Examples, Definitions, and Fallacy in Plato

Originally written for PHIL 1110B Plato with Prof. Justin Broackes.

In a commentary on the Euthyphro, Peter Geach ascribed the following two claims to Socrates in the dialogue, which he dubbed the “Socratic fallacy”: “(A) that if you know that you are correctly predicating a given term ‘T’ you must ‘know what it is to be a T,’ in the sense of being able to give a general criterion for a thing’s being T, and (B) that it is no use to try and arrive at the meaning of ‘T’ by giving examples of things that are T” (pg. 371.) There has been much discussion since about whether these claims accurately reflect the views of Socrates and Plato. I will touch on this question (in particular whether this is an accurate representation the Socrates of the Meno and the Euthyphro), mostly drawing on discussion by Gerasimo Santas. I will argue that the purely skeptical position Santas attempts to ascribe to Socrates is effectively equivalent to the position Geach criticized. Above and beyond the exegetical question, however, I will address the issue of whether the position characterized by Geach’s two claims is in fact a fallacy, concluding, contrary to an argument given by William Prior, that it is.

Indisputably, the methodology that Socrates pursues in early dialogues such as the Euthyphro and the Meno places considerable weight on definitions. In the Euthyphro, Socrates moves very quickly from the discussion of the particular case that Euthyphro brings up (in which he is prosecuting his own father) to pressing Euthyphro for a general definition of piety (5d.) Likewise, in the Meno, Socrates strongly resists Meno’s attempts to investigate whether virtue is teachable without first establishing a firm definition of virtue (for example, in 71d and 86d.) The question, then, is whether this methodological insistence on definition brings with it specific claims about the relationship between knowledge of a definition and other forms of knowledge about a concept. Geach’s claim (A), which Prior refers to as the “priority of definition,” can be rephrased as the idea that the evaluation of a particular case of a concept can only be carried out after the establishment of the concept’s definition. This is not the only way one might translate the definition-based methodology into a claim about knowledge, however, and many related (usually weaker) claims have been discussed in the literature. For instance, definitions might not be important because they take priority over every case, but only because it is impossible to decide some particularly challenging cases without establishing a definition (Benson’s claim D (pg. 34).) Alternatively, it may be that definitional knowledge is required to know any properties of the concept (Prior’s claim A2, which he attributes to Beversluis (pg. 100)) or that without it knowledge of cases is merely undermined and mudded, but not strictly rendered impossible (Santas pg. 139-141.)

Since Socrates never makes his stance on the philosophical importance of definition explicitly, we can only infer it from the dialectical position it is endowed. When Socrates proclaims “I blame myself for my complete ignorance about virtue. If I do not know what something is, how could I know what qualities it possesses?” (71b) he implies that not knowing “what virtue is,” or in other words a definition or general criterion of virtue, renders him completely ignorant of virtue. He directly implies that this means he cannot know whether it is teachable, but it is hard not to take this claim of complete ignorance as meaning that he cannot confidently claim knowledge about the classification of any particular case, as well. When Euthyphro claims to be confident about the piety of prosecuting his father for the neglectful death of his servant, Socrates interprets the claim about knowledge of the particular case as a claim about knowledge of definitions: “So tell me now… what you just now maintained you clearly knew: what kind of thing do you say that godliness and ungodliness are…?” (5c.) Clearly, Socrates wants to severely undermine purported knowledge about concepts like virtue and piety made in the absence of clear definition. Claims about cases, or particular features of the concept, are implicitly backstopped, for Socrates by general definitional knowledge.

According to the interpretation given by Santas, these undermining moments cannot be used to give Socrates a positive view about the priority of definitions like Geach’s (A), but rather they should be distilled as aporetic skepticism about knowledge of cases. I think such a distinction makes little difference. If the matter is settled definitively against (A), then the equivalent skeptical question is also no longer open. In other words, if we can be assured of knowledge in some case absent definitional knowledge, then it must both be the case that (A) is incorrect, and that we should no longer be, in general, skeptical of particular knowledge not backed up by general knowledge. Of course, one might still have the weaker skepticism of whether the answer in every case is knowable without a guiding definitional criterion. However, I think the stronger skepticism equivalent to (A) is a more natural reading of Santas. Santas notes that “the ‘paradigm case argument’ or something like it apparently did not occur to Plato… but there is more to it than this… Socrates believed that one is in difficulty when it comes to defending one’s claim of an example when one does not know the definition” (pg. 139.) In other words, despite the absence of an account of paradigm cases, the Socratic skepticism is still reasonable because it amount to a justificatory, rather than purely classificatory, skepticism. The need for definitional knowledge, for Santas, is highlighted by pushing on the defense of claims about specific cases.

