If the slave-boy had some inkling of Pythagorean doctrine, it may be that he could not only have learned to make a square double the area of an original square of 4, i.e. a square of 8, but he could also have glimpsed the Pythagorean theorem itself, for it turns out that the square built upon the diagonal of the original square of 4, *i.e.* the hypotenuse of the isosceles right triangles formed by that diagonal, is the side of the desired square that is twice the area of the original. The square of each of the other two sides of the isosceles triangle added together are 8, the same as the square built upon the hypotenuse, i.e. the diagonal. A more knowledgeable witness might have made a connection here between this unspoken reference to Pythagoras and the theory of the transmigration of souls and the theory of recollection that Socrates is supposedly demonstrating. That the length of the diagonal turns out to be 2 x square root of 2 suggests that Socrates is additionally hinting at an esoteric Pythagorean discovery, the existence of an irrational number, i.e. the square of 2, a real number that cannot be expressed as a ratio of integers. This perhaps relates by analogy to Meno's paradox and the difference between true opinion and actual knowledge that is discussed in the remainder of the *Meno*.

See related posts: Meno's Paradox and A Classroom Version of the Slave Boy Scene in Plato's A classroom version of the slave boy scene in Plato's Meno

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