fine, gal - aristotle's two worlds - knowledge and belief in posterior analytics i.33

Meeting of the Aristotelian Society held at Senate House, University of London, on 7 June 2010 at 4:15pm.

©2010 The Aristotelian SocietyProceedings of the Aristotelian Society, Vol. cx, Part 3

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XIV—ARISTOTLE’S TWO WORLDS: KNOWLEDGE AND BELIEF IN POSTERIOR ANALYTICS 1.33

GAIL FINE

At the end of Republic 5, Plato distinguishes epistêmê from doxa, knowl-edge from belief. In Posterior Analytics 1.33, Aristotle provides his owndistinction between epistêmê and doxa. I explore his way of distinguishingthem and compare it with Plato’s.

I

In a famous and much-discussed passage in Republic 5, Plato distin-guishes epistêmê from doxa—knowledge from belief. What’s lesswell known is that Aristotle devotes a chapter of the Posterior Ana-lytics (1.33) to drawing his own distinction between epistêmê anddoxa. In this paper, I explore his way of distinguishing them andcompare it with Plato’s. About Plato, however, I shall have to bebrief.1

II

On a familiar interpretation of the argument in Republic 5, Plato dis-tinguishes knowledge from belief in terms of their disjoint objects:knowledge is of forms, belief is of sensibles. If one has knowledge, it’sonly about forms; if one has a belief, it’s only about sensibles. Onecan’t have any knowledge about sensibles, or any beliefs aboutforms. I’ll call this a Strong Two Worlds Theory for Objects (stwo).

On a second view, Plato favours a Weak Two Worlds Theory forObjects (stwo), according to which, though one can’t know sensi-bles, one can have beliefs about forms. On this view, the set of ob-

1 I discuss Plato in Fine (1978) and Fine (1990).

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jects one can know and the set of objects one can have beliefs aboutare different but not disjoint.

I favour a third view, according to which Plato distinguishesknowledge from belief, not in terms of their disjoint or even differ-ent objects, but in terms of the truth implications of their contents:knowledge but not belief implies truth. I’ll call this the Propositionalreading (p).2

To say that Plato distinguishes knowledge from belief in terms ofthe different truth implications of their contents is not to say that hethinks knowledge and belief are of propositions rather than of ob-jects. Rather, he thinks one knows an object by knowing that it isthus and so: by knowing that certain propositions are true of it.Similarly, one has beliefs about an object by believing that it is thusand so: by believing that certain propositions are true of it.

p leaves open the possibility, though it does not imply, that the ob-jects that can be known and that one can have beliefs about are thesame. Hence, on p, the argument in Republic 5 doesn’t commit Platoto either stwo or wtwo. Nor, on p, does it commit him to either aStrong or a Weak Two Worlds Theory for Propositions (stwp orwtwp): that is, it doesn’t commit him either to the view that noproposition that can be known can be believed or to the view thatsome propositions can be known but not believed. p leaves open thepossibility that every proposition that can be known can be believed.(However, p of course doesn’t leave open the possibility that everyproposition that can be believed can be known. For there are falsebeliefs; they can’t be known since knowledge is truth-entailing.)

One key piece of evidence in deciding how Plato distinguishesknowledge from belief is his opening claim (Rep. 476e10–477a4)that knowledge is set over what is (epi to(i) onti), coupled with hisclaim that belief is set over what is and is not.3 On one view, Platouses ‘is’ existentially, to make the point that knowledge is restrictedto objects that exist (which turn out to be forms), whereas belief isrestricted to objects that both do and don’t exist, or that half exist

2 I defend this interpretation in the articles cited in note 1. Propositions have been under-stood in many ways. As I use the term, propositions are truth evaluable. Sentences express,but are different from, propositions. Propositions also differ from states of affairs: theformer are made true by the latter; the proposition that fire is hot is made true by the stateof affairs of fire’s being hot.3 In Fine (1990), I incorrectly say that the claim about belief is an opening premiss. In fact,as I see in Fine (1978), it is elaborately argued for.

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(which turn out to be sensibles). On what is probably the most pop-ular interpretation, Plato uses ‘is’ predicatively, to make the pointthat knowledge is set over objects that are F (and not also not F),which turn out to be forms; whereas belief is set over objects thatare both F and not F, which turn out to be sensible or perceptibleparticulars (e.g. the Parthenon) and/or sensible or perceptible prop-erties (e.g. bright colour). The form of beauty, for example, is beau-tiful but not also ugly, whereas bright colour is both beautiful (inthis Klee painting) and ugly (when added to a sombre Rembrandt).On p, which is the view I favour and shall assume here, Plato uses‘is’ veridically, to make the point that knowledge but not belief im-plies truth.4

Though Plato says that knowledge implies truth, he doesn’t saythat it implies necessary truth.5 To be sure, at Rep. 477e7 he saysthat knowledge but not belief is infallible (anhamartêton). But all hemeans is that necessarily, if one knows that p, then p, whereas it isnot the case that necessarily, if one believes that p, then p. If this iswhat he means, then he does not make the mistake allegedly ‘madeevery five years in Mind’, that of inferring from the necessity of theconditional to the necessity of the consequent.6

In arguing that knowledge but not belief implies truth, Plato is dis-tinguishing knowledge as such from belief as such, where this leavesopen the possibility that knowledge is a species of belief. However, atsome points in the argument he uses ‘belief’ (doxa) for mere belief:for belief that necessarily falls short of knowledge. He uses ‘belief’ inthis way when he argues that the so-called sightlovers—who ac-knowledge sensibles but not forms—have belief but not knowledge.When belief is so conceived, knowledge is not a species of, and doesnot imply, belief. On the contrary, when belief is mere belief, thesame person can’t, at t1, both know and believe that p. But evenwhen belief is mere belief, it remains possible that every propositionthat can be known can be believed. It’s just that, if p is both knownand believed, it will be either by same person at different times or bydifferent people at the same time or at different times.

4 However, he uses ‘is’ predicatively in Rep. 478d–479e. There is no confusion, but a con-necting link: see the articles cited in note1.5 Contrast Vlastos (1985, §ii).6 Barnes (1975, p. 97) says that it is ‘quite conceivable’ that Aristotle makes this mistake;however, he also suggests an alternative explanation of why Aristotle restricts knowledge towhat’s necessary. The remark is omitted in Barnes (1993).

