Let no one ignorant of geometry enter here

Legend has it that the above words were written over the entrance to Plato's Academy. Whether that is true or not, the legend reflects the fact that Plato valued mathematical training for philosophers. But why?

The usual suggestion is that he thought it "trained the mind." But this is a rather modern spin on education, I suspect. I think the real reason is closer to this: Plato lived at a time when sophism was rampant in Athens. The sophists generally were moral subjectivists. What mathematical training could do, in my opinion, is convince students that there are truths about the mental world that are not just matters of opinion. That having occurred, they ought to then be more open to the idea that there are moral truths that are not simply a matter of opinion as well.


  1. This is a very interesting idea. I'm not convinced (yet), but even aside from the Plato angle it's an interesting idea.

  2. The definition of a sophist that I am familiar with is someone who setups arguments purposely so they can win them. So who were some of the sophists of ancient Greece and how do we know that they were relativists?

    1. Here.

      Socrates was often doing battle with them in Plato's dialogues: see, for instance, Thrasymachus in The Republic.


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