Erudite Relics of Loc Huu Ho

Definitions

• abet: act of abetting; aid; To assist or encourage by aid or countenance, especially in crime; To support, uphold, or aid; to maintain
• dialectical: is controversy: the exchange of arguments and counter-arguments respectively advocating propositions (theses) and counter-propositions (antitheses). The outcome of the exercise might not simply be the refutation of one of the relevant points of view, but a synthesis or combination of the opposing assertions, or at least a qualitative transformation in the direction of the dialogue.The presupposition of a dialectical dialogue is that the participants share at least some meanings and principles of valid inference, even if they do not agree
  
• reductio ad absurdum: The method of proving a statement by assuming the statement is false and, with that assumption, arriving at a blatant contradiction
  

Notes

• As Gregory Vlastos ( 1991: 107) put it, Plato ‘ was able to associate in the Academy on easy terms with the finest mathematicians of his time, sharing and abetting their enthusiasm for their work’.
• Plato notes in passing that mathematics is ‘universally useful in all crafts and in every form of knowledge and intellectual operation-the first thing everyone has to learn’ (Republic, 523).
• Plato realized that one needs intense and prolonged study for any ‘form of knowledge and intellectual operation’. Especially philosophy.
• Everyone does only what he or she does best. Philosophy too is left to the experts-the Guardians. To rule well, the Guardians need to turn their focus from the world of Becoming to the world of Being. Thus, a crucial part of their education has to ‘turn the soul from a day that is as dark as night to the true day, that journey up to the veritable world which we shall call the true pursuit of wisdom’ (Republic, 521). Mathematics ‘draws the soul from the world of change to reality’. It ‘naturally awakes the power of thought…to draw us towards reality’-at least for the few souls capable of such ascent.
• Plato saw mathematics as the gateway into the world of Being, a gateway that must be passed if one is to have any hope of understanding anything real. Recall the sign at the entrance to the Academy: ‘Let no one ignorant of geometry enter here.’ Mathematics, the prerequisite to philosophical study, demands a long period of intense study. No wonder that most of us have to live our lives in ignorance of true reality, and must rely on Guardians for direction as to how to live well.
• Mathematics proceeds via proof, not mere trial and error.
• In the Meno, Plato uses geometric knowledge, and geometric demonstration, as the paradigm for all knowledge, including moral knowledge and metaphysics.
• In sum, for Plato the fumbling but exciting and egalitarian Socratic method first gives way to the elite rigour of Greek mathematical demonstration. This is then replaced with an even more elite ‘dialectical’ encounter with the Forms.