Knowledge and Truth in the Greatest Difficulty Argument: Parmenides 133b4–134b5

One of Plato’s central tenets is that we can know forms. In Parmenides 133b4–134b5, Plato presents an argument whose sceptical conclusion is that we can’t know forms. Although he indicates that the argument doesn’t succeed, he also says it’s difficult to explain how it fails. Commentators have suggested a variety of flaws. I argue that the argument can be defended against some, though not all, of the alleged flaws. But I also argue that Plato hints at a crucial distinction that hasn’t been brought to bear in this context, and that indeed he is sometimes thought not to draw: that between the content and object of knowledge. Once we are clear about this distinction, we can see that the sceptical argument doesn’t imply that we can’t know forms.


Introduction
The first part of the Parmenides raises a series of difficulties, or aporiai (133a8, b1), for the-or a-theory of forms. The last of these is singled out as being "the greatest" (megiston, 133b4); hence it's usually called "the greatest difficulty"1 ("gd" hereinafter). gd can be divided into two: gd1 and gd2. gd1 argues that we can't know forms.2 gd2 argues that gods can't know us or, more generally, fine International Journal for the Study of Skepticism 10 (2020) 209-234 210 "things among us";3 nor can they be our masters. Though gd1 and gd2 are collectively called "the greatest difficulty," gd2 is singled out as being more formidable (deinoteron, 134c4). Nonetheless, gd1 has received the lion's share of the attention, and it will be my focus here. gd1 can itself be divided into two parts, which Sandra Peterson, in her seminal 1981 article, calls the active and the passive routes. The active route argues that we can't know forms; the passive route argues that forms aren't knowable by us. The active route concludes at 134b5; the passive route concludes at 134c3. Though the two conclusions are phrased differently, they are equivalent. In what follows, I focus on the active route.
gd challenges a central claim of the middle dialogues. For they assume that it's possible for us to know forms. For example, according to a famous argument at the end of Republic 5 (an argument that is lurking in the background here and that I touch on briefly below), we can have knowledge only if there are forms; we can have knowledge; so forms exist and we can know them.4 And in Phaedo 74b Simmias says that "we know what the equal itself is": that is, we Platonists can 2 Parmenides begins by saying that gd shows that forms are unknowable (133b4-c1), which might seem to go beyond the claim that we can't know them. And Lewis (1979: 120-122) argues that gd2 seems to imply that god can't know forms either-though, as he says, this conclusion is never explicitly drawn. Mueller (1983: 3), by contrast, takes gd2 to say that gods can know forms. Whether or not gd implies more than that we can't know forms, 135a5 makes it clear that it aims to show at least that: anthrôpine phusei agnôsta; and that's the conclusion I'll focus on. 3 Ta par'hêmin. It's not clear how many things are par'hêmin, but I assume that sensibles are included (though gd never uses the term aisthêta), whereas forms and god are not. (Cf. gd2, 134d9, which contrasts para tô(i) theô(i) ["among the divine," i.e. gods] with ta par'hêmin.) (In saying this, I assume that par'hêmin is here being used ontologically, not epistemologically. I explain this distinction in Section 10 below.) It's not clear where human souls belong: gd doesn't explicitly mention them. Lewis (1979: 110) seems to equate non-forms with sensibles, in which case souls would be sensibles and so among ta par'hêmin. However, if all non-forms were par'hêmin, gods would be par'hêmin; but gd2 makes it clear that they aren't. Cornford (1939: 99) thinks souls "are an intermediate order of existents, having a foot in both worlds." If we are identical to our souls and they can be 'there' , gd1 doesn't imply that we can't know forms when we are 'there' , i.e. when we are discarnate. The Phaedo is sometimes thought to argue that we can have knowledge only when we are discarnate. For anyone who holds this view, the conclusion of gd1 isn't troubling if all it means is that we can't know forms when we are incarnate. In addition to using par'hêmin, gd also uses en hêmin (133c5, 133e5; cf. 131a8). Throughout, I translate par'hêmin as 'among us' , and en hêmin as 'in us' . So far as I can tell, Plato uses the phrases interchangeably for things among us in general. (However, as we shall see, the Epistemological Argument might use par'hêmin both ontologically and epistemologically, but it uses en hêmin just ontologically. See Section 10.) 4 I discuss this argument in detail in Fine (2003bFine ( , 2003c. My discussion of Rep. 5 below draws on these articles. 5 The interpretation of this passage is disputed. I defend my interpretation in Fine (2020aFine ( , 2020b. 6 It's unclear whether gd allows us to know sensibles. It says that any knowledge among us is of things among us, which might seem to imply that we can know things among us. However, the point might be that if there is knowledge among us, it is of things among us; that doesn't by itself imply that there is or can be any such knowledge. 7 Surprisingly, however, the argument is sometimes taken to be of little or no interest to epistemology. Mueller (1983: 3), for example, says that "Parmenides' argument rests on relatively abstract considerations which are independent of specifically epistemological ideas." Or again, Lewis says that "[t]he fallacy the argument commits is perhaps of some interest in the theory of relations, or in deciding the logical form of certain sentences-but intrinsically it has little bearing on questions of epistemology " (1979: 118). (Despite saying this, he goes on to suggest a way in which gd is of epistemological interest: "Roughly put, forms and sensibles are so different, that it may seem a puzzle how there could be a relation that holds between entities of these two kinds. And so it may also seem a puzzle, supposing knowledge to be a relation between entities, how a sensible can have knowledge of forms (or god have knowledge of sensibles)" (1979: 118).) 8 Or, at any rate, views the character Socrates appears to accept in the middle dialogues. I won't ask here whether Plato accepts those views, or attributes them to Socrates for other reasons. 9 Vlastos first introduces the phrase "record of honest perplexity" in Vlastos (1965: 254-255); he discusses gd in Vlastos (1965: 257-258 We can rule out the view that Plato thinks gd is sound.11 For in 133b, he says that it would take a gifted person to understand the refutation of the argument; this suggests that he thinks it can be refuted. In 135b, he repeats that claim and adds that it would take an even more remarkable person both to discover where the argument goes wrong and also to be able to teach this to someone else who has thoroughly sifted through all these difficulties for himself. Nonetheless, he concedes that whoever says that forms "do not exist and that, even if they do, they must, quite necessarily, be unknowable by human nature … seems (dokei) to have a point" (135a4-6).12 Since Plato thinks the argument can be refuted, we should expect to find either a false premise or an invalid inference-or a premise it's reasonable to think Plato takes to be false, or an inference it's reasonable to think he finds fallacious. (Of course, there might be more than one such premise or inference.) But, at the same time, we should guard against interpretations on which the argument is, as Cornford (1939: 98) takes it to be, "almost grossly fallacious"13-though, of course, what strikes us as grossly fallacious might not strike Plato that way. What we ideally want is an interpretation on which the argument seems plausible and is difficult to refute, though, in the end, it can be refuted. Either there's at least one false premise, but one (or ones) whose falsity Plato thinks it is difficult to detect; or else there's at 10 Yet another possibility, suggested by Meinwald (1991: 17-18, 159-162;1992: 365-396) is that the middle dialogues' theory of forms is indeterminate, and gd criticizes one possible reading that is left open but not required. If this is right, Plato might reply by providing an account of forms that is determinate, invulnerable to gd, and left open by the middle dialogues. 11 Proclus, however, thinks the argument is sound insofar as he thinks that there is a kind of form that isn't among us and that we (therefore?) can't know (at least, not with the sort of knowledge at issue in gd). But he thinks both that there are other sorts of forms that are among us that we can (therefore?) know, and also that we can know some forms that aren't in us, through the likenesses (eikones) of them that are in us. Hence, he doesn't take gd to be sound tout court, since he thinks both that some forms are among us and also that we can know some forms that aren't among us. See his Commentary on Plato's Parmenides, 4.919-977. Duncombe seems committed to saying that Plato takes gd to be sound; see below, n. 14. His reasons are very different from Proclus's qualified endorsement. 12 Unless otherwise indicated, all translations are my own, though I have consulted Cornford (1939), Diès (2011), Peterson (1981 (who translates part but not all of the argument), and Gill & Ryan (1996). For the Greek text, I rely on the oct (Burnet 1901), though I have also consulted the Budé (Diès 2011). 13 I discuss his reason briefly below.