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III

With this background in mind, let’s now turn to Posterior Analytics1.33. Aristotle begins by saying:7

What can be known (to epistêton) and knowledge (epistêmê) differfrom what can be believed (to doxaston) and belief (doxa) becauseknowledge is universal and through (di’) necessities; and what is nec-essary cannot be otherwise. But there are some things that are true andare beings (esti de tina alêthê men kai onta), but that can also beotherwise. So it is clear that knowledge cannot be about (peri) thesethings; for then what can be otherwise could not be otherwise. But noris understanding (nous) [about them] (for by ‘understanding’ I mean aprinciple of knowledge), nor non-demonstrative knowledge. (This issupposition (hupolêpsis) of an immediate proposition (protasis).) Butit is understanding, knowledge, belief, and what is called after them,that are true. Hence it remains that belief is about what is true or falsebut can also be otherwise. This is supposition of a proposition that isimmediate and not necessary. (APo. 88b30–89a4)

Like Plato in Republic 5, Aristotle contrasts epistêmê and doxa. Aswe’ve seen, Plato’s contrast, at least at some stages of his argument,is between knowledge and belief as such. That, however, is not thecontrast Aristotle is drawing. First, he is not using epistêmê for allknowledge as he conceives of it, but only for what I shall call High-Level Knowledge (hlk): that is, for knowledge of the premisses andconclusions of demonstrations grasped as such.8 Aristotle thinksknowledge is more extensive than hlk. But in this chapter he leaveslower-level sorts of knowledge to one side.9

7 I generally follow the translations in either Barnes (1975) or Barnes (1993), though I some-times alter them without comment. I take it that in saying that epistêmê is universal andthrough necessities, Aristotle means that the conclusions of demonstrations are universalpropositions that have been inferred from premisses that are necessarily true. (Here it’sworth recalling that Aristotle doesn’t restrict necessity to logical necessity.)8 Aristotle initially uses epistêmê just for the cognitive condition that apprehends the con-clusions of demonstrations as such, reserving nous for the apprehension of immediates,which are, or at least include, real definitions. However, he also calls nous non-demonstra-tive epistêmê (APo. 88b36). (I agree with Ross (1949, pp. 606–7), and Barnes (1975,p. 190) that ‘nor’ (oude) in 88b36 is epexegetic.) So he uses epistêmê both narrowly, for thecognitive condition that apprehends the conclusions of demonstrations, and also morebroadly, to include nous.9 I discuss Aristotle on the scope of knowledge in Fine (2010). If lower-level knowledge fallsunder doxa, Aristotle’s distinction between epistêmê and doxa is exhaustive; otherwise, itisn’t.



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Secondly, in APo. 1.33 Aristotle uses doxa just for mere belief: forbelief that necessarily falls short of knowledge. He uses ‘supposi-tion’ (hupolêpsis) for the genus of which doxa and epistêmê are spe-cies.10 As mentioned above, when doxa is mere belief, knowledgeisn’t a species of, and doesn’t imply, doxa. It doesn’t follow, howev-er, that if a proposition can be known it can’t be believed. All thatfollows is that if it is both known and believed, it will be either bythe same person at different times or by different people at the sametime or at different times. Nor does it follow from the fact that Aris-totle uses doxa for mere belief that he doesn’t think knowledge is aspecies of belief as we understand belief: as taking a proposition tobe true.11 On the contrary, in saying that doxa is a species of suppo-sition, he implies that it is a species of belief in ‘our’ sense of theterm.

Though Aristotle’s contrast is between hlk and mere belief, rath-er than between knowledge and belief as such, for the sake of con-venience I shall nonetheless from now on generally ask how hedistinguishes knowledge from belief.

IV

At the beginning of the chapter, Aristotle plainly restricts knowledgeto what’s universal and necessary. But it’s not clear whether he re-stricts belief to what’s contingent or merely means that belief in-cludes what’s contingent. Nor is it clear whether he is distinguishingknowledge from belief in terms of their different or disjoint proposi-tions or in terms of their different or disjoint objects. There are atleast three possibilities:

(a) Only propositions are at issue: knowledge is of universal(i.e. general) propositions that are necessarily true, whereasbelief is either wholly or partly of propositions that arecontingently true and contingently false.12

10 Cf. De An. 427b25.11 For this conception of belief, see Velleman (2000, pp. 244–81).12 Contingently true and false propositions include some general propositions: e.g. ‘Somemen are tall’, which is about a universal not spoken of universally. See De Int. 7, 17b7–12.

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(b) Only objects are at issue: knowledge is of universals (whichare beings, onta) that necessarily exist; belief is either whol-ly or partly of objects whose existence is contingent.

(c) Both propositions and objects are at issue: knowledge isboth of universal propositions that are necessarily true andalso of universal objects that necessarily exist. Belief is ei-ther wholly or partly of true and false propositions, and ofobjects whose existence is contingent.

On (a), Aristotle distinguishes knowledge from belief in terms of thetruth implications of their contents. On (b), he distinguishes knowl-edge from belief in terms of the sorts of objects one can know andhave beliefs about. On (c), he distinguishes knowledge from beliefboth in terms of the truth implications of their contents and also interms of their objects. As we’ve seen, there are disputes about wheth-er Plato, in Republic 5, distinguishes knowledge from belief in termsof their different truth implications or in terms of their different ordisjoint objects. The same issue arises in interpreting APo. 1.33.

