility of Anaximander’s apeiron

http://slidepdf.com/reader/full/aristotle-on-the-impossibility-of-anaximanders-apeiron 10/15

26  M. Wedin / Phronesis 58 (2013) 17-31

also is it water with a contrary; and just as what is between air and fire isfire with a contrary, so also is it air with a contrary. Aristotle does not need

to add these cases because they are equivalent to the cases he does give us.For what is water with a contrary is just (wet + cold) + dry and this yields(7a*), and what is air with a contrary is (dry + cold) + hot, and this yields(7b*). Note, secondly, that the argument explicitly omits the elementearth. But, again, the omission is harmless because the argument appliesequally to what is between water and earth. For this will be (wet + cold)together with (cold + dry) and this reduces to what is (cold + wet) + dry and so gives us something that is wet + dry, just what (7b*) records.

 A more substantive point concerns what might be called the ‘modality’of Aristotle’s conclusion. Te intermediate, he concludes, can never existby itself.12 Now, of course, one might ask why the apeiron must exist by itself. After all, in its role as the underlying stuff one might suppose that itdoes not occur by itself. But Anaximander’s single underlying stuff alsooccurs as the ‘surrounding’, and in this function the apeiron presumably occurs as a kind of free-standing stuff. Here Aristotle’s argument gains trac-tion. For we can take him to argue, counterfactually, that as free-standing stuff the intermediate would actually exist as something that is betweenfire and air or air and water and so would be something that is actually hotand cold or actually wet and dry. But this is plainly impossible as his argu-ment shows. Since the stuff that surrounds is no different from the stuff that underlies, the latter too must be declared impossible. In both cases, what is banned is the compresence of contraries ‘existing in their full real-ity without qualification’ (334b10-13).

Tere is, however, more to be said about the intermediate’s function assurrounding stuff, a role Aristotle deems impossible. Tus, consider the

point that a standard element such as air can occur as a free-standing ele-ment. As such, it will have the distinctive properties that comprise it, inthis case hot and wet, and it will have them without qualification. Since Anaximander’s intermediate occurs as a free-standing stuff, it also mustpossess its distinctive properties without qualification. Tis, of course,means that it will have the contrary properties reported in (7a*) and (7b*) without qualification. Now these resulted from combining the defining properties of the flanking elements, i.e. the elements between which the

12) Graham 2010, 53: ‘So it is never possible for the alleged source to exist by itself.’ Joachim 1922 ad loc.: ‘the intermediate never can exist . . . in isolation.’

Page 11: Aristotle on the Impossibility  of Anaximander’s apeiron

7/27/2019 Aristotle on the Impossibility of Anaximander’s apeiron

http://slidepdf.com/reader/full/aristotle-on-the-impossibility-of-anaximanders-apeiron 11/15

M. Wedin / Phronesis 58 (2013) 17-31 27

intermediate falls. So while the intermediate is not the product of combin-ing standard elements, it will have to be constituted by some combination

of the defining properties of these elements. It is this requirement, appar-ently imposed by Aristotle, that ushers in the disqualifying contradiction.13 Tus nothing can be, for example, hot without qualification and also cold without qualification, but Anaximander’s intermediate must be bothbecause it functions as an (or the) element and elements by definition arethings that can have their defining properties without qualification. Hence,it cannot be the underlying element of anything.14

Its probative virtue notwithstanding, Aristotle’s argument invites a 

complication. For his complaint against the apeiron as an intermediatestuff requires that Anaximander combine what cannot be combined,namely, distinct elements or at least the defining properties of such ele-ments. Yet Aristotle himself appears to embrace just such combinations.Tus, he clearly allows that earth and fire may be mixed but he must deny that this results in the impossibility facing Anaximander. He does this by claiming that, when two elements are mixed, they do not actually exist assuch in the resulting mixture; rather, they exist in it potentially , in the sensethat they can be ‘recovered’ from the mixture as stand-alone stuffs. For thedefining properties of such elements, a parallel account holds. Tus whenfire combines with water, for instance, the hot of fire will be cold and thecold of water will be hot – not cold or hot ‘without qualification’ but coldfor fire and hot for water.15 Likewise, hot without qualification existspotentially in the mixture because the hot that is cold is potentially hot without qualification and the cold that is hot is potentially cold withoutqualification. Tese potentialities are actualized when fire and water, the

13) Te requirement is actually quite strong for in effect it legislates that all differencesbetween stuffs is to be explained by differing proportions of the fundamental properties,hot, cold, wet, and dry. So these serve as something like the ‘building blocks’ for stuffs,elemental and other.14) I hasten to add that it is not at all clear that the historical Anaximander would view hisintermediate as analogous to an Aristotelian element.15) As Aristotle puts it, in Joachim’s translation: ‘. . . so that there exist instead a hot which(for a “hot”) is cold and a cold which (for a “cold”) is hot’ (On Generation and Corruption 334b10-12).Tis uncharacteristically colorful language may be unpacked in more pedes-trian terms: the hotness that is in the mixture is not as hot as the hotness of the hot whenit occurs free of cold; likewise, the cold that is in the mixture is not as cold as the coldnessof the cold when it occurs free of hot.