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International Journal for the Study of Skepticism 10 (2020) 209-234 knowledge and truth in the greatest difficulty argument least one invalid inference but, again, one (or ones) that Plato thinks it is difficult to detect.14 With this background in mind, let's now turn to gd: or rather, to gd1's active route.
First, though, a word about my strategy. I shall call the last stages of the argument-steps 7-12-the Epistemological Argument (ea). I'll argue that the-or least a-crucial flaw in gd1, so far as our ability to know forms goes, comes late in ea. However, most commentators find the crucial flaw(s) in steps or inferences that precede ea. Some of those steps and inferences are indeed flawed; but they don't explain what's wrong with ea-or, at least, they don't explain everything that's wrong with it. In other cases, steps or inferences that have been taken to be flawed either turn out not to be once they are properly understood, or else aren't actually involved. In order to defend this view, I need to discuss these earlier stages. But in order to have sufficient time to discuss ea, I'll be relatively brief about them.

Steps 1-3: Being Itself in Itself and Non-immanence
The argument begins as follows: Because, Socrates, I think that both you and anyone else-whoever posits for each thing15 some being (ousia) itself by itself-would agree, first, that none of them is in us. (133c3-5) We can formalize this as follows: 14 Commentators who think that the argument is unsound disagree about whether it is valid. Forrester (1974) and Lewis (1979) think it is invalid. Peterson thinks "that the inferential moves in the argument are reasonable," though she adds that "there is no generally valid form exhibited by the argument" (1981: 15): so she seems to think it is invalid. (However, she seems to make this claim just about the passive route, not about the active route.) She also identifies one explicit and one implicit premise that she thinks "seem weaker than the other premises," though she doesn't "have an account of what Plato might have thought were their flaws" (1981: 16); one of these premises figures in the active route, so she thinks it is at least unsound. Duncombe twice says that the argument isn't invalid in the ways in which it is sometimes thought to be (2013: 43, 60). That falls short of saying that it is valid, but on page 60 he says he's shown that the argument is "not formally invalid." He also says that the argument isn't question-begging, insofar as it doesn't involve assumptions Plato would reject. This seems to commit Duncombe to the view that Plato takes the argument to be sound. 15 I.e., for each kind of thing that has a form. There is some being of each thing, itself by itself (ii = being itself in itself). 2. If F is itself by itself, F isn't in us. 3. Therefore, these beings aren't in us.
Assuming the key terms are used univocally, this argument is valid. But neither ii nor not being in us (i.e. not being immanent) is explained. However, both earlier in the Parmenides, and also in some passages in the middle dialogues, forms are characterized as being both ii and immanent. So we should look at those contexts to see how they understand ii and immanence, and whether they take ii to imply non-immanence (or whether ii in fact implies non-immanence, whether or not it is said to do so).
Let's first look briefly at immanence. Though some passages in the middle dialogues describe forms as being immanent (e.g. Phd. 102), Plato doesn't say exactly what that amounts to. Perhaps it will do for present purposes to say that if the form of F is in x, x is F, and the form of F is that in virtue of which x is F and is where x is.
This might seem problematical, however: how can immaterial forms be anywhere? Presumably this worry lies behind Zeno's criticism, earlier in the Parmenides (130e-131e), of the view that forms are in things. He argues that neither the whole nor a part of a form can be in things. But his argument relies on a crudely physicalistic account of immanence that we need not accept. Since the Whole-Part Dilemma argues against just one way of understanding immanence, it's not surprising that, in response to it, Socrates says, not that immanence has been ruled out, but that "it strikes me that it's not at all easy to determine" how to understand it (131e6-7). This suggests that he leaves open the possibility that either the Whole-Part dilemma can be disarmed or else some other account of immanence is possible. And indeed, soon after the Whole-Part Dilemma, they consider the view that forms are thoughts in minds (132b-c). To be sure, that view is also refuted. But the reason isn't that forms can't be in things. The reason is that forms aren't themselves thoughts, but what thoughts are of or about. So it remains possible that forms can be in things in some other way.16 Let's now look at ii. I've argued elsewhere that, as ii is understood in the middle dialogues, it is the view that forms escape compresence of opposites: the form of beauty, for example, isn't both beautiful and ugly, in the sense that anything that participates in it is thereby beautiful but isn't thereby 16 Even if forms aren't immanent, things among us might participate in forms in some other way, e.g. by being likenesses of forms, a possibility Plato explores, but argues against, in Parm. 132d1-133a3. It's not clear that Plato takes the argument to be sound; but even if he does, still, he might think things among us participate in forms in some other way.
ugly. Something that participates in the form of beauty might be ugly; but if it is, that's not because it participates in the form of beauty. By contrast, sensible properties like bright color are both beautiful and ugly in that some brightly colored things are beautiful, whereas others are ugly. For forms to be ii also involves them being unmixed with anything sensible, not in the sense that they aren't immanent in sensibles, but in the sense that their natures are wholly non-sensible. If this is what it is for a form to be "itself by itself," it doesn't imply non-immanence (see Fine 1984Fine , 1987Fine , 1993.17 Nor does ii, as it is understood earlier in the Parmenides (128e6-129a1, 129d7-8, and 130b8), imply non-immanence. For there the phrase is used just to indicate that we should focus on the form as it is in itself: we should consider justice as such, not this or that just person or action. It plays what Peterson (2008: 389) calls a topic-narrowing and, sometimes, definition-seeking, role.