This position is further clarified when Santas distinguishes a lack of knowledge from total ignorance. Santas characterizes Meno as being able to accurately tell what is virtuous in various examples, and that “if [Socrates’ interlocutors] don’t know the definition, and are also completely ignorant of examples, how on earth are they supposed to get started?” (pg. 140.) Santas is careful to note that Meno “might not have knowledge of the examples in some Platonic sense of ‘knowledge’… but [he is] not totally ignorant of the examples either” (pg. 140.) Setting aside Socrates’ professed total ignorance of virtue himself early in the dialogue (as discussed above) this move of exporting the burden onto knowledge is ineffective. Even if the skepticism is just about knowledge of the cases, this is still perfectly compatible with it reducing to equivalence with (A), since “knowledge” appears there too. Determining whether or not (A) is correct, insofar as it is a claim about knowledge, crucially involves deciding whether a Platonic analysis of knowledge is appropriate. Thus, skepticism about whether someone can have a Platonic knowledge in a particular case without definitional knowledge is either worthless, if the Platonic analysis is not appropriate for knowledge, or equivalent to a denial that the case has been settled against (A), if it is.

Thus, I think Santas’ claims are better understood as a dispute about the “fallacious” status of (A) rather than a non-intuitive reading of Plato. Suppose the position characterized by (A) were clearly fallacious. Then skepticism of the kind Santas attributes to Socrates, i.e. wide-ranging skepticism about exemplary knowledge sans definitional knowledge, would be equivalent to a denial of this fact and an insistence that a clearly fallacious position be given further consideration. Even if Santas thinks the positive claim of (A) is absent from the dialogues, a skepticism on the issue would mean that (A) is compatible with Socrates’ account, and so it would be just as damaging to Socrates if (A) were fallacious.

Thus, we are naturally pushed to consider whether the “Socratic fallacy” is fallacious after all. Prior notes that despite significant exegetical disagreement about Geach’s reading of Plato’s Socrates, “almost all scholars agree, however, that the “Socratic fallacy” is a bad thing and that Socrates has good reason to avoid commitment to [it]” (pg. 99) Prior, on the other hand, disagrees. He concedes that the priority of definition outlined in (A) is, in fact, Socrates’ view, but argues that such a view actually has nothing particularly wrong with it.

Let us first consider the situation of paradigm cases. If one wants to deny knowledge of cases by endorsing (A), this must extend even to cases which are typically thought of as central to the understanding of the concept. For instance, we might be completely certain that a desk chair is a chair, but giving a precise definition that includes all such paradigm chair and excludes things like sofas and saddles is notoriously difficult. A rejection of exemplary knowledge as in (A) not only, then, says that to decide whether borderline cases like a stool or a recliner are chair we must first have the definition in hand, but that without it we cannot even know that the desk chair is a chair.

This nicely coheres with Santas’ earlier point that in the absence of classification in these base examples, it is unclear how to even begin thinking about the concept at all. In other words, then, endorsing (A) commits one to a picture of knowledge that, even if it doesn’t match Plato’s exactly, is at least significantly restrictive. If we cannot know about paradigm cases in the absence of a definition, then the collective certainty we feel about the desk chair must be lacking something that true knowledge has. To say simply that what is lacking is the definition itself seems to be question-begging, but in every other way our position on the classification of the desk chair feels no different from classification with a definition in hand.

Another crucial example of this point is that of colors. Prior wants to emphasize the borderline nature of some color classifications:“Is that color a dark shade of yellow or a light shade of orange?… How can we answer such questions if we lack criteria for determining where yellow leaves off and orange starts…? If one can’t deal with the contentious cases, the borderline or disputed cases, it is tempting to think that one doesn’t know how to use the term in question after all, or at least that one’s knowledge is incomplete” (pg. 104.) Certainly, an inability to answer questions about borderline cases almost definitionally reflects an incomplete knowledge of a concept. However, it is much more difficult to see why it should reflect an incompleteness in the knowledge of the more central case.

To be clear, what Prior wants to dispute in such paradigmatic cases is not that we are wrong or uncertain about the classifications; “the question [Plato] would raise in such situations [of paradigm cases] is not whether the concept applied to the case but whether the cognitive certainty on the part of the observer amounted to knowledge” (pg. .) Thus, Prior seemingly wants to endorse the idea that even in the most widely agreed-upon cases, at least for moral concepts, we can not have knowledge (absent a definition) no matter how unanimous, reliable, or certain our judgements about the case are.

First, such a view must either give a good reason for asymmetry between the cases of moral and physical concepts, or else it must admit that the dismissal of knowledge of paradigm cases extends to physical concepts like colors as well. Certainly, determining whether something is yellow and determining whether someone is acting courageously are quite different tasks. Moral judgments are less perceptual, less immediate, are perhaps more sensitive to upbringing and socialization, and so forth. However, claims like “what makes for knowledge, then, is not certainty or practical reliability but the ability of the person who has knowledge to give a reasoned explanation of what he or she knows” which Prior introduces in the moral case do not seemingly have anything to do with these distinguishing features. The perceptual differences and so on do not justify why knowledge must require the ability to explicitly reason to the claim when it comes to moral concepts, but not physical ones. If a Platonist bites the bullet, then, and says that knowledge of physical concepts has equally strenuous requirements, then we consequently must be suspicious of claims like “I know this flower is yellow.” One is only licensed to make such a claim with a rationale behind it, but what could such a rationale look like? One might be able to provide a definition of “yellow” involving wavelengths of light, but not only is it impossible to choose between the manifold such candidate definitions, the claimant is extremely unlikely to be making use of such definitions as justification for the claim. Our collective certainty in the identification the color of some objects seems so pure and reliable that adding additional criteria onto it for it to be knowledge seems only to degrade the usefulness of knowledge as a concept, rather than elucidate something missing from the color identification.

