Philosophical Rigor

Larval Subjects .

There’s a model of philosophical rigor that denounces all analogies, metaphors, and examples.  It is an ancient tradition.  Plato, of course, denounces the use of examples tirelessly throughout his writings.  “I did not ask you for an example of piety, Euthyphro, but to articulate what piety itself is or what is common to all instances of piety!”  In the Republic, dianoia– mathematical reasoning –is not yet the highest form of knowledge because it relies on writing and the use of diagrams.  The symbols I use in my notation can get in the way of recognizing relationships as in the case of the near impossibility of doing even the simplest arithmetic using Roman numerals, and the diagrams I use to help me to think of a conic section or a triangle can lead me astray insofar as no matter how hard I try I can’t draw triangleness, only a triangle…

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