Since ii, as it is understood both earlier in the Parmenides and also in the middle dialogues, doesn't imply non-immanence, Socrates' quick agreement, at the beginning of gd, that ii is incompatible with immanence is surprising.18 One might then think to fault the argument here: either 2 is false; or, if being ii is understood such that it implies non-immanence, it doesn't capture Plato's own understanding of ii. Perhaps that's the point, to show us how not to understand being ii. However, even if this is a flaw in the argument, we shouldn't stop here. For one thing, one can accept 3 without inferring it from 1 and 2. It's often thought that Plato doesn't take forms to be immanent; but not everyone who holds this view infers it from the fact that forms are said to be ii. Further, even if the inference from 1 and 2 to 3 is invalid, many have found fault with the argument elsewhere. So let's see what happens next.
17 To say that forms being auta kath'hauta doesn't imply non-immanence isn't to say that forms are immanent; the claim that forms are auta kath'hauta is neutral as regards immanence. Devereux (1994), by contrast, argues that forms being auta kath'hauta implies that they aren't immanent. If one accepts that view, one won't be troubled by 1-3, but might, for all that, be troubled by other aspects of the argument. 18 Gill (1996: 45-46) thinks that, by this point in the dialogue, they have given up on the idea that forms are immanent, as well as on the idea that things among us participate in forms in some other way. She thinks gd considers what happens if things among us bear no relations to forms, a view that is sometimes called "radical separation." For criticism of the view that gd assumes radical separation, see Peterson (1981) and Duncombe (2013). As I reconstruct the argument below, radical separation is not involved; indeed, premise 4 is incompatible with it. See next note. There's dispute both about whether Parmenides says that 3 implies 4, and about whether it in fact does so.20 Fortunately, this is another issue we can set to one side. For, as we shall see, in ea 3 is not used to justify 4. So let's just focus on 4 on its own. It will be helpful to divide 4 into two parts, 4a and 4b. Let's look at 4a first. It has been formulated in various ways.21 I'll formulate it as follows: 4a. If F is a form and is what it is pros G, then G is a form.
4a concerns only those forms that "are the ones that they are in relation to each other" (pros allêlas eisin hai eisin); such forms have their being (ousia) in relation to themselves, not in relation to things among us. It's often thought that Plato intends a restriction to cases where F and G are correlatives of one another (see, e.g., Duncombe 2013). In favour of this view is the fact that Socrates initially illustrates 4 with the example of master and slave, which are correlatives of one another. However, Socrates' second illustration is of knowledge and truth, which are not correlatives of one another. To be sure, knowledge is a correlative. But its correlative is not truth; nor is truth a correlative. 19 There is dispute about whether the antecedent of the relative pronoun hôn is hosai tôn ideôn or ta par'hêmin. On the first view, which I favour, the passage says that we participate in forms. On the second view, favoured by e.g. Gill and Ryan, it says that we participate in ta par'hêmin, which they take to be so-called immanent characters, e.g. the largeness in me. 20 Oukoun can but need not be inferential. This occurrence of it has been understood in both ways. 21 My formulation is closest to Rickless' (2007: 87), though I prefer 'F' and 'G' to his 'X' and 'Y' . knowledge and truth in the greatest difficulty argument To get around this objection, some commentators suggest that 'truth' here means 'object of knowledge' , 'the known' , or 'the knowable' (see, e.g., Forrester 1974, Duncombe 2013. But these are not natural ways of understanding 'truth' (alêtheia). Nor do we need to have recourse to any of them. For, as we shall see, ea doesn't require knowledge and truth to be correlatives of one another.
If 4a isn't about correlatives, what then is it for a form, F, to be the one that it is, and to have its being, in relation to another form, G? There are at least three possibilities. Firstly, perhaps the point concerns definition: any form that occupies the F-place is defined in terms of a form that occupies (or in terms of forms that occupy) the G-place. On this interpretation, 4a expresses what Peterson (1981: 1 and passim) calls definitional isolation: some forms are defined in terms of other forms.22 Looking ahead to Plato's first illustration of 4a, on this reading the point is that the form of master is defined in terms of the form of slave or, otherwise put, mastery is defined in terms of slavery. So understood, 4a is arguably true and would be taken by Plato to be true.
Secondly, the point might concern, not how any forms are defined, but what properties they have. In terms of Plato's first illustration of 4a, the point, on this interpretation, is that the form of master is the master of the form of slave: it has the property of being a master of the form of slave. So understood, 4a involves Self-Predication (sp), the view that any form of F is predicatively F: it has the property of being F. sp has been interpreted in many ways. On one interpretation, which I have elsewhere called Narrow Self-Predication (nsp), the claim is that the form of master (for example) is a master in something like the way in which some humans are masters. If 4a is so understood, it is false, since the form of master isn't the sort of thing that could be a master in the way in which human beings (unfortunately) can be (Fine 1987(Fine , 1993.23 It's because Cornford understands 4a this way that he takes gd to be "almost grossly fallacious" (1939: 98-99).24 Thirdly, perhaps 4a equivocates between, or conflates, these two readings. It is true on one of them, false on the other.25 fine International Journal for the Study of Skepticism 10 (2020) 209-234 218 I favour the first interpretation. A count in its favour is that 4a involves those forms that have their being (ousia) in relation to other forms. Plato often uses ousia for essence which, in turn, is tied to definition: the definition of something specifies its essence (where these are real, not nominal, definitions and essences). Further, this reading of 4a is adequate for the purposes of the argument.26 It also has the advantage over the second and third interpretations of being true. Further, I've argued elsewhere that Plato doesn't endorse nsp. If nsp is not only false but also never endorsed by Plato, and if the argument doesn't require it, we shouldn't have recourse to it. A fortiori, we need not assume that 4a equivocates between the true definitional claim and the false sp claim.27 I shall assume, then, that 4a means just that a certain range of forms are defined in terms of other forms.

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Step 4: Things among Us Let's now turn to 4b which, as Peterson (1981: 3) remarks, is "more difficult to grasp" than 4a is. I shall formulate it as follows:28 4b. If F is among us and is pros G, then G is among us.
Given the similarity in language between 4a and 4b, one might think they should be interpreted in exactly the same way such that if 4a is about definitional isolation, so too is 4b; whereas, if 4a is about property exemplification, so too is 4b; and if 4a equivocates between or confuses these two readings, so too does 4b. In fact, the language is not exactly the same. In particular, 4a, but not 4b, has tên ousian. Perhaps this indicates that, though 4a is about definition, 4b is about predication (x is F) that doesn't, or at least needn't, advert to essence. This doesn't mean there is an equivocation as between 4a and 4b; rather, Plato uses different language to indicate that pros is being used in two different 26 Peterson (1981) argues persuasively that the active route makes no use of any version of sp.
