Următoarea conferință din cadrul seminarului de cercetare al Departamentului de Filosofie Teoretică în parteneriat cu CELFIS va fi susținută de Antonio Piccolomini d’Aragona, cercetător la Universitatea din Siena, dar afiliat  şi Aix-Marseille Univ. si Univ. din Viena. Mai multe detalii sunt disponibile aici: https://sites.google.com/site/piccdarag 

Comunicarea acestuia este parte dintr-un ciclu de conferințe asociat programului masteral Analytic Philosophy, cu predare în limba engleză. Toate aceste evenimente sunt deschise studenților în filosofie, științele exacte, digital humanities, științele comunicării, și multe altele. Detaliile programului sunt disponibile aici: https://filosofie.unibuc.ro/master-of-arts-in-analytic-philosophy/ 

Prezentarea profesorului Piccolomini d’Aragona se intitulează „Proof-theoretic squeezing„. Iată un rezumat al acesteia, urmat de referințele bibliografice cheie:

„According to an interpretative line first put forward by [Crocco 2019], Kreisel’s notion of informal rigour [Kreisel 1967] can be understood as pointing to the importance and fruitfulness of an analysis of the dialectical interplay between a formal and an informal approach to such concepts as provability, definability, set, etc. The formal moment makes those concepts precise, but is also essentially incomplete. The precisification, however, permits one to single out principles which may be used informally to improve the formal analysis itself, thus broadening its scope towards stronger and stronger formalisations. At the same time, the informal view is informed by the structure of the formal level, i.e., by the results and notions it allows for. Kreisel’s celebrated squeezing argument, relating an informal notion of validity to suitable formal counterparts of it, as well as to existing completeness results, may be understood as a paradigmatic example of application of such a dialectical methodology.

As I have already argued elsewhere [Montesi & Piccolomini d’Aragona 2022], Prawitz’s proof-theoretic semantics, a constructivist semantics stemming from Prawitz’s own normalisation results in Gentzen’s natural deduction [Prawitz 1965, 1973], may be read along the lines of Kreisel’s informal rigour. Prawitz aims at providing a semantic generalisation of some results and properties he had obtained at the level of proof-theoretic analysis of formal systems. As led by informal principles about provability and its relation with meaning, such a generalisation naturally tends towards a class of stronger and stronger systems where the notions of derivability and provability approximate to each other.

In my talk, I will address the question whether, based on this Kreselian interpretation of proof-theoretic semantics, a “proof-theoretic squeezing argument” may be put forward, by relating informal notions of semantic provability to a hierarchy of formal systems which provide partial, albeit increasingly strong formal instances of those notions. I will end up by discussing some differences between Kreisel’s squeezing and the (tentative) proof-theoretic version of it. In particular, I will argue that most of these differences may stem from the fact that Prawitzian validity is relative, not to (set-theoretic) structures, as in Kreisel, but to underlying atomic axiomatic theories, as well as from the fact that no uniform completeness result is available (nor can it be) for Prawitz’s semantics.

References

• G. Crocco (2019), Informal and absolute proofs: some remarks from a Gödelian perspective, in Topoi
• G. Kreisel (1967), Informal rigour and completeness proofs, in I. Lakatos, Problems in the philosophy of mathematics
• F. Montesi & A. Piccolomini d’Aragona (2022), Prawitz’s semantics and Walton’s argument schemes: a tentative reading and application of Kreisel’s informal rigour, in Noésis
• D. Prawitz (1965), Natural deduction. A proof-theoretical study
• D. Prawitz (1973), Towards a foundation of a general proof theory, in P. Suppes et al., Proceedings of the Fourth International Congress for Logic, Methodology and Philosophy of Science, Bucharest, 1971″

Conferința se va desfășura azi, marți, 21 mai, orele 16.00-18.00, în sala „Tudor Vianu” de la etajul 1 al Facultății de Filosofie din Splaiul Independenței nr. 204, București 060024. Pentru mai multe detalii, vă rugăm urmăriți pagina Facebook „Seminarul Departamentului de Filosofie Teoretica UniBuc”.

Morality can be seen as arduous, demanding, centered on obligations and rules and usually going against the personal interest of the agent. Alternatively, it can be seen as going along with the interest of the agent, contributing to personal development, not centered upon obligations, but on aspirations, and only accidentally difficult.

Therefore, we might end up with two main ways of seeing morality: morality as a difficult enterprise, usually going against the interest and the well-being of the moral agent; or, morality as a not-so-difficult enterprise, because usually not going against the interest of the moral agent (i.e. morality as something that comes, in some sense, naturally to the moral agent). I have called the first kind ‘morality of law’ because in order to secure the moral agent’s compliance it relies on rules and obligations as its core. I have contrasted this way of seeing morality with a view usually called ‘morality of virtue’ which does not rely on rules and obligations as its main instruments, but relies rather on moral aspirations and moral ideals. This contrast is, obviously, not new. I am borrowing the labels ‘morality of law’ and ‘morality of virtue’ from MacIntyre inAfter Virtue, even if I do not fully employ his way of depicting the contrast between the two. Another similar distinction is made by Korsgaard inThe Sources of Normativity(1996).