The Metaphysics of Paradox (vol. 1)

A Barber was Thinking

It’s getting up, it’s still dark; the paradoxes begin! Who then gets up, all the cells of his body having been renewed (paradox of the boat of Theseus*¹ or Chisholm*)? And shouldn’t it be day at night (Olbers’ paradox*)?

He does not say hello to his wife because he is not married, arranged marriages no longer exist and free marriages being more subject to divorce than arranged marriages (Toqueville* paradox). He does not shave, because, as a barber himself, he has been foolishly defined as the one who (only) shaves those who do not shave themselves (Barber’s paradox*). Moreover, he is a good barber and, to become one, he did like his master, he did not imitate anyone (paradox of Consuelo* Casula). [Foreword, p. 13]

A Classification of Paradoxes: Paralogy, Paracosmia, Paradoxia

Whether the aim is to contradict intuition or logic, to entertain or to mark progress in the sciences, not all paradoxes are approached in the same way. Following Delmas-Rigoutsos, we can distinguish them according to the source of the contradiction expressed:

1. If the incompatible realities presented are undeniable, but specious reasoning is the cause of the contradiction, we’re dealing with a logical paradox, a paralogy (or paralogism); for example, the light-hearted joke: Socrates is mortal, the horse is mortal, therefore Socrates is a horse. The apparent demonstration that leads to the contradiction has in fact not taken place. While paralogy is a logical fallacy, sophistry, which is also a logical fallacy, differs in its intention to deceive. It was the struggle of Greek philosophers against the sophists, who taught the art of convincing by any means, that led Aristotle to found logic (his Organon) and define the types and forms of valid reasoning. In addition to this inaugural period (in the West), paradoxes of this kind fuelled the vast logical investigations of medieval thinkers (under the name of “insolubilia”) and, in the 20th century, those of philosophers of language.
2. If the reasoning is irreproachable, and the source of the contradiction lies in the bringing together of two incompatible realities, then we’re dealing with a cognitive paradox, a paracosmia; for example, Olbers*’s “sky on fire”, who is astonished that the sky is black at night. It is this type of paradox, often the assertion of a counter-intuitive fact, that has always flourished in the sciences, so much so that they are often referred to as scientific paradoxes. However, it should not be thought that these types of paradoxes emerge like sudden illuminations in the face of the flaw in an established theory; they accompany, and follow, theoretical developments, and are, moreover, as Delmas-Rigoutsos points out, “generally disseminated with a solution” and an explicit theoretical frame of reference.
3. If the realities presented and the reasoning are all correct, but no reasonable conclusion can be reached, we can speak of a paradoxia, or a logical dilemma, or simply a dilemma (or even an antinomy). The most emblematic example of a paradoxia is the Liar’s paradox*. Although it only really acquired this status in modern times, the first written trace of the discussion of a logical dilemma can already be found in Aristotle, with reference to an earlier discussion. Like paralogies, dilemmas have occupied thinkers in the three great periods of logic (Antiquity, the Scholastic Middle Ages, the 20th and 21st centuries), with discussions starting all over again “quasi tabula rasa”. [Chap. 1, pp. 30-32]