She also argues persuasively that even if some version of sp is relevant elsewhere, it is just a harmless version of it. 27 It's sometimes thought that Plato accepts, or is committed to, nsp in the middle dialogues.
I argue against that view in Fine (1987Fine ( , 1993; see also Peterson (1973). Of course, one might argue that gd adverts to nsp, not because Plato ever accepted it, but in order to make it clear how not to interpret him. However, it's worth seeing how many premises can be made plausible; and we can make 4a plausible if we set both sp, and the suggestion that 4a equivocates, to one side. 28 My formulation is close to Peterson's (1981) formulation. knowledge and truth in the greatest difficulty argument ways-first for definitional isolation, then for predication.29 This is suggested not only by the fact that 4b doesn't have ousia, but also by Plato's illustrations of 4a and 4b.
If, as I've suggested, 4b is about predication (x is F)-or, otherwise put, about property possession for things among us-Plato would think it is false. For he doesn't think that, in every case, if x is predicatively F, where that involves x's being F in relation to something else y, and x is among us, y is also among us. For example, as we've noted, he doesn't think that human slaves are slaves just of human masters; they (like all of us) are slaves of the gods. We seem, then, to have uncovered a false premise, one Plato would also take to be false. 30 We shall need to see how if at all this affects ea. However, though 4b is false, it has some true instances. For example, every human master is the master just of a human slave.
It's been argued that 4b is not only false but also fallaciously inferred from 4a.31 However, the argument doesn't infer from 4a to 4b, so we shouldn't fault the argument on that score.

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Steps 5-6: Master and Slave Given how difficult it is to understand 4, it's not surprising that Socrates professes not to understand it. In reply, as we've seen, Parmenides first illustrates it with the case of master and slave. We've already glanced at this illustration; but a more detailed exploration is in order.
29 To say that it is used in different ways is not to say that it is used in different senses. But whether ways, or senses, are involved, there is no equivocation if Plato makes the difference clear. 'Bank' is used in different senses in 'The bank of the Cherwell overflowed' and 'I went to Barclays' bank today' . But there's no equivocation in saying 'I walked along the Cherwell river today; its banks overflowed. Then I went on to Barclays' bank, to deposit some money' . 30 Plato would also take 4b to be false if it is understood in terms of definition. For in his view, if anything among us can be defined, and also has a corresponding form, it would be defined, at least in part, in terms of that form. (There is also the question of whether he thinks things among us can be defined, but I leave that issue to one side here.) So whereas 4a is true read in terms of definition but false read in terms of property exemplification, Plato would take 4b to be false whichever of those two ways it is read. And, of course, 4b is also false if it confuses property exemplification and definition. 31 Lewis (1979) thinks the argument infers 4b from 4a, and he takes the inference to be valid. Yi and Bae (1998) agree that the argument infers 4b from 4a, but they argue persuasively that the inference is invalid. In brief, 4a implies a claim about the correlation of instances of F and G; but 4b makes a claim about the correlation of things among us. Yet instances of forms are not always restricted to things among us; for example, several forms instantiate the form of odd (the form of three, of five, and so on). For instance, if one of us is a master or slave of someone, he is presumably not a slave of master itself-of that which is master-nor is a master a master of slave itself-of that which is slave-but, being a human being, he is master or slave of a human being. But mastery itself is what it is of slavery itself; and, in the same way, slavery itself is slavery of mastery itself. (133d7-e4) This includes two claims, which we may formulate as follows: 5. Mastery itself is what it is of slavery itself; and slavery itself is slavery of mastery itself. 6. (a) Human masters are masters (only) of human slaves; and human slaves are slaves (only) of human masters. (b) No human master is master of slave itself, nor is any human slave a slave of master itself.
5 is meant to illustrate 4a. I interpreted 4a in terms of definitional isolation. So if 5 is an illustration of 4a, it says that mastery is defined in terms of slavery, and that slavery is defined in terms of mastery. So read, it is true. What about 6, which is supposed to illustrate 4b? I argued that 4b is about predication; so we should understand 6 that way too. So read, Plato accepts 6b. He also accepts part, but not all, of 6a. He agrees that human masters are masters, i.e. have the property of being masters, just of human slaves. But, as we've noted, he thinks human slaves are slaves not only of human masters but also of the gods. So although 4b is false, it has some true instances. 5 doesn't imply 6. As Peterson explains, 5 implies that no mention of human masters or slaves will figure in the definition of mastery or slavery. But that doesn't imply "that our neighborhood master is not a master of what a slave is" (2008: 400). Of course, we don't think our neighborhood master is a master of what a slave is. But that doesn't affect the fact that 5 doesn't imply this, yet 6 disallows it. But we need not say that there is therefore a fallacious inference here. For just as Plato doesn't say that 4a implies 4b, so he doesn't say that 5 implies 6.

A Rephrasing of Step 4
Having mentioned 5 and 6, Parmenides rephrases 4: But things in us do not have their force (dunamis) pros them (ekeina = forms), nor do those things <have their force> pros us; but, as I say (all' ho legô(i)), knowledge and truth in the greatest difficulty argument those things [forms] are themselves of themselves and pros themselves, and things among us are, in the same way (hôsautôs), pros themselves. (133e4-134a1) Here, rather than saying just that some forms are what they are pros other forms, and that some things among us are pros other things among us, Parmenides speaks of forms having their dunamis pros one another, and of things among us having their dunamis pros one another. But I take it that 133e4-134a1 just rephrases 4; it doesn't make any new points.32

8
Step 7 32 This is suggested by "but, as I say," which is usually anaphoric. The use of dunamis here is sometimes linked to its use in Republic 5 (where epistêmê and doxa are said to be dunameis) and to the battle of the gods and giants in the Sophist. See e.g. McPherran (1999). In my view, there is no significant connection to either of these two passages, but it would take me too far afield to defend that claim here. 33 Oukoun seems to be inferential here in the sense that 7 and 8 are, or purport to be, instances of 4a; and 9 and 10 are, or purport to be, instances of 4b. 34 Cornford (1939), Diès (2011), and Gill and Ryan (1996) all take sumbainoi to be inferential. If it is, presumably the point is that 9 and 10 are inferred from 4b in the sense that they are, or purport to be, instances of it. However, like oukoun, sumbainoi need not be inferential: it can mean 'turn out' or 'happen' , as in it turns out, or happens, to be the case. We can formulate this as follows: 7. Knowledge itself is of truth itself. 8. Each of the knowledges is of a given being, what it is. 9. Knowledge among us is of truth among us. 10. Each knowledge among us is of a given being among us. 11. We don't have the forms, nor can they be among us.35 [12. Therefore, we don't know forms.]36 Just as 5 is meant to be an instance of 4a, so too are 7 and 8; and just as 6 is meant to be an instance of 4b, so too are 9 and 10. But how exactly should we understand 7-12? Let's begin with 7. 7 tells us that knowledge (epistêmê) itself is defined in terms of truth itself. I take it that just as mastery itself and slavery itself, in 5, are forms, so knowledge itself and truth itself are forms. These are not forms Plato focuses on elsewhere. They aren't, for example, among the forms mentioned earlier in the Parmenides. But it has been argued that he mentions them elsewhere.37 Whether or not he does so, he mentions them here.