One piece of evidence occurs in APo. 88b32–3, where Aristotleuses the phrase ‘there are some things that are true and are beings’.13

One might take ‘and’ to be epexegetic, and argue that ‘true’ is beingused for beings, in the sense of objects whose existence is contingent.That would favour (b).14 However, at least two other readings of thephrase are possible. First, perhaps ‘and’ is epexegetic in the other di-rection, such that ‘beings’ is used veridically, for truth.15 That wouldfavour (a). Alternatively, perhaps ‘and’ is conjunctive: belief is eitherwholly or partly both of contingent truths and falsehoods and alsoof objects whose existence is contingent. That would favour (c).16

Of these three readings, I favour the second, according to which‘beings’ is used veridically for truth. For Aristotle says that under-standing is the supposition of an immediate proposition (protasis),and that belief is the supposition of an immediate proposition that is

13 Cf. Rep. 508d4: alêtheia te kai to on; Tht. 178b6–7: alêthê te oietai hauto(i) kai onta.14 For this interpretation, see Mignucci (1975, p. 647). The main passages that have beenthought to show that Aristotle uses ‘true’ for objects (sometimes construed broadly so as toinclude states of affairs) are Met. 5.29 and Met. 9.10, 1051a34–1051b9.15 This is how it is used in, for example, Met. 1017a31–35. Cf. APo. 71b25–6.16 According to Philoponus (1909, pp. 323.15–27), Alexander favours this interpretation(in his commentary on the Posterior Analytics, which unfortunately is no longer extant).Philoponus also seems sympathetic to it.



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not necessary.17 If understanding and belief are supposition of aproposition, so too, presumably, is knowledge.18 Aristotle also saysthat knowledge, understanding, belief, and what is named fromthem (i.e. what can be known, understood, and believed), are true,and that belief is about what is true or false and can be otherwise(APo. 89a2–3). In speaking of knowledge, understanding, and beliefas true, Aristotle means that these cognitive conditions can be spo-ken of as being true; and, he goes on to imply, belief can also be spo-ken of as being false. They are so called in virtue of the fact thatwhat they are of is true or, in the case of belief, either true or false;and he makes it clear that these are propositions. Hence Aristotle isthinking of propositional truth and falsity.

Aristotle’s claim, then, is that knowledge and understanding (thatis, non-demonstrative epistêmê, i.e. epistêmê that can’t itself bedemonstrated) imply truth, indeed necessary truth; whereas belief iseither restricted to, or at least includes, contingent truths and false-hoods. So Aristotle—like Plato on my interpretation of him—distinguishes knowledge from belief in terms of their different truthimplications; and they both do so by using einai veridically (thoughAristotle clarifies the point by adding alêthê). They differ, however,in that Plato merely says that, necessarily, knowledge implies truth,whereas Aristotle says that knowledge implies necessary truth. (Itdoesn’t follow that he makes the mistake allegedly ‘made every fiveyears in Mind’: he might hold the view on other grounds.)

V

Aristotle next defends his way of distinguishing knowledge from be-lief by saying that it agrees with two appearances (phainomena)(APo. 89a4–5). Perhaps looking at them will help us decide whetherhe thinks belief merely includes, or is restricted to, contingent truths

17 It’s not clear why Aristotle says this about belief. But the crucial point is that he correlatesbelief with a certain sort of protasis, and so with a certain sort of proposition. Aristotlesometimes uses protasis for premisses rather than for propositions as such; but I don’t thinkhe does so here. But even if he does so, still, premisses are a kind of proposition. So eitherway, belief is correlated with a certain kind of proposition.18 If protasis is being used for premisses, and knowledge is restricted to the conclusions ofdemonstrations, then knowledge isn’t a supposition of a protasis. But if Aristotle correlatesbelief and understanding with certain sorts of premisses, presumably he correlates knowl-edge with conclusions and so with a certain sort of proposition. See previous note.

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and falsehoods. Perhaps it will also either reinforce or challenge mysuggestion that he distinguishes knowledge from belief in terms ofthe truth implications of their contents.

According to the first appearance, belief is unstable (abebaios).19

Aristotle doesn’t say what stability amounts to here. It can be under-stood in at least three ways.

First, at the end of APo. 1.2, Aristotle says ‘it is not possible to bemore confident (pisteuomen mallon) of what one in fact neitherknows (eidenai) nor is more happily disposed towards than if one infact knew it, than one is of what one knows’ (APo. 72a32–4); some-one who has knowledge can’t be persuaded out of it (ametapeiston:APo. 72b3–4). Since one is more confident of what one knows thanof what one merely believes, one is less likely to lose one’s knowledgethan one’s mere beliefs; hence knowledge is more stable than belief.

The point can be put in terms of the cognitive condition: I’m moreliable to cease being in the cognitive condition of believing that pthan to cease being in the cognitive condition of knowing that p. Itcan also be put in terms of the propositions that are known and be-lieved: if I know that p, p is stable in the sense that it isn’t likely tocease being known by me; whereas, if I merely believe that p, p is un-stable in the sense that it is more likely to cease being believed by me.

What’s at issue here is rational confidence, not subjective certain-ty. A proposition p is stable for the person who knows that p, be-cause she sees why p is true; hence she is unlikely to abandon p inthe face of counterarguments. A dogmatic believer who holds on toher beliefs come what may isn’t in a stable condition in the relevantsense.20

If this is Aristotle’s point, it leaves open the possibility, though itdoesn’t imply, that there can be belief about every proposition thatcan be known. For the claim is just that if one knows that p, one’ssupposition that p is stable in the right way; whereas, if one merelybelieves that p, it isn’t.

A second interpretation rests on Aristotle’s view that some propo-

19 Aristotle adds: ‘and that sort of nature’ (kai hê phusis hê toiautê). b1 translates: ‘and so toois the nature of the things in question’, which suggests that both the cognitive condition andwhat it is of are unstable. But Aristotle need not be so understood: he might mean that just asbelief is unstable, so too is whatever is relevantly like belief. However, see EN 1139a6–11.20 Cf. EN 1146b29–31; MM 1200b36; Cat. 8b27–8. This is the point Plato has in mindwhen he argues in the Meno that knowledge enjoys a sort of stability (monimoi: Meno98a6) that mere true belief lacks. See Fine (2004).



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sitions can change their truth-value.21 For example, the propositionthat Socrates is standing is true when he is standing; but it changesto being false when he sits down. If Aristotle has this point in mind,perhaps the first appearance means that if A knows that p, p isstable in the sense that it is always true and can’t change from beingtrue to being false. By contrast, if p can change its truth-value, itcan’t be known even when it’s true; one can in this case at most be-lieve that p.

