A year ago on July 18 2014 the logician and philosopher Carlo Dalla Pozza died.
An important part of his thought should soon be available in Italian with the publication by the publisher Carrocci of the book "Il Problema della Demarcazione: Verificabilità, Falsificabilità e Confermabilità Bayesiana a confronto”, with co-author Antonio Negro. The thesis that scientific statements are those to whom Bayesian probability can be assigned as a function of experimental results is the conclusion of Dalla Pozza’s epistemological thinking. Throughout his work he has been revisiting the tradition of Rudolph Carnap, Hans Reichenbach and of logical empiricism with original reflections on modern philosophies of logic and an intelligent attention to the debate on the foundations of physics.
From the viewpoint of the philosophy of logic the “pragmatic interpretation” of non-classical logics (A pragmatic interpretation of intuitionistic propositional logic, with C. Garola, Erkenntnis, 48, 1995 pp.81-109) may be seen as a programme to guarantee the fundamental role of classical logic as the logic of truth and to explain the justification of judgements using notions from pragmatics, namely, starting from the commitment made in elementary judgements: these are illocutionary acts of assertion, of making hypotheses, objections, denials. As judgements are “justified” or “unjustified”, and only their propositional content may be true or false, in a “logic of judgement” connectives cannot be truth-functional and are best explained according to the Brouwer-Heyting-Kolmogorov interpretation. In this way also the epistemic components of meaning can be accounted for without adopting a verificationist viewpoint in the theory of meaning, which Dalla Pozza does not accept. The distinction between logic of truth and logic of justification has found a counterpart in theoretical work by Claudio Garola on the foundation of physics and the logic of quantum mechanics.
Carlo Dalla Pozza has also extended his “pragmatic approach” to deontic logic and the philosophy of laws, in response to a problem raised and discussed by von Wright, Alchourron and Bulygin. Dalla Pozza develops the distinction between the “expressive” use of normative expressions, carrying the illocutionary force of an obligation, and their “descriptive” use, e.g., referring to the propositional content of a norm or to its existence in a normative system. (Una logica pragmatica per la concezione “espressiva” delle norme, in Martino A.(ed.) Logica delle Norme, SEU, Pisa, 1997). Again intuitionistic logic is appropriate in the “expressive” discourse about norms. Dalla Pozza’s approach has been developed formally in work with Gianluigi Bellin (A Pragmatic Interpretation of Substructural Logics, In: Reflections on the Foundations of Mathematics. Essays in Honour of of Solomon Feferman, ASL, Lecture Notes in Logic vol 15, pp.139-163, 2002) and in Kurt Ranalter’s dissertation (see “A Semantic Analysis of a Logic for Pragmatics with Assertions, Obligations and Causal Implication, Fundamenta Informaticae 84, pp.443-470, 2008). At the same time, Dalla Pozza continued to follow and to contribute to work on the foundations of laws, especially in an active dialogue with Luigi Ferrajoli.
A “pragmatic interpretation” of co-intuitionistic logic has been proposed by Gianluigi Bellin and others in order to understand notions of duality between intuitionism and co-intuitionism (G.Bellin. Assertions, hypotheses, conjectures, expectations: rough-sets semantics and proof-theory. In Advances in Natural Deduction. A Celebration of Dag Prawits Work. Trends in Logic 39, Springer 2014, pp.193-241). Intuitionistic conjunction and implication are “dual” to co-intuitionistic disjunction and subtraction B - A (“B excludes A”) in a precise mathematical sense [subtraction is defined as the left adjoint of disjunction while intuitionistic implication is defined as the right adjoint of conjunction]. Bi-intuitionistic logic in the tradition of C.Rauszer extends intuitionistic logic with subtraction. This system has found applications in computer science but important structure of is lost: in particular, it has no nontrivial categorical model. Thus there are mathematical reasons to study the two logics where duality is extended to atomic sentences. A “pragmatic conjecture” is that co-intuitionism is about hypothetical reasoning while intuitionistic logic is about assertive reasoning . Recent work by Bellin, Carrara, Chiffi and Menti (“Pragmatic and Dialogic Interpretations of Bi-Intuitionism, Part I, Logic and Logical Philosophy, 23, 4, 2014, pp.473-506. Errata Corrige DOI: 10.12775/LLP.2015.003, Bellin, Carrara, Chiffi “On an intuitionistic logic for pragmatics”, Journal of Logic and Computation 2015; doi: 10.1093/logcom/exv036) considers “dialogical” notions of duality between assertions and negative hypotheses (“objections”) and also between hypotheses and negative assertions (“denials”). Here research faces the philosophical difficulty of explaining what a justification of a hypothesis is. The justification of the process of revision of hypotheses in terms of Bayesian confirmation as proposed by Dalla Pozza and Negro may provide a response to such a difficulty. The Bayesian approach has successful applications in formal epistemology and in computer science.
Those who had the privilege of having Carlo Dalla Pozza as a friend, always available to listen and advise in moment of personal difficulty, the loss has no remedy. His rational and realist approach to human situations, always sensitive to psychological complexities and to ethical aspects of personal choices was a reference point, an irreplaceable compass in facing the trouble of each day.
Gianluigi Bellin July 13 2015