35 Two questions about 11. First, why does it say that we don't have the forms, rather than, as heretofore, that forms aren't in or among us? Either it is just another terminological variant, or else it indicates a subclass of things that aren't in or among us, viz. those that aren't features of e.g. you or me, as opposed to features of 'this' world that aren't features of humans in particular. In the second case, the second clause of 11 generalizes. Secondly, why does 11 say, not (as 3 does) that forms aren't in us, but that they can't be among us? Perhaps 'can't' alludes to the fact that 3 is inferred from 1 and 2. However, as I've noted, one can defend 3 without relying on 1 and 2. 36 This step is licensed but not explicit. It is the conclusion of the active route: see n. 2. 37 The end of the Crat. seems to have a form of knowledge, though it's been argued that it describes forms differently from how they are described in the middle dialogues and/or in the first part of the Parmenides. See also Phdrs. 247de (though see Rowe 1986: note ad loc.) and, possibly, So. 257d (which may have not only a single generic form of knowledge, but also forms of kinds of knowledge). Aristotle, Met. 1050b34-1051a1, implies that Plato posits a form of epistêmê. Hestir (2016: 5 n. 17) cites the following passages as indirect evidence that Plato posits a form of truth: Phd. 115a1; Rep. 487a5, 511e1, 526b1-2; Phil. 65a1-2. (On 238 n. 18, he mentions only the first two of these passages.) I'm not sure any of these passages mentions a form of truth. If they don't do so, gd is the only place where Plato explicitly mentions it. Perhaps this is significant; perhaps we are meant to see that there are difficulties in positing knowledge and truth in the greatest difficulty argument As is well known, epistêmê can be used both for the cognitive condition of a person who has knowledge and also for propositions, where that includes both individual propositions that are known and also bodies of propositions that constitute a branch of knowledge.38 Not only can we speak of Joe's epistêmê (that is, his cognitive condition, his state of knowing); but we can also say that 2 + 3 = 5 is a piece of knowledge (i.e. a proposition that is known), and that medicine and geometry are branches of knowledge (epistêmai). In ea, epistêmê isn't used for any of these things; rather, it is used for the form of knowledge. If, as I believe, forms are properties, then the form of knowledge is the property of knowledge.39 That, however, leaves it unclear exactly what instantiates or participates in it: just beings who have knowledge, i.e. knowers? Or also or instead individual propositions that are known and/or branches of knowledge? On the reasonable assumption that Plato takes epistêmê to be univocal and thinks that the form of F is that by which all F things are F, he presumably takes all these things to instantiate or participate in the form of knowledge.40 Let's now ask how we should we understand 'truth' in 7. Plato uses alêtheia, and alethic terms in general, in various ways, but they all fall into two broad groups: ontological and semantic.41 For example, in Rep. 515d7 Socrates says that the prisoner who is released in the cave will initially think the shadows are truer (alêthestera) than the things that cast the shadows. This is an ontological use: shadows are less true than what casts the shadows. In Tht. 152c10, Socrates asks whether Protagoras spoke the truth (tên alêtheian) in secret: this is a semantic use. In Phdrs. 247c4-6 Socrates says that "one must be bold enough to say what is true, especially when speaking about truth (tolmêteon gar oun to ge alêthes such a form. However, even if (apart from gd) Plato doesn't explicitly mention a form of truth, he might be committed to one, given his general arguments for the existence of forms. After all, he doesn't usually give an exhaustive list of the forms he recognizes; rather, he mentions some general considerations and/or salient examples. 38 See e.g. Burnyeat (1981). Though he notes that epistêmê can be used both for a cognitive condition and for a body of propositions, he doesn't mention that it can also be used for an individual proposition (or sentence or statement) that is known. For that usage, see e.g. Tht. 197e-198a. 39 I defend the view that forms are properties in Fine (1993). 40 Yi and Bae (1998: 282), however, seem to think that instances of epistêmê are just knowers, whereas Peterson (1981: 4) seems to think they are just branches of knowledge. 41 Or so I am inclined to think. But some think he acknowledges further kinds of truth (or senses of 'truth'). See e.g. Szaif (1996Szaif ( , 2018 A choice between 7O and 7S should take into account how 7 fits into the argument as a whole. But a few preliminary points can be made here. Firstly, 7 implies, even if it doesn't mean, that whoever knows something, knows something real (7O) or true (7S). Secondly, 7 is an instance of 4a, whether it is read as 7O or as 7S; so there is nothing to choose between them on that score.
Thirdly, there is room for dispute about what the form of reality is (if it is at issue here, a matter we haven't yet decided about). It might be the form of being, in which case everything that is, is an instance of it. Or it might be the form of the really real, such that only forms are instances of it.44 Fourthly, though it's controversial to say so, in my view Plato never defines knowledge in terms of forms; nor does he restrict knowledge to forms. Nor does he define knowledge in terms of what's really real or in terms of reality. By contrast, he thinks knowledge is defined (at least in part) in terms of semantic are, rather, the contents of propositional attitudes such as knowledge and belief, and what assertions, utterances, and sentences express (which is not to say that they are mind-or language-dependent). Though sentences e.g. are not themselves propositions, I count them as being semantically true when they express true propositions. 42 Ontological truth is not restricted to forms. In Rep. 515d7, what casts the shadows are said to be truer than the shadows, which implies that shadows have some degree of truth. 43 I'll use 'reality' for ontological truth, and 'truth' for semantic truth (and, sometimes, to render alêtheia, without taking a stand on whether it is being used ontologically or semantically). Neither semantic truth nor reality is the correlative of knowledge. Another possibility, beyond 7O and 7S, is that 'truth' , in 7, is a generic form of truth, of which the forms of ontological and semantic truth are both instances. I don't know of anyone who defends this possibility, and I'll leave it to one side here. Perhaps one reason no one has explicitly considered it is that it's generally thought that only ontological truth is relevant here. 44 Commentators have not been very forthcoming about this issue. Cornford (1939), for example, doesn't even mention it. Yi and Bae (1998: 277 with n. 14) mention it, but don't take a stand.