Can one not only know but also believe propositions that are al-ways true and that can’t change from being true to being false? SoAristotle seems to allow in Met. 1051b15–17: ‘beliefs (doxa) andstatements (logos) about things that cannot be otherwise do notcome to be at one time true and at another time false, but the sameones are always true and always false’. Here Aristotle allows one tobelieve that p even if p is always true.22

On a third interpretation, the first appearance says that the onlyobjects one can know are stable, whereas the objects one can havebeliefs about are either restricted to, or include, objects that are notstable. Aristotle does sometimes restrict knowledge to what’s stablein the sense of being everlasting.23 But when he does so, he doesn’trestrict belief to objects that aren’t everlasting. Usually he doesn’taddress the issue one way or the other. But in EN 1111b31–3 he ex-plicitly allows beliefs about what’s everlasting: ‘belief (doxa) seemsto be about everything, no less about things that are everlasting (taaidia) and things that are impossible [for us] than about things thatare up to us’ (Irwin translation, somewhat revised).24

The first appearance, then, doesn’t help us decide whether Aristo-tle distinguishes knowledge from belief in terms of objects, proposi-tions, or both. For elsewhere he makes a stability point both aboutpropositions and about objects (and about cognitive conditions).When he makes one or another stability point elsewhere, he doesn’trestrict belief to what’s unstable. Indeed, in some passages he explic-

21 Cat. 4a34–b13; Top. 123a15–17; SE 178b25–9; Met. 1051b13–18. Cf. Barnes (1975,pp. 189, 126).22 However, doxa might be being used here for belief as such rather than for mere belief. Ifso, the passage doesn’t show that one can merely believe a proposition that is always true.23 See e.g. APo. 1.8 (where, however, the perishability at issue involves propositional truth);Met. 1040a; EN 1139b22–4.24 Here, again, though, doxa might be belief as such; if so, the point made in note 22 applieshere as well.

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itly allows belief about what’s stable in the sense at issue there. Thefirst appearance doesn’t explicitly say there can be belief aboutwhat’s stable. But it seems to leave that possibility open.25

VI

Let’s now turn to the second appearance:

No one thinks (oiêtai) he believes something when he thinks it can’t beotherwise; rather, he thinks he knows it. But when he thinks it is sobut nothing prevents it from being otherwise, he thinks he believes it,assuming that belief is of this sort of thing and that knowledge is ofwhat is necessary. (APo. 89a7–10)

Aristotle claims that when someone takes p to be a necessary truth,she takes herself to know it and not to believe it; and when she takesp to be a contingent truth, she takes herself to believe it and not toknow it. Why do people reason in this way? Because they think be-lief is restricted to what’s contingently true or false, knowledge towhat’s necessarily true.

In fact, not everyone thinks knowledge is restricted to what’s nec-essarily true, belief to what’s contingently true or false. Some peoplethink contingent truths can be known. And some people think onecan merely believe a proposition that’s necessarily true. One might,for example, believe that Fermat’s last theorem is necessarily true,but deny that one knows that it is, since (unlike Andrew Wiles) onecan’t prove that it is.

Further, even if one thinks knowledge is restricted to what’s neces-sarily true, belief to what’s contingently true or false, one should notinfer from one’s thinking that p is a necessary truth that one knowsit, or from one’s thinking that p is a contingent truth that one merelybelieves it. For one might be wrong about its modal status.

Be that as it may, the crucial point for our purposes is that, ac-cording to the second appearance, knowledge is restricted to what’snecessary, belief to what’s contingent. Hence, if Aristotle accepts itwholesale, he’s committed to some version of a Strong Two WorldsTheory, on which what can be known and believed are disjoint. If,as I’ve assumed so far, propositions are at issue, the second appear-

25 But see notes 22 and 24.



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ance assumes stwp, on which the propositions that can be knownand believed are disjoint. However, the second appearance can alsobe explained in terms of objects. The idea, in this case, would bethat one can know an object only if it necessarily exists; if an ob-ject’s existence is contingent, one can at best have beliefs about thatobject. Further, one can’t have beliefs about any object whose exist-ence is necessary. So, though the second appearance assumes aStrong Two Worlds Theory, it’s not clear whether it assumes stwo,stwp, or both.

But before assuming that Aristotle accepts either appearancewholesale, we should see what happens next. For, though Aristotledoesn’t express any misgivings about either appearance here, hesometimes modifies or clarifies appearances.

VII

Aristotle proceeds to ask two questions:

In what way (pôs), then, is it possible to believe and to know the samething (to auto)? And why will belief not be knowledge, if one positsthat it’s possible to believe everything one knows (oiden)? (APo.89a11–13)

The first question asks whether, despite what’s been argued so far,there’s nonetheless a way in which it’s possible to believe and toknow the same thing. The question is indeterminate in at least twoways. First, it’s not clear whether objects and/or propositions are atissue. Secondly, it’s not clear if the question is whether there can bebelief about everything, or about anything, that can be known.

However we resolve these issues, perhaps Aristotle raises the firstquestion because he realizes that he seems to have argued that noth-ing that can be known can be believed; he sees that that’s counter-intuitive and wonders whether there’s a way out. The second ques-tion suggests that at least one way out leads to difficulty: for it sug-gests that if every proposition that can be known can be believed,belief will be knowledge.

The two questions taken together therefore raise an aporia: diffi-culties arise whether or not we say that what can be known can bebelieved. The rest of the chapter is devoted to resolving this aporia.

It may seem clear that even if every proposition that can be

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known can be believed, belief would not be knowledge. For, as Platoand Aristotle agree, there are false propositions and they can’t beknown. However, the second question seems to be asking whethertrue belief would be knowledge, if every proposition that can beknown can be believed. For if p can be known, it’s true. Hence ifsomeone believes that p, her belief is true. What, then, determineswhether she knows, or just has a true belief, that p? Nonetheless, I’llcontinue to follow Aristotle’s lead and ask, as he does, how to dis-tinguish belief from knowledge.

Before replying to either question, Aristotle explains why it mightseem problematical to allow that everything that can be known canbe believed:

For the knower (eidôs) and the believer will follow [the same steps]through the middle terms until they come to the immediates; so that(hôste) since the former knows, the believer also knows. For just asone can believe the fact (to hoti), so too [one can believe] the reasonwhy (to dihoti); and that is the middle term. (APo. 89a13–16)

Aristotle plainly has propositions in mind here: he’s considering acase in which two people—a knower and an alleged mere believer —consider a demonstrated conclusion and trace it back to its grounds,eventually to its ultimate grounds. The suggestion is that, in thiscase, the alleged mere believer has knowledge. For he accepts exactlythe same propositions as the knower does. Hence, if every proposi-tion that can be known can be believed, belief will be knowledge.

