Plato's mathematical imagination: The mathematical passages by Robert Sherrick Brumbaugh

By Robert Sherrick Brumbaugh

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Extra info for Plato's mathematical imagination: The mathematical passages in the dialogues and their interpretation (Indiana University publications : Humanities series)

Sample text

Is he not better off in knowing his ignorance? lVIENO: I think that he is. : If we have made hitn doubt, and given him the 'torpedo's shock,' have we done him any harm? MENO: I think not. : We have certainly, as would seem, assisted him in some degree to the discovery of the truth; and now he will wish to remedy his ignorance, but then he would have been ready to tell all the world again and again that the double space should have a double side. MENO: True. : But do you suppose that he would ever have enquired into or learned what he fancied that he knew, though he was really ignorant of it, until he had fallen into perplexity under the idea that he did not know, and had desired to know?

In Euclid iii. 35, the case of two intersecting lines in a circle which coincide with perpendicular diameters is treated separately as the initial case in the proof of the theorem. 28 There is no reason why Socrates, if he had the more general problem in mind, should EXAMPLES FROM PURE MATHEMATICS OF METHODS AND CLASS-RELATIONS 35 not have presented to Meno tIle most intuitively evident special case from a cOlnplete demonstration which Meno could not have understood. This suggestion combines the merits of Benecke's insistence on consistency of character and economy of imagery, and the suggestion of the second group of interpreters, that some more general theorem is required to make the example mathematically interesting or meaningful.

And now I add another square equal to the former one? [BEFC} Fig. 9] BOY: Yes. : And a third, which is equal to either of them? [DEHG J Fig. 9] Plato's Mathematical Imagination 26 BOY: Yes. : Suppose that we fill up the vacant corner? [EFIH, Fig. 9] BOY: Very good. : Here, then, there are four equal spaces? BOY: Yes. : And how many times larger is this space than this other? BOY: Four times. : But it ought to have been twice only, as you will remember. BOY: True. : And does not this line, reaching from corner to corner, bisect each of these spaces?

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