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Can we treat contradiction? Is it possible to justify a contradiction from a logical point of view? Does contradiction force us to abandon logic? From a logical point of view, a formal system S implanted in language L is said to be consistent or non-contradictory if it never allows the demonstration and refutation of a formula at the same time, in other words, a contradiction. 1 If instead such is said to be the case, then S is said to be inconsistent or contradictory. It is said to be trivial if and only if it allows the demonstration of all the formulas of L. The trivialist claims that all the contradictions are true and, thus, that everything is true. In the case that the system used entails negation, it is said to be banal, because it demonstrates everything and the contrary of everything: a ∧ ¬ a → b. The connection between inconsistency and triviality is explained by the law of Pseudo-Scotus: ex contradicione quodlibet, from contradiction anything follows. Technically, in the natural deduction calculus, the Pseudo-Scotus is obtained by means of the rule of the elimination of negation (E ¬) with the further step of the introduction of the conditional (I →). It is the negative version of the paradox of material implication [¬ p → (p → q)]: the false, the absurd, implies anything. Paraconsistent logics both deepen and put this conviction to the test. The Pseudo-Scotus is called "the principle of explosion" to convey the idea of the destructive power of a contradiction within a formal system. If a formal system allows even one contradiction, the consequences are disastrous, and the system becomes deductively useless. 2 A paraconsistent logic avoids explosion. 3 We can admit contradictions, without trivializing the 1 Defining what a contradiction is, is an enormous problem. Contradiction is a dichotomous situation: a statement and its negative counterpart. In technical terms, a contradiction is the conjunction of two statements, and one is the negation of the other. We could also say, in a formulation that is distributive rather than collective, that a contradiction is a pair of statements of which one negates the other, eliminating the reference to the conjugation. From a semantic perspective, contradiction is the conjugation (or pair) of statements that cannot be neither both true (subcontrary) nor both false (contrary). In metaphysics, a contradiction is rather a situation in which an object at the same time possesses and does not possess a certain property. From here arises the hypothesis of contradicting worlds. The principle of non-contradiction negates the possibility of contradictions at the syntactic, semantic, ontological, and psychological level. As Aristotle says: "It is impossible to be and not to be at the same time" (Met. 1006a 1-5). 2 Berto (2006, 99-100). 3 Paraconsistency is not a new argument in philosophy. Aristotle's syllogisms were already an example of paraconsistent logic. Even the stoics did not seem to recognize the necessity of the explosiveness of contradiction. Such necessity rather become crucial in classical logic. The rediscovery of paraconsistency occurred in the second half of the 20th century, through the discussive logic of Jaśkowski (a nonadditive approach), as well as from the strategy to the fragmentation of David Lewis, the theses of Rescher and Brandon, da Costa's work, adaptive logics, Routley's relevant logics, and the approach of Priest. From a semantic point of view, in paraconsistent logics, the validity of an argument is defined in terms of the truth-according-to certain interpretations. Semantic models are adopted, therefore, in which it is possible to give an interpretation of the terms used (constants, variables, connectives, quantifiers), on the basis of which a and ¬ a can both be true. One way is to use the logic of three values: 'true', 'false', and 'true and false', an approach taken by Priest.

Le tecnologie digitali hanno trasformato la maniera in cui ci rapportiamo col mondo, nel triplice senso del Selbstwel, Mitwel e Umwelt. Si pensi alla quantificazione del sé, al numero di followers e likes nei social media o ancora l’uso di Google Maps e strumenti simili per orientarsi in una città, per trovare un buon ristorante, eccetera. Si potrebbe dire che le tecnologie digitali hanno trasformato la nostra interpretazione, la nostra comprensione e il nostro accesso al mondo. Ora, se l’ermeneutica è la filosofia dell’interpretazione, allora dovremmo supporre che l’ermeneutica dovrebbe essere attenta a queste trasformazioni. Secondo noi, l’ermeneutica digitale è precisamente lo studio della maniera in cui le tecnologie digitali mediano tra gli uomini e il mondo. Si tratta anche dello studio della maniera in cui le tecnologie digitali si articolano con relazioni di natura non tecnologica tra gli esseri umani e il mondo – relazioni psicologiche, sociali, culturali e così via [...], Critical Hermeneutics, V. 4, N. 1 (2020): Digital Hermeneutics

Recensione al volume: F. Berto, L. Bottai, Che cos'è una contraddizione, Roma, Carocci, 2015, pp. 123.