On the assumption that belief is not knowledge, there are twoways of responding to this argument. First, one might accept theconditional and argue that not every proposition that can be knowncan be believed. There are at least some propositions that can beknown but not believed. If one accepts such a proposition, onethereby knows it; mere belief isn’t an option.26 Secondly, one mightreject the conditional and argue that belief would not be knowledgeeven if every proposition that can be known can be believed.27

26 For recent discussion and criticism of the closely related view that there are some propo-sitions such that to understand them is to know them, see Williamson (2007).27 One might also challenge the argument Aristotle gives on behalf of the conditional, but Ishall not do so here. It compares interestingly with the geometrical discussion in the Meno:though the slave in some sense follows a proof, Socrates denies that he as yet knows theanswer (Meno 85bd).



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VIII

Which of these replies does Aristotle favour? He begins by saying:28

Or (ê) if he supposes something about what cannot be otherwise in theway in which he grasps (echei) the definitions through which demon-strations [proceed], won’t he not believe (doxasei) but know it? Whileif he supposes that they are true but not that they belong to them invirtue of their essence and form (kat’ousian kai kata to eidos), won’the believe and not truly know—both the fact and the reason why, ifhe believes through the immediates, but if not through the immediates,he will believe only the fact? (APo. 89a16–23)

The passage is terse and difficult to interpret. But on what is per-haps the most natural interpretation, Aristotle is asking whether weshould say that, where p is a necessary truth, one knows, anddoesn’t believe, that p when one grasps that it is a necessary truth,whereas one believes but doesn’t know that p when one doesn’tgrasp that it is a necessary truth.29 On this interpretation, if Aristotleanswers ‘yes’ to the question he asks here, he rejects the conditionalconsidered in APo. 89a11–13. He would be suggesting that even ifevery proposition that can be known can be believed, belief wouldnot be knowledge. Whether a given necessary truth p is known orbelieved depends on whether one grasps that it is a necessary truth.

But it’s not clear that Aristotle endorses the suggestion he consid-ers here; to see whether he does so, we need to look at what he saysnext. Before doing so, however, it’s worth noting that if he does en-dorse the suggestion, he is committed to the view that if p is neces-sarily true and one supposes that it is necessarily true, one therebyknows that p. Yet it seems that any proposition can be accepted oninadequate grounds. For example, I might suppose that p is necessar-ily true (when it is) because I read that it is in a well-respected jour-nal. Unbeknownst to me, however, there was a typo, and the authormeant to claim that the proposition is not necessarily true. If Aristo-tle believes that taking a proposition to be necessarily true, when it is,is sufficient for knowing that it is true, we should be disappointed.30

28 I retain echei. Though the oct deletes it, it is found in most mss.29 Aristotle speaks both of what can’t be otherwise (i.e. of what’s necessary) and of essence.I shall focus on necessity.30 Cf. Barnes (1975, p. 190).

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IX

Aristotle proceeds to argue—characteristically—that ‘there is notbelief and knowledge of the same thing (tou autou) in every way’(APo. 89a23–4). But neither, he argues, do they exclude one anotherin every way. For just as there’s a way in which there can be true andfalse belief about the same thing, so there’s a way in which there canbe knowledge and belief about the same thing. So his resolution ofthe aporia raised by the two questions in APo. 89a11–13 is: there’sa way in which one can believe and know the same thing, and a wayin which one can’t. What are these ways?

Let’s look first at Aristotle’s explanation of how there can be trueand false belief about the same thing. For it is meant to illuminatethe way in which there can be knowledge and belief about the samething. Aristotle explains that:31

to believe truly that the diagonal is commensurate is absurd. But be-cause the diagonal that the beliefs are about (peri) is the same, in thisway they are of the same thing, though what it is to be each of them inrespect of its account is not the same. (APo. 89a29–32)

One can’t believe truly that the diagonal is commensurate (sc. be-cause it isn’t). But one can have the false belief that the diagonal iscommensurate. One can also have the true belief that it is incom-mensurate. That is, one person can have the true belief that it is in-commensurate, and someone else can have the false belief that it iscommensurate; or the same person can have first one of these be-liefs, then the other. Here the ‘same thing’ is an object, the diagonal.The propositions expressing true and false belief are different; butthey are about the same object.

Aristotle’s language is reminiscent of the Sophist, which explainsfalse belief as believing, of x, what isn’t true of x.32 At t1, I mightfalsely believe, of Theaetetus, that he is flying; and you might be-lieve truly, of him, that he is sitting. The thing, x, is the same, butthe propositions about x are different.

Aristotle proceeds to use this account of how there can be true

31 Aristotle offers two accounts of false belief, rejecting the first but accepting the second. Ifocus on the second account.32 Sophist 262e–264b. There’s considerable dispute about precisely how the Sophistexplains false statement and belief. Fortunately, this need not concern us here.



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and false belief about the same thing, to show how there can be be-lief about what can be known:

[Knowledge] is of the animal33 in such a way that it is not possible forit not to be an animal, and [belief is of the animal] in such a way thatit is possible—e.g. if the former is of just what is man (hoper an-thrôpou esti), and the latter is of man but not of just what is man. Forthey are the same,34 because man [is the same]; but they are not thesame in the way (hôs) they take man [to be]. (APo. 89a33–7)

Aristotle immediately infers:

It is clear from this that it is not possible to believe and to know thesame thing at the same time. For then one would at the same timehave the supposition that the same thing can be otherwise and that itcannot be otherwise—which is not possible. In different people it ispossible for there to be each [of these attitudes] with regard to thesame thing, as has been said. But in the same person it is not possibleeven in this way. For he would at the same time have the suppositionthat e.g. a man is just what is an animal (for this is what it is for it notto be possible for a man not to be an animal), and also the supposition[that man is] not just what is an animal (for let that be what it is for itto be possible). (APo. 89a38–b6)

Aristotle has now provided his considered account of the way inwhich there can, and the way in which there can’t, be knowledgeand belief of the same thing.

