When do you expect these students to have the chance to implement their systems?
Actually, math is too mechanical. It does not truly involve the evaluation of ideas.
Well, I cannot answer for you, but I have no idea what critical thinking would be if it were not essentially dialectical. Basically, one might characterize dialectic as the hypothetical method, a specialized version of which became "the scientific method". One looks for the difficulties in a subject, floats possible solutions, examines the pros and cons, and finally either accepts, modifies, or discards the proposed solution. It is the devising of tests for hypotheses. For example, in the Meno, Socrates asks: "Can virtue be taught?" Supposing it can, he notes a couple of prominent instances where good men had rotten sons. Since they were good, and would be presumed to be anxious to teach virtue if they could, the idea of teachability is refuted. In the Republic, someone proposes that justice is "giving to each his due". But how do you determine what is someone's due? For example, suppose someone gives weapons to you for safekeeping. A month latter, he goes insane, and in his mania demands the weapons so that he can attack someone innocent. The weapons are his, but justice is supposed to be a good, and giving him the weapons would promote a great injustice and evil. Thus, "giving to each his due", though plausible, in inadequate, and at least requires modification. You get the idea, I am sure....... |