truth. So, for example, at the end of Rep. 5,45 Plato says that knowledge is set over what is (epi tô(i) onti). As is well known, 'to be' (einai) can be used in various ways: for example, veridically (p is true), predicatively (x is F), and existentially (x exists). I've argued elsewhere that in saying that knowledge is set over what is, Plato means that it is defined, at least in part, in terms of what is semantically true. However, my view is controversial; many commentators think that 'to be' , in the claim that knowledge is set over what is, is predicative, so that the claim is that knowledge is set over what is F (and not also not F), which turns out to be forms (see e.g. Annas 1981). I agree that 'is' is used predicatively at some points in the argument (see e.g. 478e5-479d1)-but not in the claim that knowledge is set over what is. Despite the fact that the argument uses forms of 'to be' in two different ways, there is no equivocation; rather, Plato posits a connecting link. It is tempting to think that in premise 7 of gd, Plato uses alêtheia, rather than a form of einai, to make it clear that he has semantic truth in mind (although, to be sure, we have seen that alêtheia can also be used for ontological truth). Of course, even if, as I think, Plato accepts 7S but not 7O, he might nonetheless intend 7O here: perhaps he wants us to see that it is problematic. Still, as before, it's worth considering whether we can make the various premises and inferences plausible, and/or acceptable to Plato. In the present case, we can accomplish both of these things by understanding 7 as 7S.
However, every commentator I know of seems to interpret 7 as 7O. Jan Szaif, for example, says that Parm. 134a-b (= premise 8) "assumes that each species of knowledge correlates with a Form … while the universal genus knowledge has truth as such as its defining object. This implies that the Forms are understood as specifications of 'the truth'" (2018: n. 23).46 If forms are specifications of truth as it is understood in 7, then truth, in 7, is ontological, not semantic.
Though all the commentators I know of seem to favor 7O, some of them conflate 7O and 7S. Ian Mueller, for example, says that "it seems correct to say that 45 See also Meno 98a. (I discuss Plato's account of knowledge in the Meno in Fine (2004).) See also Gorg. 454d-e. (One might argue that the Gorg. says only that knowledge implies truth. Even if that's so, still, the passage has semantic truth in mind.) The Tht. also takes knowledge to imply, but also, I think, to be defined, at least in part, in terms of semantic truth; and it explicitly rejects the view that knowledge should be defined in terms of its objects. Contrast Sedley (2004: 180). One might argue that only propositional knowledge is defined in terms of propositional (or semantic) truth, and that Plato recognizes other kinds of knowledge that aren't so defined. I won't engage with that issue here, though see n. 50. 46 See also Hestir (2004: 119;2016: 89 n. 19), Mueller (1983: 4), and Cornford (1939: 97) knowledge is knowledge of (some) truth" (1983: 5). But he also takes 7 to say that "Knowledge itself is what it is in relation to Truth itself (the forms)" (1983: 4). It is indeed correct to say that knowledge is defined in terms of (semantic) truth; but it is not correct to say that knowledge is defined in terms of forms. We need to distinguish the content from the object of knowledge. The content of knowledge is semantic truth. What those truths are about is another matter. 7S specifies the content of knowledge, and is true. 7O makes a claim about its objects, and Plato takes it to be false since, I've suggested, he doesn't define knowledge in terms of its objects.47

9
Step 8: Each of the Knowledges and Beings Let's now turn to 8. It differs from 7 in two ways. Firstly, it mentions, not knowledge itself, but "each of the knowledges" (hekastê tôn epistêmôn). These knowledges, like the form of knowledge, are forms-e.g. the form of medical knowledge (i.e. of medicine). Secondly, whereas 7 says that knowledge itself is of truth itself, 8 says that each of the knowledges is of a given being (on), what it is. As we've seen, einai, like alêtheia, can be used for both semantic truth, and ontologically. If we favor 7S, we might think onta, in 8, is used for semantic truth. 8 would then say that each of the knowledges is defined in terms of the truths in its domain. Medical knowledge, for example, is defined in terms of truths about health. As Peterson puts it: "if knowledge itself is of truth itself, then knowledge-about-geometry itself would be of truth-about-geometry itself": (1981: n. 4, though this isn't clearly her explication of premise 8).
For reasons that will emerge shortly, I think this is what 8 means, or at least implies when taken together with 7. However, that's not because I think 8 uses onta for semantic truth. Rather, it uses it for forms.48 We might then infer that truth, 47 Although Szaif is himself very clear about the distinction between content and object, he thinks that, in Plato, "it is not possible clearly to distinguish between the object and the content of knowledge in the case of knowing a Form because the Forms are nothing but reified essences, hence reified descriptive content" (2018: 19). I agree that forms are reified essences, if that means that they are real essences, such that the form of beauty e.g. is what beauty really is. However, that doesn't imply that they are the contents of knowledge; nor, in my view, does Plato think-for that or other reasons-that they are. 48 One reason to think this is that the corresponding claim in the passive route mentions, not onta, but ta genê (134b7). We saw that Rep. 5 uses forms of einai both veridically and predicatively, and so both semantically and ontologically. By contrast, 7 uses one word ('truth') semantically, and 8 uses a different word ('beings') ontologically. Perhaps this is quite deliberate. knowledge and truth in the greatest difficulty argument in 7, is ontological. The point of 7 and 8, on this reading, would be that knowledge as such is of forms (= 7), whereas each of the knowledges is of the form specifying its domain (= 8), so that medicine, for example, is defined in terms of health.49 However, even if we so understand 8, we can still take 7 to say that knowledge is defined in terms of semantic truth. So read, and taken together with 8, it follows that medicine, for example, i.e. medical knowledge, is of truths in the domain of health. It's not that 8 directly says this; but coupled with 7S, it implies this. Or perhaps 8 does say this directly. For contrary to what is generally assumed, it doesn't say that medicine (e.g.) is of health. It says that it is of health, what it is. Perhaps the point is that to have medical knowledge, one needs to know, not any old thing about health, but what health essentially is. To know what health essentially is, is to know the answer to the 'What is F?' question about it, which is propositional. In this sense, 8 involves semantic truth, not in using onta, but in adverting to the 'What is F?' question.50 If we understand 7 and 8 as I have proposed, each of them is, as it purports to be, an instance of 4a. Further, each of them is arguably true. However, neither of them, either on its own or taken together with earlier steps, precludes our knowing forms. All that follows so far is that whoever knows, knows a semantic truth; and that if one has (e.g.) medical knowledge, one knows something in the domain of health (by knowing a truth about it) and/ or knows what health is.
Not only do 7 and 8, even when taken together with earlier steps, not preclude our knowing forms; but also, as we shall now see, neither are they necessary for that conclusion.