X

But what are these ways? Aristotle summarizes them in APo. 89a36–7: knowledge and belief can both be of the same thing, e.g. man. But‘they are not the same in the way they take man [to be]’.

On the most natural interpretation of this remark, the point isthat if to auto is an object, there can be belief about everything thatcan be known: one can both know, and have beliefs about, e.g. man.If, however, to auto is a proposition, nothing that can be known canbe believed. Consider, for example, suppositions about what man is.

33 In speaking of ‘the animal’, Aristotle means e.g. man, which he goes on to discuss.34 To auto. Here we might have expected tou autou, for Aristotle’s point is not that knowl-edge and belief are the same, but that what can be known and believed is the same.

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If one’s supposition amounts to knowledge, one knows the proposi-tion ‘Man is necessarily an animal’. If, however, one’s supposition isa mere belief, one believes that, as Aristotle puts it, ‘the same thing[man] can be otherwise’: that is, one believes the proposition ‘Manis not necessarily an animal’. Strictly speaking, knowledge is of theform ‘x is necessarily F’, and belief is of the form ‘x is not necessari-ly F’ (or: ‘x is contingently F’). Let’s call this the Same Object, Dif-ferent Proposition view (sodp). On it, Aristotle claims that nopropositions can be both known and believed. If Aristotle advocatessodp, his answer to the question raised in APo. 89a16–23 is ‘no’.He pulls back, and suggests a different view (though one that stillassumes that, if one supposes that p is necessarily true, when it is,one thereby knows that p).

sodp has much to recommend it (as an interpretation of thechapter: whether it is philosophically plausible is another matter).First, APo. 89a36–7 says that knowledge and belief are of the samething, because man is the same; they differ in how they take man tobe. This is most naturally taken to mean that, though the same ob-ject (e.g. man) can be both known and believed, the propositions ex-pressing knowledge and belief are different.

Secondly, we should expect Aristotle’s considered view to turn ona difference between objects and propositions. For he uses his ac-count of true and false belief to explain how there can be beliefabout everything that can be known; and the key move in that ac-count is to distinguish between propositions and objects. He thenuses that account to explain that, just as there can be true and falsebeliefs about the same objects, though the propositions by whichone does so are disjoint, so there can be knowledge and belief aboutthe same objects, though the propositions by which one does so aredisjoint.

Thirdly, sodp provides a clear account of how Aristotle answersthe two questions raised at APo. 89a11–13. The first question,we’ve seen, asks how it’s possible to know and believe the samething. According to sodp, one can do so if ‘the same thing’ is anobject, but not if it is a proposition. The second question, we’veseen, asks whether belief would be knowledge if every propositionthat can be known can be believed. sodp accepts this conditional;to avoid the consequent, it says that no propositions can be bothknown and believed.

Fourthly, notice that in the example Aristotle gives, the belief



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about what man is is false. Why does Aristotle suggest this? sodpprovides an answer. For if Aristotle thinks that no propositions canbe both known and believed, there can’t be both knowledge andtrue belief about any proposition saying what man is. Aristotlethinks there can be knowledge about what man is. Hence there can’talso be true belief about what man is. So either there are no beliefsabout what man is or else there can be false beliefs here. Aristotleplumps for the latter option.35

Even if there can’t be any mere true beliefs about what man is (forhere one has either knowledge or a false belief), there can be meretrue beliefs about man. One might, for example, have the true beliefthat man is tall (i.e. that some men are tall).

Fifthly, Aristotle says that ‘it is clear from this that it is not possi-ble to believe and to know the same thing at the same time’ (APo.89a38–9). We might have expected him to say that the reason is thatno one can simultaneously know, and merely believe, that p. For, aswe’ve seen, ‘belief’, here, is mere belief; and one can’t, at t1, bothknow and merely believe that p. But that is not the reason he gives.Rather, he says that if one knew and believed the same thing at thesame time, one would be supposing that the same thing, x, both canand can’t be otherwise: one would simultaneously accept the propo-sitions that (e.g.) ‘Man is necessarily an animal’ and ‘Man is notnecessarily an animal’; one would be committed to accepting con-tradictory claims. This suggests that knowledge is always of theform ‘x is necessarily F’, whereas belief is always of the form ‘x isnot necessarily F’. On sodp, it’s clear why Aristotle says this: hethinks belief would be knowledge if every proposition that can beknown can be believed. To avoid that result, he suggests that thepropositions that can be known and believed are disjoint.

Sixthly, on sodp the chapter is clear and straightforward: we cannow see that Aristotle’s opening remarks say that knowledge is re-stricted to necessary truths, belief to contingent truths. Aristotlethen supports that view with two appearances, the second of whichrelies on the assumption that everyone thinks that belief is restrictedto contingent truths, knowledge to necessary truths. Aristotledoesn’t revise or modify that view; he accepts it as is. He proceeds tonote, however, that his view seems to conflict with the intuition that

35 Cf. Met. 9.10, where Aristotle seems to say that in the case of essences, one either graspsthe truth or is out of touch; error is impossible, except accidentally.

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the same thing can be known and believed. To avoid the conflict, heturns from propositions to objects.

Though sodp fits the chapter well, one might think it has at leasttwo disadvantages. First, Aristotle is often thought to believe that,where p is a proposition that can be known, one first believes that pis true, and then acquires high-level knowledge that it is true either(if p is demonstrable) by demonstrating it or (if it is a first principle)by coming to have nous of it. On sodp, Aristotle would be speak-ing loosely when he speaks that way. Strictly speaking, one first be-lieves one proposition, and then comes to know a differentproposition.36 Secondly, one might find sodp philosophically unat-tractive; for one might think that propositions that can be knowncan be believed.

