In their discussions of logic and set theory, Willard Quine and Alonzo Church distinguish between a paradox, an affront against unschooled intuition, and an antinomy, an outright contradiction, an offense against the laws of reason. Both of these predicaments are rooted in classical antiquity. The term aporia (literally, “no way”, or “cul-de-sac”), derived from poros (passage), already occurs in the writings of Democritus. Plato relates it to dialectic. The aporetic situation arises as an intermediate consequence of elenchus, the Socratic method of eliciting truth by means of brief questions and answers. One characteristic instance witnesses Socrates eliciting doubts from his interlocutors by being more in doubt than anyone else. (See Meno 80c.) According to Aristotle, an aporia results when a gratuitously clever sophistic argument from received premisses (τὰ ἔνδοξα), leads to an impasse, wherein “thought is bound fast when it will not rest because the conclusion does not satisfy it, and cannot advance because it cannot refute the argument”. (See the Nicomachean Ethics, VII.2 1146a 24.) It is defined as a condition of perplexity, which obtains “when we reflect on both sides of the question and find everything alike to be in keeping with either course that we are perplexed which of the two we are to do”. (See Topics, VI.6.145b 17–20.) However, the diaporematic method can also be used in the task of attaining knowledge, as is famously declared in the beginning of the book B of Metaphysics:
We must, with a view to the science which we are seeking, first recount the subject that should be first discussed. These include both the other opinions that some have held on certain points, and any points beside these that happen to have been overlooked. For those who wish to get clear of difficulties it is advantageous to state the difficulties well; for the subsequent free play of thought implies the solution of the previous difficulties, and it is not possible to untie a knot which one does not know. But the difficulty of our thinking points to a knot in the object; for in so far as our thought is in difficulties, it is in like case with those who are tied up; for in either case it is impossible to go forward. (Metaphysics III(B) 3.995a 24-34.)
Accordingly, the goal of the diaporematic method consists in liberating man from the bondage of his perplexity.
In the Roman rhetoric, the figure of aporia or diaporesis has been rendered as dubitatio, or indecision, whereby a speaker seems to ask the audience which of the two or more words (verba) he had better use, or which things (res) he had better talk about. (See Cicero, Ad Herennium, IV.xxix.40.) In his pithy manner, Quintilian observes the deceptive capacity of dubitatio: “Hoc etiam in praeteritum valet; nam et dubitasse nos fingimus.” (See Institutio Oratoria IX.i.30,35; IX.ii.19–20, IX.iii.88.) It was said that indecision may lend an impression of truth to his statements, or even assist him in covering up his past with a pretense. Thus the practically oriented orator found advantageous the bondage that Aristotle strove to overcome through the process of rational inquiry.
In words, as in deeds, Michael aims to escape the bounds of his perplexity. He reflects on the words of Edgar Allan Poe: “every work of art should contain within itself all that is necessary for its own comprehension.” If this is true, it is only in virtue of the work containing within itself a microcosm that reflects the innermost principle of its composition, just as the nucleus of a living cell contains genetic code responsible for defining its function. And just as the study of genetics depends on the prior understanding of scientific bases of physical and chemical interactions, so does art, howsoever self-sufficient, depend in its essence on the understanding of its origins and its environment. As with art, so with life. In achieving an understanding of a self-contained fragment, Michael hopes to gain an insight into the workings of the extensive whole. It will only take a lifetime.