Page 12: Aristotle on the Impossibility  of Anaximander’s apeiron

7/27/2019 Aristotle on the Impossibility of Anaximander’s apeiron

http://slidepdf.com/reader/full/aristotle-on-the-impossibility-of-anaximanders-apeiron 12/15

28  M. Wedin / Phronesis 58 (2013) 17-31

elements of the combination, are recovered from the combination. Forthen we have both defining properties existing as such without qualifica-

tion. So hot and cold cannot be combined.Moreover, when hot and cold are combined in this manner (as when

fire and water are combined), Aristotle says that the result is an intermedi-ate entity, something that is, for example, potentially more hot that cold.So Aristotle’s version of an intermediate stuff is acceptable but Anaxi-mander’s is not. How is this to be allowed? Well, it appears that Aristotlemust reject Anaximander’s apeiron for either of two reasons. On the onehand, as we have suggested, he may simply reject the existence of an alleged

stuff besides the standard elements because when characterized as in (3)such stuff would consist of properties that are contraries and cannot becombined. Lacking the distinction between actuality and potentiality, Anaximander’s hot and cold can exist in the combination only in their fullactuality. On the other hand, Aristotle might adopt a somewhat moreconcessive tone, allowing Anaximander to combine defining propertiessuch as hot and cold but insisting that this can only work if it accords withhis own account – an account that does not call for an additional stuff besides the standard elements. On this reading, Anaximander makes a  worthy effort but needs Aristotle to show him how such combinations work.16

Finally, there is a point of interest concerning Aristotle and the notionof prime matter. Should such a thing exist, it would underlie the mostfundamental changes – perhaps, changes between elements. Aristotle’sallegiance to the notion is, of course, not a settled matter, and On Genera-tion and Corruption itself discusses at some length the transformation of one element into another in terms that may not require prime matter. But

if prime matter exists, it is at least clear that it is strictly a potentiality, whether a potentiality of a fundamental stuff to change, or the matter of the most fundamental stuffs – earth, air, fire, and water. It will, then, enjoy the potentiality canonically associated with matter and because it is thefundamental underlying stuff, it will have nothing underlying it.

16) How Aristotle’s account works, of course, is hardly pellucid. Indeed, it is fraught withdifficulties. o get a handle on the difficulties see the excellent accounts of Fine, Code andBogen in Lewis and Bolton 1995, and the earlier account in Gill 1989. On prime matterin On Generation and Corruption, see the Appendix in Williams 1982. For astute guidanceon the complexities of Aristotle’s theory of mixture see Fine 1995.

Page 13: Aristotle on the Impossibility  of Anaximander’s apeiron

7/27/2019 Aristotle on the Impossibility of Anaximander’s apeiron

http://slidepdf.com/reader/full/aristotle-on-the-impossibility-of-anaximanders-apeiron 13/15

M. Wedin / Phronesis 58 (2013) 17-31 29

So Aristotle’s prime matter is pure potentiality. As such, it is nothing that actually exists or, at any rate, nothing that actually exists on its own as

such. By contrast, then, where P  is the fundamental underlying stuff, Anaximander apparently is held to:

(13) P underlies everything → P actually exists as such.17 

 As we have seen, (13) can be attributed to Anaximander because he holdsthat the intermediate, as the ‘surrounding’, exists on its own as a stand-alone stuff and also underlies everything else. Since it exists on its own, the

intermediate could qualify as an element because for Aristotle an elementmust be capable of existing as a stand-alone stuff.18 For Aristotle some-thing like this occurs when an element ceases to underlie, i.e. when it isrecovered from a mixture. Tis maneuver exceeds Anaximander’s concep-tual range. Plus, in any case, Aristotle’s version of an ultimate underlying stuff is not subject to this constraint. Terefore, he may deny (13) and helphimself to:

(14) P underlies everything → P does not actually exist as such,

 which is consistent with the thesis that prime matter exists as a purepotentiality.19 From this point of view, Anaximander’s apeiron is less a 

17) According to Williams (1982, 214), at 332a35-b1 Aristotle takes another swipe at Anaximander by asserting that the apeiron was held to be both perceptible and prior to theelements, whereas in fact nothing that is prior to the elements, the ultimate perceptibleitems, could be perceptible. It is not completely clear that Aristotle is addressing Anaxi-mander’s singleton in this passage as opposed to drawing a consequence for his own view,namely, that what would be intermediate between the elements would have to be imper-ceptible and inseparable. In attributing (13) to Anaximander, Aristotle takes him to awardseparate existence to the apeiron. It is, however, unclear that this, in turn, entails that theapeiron be perceptible, for in Aristotle’s scheme something can be actual without being perceptible. Perhaps, its status as an actual material or stuff-like thing is sufficient to gener-ate the entailment. Tis would give him the requisite contrast with Anaximander’s single-ton, namely, his own candidate, prime matter.18) Note here that (13) does not require that P , in its role as the underlying stuff, actually exists as such (though it may, for all I know). It is enough that what serves in this role iscapable, independently, of existing on its own.19) Tis claim invites comment. Consider, for instance, the fact that prime matter, as a strict potentiality, is arguably nothing actual. Tere are two worries about this. First, it may 