Neither objection is as serious as it might seem to be. As to thefirst, at most once in the Analytics (at 76b28–34) does Aristotle sug-gest that one can first have the doxa that p and then come to knowthat p.37 And perhaps Aristotle is speaking loosely there: the passageoccurs before APo. 1.33; and he sometimes speaks loosely beforeturning to a deeper and more technical discussion. As to the secondobjection, while it’s true that, on sodp, no proposition that can beknown can be believed, that doesn’t imply that the same propositioncan’t be grasped in more than one way. Perhaps, for example, beforedemonstrating that p, one can entertain p, or consider it, or wonderwhether it’s true.38

Still, it may be worthwhile to consider a second interpretation.Perhaps Aristotle thinks that every proposition that can be knowncan be believed, but the knower and believer accept the same propo-sitions in different ways. One can, for example, both know and be-lieve the proposition ‘Man is an animal’. When one knows it, onesees that it expresses a necessary truth. When one believes it, onedoes not see this: one either has no views about its modality or elsetakes it to express a contingent truth. (In fact, as we’ve seen, Aristo-tle plumps for the latter option, since he says that the believer sup-poses that man is not just what is an animal, and that it is possible

36 Cf. Ackrill (1981, pp. 367–8).37 Thanks to David Bronstein for calling this passage to my attention. Though Aristotledoesn’t elsewhere say that one can first have the doxa that p and then come to know that p,he does elsewhere say that one can first know (eidenai) that p and then come to know whyp is so. See e.g. APo. 2.1., 89b29–31; cf. 38–9 (gnôntes).38 Thanks to Linda Zagzebski and Ursula Coope for discussion of this point.



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for man not to be an animal.) Let’s call this the Same Proposition,Different Mode of Apprehension view (spdm).39

On spdm, Aristotle answers the first question raised in APo.89a11–13, about whether the same thing can be known and be-lieved, by saying that every proposition that can be known can bebelieved. And it answers the second question raised there by reject-ing the conditional and saying that, though every proposition thatcan be known can also be believed, belief isn’t knowledge becausethe modes of apprehension differ.

In favour of sodp is the fact that it allows Aristotle to say thatone can first believe that p and then come to know that p. For onemight hope he allows this, even though he rarely speaks that way.One might also favour sodp if one thinks Aristotle answers ‘yes’ tothe question raised in APo. 89a16–23.

However, spdm has disadvantages. First, we’ve seen that Aristo-tle’s account of true and false belief relies crucially on a distinctionbetween objects and propositions. On spdm, the role played by ob-jects is played by propositions; and the role played by propositionsis played by modes of apprehension. The parallelism is not nearly asneat as it is on sodp; indeed, on spdm the discussion of true andfalse belief might seem misleading.

Secondly, when Aristotle introduces the second appearance, hedoesn’t express any misgivings about it. But on spdm he rejects itoutright. If he were going to do so, it would be odd that he initiallymentions the second appearance in support of his own view.

Thirdly, we’ve seen that Aristotle suggests that mere beliefs aboutwhat man is are false. On spdm, he should say instead just that themere believer believes that man is an animal. He need not say thatthe mere believer falsely believes that man is not necessarily an ani-mal. Yet that is what he says.

Further, spdm aims to show how every proposition that can beknown can be believed. But even if it shows how ‘Man is an animal’can be both known and believed, it doesn’t seem to show how ‘Manis necessarily an animal’ can be both known and believed. For heremodality is part of the content of the proposition. We could stipu-late that modality is never part of the content of a proposition. Butthat seems ad hoc. Nor does it seem to be Aristotle’s usual view. In

39 This interpretation may be favoured by Philoponus (1909, pp. 328.14–329.2) and byZabarella (1597/1966, esp. p. 1025), though I am not sure about that. They may insteadfavour tfp, which I consider shortly.

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his modal syllogistic, for example, modality seems to be a part ofsome propositions.

So let’s consider a third interpretation, according to which somebut not all of the propositions that can be known can be believed.Propositions like ‘Man is an animal’ can be both known and be-lieved, but propositions like ‘Man is necessarily an animal’ can beknown but not believed. Let’s call propositions of the former sort‘truncated propositions’, and propositions of the latter sort ‘fullpropositions’. According to the third interpretation, every truncatedproposition that can be known can be believed, but no full proposi-tion can be both known and believed. Let’s call this the Truncatedversus Full Proposition view (tfp).

tfp answers the first question in 89a11–13 by saying that everytruncated proposition that can be known can be believed, but nofull proposition that can be known can be believed. It answers thesecond question in APo. 89a11–13 by rejecting the conditional if itis read in terms of truncated propositions, but by accepting it if it isread in terms of full propositions.

tfp fares better than spdm does. First, whereas spdm rejects thesecond appearance, tfp modifies or clarifies it: it is false understoodin terms of truncated propositions, but true understood in terms offull propositions. Though it would be odd if Aristotle rejected thesecond appearance outright, it would not be odd if he modified orclarified it. Secondly, tfp allows Aristotle to say that, though thebeliever believes that man is an animal (and so to that extent has atrue belief), he is committed to accepting the corresponding fullproposition that ‘Man is not necessarily an animal’, which is false.So it fits better than spdm does with Aristotle’s suggestion thatmere beliefs about what man is are false. Thirdly, tfp doesn’t needto say that modality is never part of a proposition.

Though tfp fares better than spdm does, it doesn’t fit the chap-ter as well as sodp does. First, we’ve seen that the crucial distinc-tion in the discussion of true and false belief is between objects andpropositions. tfp transfers the role played by objects to truncatedpropositions, and the role played by propositions to full proposi-tions. The parallelism is not as neat on tfp as it is on sodp. Sec-ondly, Aristotle says that knowledge and belief are of the same thingbecause they are both of man. On tfp, one would expect him to sayinstead that they are of the same thing because they are both of theproposition that man is an animal. But that is not what he says.



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Thirdly, though it would not in principle be problematic were Aris-totle to modify or clarify an appearance, the chapter reads moresmoothly if he doesn’t modify the ones at issue here. Rather, he ad-duces them in his support, and then moves on to other issues. Andthat’s what happens on sodp. On tfp, by contrast, he modifies orclarifies the second appearance without calling attention to the fact.Fourthly, tfp may seem little more than a sop to those who find itcounter-intuitive to suppose that no propositions can be bothknown and believed. To them, Aristotle says: the same truncatedpropositions can be both known and believed. But he then addsthat, strictly speaking, no one ever supposes just a truncated propo-sition; in accepting any proposition, one is committed to accepting afull proposition. This doesn’t show that tfp doesn’t fit the chapter.But it perhaps gives us a reason to doubt its philosophical creden-tials; and that, in turn, might make us more inclined to favour themore straightforward sodp.