Of course, Prior acknowledges that many of the claims that naturally follow from (A) fail for some senses of the word “know” but, according to him, this is no problem since the relevant sense here is only the Platonist one. This is a claim, however, that requires argument. Just because there is some concept that one might be able to identify in Plato with the word “know” does not mean that such a concept is knowledge, or even a viable candidate for such. The claim made in (A) is not a claim about some exegetical concept “know_Plato.” The fact that one cannot know_Plato about examples without having knowledge_Plato of the definition is only equivalent with (A) if knowledge, actual knowledge, is accurately captured by the concept of knowledge_Plato. Perhaps that identification is a good one (although at least for the physical case we have good reason to doubt it), but it needs to be established. Much of Prior’s argument, for example his dismissal of Geach’s original criticism since “Geach’s view is indebted to Wittgenstein’s philosophy of language. [(A)] is implausible on this reading of the verb “to know,” but not on Plato’s” (pg. 97) rests on this identification, but little is provided in the way of argument for it.

Let us now turn to another dimension of the fallacy. Although Prior concedes (A) as an accurate summary of Socrates, he does not concede (B). In his original presentation, Geach characterized (B) as following from (A), hence much subsequent discussion has focused on (A) and propositions like it. Prior questions this logical connection between (A) and (B), however. Like Santas, Prior points to the actual usefulness of examples in the Socratic dialogues and the distinction between a lack of knowledge and a complete lack of understanding: “I think that, for Geach’s objection to hold, and for (B) to follow from (A), it would have to be the case that a lack of a general criterion for what it is to be a T must produce in the investigator such a degree of confusion that he or she is unable even tentatively to identify examples of T. We have seen that this is not the case” (pg. 112.) If we read (B) as saying that examples are categorically useless, then it certainly does not follow from (A), precisely because (A) contains the term “know” which is clearly up for debate. If, instead, we read the claim in (B) that we cannot use examples to “arrive at the meaning of T” as the claim that we cannot acquire knowledge of the definition of T, then the connection is reforged.

This leads to the more general question: if knowledge is supposed to be such a high bar that we do not possess it at first even in paradigm cases, how can we come to obtain knowledge of the definition, from which knowledge in cases would flow? The dialectical demonstration that Socrates delivers involves working from the cases, which Santas and Prior are quick to point out. However, if such a method eventually did conclude with a definition that covered our starting positive cases and excluded our negative ones, would we then have knowledge of the concept? If knowledge has the justificatory element that Prior claims it does, then we might at first think that the dialectical journey itself would constitute the “reasoned explanation” of belief in the definition. If, however, examples are foundational to the dialectic, and we are not supposed to be able to provide good reasons for our classifications of examples without using the definition, then why should our reasons for the definition be good? In other words, if we have a definition that fits our examples and counterexamples well, we should only be as satisfied with this as a reasoned justification of the definition as we are with the reasoning behind those examples and counterexamples.

It is not, then, that cases are useless completely. Seemingly, both sides of the debate agree that one can begin with cognitive certainty about cases, and from there move to certainty about definitions. The problem enters when, like Prior, one wants to preclude any knowledge about the cases, but still hopes for knowledge about the definitions at the end. I think there is a hint of equivocation about knowledge in a move from mere certainty about cases to knowledge about definitions. Thus, (A) does seem to entail (B) after all, and (B) too seems to be a consequence of the Socratic view insofar as it precludes knowledge of definitions via the method of examples. This seemingly contradicts Socrates’ dialectical practice, but as Prior admits (as an imagined response from Geach), “So much the worse for Socrates’ practice. If (B) follows from (A), Socrates is not entitled to make use of examples in any of these ways” (pg. 110.)

In sum, I hope to have shown (in agreement with Prior) that the attempt to defend Plato and Socrates from the “Socratic fallacy” by arguing that Geach’s claims do not accurately reflect the dialogues is a mistaken framing, at least in the case of Santas’ work. Furthermore, I hope to have given good argument (against Prior) that the position is, in fact, fallacious, and that the account of knowledge it rests on is on somewhat shaky foundations and requires some equivocation on the part of its defenders.

Works Cited

Benson, Hugh G. (1990). “The Priority of Definition and the Socratic Elenchus.” Oxford Studies in Ancient Philosophy 8: 19.

Geach, P. T. (1966). “Plato’s Euthyphro: An Analysis and Commentary.” The Monist 50(3): 369–382.

Plato (2002). Five Dialogues. Trans. G. M. A. Grube, ed. J. M. Cooper. 2nd ed. Indianapolis: Hackett.

Prior, William (1998). “Plato and the ‘Socratic Fallacy.’” Phronesis 43(2): 97–113.

Santas, Gerasimos Xenophon (1972). “The Socratic Fallacy.” Journal of the History of Philosophy 10(2): 127–141.