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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.

Digital media and technologies have significantly transformed the ways we relate to the world, in the triple sense of Selbstwelt, Mitwelt, and Umwelt. Think of the quantification of the self, the number of followers and likes on social media, or using Google maps and similar tools to orient ourselves in a city, to find and choose a good restaurant, and so on. One might say that digital media and technologies have actually transformed our interpretation, understanding, and access to the world. Now, if hermeneutics is the philosophy of interpretation, then we might suppose that hermeneutics should pay attention to these transformations. For us, digital hermeneutics is the study of the ways digital media and technologies mediate between humans and the world. It is also the study of the ways digital media and technologies are embedded in non-technological relations between humans and the world – psychological, social, cultural, and so on., Critical Hermeneutics, V. 4, N. 1 (2020): Digital Hermeneutics

In this paper we present a set of philosophical analyses to defend the thesis that computational reason is founded in writing; only what can be written is computable. We will focus on the relations among three main concepts: recursion, writing and iteration. The most important questions we will address are: What does it mean to compute something?What is a recursive structure? Can we clarify the nature of recursion by investigating writing?What kind of identity is presupposed by a recursive structure and by computation?Our theoretical path will lead us to a radical revision of the philosophical notion of identity. The act of iterating is rooted in an abstract space – we will try to outline a topological description of iteration. Writing and computation are two different interpretations of this imaginary use of space. So I want to propose a minimal philosophical account1 of computational reason.One of the main guiding ideas of this paper is that we need new philosophical tools to understand the roots of computation and computer science. It would be useful to apply mathematical models to express and clarify philosophical problems, but this would entail major consequences for our formulation of those problems.I will proceed as follows. The first part will be about recursion and the rule-following paradox elaborated by Kripke. I will give some basic definitions of recursion and algorithms, and I will present the paradox. The second part will treat the connection between recursion and writing from the point of view of the French philosophy of technology elaborated by Bruno Bachimont. The third part will focus on iteration and will include a formal definition of iteration.

In this paper we present a set of philosophical analyses to defend the thesis that computational reason is founded in writing; only what can be written is computable. We will focus on the relations among three main concepts: recursion, writing and iteration. The most important questions we will address are: What does it mean to compute something?What is a recursive structure? Can we clarify the nature of recursion by investigating writing?What kind of identity is presupposed by a recursive structure and by computation?Our theoretical path will lead us to a radical revision of the philosophical notion of identity. The act of iterating is rooted in an abstract space – we will try to outline a topological description of iteration. Writing and computation are two different interpretations of this imaginary use of space. So I want to propose a minimal philosophical account1 of computational reason.One of the main guiding ideas of this paper is that we need new philosophical tools to understand the roots of computation and computer science. It would be useful to apply mathematical models to express and clarify philosophical problems, but this would entail major consequences for our formulation of those problems.I will proceed as follows. The first part will be about recursion and the rule-following paradox elaborated by Kripke. I will give some basic definitions of recursion and algorithms, and I will present the paradox. The second part will treat the connection between recursion and writing from the point of view of the French philosophy of technology elaborated by Bruno Bachimont. The third part will focus on iteration and will include a formal definition of iteration.