The extent of Plato’s knowledge of mathematics is made apparent through his use of the subject within his written works. In Ion, an early dialog of Plato 's, Socrates uses analogical argument to get his point across. The thing that makes these arguments suitable for this paper is that they heavily rely on mathematics for the source of the example (Roochnik, p. 548). In Elenchus and Mathematics: A Turning-Point in Plato 's Philosophical Development, Vlastos gives a translated version of a section of Plato 's Meno:
By 'investigating from a hypothesis ' I refer to the way the geometricians frequently investigate. When they are asked, for example, as regards a given area, whether it is possible for this area to be inscribed in the form of a triangle in a given circle, they may reply: 'I don 't yet know whether this area is such as can be so inscribed. But I think that a certain hypothesis would be helpful for that purpose. I mean the following: If the given area is such that when it has been applied (as a rectangle) to the given straight line in the circle, it is deficient by a figure similar to …show more content…
80-81). Furthermore, he spoke of Hippias of Elis as a “vain man, given to arrogance and boasting” (Smith, 1951, p. 82). As he was critical of the business of others, one might suppose that the man himself would likely try to avoid such acts within his own work. This is of course unless he felt that his statements were in reality the truth rather than simple arrogance. It should be noted that Plato makes the claim in the Euthydemus as a philosopher rather than as a mathematician. This distinction is necessary as he isn 't saying that the mathematician’s results aren 't useful or important, only that they lack the ability to make use of them on a philosophical
By 'investigating from a hypothesis ' I refer to the way the geometricians frequently investigate. When they are asked, for example, as regards a given area, whether it is possible for this area to be inscribed in the form of a triangle in a given circle, they may reply: 'I don 't yet know whether this area is such as can be so inscribed. But I think that a certain hypothesis would be helpful for that purpose. I mean the following: If the given area is such that when it has been applied (as a rectangle) to the given straight line in the circle, it is deficient by a figure similar to …show more content…
80-81). Furthermore, he spoke of Hippias of Elis as a “vain man, given to arrogance and boasting” (Smith, 1951, p. 82). As he was critical of the business of others, one might suppose that the man himself would likely try to avoid such acts within his own work. This is of course unless he felt that his statements were in reality the truth rather than simple arrogance. It should be noted that Plato makes the claim in the Euthydemus as a philosopher rather than as a mathematician. This distinction is necessary as he isn 't saying that the mathematician’s results aren 't useful or important, only that they lack the ability to make use of them on a philosophical