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## How Is a Rational Discussion Possible?One essential ingredient of the solution I have proposed is the remark that, when the logical constants are understood intuitionistically, the formalization (2t) of (RAR) becomes perfectly acceptable. On the other hand, when the logical constants are understood classically, (2) is utterly unacceptable. This situation is far from surprising; on the contrary, it illustrates a general truth reminded above: the classical meaning of the logical constants is deeply different from their intuitionistic meaning. Consider for instance the schema “ (i.e. formalized as However, this situation generates a serious problem: the problem whether a rational discussion between a supporter of classical logic and a supporter of intuitionistic logic is possible at all. How is it possible that there is real disagreement or real agreement between them, given that both disagreement and agreement about a principle presuppose that the same meaning is assigned to it by both parties, while, as we have just seen, the meaning of one and the same formula drastically changes across classical and intuitionistic readings? It seems to me that there are at least two alternative strategies to tackle the problem. The first consists in placing the discussion between the two parties (i) Which intuitive notions should be formalized? For instance: inclusive or exclusive disjunction? Which notion of implication? Which notion of truth? (ii) Which intuitive notion should be chosen as the key-notion of the theory of meaning, i.e. as the notion in terms of which the meaning of the expressions of the formal language (in particular of the logical constants) is to be characterized? For instance: (bivalent) truth (as the realist claims), or knowability/existence of a proof (as the neo-verificationist claims), or knowledge/actual proof (as the intuitionist claims)? In this case the problem can be solved, The second strategy consists in placing the discussion between the two parties I hold the first alternative is better, but I have not an a priori argument; I will argue for my thesis by considering what seems a very plausible tactics and explaining why, in my opinion, it is not viable. The tactics is based on the idea of translating one logic into the other, analogously to the case of the translation of a language into another. As a matter of fact, there are several so-called 'translations', both of classical logic/mathematics into intuitionistic logic/mathematics—the so-called negative translations (by Kolmogorov, Gödel, Gentzen, Kuroda and others); and of intuitionistic logic/mathematics into extensions of classical logic/mathematics (Shapiro, Horsten, Artemov). I shall not enter here into a detailed discussion of this tactics. I want only to stress an obvious fact: that the so-called 'translations' are not translations at all. A translation, in general, must be correct, and it is correct if it is meaning-preserving, i.e. if, for every expression
meaning as |

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