In the Theaetetus we see Socrates interacting with an up-and-coming mathematician Theaetetus with his mentor Theodorus. It's noteworthy that Plato places his dialogue about the nature of knowledge in the study of a mathematician. I think it's not unreasonable to conclude that the philosopher had a great respect for mathematics. On the other hand, I wonder if it's possible to derive a type of warning in over indulging in mathematics.

In the Theaetetus lines 162 a,b made me think that Plato was commenting that it is often the disposition of mathematicians to avoid certain conflicts, preferring to focus on the mathematics (which is simpler in the sense that the assumptions/definitions that mathematics rests on are somehow firmer). I read this passage as a type of gentle goading of mathematicians to be vulnerable and occasionally leave the realm of firm definitions to discuss important matters.

1) Is this a reasonable interpretation of this passage? I worry I am reading into it too much.

2) Is there anywhere else in Plato's writing that suggests that over-indulging in the "non-pragmatic" is a danger which is to be avoided? This is contrary to my general attitude about Socrates. He is the type of guy who tells us that we need to pause in our preparation of the troops to discuss what courage is on some essential level.

3) Is this interpretation of the Theaetetus something that appears in the literature?

The lines I am referencing follow. 162a, 162b.

Theodorus: Socrates, the man was my friend, as you just remarked. So I should hate to bring about the refutation of Protagoras by agreeing with you, and I should hate also to oppose you contrary to my real convictions. So take Theaetetus again; especially as he seemed just now to follow your suggestions very carefully.

Socrates: If you went to Sparta, Theodorus,[162b] and visited the wrestling-schools, would you think it fair to look on at other people naked, some of whom were of poor physique, without stripping and showing your own form, too?

Theodorus: Why not, if I could persuade them to allow me to do so? So now I think I shall persuade you to let me be a spectator, and not to drag me into the ring, since I am old and stiff, but to take the younger and nimbler man as your antagonist.

Socrates: Well, Theodorus, if that pleases you,

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    Sorry, I see no "gentle goading" of mathematicians, or anything directed specifically at mathematicians, in this passage. Your general impression of (Plato's) Socrates is on the right track, if anything he was concerned about geometers becoming too pragmatic in doing geometry, see When were the concepts of pure and applied Mathematics introduced? According to Plutarch, "Plato was displeased and opposed them on the ground that they destroyed and corrupted the good of geometry, which relapses from incorporeal, intelligible objects to sensibles".
    – Conifold
    Aug 28, 2018 at 5:21
  • @Conifold. Thanks! Maybe you can be convinced to promote your comment to an answer? I would comment that this is of a very few passages where we see (Plato's) Socrates speaking to an adult/pro mathematician and a mathematician of some import. That is, I imagine that Plato's readers if they knew nearly nothing of Theodorus would know that he did math... Which is why I am viewing as a potential commentary on the relationship between philosophy and mathematics.
    – Mason
    Aug 31, 2018 at 8:06


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