I’ve suggested three interpretations of Aristotle’s final view. Ac-cording to sodp, one can have beliefs about every object that canbe known, but no proposition can be both known and believed. Ac-cording to spdm, every proposition that can be known can be be-lieved; knowledge and belief differ in the way in which they acceptpropositions. According to tfp, no full proposition can be bothknown and believed; but every truncated proposition that can beknown can be believed. Each of these interpretations has advantagesand disadvantages. But all things considered, sodp seems the bestinterpretation, with tfp being the runner-up.

XI

By way of conclusion, let’s ask how Posterior Analytics 1.33 com-pares with Plato’s argument in Republic 5. As we’ve seen, the argu-ment in Republic 5 doesn’t commit Plato to either stwo or wtwo:it leaves open the possibility that there can be knowledge and beliefof exactly the same objects. Nor does the argument commit Plato toeither stwp or wtwp: it leaves open the possibility that every prop-osition that can be known can be believed.

On all the interpretations I’ve considered, APo. 1.33 rejects stwobut accepts wtwo. For it restricts the objects that can be known tothose that necessarily exist, but it allows us to have beliefs about

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them. Hence, unlike the argument in Republic 5, APo. 1.33 is com-mitted to a Weak Two Worlds Theory for Objects.40 (Of course, if,unlike me, one thinks the Republic 5 argument defends stwo, then itis committed to a more robust Two Worlds Theory for Objects thanAPo. 1.33 is. If, unlike me, one thinks the argument in Republic 5 de-fends wtwo, then it agrees with APo. 1.33 on this point. In either ofthese two cases, though, Plato and Aristotle would still differ in so faras different objects would be at issue: forms versus sensibles for Plato;what’s necessary versus what’s contingent for Aristotle.)

As to propositions, whereas Plato says just that knowledge butnot belief implies truth, Aristotle, on all the interpretations I’ve con-sidered, says that knowledge implies necessary truth. Hence, just asAPo. 1.33 has a more restrictive view than Republic 5 does aboutthe range of objects that can be known, so it has a more restrictiveview about the range of propositions that can be known. In denyingthat contingent truths can be known, APo. 1.33 is committed to aWeak Two Worlds Theory for Propositions.

What about a Strong Two Worlds Theory for Propositions? Thethree interpretations we’ve considered answer this question differ-ently. On spdm, Aristotle rejects a Strong Two Worlds Theory forPropositions. However, spdm is the least plausible interpretation.tfp avoids a Strong Two Worlds Theory for propositions in the caseof truncated propositions; but it accepts one for full propositions.sodp straightforwardly simply accepts a Strong Two Worlds Theo-ry for Propositions.

It’s often thought that, in Republic 5, Plato defends some versionof a Two Worlds Theory, though in my view he does not do so.However that may be, if the argument of this paper is correct, Aris-totle is committed to a Weak Two Worlds Theory for both Objectsand Propositions; and on the two most plausible of the three inter-pretations we’ve considered, he’s also committed to some version ofa Strong Two Worlds Theory for Propositions. It’s therefore Aristo-tle, not Plato, who defends a Two Worlds Theory.41

40 If, however, as I’ve argued, Aristotle focuses on the different truth implications of knowl-edge and belief, then his commitment to wtwo is more implied than stated.41 Earlier versions were read at Oxford, Yale, Cambridge, Bologna and the AristotelianSociety. Thanks to the audiences for helpful discussion. Thanks too to Ursula Coope, PaoloCrivelli, Dominic Scott, David Sedley and Linda Zagzebski for helpful discussion; to WalterCavini, Andrew Chignell, Michail Peramatzis and Malcolm Schofield for helpful writtencomments; and to David Bronstein for helpful written and oral comments, and for sharinghis own paper on Posterior Analytics 1.33 with me.



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Sage School of PhilosophyCornell UniversityIthaca, ny 14853

[email protected]

Merton CollegeUniversity of Oxford

Oxford ox1 4jduk

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Ackrill, J. L. 1981: ‘Aristotle’s Theory of Definition’. In Enrico Berti (ed.),Aristotle on Science, pp. 359–84. Padua: Editrice Antenore.

Barnes, Jonathan (ed.) 1975/1993: Aristotle: Posterior Analytics, 1st/2ndedns. Oxford: Clarendon Press.

Fine, Gail 1978: ‘Knowledge and Belief in Republic 5’. Reprinted in Fine2003, pp. 66–84.

——1990: ‘Knowledge and Belief in Republic 5–7’. Reprinted in Fine 2003,pp. 85–116.

——2003: Plato on Knowledge and Forms: Selected Essays. Oxford:Clarendon Press.

——2004: ‘Knowledge and True Belief in the Meno’. Oxford Studies inAncient Philosophy, 27, pp. 41–81.

——2010: ‘Aristotle on Knowledge’, Elenchos, 14, pp. 121–56.Irwin, Terence (ed.) 1999: Aristotle: Nicomachean Ethics. Indianapolis:

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mento agli Analitici Secondi. Padua: Editrice Antenore.Philoponus, John 1909: In Aristotelis Analytica posteriora commentaria

cum anonymo in librum secundum, ed. Maximilianus Wallies. Commen-taria in Aristotelem Graeca, xiii.3. Berlin: Reimer.

Ross, W. D. (ed.) 1949: Aristotle’s Prior and Posterior Analytics. Oxford:Clarendon Press.

Velleman, J. David 2000: The Possibility of Practical Reason. Oxford:Clarendon Press.

Vlastos, Gregory 1985: ‘Socrates’ Disavowal of Knowledge’. PhilosophicalQuarterly, 35, pp. 1–31.

Williamson, Timothy 2007: The Philosophy of Philosophy. Oxford: Black-well.

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Zabarella, Jacopo 1597/1966: In duos Aristotelis libros Posteriores Ana-lyticos commentarii. In Opera Logica. Hildesheim: George Olms.

fine, gal - aristotle's two worlds - knowledge and belief in posterior analytics i.33

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