The clouds and mists of their own raising

From the translators’ preface of the first English edition (1685) of Arnauld’s La Logique ou l’art du penser (1662):

The Common Treatises of Logic are almost without number, and while every Author strives to add something of his own, sometimes little to the purpose, sometimes altogether from the matter, the Art is become, not only Obscure and Tedious, but in a great measure Impertinent and Useless.

Thus the Schoolmen may be said to have clogg’d and fetter’d Reason, which ought to be free as Air, and plain as Demonstration itself, with vain misapplications of this Art to Notion and Nicety, while they make use of it only to main­tain litigious Cavils and wrangling Disputes. So that indeed the common Logics are but as so many Counterscarps to shelter the obstinate and vain-glorious, that disdain Submission and Convincement, and therefore retire within their Fortifications of difficult Terms, wrap themselves up in Quirk and Suttlety, and so escape from Reason in the Clouds and Mists of their own Raising.

The pleasure of the text

Barthes, Le Plaisir du Texte, 1973, translated by Richard Miller:

Imagine someone (a kind of Monsieur Teste in reverse) who abolishes within himself all barriers, all classes, all exclusions, not by syncretism but by simple disregard of that old specter: logical contradiction; who mixes every language, even those said to be incompatible; who silently accepts every charge of illogicality, of incongruity; who remains passive in the face of Socratic irony (leading the interlocutor to the supreme disgrace: self-contradiction) and legal terrorism (how much penal evidence is based on a psychology of consistency!). Such a man would be the mockery of our society: court, school, asylum, polite conversation would cast him out: who endures contradiction without shame? Now this anti-hero exists: he is the reader of the text at the moment he takes his pleasure.

Rigidity and continuity

John von Neumann, “The General and Logical Theory of Automata,” 1948:

There exists today a very elaborate system of formal logic, and, specifically, of logic as applied to mathematics. This is a discipline with many good sides, but also with certain serious weaknesses. This is not the occasion to enlarge upon the good sides, which I have certainly no intention to belittle. About the inadequacies, however, this may be said: Everybody who has worked in formal logic will confirm that it is one of the technically most refractory parts of mathematics. The reason for this is that it deals with rigid, all-or-none concepts, and has very little contact with the continuous concept of the real or of the complex number, that is, with mathematical analysis. Yet analysis is the technically most successful and best-elaborated part of mathematics. Thus formal logic is, by the nature of its approach, cut off from the best cultivated portions of mathematics, and forced onto the most difficult part of the mathematical terrain, into combinatorics.

The theory of automata, of the digital, all-or-none type, as discussed up to now, is certainly a chapter in formal logic. It would, therefore, seem that it will have to share this unattractive property of formal logic. It will have to be, from the mathematical point of view, combinatorial rather than analytical.

The work of reason produces monsters

Poincaré, “Mathematical definitions and education,” 1906, in Science and Method, translated by Francis Maitland:

Logic sometimes breeds monsters. For half a century there has been springing up a host of weird functions, which seem to strive to have as little resemblance as possible to honest functions that are of some use. No more continuity, or else continuity but no derivatives, etc. More than this, from the point of view of logic, it is these strange functions that are the most general; those that are met without being looked for no longer appear as more than a particular case, and they have only quite a little corner left them.

Cf. Goya’s El sueño de la razón produce monstruoscirca 1799: