Recollecting Errors

Nasanbayar Ulzii-Orshikh, 10/25/2020

Error is natural to us. We are easily deceived by small letters and think we are flying when really snoring on a bed. Even beyond peripheral perception, we often miscount 23 multiplied by 97 (try it) or infer what is not implied. Yet, when Plato claims that learning is in fact a simple recollection, tables start to turn. We think of learning as something like assembling a painting one new brushstroke at a time or expanding a network of nodes that we extract from new information. However, for Plato, learning is when the soul inside of us, having “nothing which it has not learned” (81d)^[1], invokes itself for knowledge, for it has “always" carried the “truth about reality” (86b). Then, in invoking truth how do we slip into a false opinion? If knowledge is already in us, why can’t we reach our hands into our own souls and take out the truth? If truth is innate, why do we make errors?

Before we begin our interrogation, we must agree on our definition of error. Initially, it seems to be concerned with falsehood, but it cannot be falsehood itself, for a thinker arriving at a falsehood as part of reductio ad absurdum isn’t considered to be erroneous*. Then, suppose error is something false that is believed to be true. For Plato, between knowledge and opinion, what is false is in the domain of only opinion, since knowledge is concerned with exclusively what is true. Then, error can be thought of as a false opinion enacted as knowledge.

Plato offers an insightful example of this, when Socrates leads Meno’s attendant into an error (82a-e). Take a rectangle with sides of lengths one and two. The size of the shape is clearly two. Then, double the side of length one. The size also doubles. However, it is the moment when given a shape with equal sides and twice the size of the two by two rectangle that the attendant makes an error, computing the length of its sides to be twice as long as those of the rectangle.

Making of such an error seems to be facilitated by the specific progression of questions that Socrates poses to the attendant. He intentionally presents an example of a shape with sides of length one, since any number multiplied by one keeps its identity, so it is no surprise that when that side is doubled, the size of the shape also doubles, hence ingraining in the mind of the attendant this a priori idea, or mechanism, of doubling the length and thus doubling the size for this instance. When encountered with the next shape, he then attempts to apply the same concept to ultimately make an error. If the attendant was instead introduced with an example of a two by four rectangle, increasing to four by four, then he would have had to make a different generalization. Since the example would have resembled general cases to a higher degree than those which involve sides of length one, the attendant’s answer would have accordingly resembled to a higher degree a true mathematical opinion. One might argue that the attendant had incorrectly inferred that doubling the length means doubling the size before encountering the new example and thus had already made an error at the first example, but without being questioned in any way, whether with a new example or by a request from Socrates or himself to make some inference, he had knowledge of only the first example, namely, a rectangle transforming from one by two to two by two doubles in size, which itself is indeed a true opinion. Thus, the specific order and type of questions that one strives to answer seems to help pre-determine their making of an error.

The moment of realization of the error, however, is not in the collection of questions or the conclusion that is incorrect. It is the very act of making a jump from the premises to a conclusion by the attendant that allows for slipping from true opinion into a false one. Yet, why does this happen? We must realize that there is no ground based on which the attendant can truly predict the size of the new square because the true opinions that he has about the smaller square and rectangle do not describe per se what he seeks to know, but only the examples that he has encountered so far. That is, the attendant’s knowledge of mathematical form is not predictive in nature, for it merely summarizes the paradigm in the examples that he has observed in his lifetime. Then, error is made by the act of generalizing true opinions into a broader set of instances, while the object of generalization fails to apply universally, for the knowledge is not intrinsically predictive.

At the same time, it is notable how the error seems to exist at the intersection of multiple perceptions, as an independent object of learning. The error that has been realized so far is realized only for Meno and Socrates, as they can check against the true opinion at which the attendant should have arrived instead. For the attendant, however, the error starts to realize only after Socrates elucidates for him that his conclusion is inconsistent with other instances (83a-84a), making him “perplexed and numb as torpedo fish does” (84b). In that sense, making an error helps the attendant to know that he does not know what he thought he knew and thus creates in him the capacity of, or even longing for, learning true opinions (84c). That is, for subjects that we think we know but in reality do not, if we seek to learn true opinions, we must face perplexity ourselves, whether due to error or wonder.