10
Step 9: Knowledge and Truth among Us Let's now turn to 9 and 10. Just as 7 and 8 are instances of 4a, so 9 and 10 are, or purport to be, instances of 4b. But what exactly do they say? 9 says that knowledge among us is of truth among us. I take it that knowledge among us is not a form (no forms are among us), but any knowledge we have: your knowledge (if you have any) and my knowledge (if I have any). 49 As we've seen, this is Szaif's interpretation. 50 It's not that one knows a proposition about what health is rather than health itself. Rather, to know a form is to know what it is; and to know what it is, is to know that it is thus and so where that, in turn, is to know a proposition true of it, one specifying its essence. See Fine (2003d), also Burnyeat (2011). For a different view, see McDowell (1973 But what is "truth among us"? If alêtheia is used ontologically, we might render 9 as: 9O. Knowledge among us is of reality among us.
If alêtheia is used semantically, we might render 9 as: 9S. Knowledge among us is of truth among us.
Before asking whether we should we favor 9O or 9S, we should distinguish two uses of par'hêmin, which I shall call ontological and epistemological. So far in gd, par'hêmin has been used ontologically, to indicate that forms are not among us: they are not features of the sensible world; that's not where they exist.51 But par'hêmin can also be used epistemologically, to mean 'in our view' or 'according to us' , or 'in our mental presence' .52 This distinction is analogous to, or is perhaps the same as, Descartes' distinction between objective and formal reality.53 The sun is formally in the sky: 51 The only two occurrences of en'hêmin in gd (133c5 and 133e5) are also ontological. 52 According to lsj (sv. para B), para with the dative can be used both ontologically and epistemologically. One passage lsj cites for the epistemological use is Hdt. 1.32. For epistemological uses of par'hêmin, see also Smythe (1920Smythe ( : 382, 1692, who cites Xenophon, C 1.6.19 (blameworthy in the opinion of) and Lyc. 54 (in the opinion of). For an epistemological use of par'hêmin in Plato, see So. 218c3; cf. the spurious Minos, 316b4. The Parmenides contains 14 occurrences of par'hêmin, all of which are in gd. Though gd uses en'hêmin just ontologically, the phrase can be used epistemologically: see lsj, sv. en I 6. One of the passages they cite is Sophocles, Antig. 925. See also Smythe, p. 377 #1687c, which cites Euripides, Hipp. 1320 as an epistemological use of en emoi. See also Prot. 355d4, though the interpretation of this passage is disputed; for a defense of an epistemological reading, see Vlastos (1969: n. 28). See also see the First Letter of John (1:8), which says that when we deceive ourselves, the truth isn't in us (hê alêtheia ouk estin en hêmin), i.e. we don't understand the truth. (Thanks to Terry Irwin for this last reference.) I use 'epistemological' to capture the fact that (as we might put it) mental, rather than physical, presence is at issue. Of course, p might be so in my view and be false. But that possibility isn't left open in 9 or 10, since they concern knowledge, which can't be false. If an epistemological use is at issue, the point would be that what I know (whether that's an object or a truth) is present to me in the sense that I know it. 53 In the Replies to the First Set of Objections, for example, Descartes says that "the idea of the sun is the sun itself existing in the intellect-not, of course formally existing, as it does in the heavens, but objectively existing, i.e. in the way in which objects normally are in the intellect" (atm vii 102/csm ii 75). Here, formal and objective reality are attributed to the sun. The idea of the sun also has both formal and objective reality. Its formal reality is that of a mode, since the idea is a modification of the mind. Its objective reality is that of a substance, since its object is the sun, and that's the level of formal reality that the sun itself has. See e.g. Meditation 3.
knowledge and truth in the greatest difficulty argument that's where it literally, physically, exists. It is objectively in me when I have an idea of it-that is, when I conceive of it some way. When I don't conceive of it in any old way, but know it, my idea is true; for knowledge implies truth. Formal reality is analogous to, or is perhaps the same as, the ontological use of par'hêmin. Objective reality is analogous to, or is perhaps the same as, the epistemological use (or more strictly speaking, the epistemological use is an instance of objective reality, where the mental presence involves truth).
Once we see that par'hêmin can be used in these two ways, we can see that 9O can be read in two quite different ways: 9Oo. Knowledge among us is of realities that exist among us, e.g. sensibles. 9Oe. Knowledge among us is of realities that we grasp or understand.
We can also read 9S in two ways: 9So. Knowledge among us is of truths that exist in us. 9Se. Knowledge among us is of truths that we grasp or understand.
A consideration that might seem to count in favor of an o-reading (whether 9Oo or 9So) over an e-reading (whether 9Oe or 9Se) is that 9 purports to be an instance of 4b; and it seems clear that 4b uses par'hêmin ontologically. Both o-readings (9Oo and 9S0) are instances of 4b when 4b is so understood; but neither e-reading (9Oe nor 9Se) is.
A consideration that might seem to count in favor of 9Oo over the other three readings is that gd1 concludes, in step 12, that we can't know forms. 9Oo, coupled with the claim that forms aren't among us (= 11), secures that conclusion; The distinction between being ontologically and epistemologically in something also has obvious affinities with Aristotle's distinction between forms in the soul and in matter (see e.g. Met. 7.7). Similarly, Proclus says that "all things are in us psychikôs; and because of this, we are able to know all things" (Philosophical Theology 1.16). To say that all things are in us psychikôs is to say that they are in us epistemologically, in the sense that we do, or at any rate can, grasp or represent them in some way; they are mentally present to us.
In Meno 86b1, Plato says that "the truth about beings is always in the soul" (cf. Phil. 39a1-8, which mentions logoi in the soul). I take this to mean that we always in some way do, or can, grasp the semantic truth about some range of beings. The beings aren't ontologically in the soul. Nor is clear that the truth about them is ontologically in the soul, if semantic truth, properly speaking, attaches just to propositions conceived as abstract entities. Perhaps the truth is in the soul just epistemologically. So too are the objects those propositions are about, since to know a thing is to know what it is, where that is to know that it is thus and so (see n. 50). However, 86b1 doesn't say that beings are in the soul in any way; it says only that the truth about them is in the soul. fine International Journal for the Study of Skepticism 10 (2020) 209-234 230 but the other readings of 9 don't do so. Neither 9Se nor 9So does so, because neither imposes any restrictions on what truths among us can be about. We can see that this is so if, once again, we are clear about the difference between the contents of knowledge (truths) and its objects (what those truths are about). Nor does 9Oe preclude knowledge of forms. That's so even if it is conjoined with the claim that forms aren't among us. For the claim in 11 is that forms aren't ontologically among us, whereas 9Oe involves the epistemological use of 'among us ' .54 There are also, however, reasons to favor 9Se. First, 'truth' should be understood in the same way in 7 and 9. I've argued that 'truth,' in 7, is semantic; so it should also be semantic in 9.55 Secondly, just as 7 is true when it is read as 7S, so 9 is true when it is read as 9Se. (However, this is not the only reading of 9 on which it is true.) Thirdly, of the two readings of 9S (9So and e), 9Se seems the more plausible: the issue of where semantic truths exist ontologically doesn't seem relevant; nor is it even clear what the claim means.56 So I will set 9So to one side.
