Literature Study GuidesDialogues Of PlatoRecollection Proof Summary 81e 86c Summary

## Dialogues of Plato | Study Guide

Plato

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# Dialogues of Plato | Recollection Proof Summary (81e–86c) | Summary

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## Summary

Socrates beckons over a young boy, one of Meno's servants. He then draws a figure in the sand, and asks if the boy recognizes it as a square. The boy concurs. He also agrees that a square has four equal sides, and if lines are drawn through the middle, the resulting sides are equal, as well.

Socrates now asks the boy what "the whole" would be if AB is two feet and AD is also two feet. He provides an example of a square with unequal sides: one side is two feet long, and the other is one foot long. Would not the whole of that, he asks, "be two feet taken once?" The boy agrees, and also agrees that, therefore, the whole of the square in the sand would be four.

Next, Socrates adds another square, which is "twice the size" as the present figure, with each of the sides of equal length. Its whole, the boy says, will be eight feet. When Socrates asks him how long the side of a square with an area of eight feet is, the boy thinks it is four feet. At this point, Socrates turns to Meno to ask if he is teaching the boy, and Meno agrees he is not. Moreover, Socrates points out, the boy thinks he has correctly inferred the length of the square's side from its area, or whole, but that he is in error. Meno agrees that the boy believes the side of a square with an area of eight feet is determined by multiplying four by two.

Socrates asserts that the boy is now in a position to recollect the correct formula for determining both the area of a square and the length of a given side when provided with the area. He asks the boy to consider the formula required for a square with equal sides of four feet, and to calculate the length of the sides of a square with an area of eight feet. The boy manages to figure out the first but is at a loss about how to calculate the second.

Once again, Socrates turns to Meno to review what has just happened. The boy is now in a better position than he was previously, since, although he does not know the answer to the question about the length of the sides of a square with an area of eight feet, he at least recognizes that he does not know; he is confused. Before, he was confident that he was correct, but in fact was not. This, then, is an improvement, and Meno agrees.

Moreover, in bringing the boy to this state of awareness, Socrates claims, he has not done the boy any harm. Indeed, unlike what Meno had claimed, "numbing the boy" has not only not harmed him but actually benefitted him.

Socrates now returns to the original square (ABCD), and adds three more to it. He then cuts each square by drawing a line from one corner to the other.

Socrates asks the boy for the length of the diagonal line cutting each square in two. The boy responds that it is four feet. That length, multiplied by the side of the original square's length (two feet), gets the boy to the eight feet area he initially thought he would get by applying the erroneous formula.

Socrates once again turns to Meno to confirm that the boy has not been taught, but instead found the answers on his own. This, he adds, is the process of recollection.

## Analysis

When Socrates offers the boy the example of generating the "whole," or area of a square, by multiplying sides with uneven lengths, the boy transfers a mistaken formula onto the square whose area he is to calculate. Socrates's example square has one side with a length of one foot and one side with a length of two feet. Multiplying length-times-length yields an area of four feet. The boy's square has equal sides of two feet each, and takes the formula for generating the area of a square to be two-times-whatever the other side is, rather than multiplying the two sides, whatever their length. So, when Socrates asks the boy to determine the area of a square double the size of the present figure, the boy thinks it is two-times-four, where four is the length of the larger square. Socrates works to get the boy to recognize both that the area of the square with equal length sides of four feet is 16, and that a square with an area of eight feet requires sides that are greater than two feet, but smaller than four.

The boy needs to understand the correct formula for generating the area of a square, and also the formula for reversing the direction, that is, from the area of a square to the length of its (equal) sides. If the boy answers the questions honestly, and it appears he does, then clearly there is something happening that allows him both to recognize the correct answer and to recognize when he is in error. This, Socrates thinks, is accounted for by recollection.

Not only that, but Socrates insists the process of recollecting is not harmful, but entirely beneficial. So, Meno was incorrect to accuse Socrates of doing him harm by "numbing" him with his questions. It is better, after all, to realize one's ignorance than to be ignorant but think oneself knowledgeable. Aporia, or confusion, is certainly uncomfortable, but it is better than thinking one knows when one does not.

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