Organizzazione Unità di ricerca LOG-LAB
Martedì, 17 maggio 2022 ore 15.30
Aula 7, plesso didattico di via Capponi 9
Marko Malink (New York University)
Boole, Peirce, and Schröder on Expressing Particular Propositions
Abstract:In his Laws of Thought, George Boole set out to represent Aristotle's syllogistic theory in a purely equational system of algebraic logic lacking propositional negation. In doing so, he faced the problem of how to express particular propositions of the form "Some A is B". Boole attempted to solve this problem by introducing what he called "indefinite symbols". Peirce and Schröder criticized this attempt and provided different solutions to the problem based on the theory of relations (Peirce) or propositional logic (Schröder). I will examine each of these approaches, and discuss how the debate about the representation of Aristotelian particular propositions shaped the development of algebraic logic in the second half of the 19th century. I will conclude by considering how the problem of expressing particular propositions is addressed in Alfred Tarski's calculus of relations.
Giovedì, 12 maggio 2022 ore 16:00
Plesso didattico di via Capponi 9, Aula 6
Marko Malink (New York University)
The Origins of Conditional Logic: Theophrastus on Hypothetical Syllogisms
Abstract: Ancient Peripatetic logicians such as Theophrastus sought to establish the priority of categorical over propositional logic by reducing various modes of propositional reasoning to categorical form. To this end, Theophrastus proposed that the conditional "If φ then ψ" should be interpreted as a categorical proposition "A holds of all B", in which B corresponds to the antecedent φ, and A to the consequent ψ. Under this interpretation, Aristotle’s law of subalternation (A holds of all B, therefore A holds of some B) corresponds to a version of Boethius' Thesis (If φ then ψ, therefore not: If φ then not-ψ). Jonathan Barnes has argued that this consequence renders Theophrastus' program of reducing propositional to categorical logic inconsistent. In this paper, we will challenge Barnes's verdict. We will argue that the system of conditional logic developed by Theophrastus is both non-trivial and consistent. Theophrastus achieves such consistency by limiting the system to first-degree conditionals, in which both the antecedent and the consequent are simple categorical propositions.
Venerdì, 6 maggio 2022 ore 11:00
Plesso didattico di via Capponi 9 - Aula 7
Paolo Maffezioli (Università di Torino)
Aristotle's arithmetical dictum
Abstract: In Prior Analytics Aristotle explains the universal predication by resorting to an intuitively clear, albeit quite elusive, mereological notion - that of being in the whole. Building on previous scholarly work on the mathematical origins of Aristotle's syllogistic, it is suggested that for Aristotle a universal affirmative proposition such as 'x is predicated of all y' is true if, and only if, y is a divisor of x. The adequacy of such an interpretation is assessed both theoretically and textually with respect to the other mereological interpretations of the dictum. This is a joint work with Riccardo Zanichelli.
Giovedì, 21 aprile 2022 ore 11:30
plesso didattico di via Capponi 9 - Aula 6
Jan Sprenger (Università di Torino)
Trivalent Logics for Indicative Conditionals
Abstract: There are two major research projects on indicative conditionals: the semantic project of determining their truth conditions, and the epistemological project of explaining how we should reason with them. This paper integrates both projects on the basis of a trivalent, truth-functional account of the truth conditions of conditionals. On the basis of these semantics, we generate two logics for reasoning with conditionals: (i) a conditional logic of deductive inference (i.e., with certain premises) that generalizes classical logic; and (ii) a conditional logic of probabilistic inference (i.e., with uncertain premises) that generalizes Adams' logic to arbitrary compounds of conditionals. We then apply both logics to the controversies about the validity of Modus Ponens, Import-Export, and the various triviality results for conditionals. The end product is a unified theory of the truth conditions and probability of conditionals that makes sensible predictions for natural language reasoning.
The talk based on joint research with Paul Egré and Lorenzo Rossi. Preliminary work to this research has been published in the /Journal of Philosophical Logic/ :
https://link.springer.com/article/10.1007/s10992-020-09549-6 (open access). The talk will briefly summarize our work from that paper before presenting new results.