Page 14: Aristotle on the Impossibility  of Anaximander’s apeiron

7/27/2019 Aristotle on the Impossibility of Anaximander’s apeiron

http://slidepdf.com/reader/full/aristotle-on-the-impossibility-of-anaximanders-apeiron 14/15

30  M. Wedin / Phronesis 58 (2013) 17-31

plain blunder than an honorable, if unsuccessful, precursor to Aristotle’snotion of prime matter.20

Bibliography 

Barnes, J. (1979), Te Presocratic Philosophers , vol. 1. London.Bogen, J. (1995), ‘Fire in the Belly: Aristotelian Elements, Organisms, and Chemical

Compounds’, Pacific Philosophical Quarterly 76: 370-404.Buchheim, . (2010), Aristoteles: Ueber Werden und Vergehen. Berlin.Charles, D. (2004), ‘Simple Genesis and Prime Matter’ in F. de Haas and J. Mansfeld

(eds.), Aristotle : ‘On Generation and Corruption’, Book I (Oxford), 151-69.Cherniss. H. (1935), Aristotle’s Criticism of Presocratic Philosophy . Baltimore.Code, A. (1995), ‘Potentiality in Aristotle’s Science and Metaphysics’, Pacific Philosophical 

Quarterly 76: 405-18.

strain the parallel with how matter functions in familiar cases. For even as a potentiality,ordinary matter can hardly be nothing actual. For suppose there existed nothing but oak benches and chairs. In such a circumstance there would exist no plain oak matter, only oak shaped up in pretty definite ways. But should we care to say that oak does not actually exist,then neither will there exist oaken things. And so with matter more generally, were there

no plain earth, neither would there be earthen things. And so it would seem that at themost general level of all, were there no plain matter then there would be no material things.In all these cases, it seems to me that we are inclined to affirm that the oak, the earth andthe matter is something actual. Te principle underlying this seems to be that if  x  is anactual thing with matter, m, then m is actual. So it is hard to see how prime matter couldunderlie anything actual. Yet as with Anaximander’s apeiron, so Aristotle’s prime matter isheld to enjoy just this function. Now if earth as such is something actual, then we need tomake sense of earth as such existing as such, not merely existing as this or that shaped upthing. Perhaps, we can accommodate this by appealing to the fact that earth as such wouldbe at its natural place and in this circumstance would not be shaped up as any given earthenthing. Tere is, of course, no parallel for prime matter and so this further strains the anal-ogy between it and ordinary matter.

A second and related worry is this: supposing prime matter to function as something underlying, still how can something that is a mere potentiality take on any actual proper-ties, as it must if it is to ‘be’ something actual such as fire or earth? One answer, due toLewis (2008, 125 n. 5), is that prime matter has as essential properties only dispositionalproperties. Tus, it has the disposition to be hot, and this is realized when it serves as thematter of fire. I leave to the reader whether, and to what extent, this might strain the paral-lel with how more ordinary matter accommodates dispositional properties. More generally,I leave to bolder hands the nuances attending Aristotle’s notion of an ultimate and strictly potential thing. Here Lewis 2008, Charles 2004, and Code1995 are adept guides.20) Tis may offset Barnes’s appraisal (1979, 37) that with Anaximander’s notion of theapeiron, ‘we find ourselves in a desert of ignorance and uncertainty.’

Page 15: Aristotle on the Impossibility  of Anaximander’s apeiron

7/27/2019 Aristotle on the Impossibility of Anaximander’s apeiron

http://slidepdf.com/reader/full/aristotle-on-the-impossibility-of-anaximanders-apeiron 15/15

M. Wedin / Phronesis 58 (2013) 17-31 31

Fine, K. (1995), ‘Te Problem of Mixture’, Pacific Philosophical Quarterly 76: 266-369.Gill, M. L. (1989), Aristotle on Substance: Te Paradox of Unity . Princeton.

Graham, D. (2010), Te exts of Early Greek Philosophy , Part 1. Cambridge. Joachim, H. H. (1922), Aristotle on Coming to Be and Passing Away . Oxford.Kahn, C. (1960), Anaximander and the Origins of Greek Cosmology . New York.Kirk, G. S., Raven, J. E., and Schofield, M., Te Presocratic Philosophers . 2nd ed. Cambridge.Lewis, F. A. (2008), ‘What’s the Matter with Prime Matter?’, Oxford Studies in Ancient 

Philosophy 34: 123-46.Seligman, P. (1962), Te ‘Apeiron’ of Anaximander . London. Williams, C. J. F. (1982) (tr.), Aristotle’s De  Generatione  et  Corruptione . Oxford.