A reason to favor 9Se over 9Oe is that 9Oe just says that when we have knowledge, we know objects among us. It doesn't say how we manage to do that, or what it involves or consists in. At least a partial answer is that we do so by grasping semantic truths about them. For Plato thinks that, to know x, is to know what it is, where that involves knowing that it is thus and so (see note 51). 9Se is therefore explanatorily prior to 9Oe: it tells us what knowing something consists in.

11
Step 10: Knowledge and Beings among Us Let's now turn to 10. Unlike 9, 10 doesn't mention truth. Rather, like 8, it uses onta; and, like 8, it uses the term ontologically, not semantically.57 There are 54 It's clear that 11 involves the ontological use. For it repeats 3, and that's what it means there: see n. 40. Further, if we take par'hêmin in 11 epistemologically, it says that we can't grasp forms, which is the conclusion of gd1. But 11 is supposed to be a premise that, combined with other premises, yields that conclusion; it doesn't itself state it. 55 If so, however, one might argue that par'hêmin is used ontologically throughout, since that's how it's used until ea: why think its use changes in the argument, whereas the use of truth doesn't do so? The reason is that that's the whole point of the argument: to get us to see the difference between epistemological and ontological immanence, a distinction that goes naturally with, but is not the same as, the distinction between semantic and ontological truth. 56 For one thing, it's not clear that semantic truths are the sorts of things that can exist ontologically in the soul. See n. 53. 57 One difference between 8 and 10 is that the former has 'each of the knowledges' , whereas the latter has 'each knowledge' . So far as I can tell, this difference is not significant. Another knowledge and truth in the greatest difficulty argument nonetheless two readings of 10, depending on whether par'hêmin is used ontologically or epistemologically: 10Oo. Each knowledge among us is of a given being among us. 10Oe. Each knowledge among us is of a given being we grasp or understand.
According to 10Oo, medical knowledge among us is of health among us: e.g. Simmias' health, or that penicillin has cured some range of people.58 That doesn't, by itself, preclude knowledge of forms. For perhaps forms are also among us. However, that was ruled out long ago (in 3) and is repeated in 11.59 10Oo and 11, taken together, preclude our knowing forms. By contrast, 10Oe, even when coupled with 11, doesn't preclude our knowing forms; for perhaps, even if they aren't among us ontologically, they are among the beings I grasp or understand. However, if we combine 10Oe with 11, the argument equivocates on 'among us' , first using it ontologically, and then using it epistemologically. It looks, then, as though ea is either valid but unsound (because it uses 9Oo and 10Oo); or else it has all true premises but equivocates on par'hêmin. But perhaps that is precisely what Plato wants us to see: that once we clearly distinguish content from object, and different ways of being par'hêmin, we can see that forms don't need to be in us ontologically in order for us to know them. We know them, so long as they are in us epistemologically, in virtue of our grasping the semantic truth about them.60

Conclusion
Let us now take stock. In working our way through gd1, we've noted that some of its premises are true: for example, 4a, 5, 7, and 8. However, these premises aren't necessary for deriving the conclusion that we can't know forms. We've difference is that unlike 8, 10 has just 'a given being'; it doesn't repeat 'what it is' . This difference might indicate that whereas 8 is about definition or essence, 10 is not. That corresponds to the difference we've noted between 4a and 4b. 58 Ta par'hêmin can include low-level types or universals, so long as they aren't forms. 59 However, 3 uses en hêmin, whereas 11 uses par'hêmin. I take it that 11 uses the phrase ontologically. 60 My view stands in striking contrast to one held by Gerson (2003). Whereas I have suggested that we can avoid gd's sceptical conclusion by distinguishing the content from the object of knowledge, Gerson argues that distinguishing the content from the object of knowledge leads to scepticism. His argument, baldly stated, is that Plato takes knowledge to be infallible which, in turn, requires it to be non-representational and so non-propositional.

fine
International Journal for the Study of Skepticism 10 (2020) 209-234 232 also noted that in some cases, purported flaws aren't really there. For example, gd doesn't infer from 4a to 4b; nor does gd involve nsp (see note 30 above). In other cases, there might be a genuine flaw that, however, we can leave to one side since it doesn't explain what's fundamentally wrong with ea. For example, premise 2 might be false. But Plato might accept 3 without accepting 2. We did detect one false premise early on: 4b. But, though 4b is false, it has some true instances. So simply pointing out that 4b is false isn't sufficient for disarming ea: we need an account of what if anything is wrong with 9 and 10, which are, or purport to be, instances of 4b. That's what I've tried to provide.
There are two ways to understand my solution. The first focuses on the shift from alêtheia to onta. Plato wants us to see that, while the content of knowledge consists of semantic truths, that doesn't, by itself, restrict the objects we can know. For all gd shows, we can know forms, so long as we grasp the relevant truths about them. gd tries to persuade us that we can't know forms by using alêtheia in 7 and 9, and then shifting to onta in 8 and 10 without highlighting their difference; and, as we've seen, other commentators haven't distinguished them. But in using both words, Plato hints at how to avoid gd s conclusion.
The second way of explaining the, or a, crucial flaw in gd doesn't depend on taking alêtheia semantically.61 For whether or not alêtheia is semantic, ea might use par'hêmin both epistemologically (in 9 and/or 10) and ontologically (in 11). If it is used in both ways, the argument equivocates. To get a valid argument, we need to understand 'among us' ontologically throughout; but then the argument is unsound.
Though this second explanation doesn't require us to take alêtheia to be semantic in 7 and 9, it brings semantic truth in by the back door. For to know something among us epistemologically is to grasp a semantic truth about it. Hence the ultimate solution to ea is to distinguish the content of knowledge from what the content is about. That makes it tempting to think that Plato hints at this solution by using both alêtheia (for semantic truth) and onta (for beings, understood ontologically).
Interestingly, although the argument in Rep. 5 uses forms of einai both ontologically and for semantic truth, and doesn't use alêtheia, it is clear about the difference between knowledge being of semantic truth and its having certain He also argues that knowers are identical to the objects of knowledge, which he thinks are restricted to forms. I don't have the space to engage with his argument here, but for penetrating criticism, which I endorse, see Taylor (2004: 541-545). It's worth noting that one can, of course, argue that Plato identifies the content with the object of knowledge, without thinking the identification would lead to scepticism, and without thinking that knowledge must be non-representational. See e.g. Szaif, discussed briefly above in n. 47. 61 Here I am indebted to Lesley Brown. objects; it distinguishes the content from the objects of knowledge. But the argument is difficult. Perhaps one point of gd is to caution us against a popular misreading of the argument in Rep. 5.62