Regardless, our soul is supposed to contain all the truth, isn’t it? If the relevant knowledge, predictive in essence, is already in us, why are we unable to invoke it in this case? Perhaps, the soul simply does not contain this specific truth, although it is unclear if Meno seems to allow for such a diversity of innate knowledge across individuals, since Plato claims that the soul must have learnt what it knows before the attendant’s present life but does not specify if each soul experiences the same learning (86a). Since all knowledge is recollected from the soul, lacking this truth means that the attendant could not have learnt the knowledge in the first place. However, once Socrates further questions him with a different progression of ideas, focusing on the connection between the diagonal and size of a shape, the same attendant is able to recollect the true opinion that his soul supposedly lacked. Thus, regardless of whether a diversity in the volume of innate knowledge is possible, the attendant’s soul must have known the truth.

Yet, this is true assuming that he has indeed learnt knowledge of some mathematics, but could we actually claim that? Certainly, he does arrive at some true opinions, but when you focus on the answers that the attendant is giving, you realize it is one of the following: “yes” or “no”, generally indicating some agreement with Socrates; a specific number, which he computes given two numbers or a shape; “I do not know”, which implies that he has no true opinion; or pointing to a line in Socrates’ diagram. The first time he points to a line, that is, states the conclusive opinion, he arrives at a false one for how Socrates sets up his diagram and reasoning. The second time, he is correct, but for the same reason. The practice of mathematics, or the logical flow of the recollection, is performed almost entirely by Socrates. In fact, all of the higher calculations is clearly fed into the attendant for either agreement or non-agreement to have him arrive at a true opinion. However, is the mere awareness of true opinion real knowledge? At least, true opinion is not something that colleges usually test for. Rather, they test for what we do not know from prior instances: we are given with new examples to which we are supposed to apply what is known. In agreement, Socrates seems to think that the attendant’s true opinions do not qualify for knowledge. Although he has true opinions in his responses to Socrates’ questions, he would have to be “repeatedly asked these same questions in various ways” to “in the end” arrive at “knowledge … as accurate as anyone’s” (85d). Indeed, reframing true opinions under further questioning is required for true opinions to transform into knowledge with the conclusive true opinion as the result of it, and thus we cannot claim that the attendant has learnt mathematical knowledge, but only true opinions, including both the premises and the conclusion. This means that it is unclear whether he has innate knowledge of this specific mathematics in his soul, but he does have innate true opinion, which he recollects based on Socrates’ reasoning.

However, especially if it is innate true opinion and not some complex knowledge that the attendant seeks, why did he err when making an inference between shapes? Why can’t he simply recollect the true opinion, if it is already in him? The answer might lie in how recollection is being defined. We usually think of recollection as remembering something: we recollect what happened in our childhood, who told us what, or what we did the previous week, for they have been entirely or partially forgotten yet are recollectible. Although there is an element of creative recombination of these memories during recollection, the process is passive in character, since the aim of such recollection is arriving at some happenstance from the past and not producing analytic theory. For Socrates, in contrast, recollection is “finding knowledge within oneself” (85d) through a questioning from one opinion to another. That is, to arrive at a conclusive true opinion, one must make jumps from one true opinion to another, as knowledge is not only a set of true opinions, but also the relations between each pair.

However, just as when presented with a clear and complete mathematical proof, we err in grasping the flow of logic, let alone recreating it, one could have all the true opinions yet err in making a sequence of jumps to arrive at the conclusive true opinion. Since one inevitably has to make such jumps to arrive at a true opinion, the capacity to make an incorrect jump in doing so, whether due to miscalculation or misinterpretation, must be the reason why one can err when recollecting a true opinion that is already innate to the soul.

Indeed, in the case of the attendant, all of his responses, including the true conclusion, were his own opinions, which means, although initially he did not know them, they were in him. However, to arrive at the conclusive true opinion, instead of building a body knowledge for himself by synthesizing the a priori true opinions through a line of questioning all under one recollection, he relies on Socrates’ knowledge. As we have seen, during this process, the attendant easily slipped into a false opinion because he tried to extrapolate what is not known based on opinions that were not predictive in nature.

In this essay, then, we have explored the cause of error despite the innateness of true opinions. As shown by Socrates, such opinions are indeed carried by the soul, but true opinions do not qualify for knowledge if they are, despite being true and of one body of knowledge, fragmented. We learn true opinions through recollection, that is, based on knowledge built by a repeated questioning of a priori true opinions within oneself. Since this process involves connecting one truth with another, doing so on a basis, not predictive in nature, allows the thinker to err, for knowledge is not innate to us, but true opinion is.

* “Thinker” instead of “mathematician", since for Plato that who can make errors is not a mathematician.

Citations:

^[1] Plato, Complete Works, edited by John M. Cooper (Hackett, 1997). All references are to this edition of Plato’s texts, unless noted otherwise.