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Phædrus (Pirsig's name for his old self) was confronted by his academic peers and presented with a dilemma.
A dilemma, which is Greek for "two premises", has been likened to the front end of an angry and charging bull.
Phædrus, however, because of his training in logic, was aware that every dilemma affords not two but three classic refutations, and he also knew of a few that weren't so classic... He could take the left horn .... Or, he could take the right horn.... Or he could go between the horns and deny that (there are only two choices).
In addition to these three classical logical refutations there are some "illogical", rhetorical ones. Phædrus, being a rhetorician, had these available too.
One may throw sand in the bull's eyes. It's an old rule of logic that the competence of a speaker has no relevance to the truth of what he says, and so talk of incompetence (is) pure sand. Socrates, that ancient enemy of rhetorical argument, would have sent Phædrus flying for this one, saying, "Yes, I accept your premise that I'm incompetent on the matter.... Now please show an incompetent old man what (your argument) is."
One may attempt to sing the bull to sleep. Phædrus could have told his questioners that the answer to this dilemma was beyond his humble powers of solution, but the fact that he couldn't find an answer was no logical proof that an answer couldn't be found. Wouldn't they, with their broader experience, try to help him find this answer?
A third rhetorical alternative to the dilemma... (is) to refuse to enter the arena...(and claim that logic does not apply to the matter).
(Phædrus) chose to respond to this dilemma logically and dialectically rather than take the easy escape of mysticism.... I think first of all that he felt the whole Church of Reason was irreversibly in the arena of logic, that when one put oneself outside logical disputation, one put oneself outside any academic consideration whatsoever. Philosophical mysticism, the idea that truth is indefinable and can be apprehended only by nonrational means, has been with us since the beginning of history. It's the basis of Zen practice. But it's not an academic subject. The academy, the Church of Reason, is concerned exclusively with those things that can be defined, and if one wants to be a mystic, his place is in a monastery, not a University. Universities are places where things should be spelled out.
- — adapted from Pirsig, Robert M. (1974). Zen and the Art of Motorcycle Maintenance. William Morrow & Company. ISBN 0-688-00230-7.