Advanced search
Start date
Betweenand

Arbitrariness and genericity: or on how to speak of the unspeakable

Abstract

With this project, I propose to investigate the notion of arbitrary object using historical, philosophical and logical methodologies. The privileged perspective from which the analysis will be conducted is that of set theory. The project is divided in three complementary axes. First, we propose a general reconstruction of the theorization about arbitrary objects, stressing the role that concepts and their extensions played in shaping axiomatic set theory. Moreover, we plan to reconstruct the origin, and to understand the meaning, of the use of generic objects in the more abstract fields of contemporary Mathematical practice. Later, from a more philosophical perspective, we plan to to confront the concept of arbitrary set with the notions of set based either on Goedel's iterative conception or on Cantor's principle of limitation of size. From a more intensional perspective on the theory of sets, we plan to study whether arbitrary objects or arbitrary reference may clarify the ontological or semantical problems of a process of abstraction à la Frege. To this aim, we propose a philosophy of Mathematical language inspired by Searle's theory of speech acts. Finally, we plan to analyze more formally the notion of arbitrariness by means of that of genericity, on which the technique of Forcing rests. We propose to axiomatize genericity in an abstract setting. Moreover we intent to apply modal logic (RI-logics) in order to capture what is invariant under Forcing (Omega-logic), in the attempt to obtain insights in the solution of the Omega-conjecture. Finally, we propose to use Forcing itself in order to study the relative or absolute character of the notion of genericity. (AU)

Articles published in Agência FAPESP Newsletter about the research grant:
Articles published in other media outlets (0 total):
More itemsLess items
VEICULO: TITULO (DATA)
VEICULO: TITULO (DATA)

Scientific publications (23)
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
JOCKWICH MARTINEZ, S.; VENTURI, G.. Non-classical Models of ZF. STUDIA LOGICA, v. 109, n. 3, . (16/25891-3, 17/23853-0)
KUBYSHKINA, EKATERINA; PETROLO, MATTIA. A logic for factive ignorance. SYNTHESE, v. 198, n. 6, . (16/25891-3, 18/25501-6)
BEZERRA, E.; VENTURI, G.. A Non-Standard Kripke Semantics for the Minimal Deontic Logic. LOGIC AND LOGICAL PHILOSOPHY, v. 30, n. 1, p. 125-135, . (16/25891-3)
RUFFINO, MARCO; SAN MAURO, LUCA; VENTURI, GIORGIO. Speech acts in mathematics. SYNTHESE, . (16/25891-3, 18/17011-9)
RUFFINO, MARCO; SAN MAURO, LUCA; VENTURI, GIORGIO. At least one black sheep: Pragmatics and mathematical language. JOURNAL OF PRAGMATICS, v. 160, p. 114-119, . (16/25891-3)
BEZERRA, EDSON; VENTURI, GIORGIO. SQUEEZING ARGUMENTS AND THE PLURALITY OF INFORMAL NOTIONS. JOURNAL OF APPLIED LOGICS-IFCOLOG JOURNAL OF LOGICS AND THEIR APPLICATIONS, v. 8, n. 7, p. 1899-1916, . (16/25891-3)
JOCKWICH, SANTIAGO; TARAFDER, SOURAV; VENTURI, GIORGIO. Ideal Objects for Set Theory. JOURNAL OF PHILOSOPHICAL LOGIC, . (16/25891-3, 17/23853-0)
VENTURI, GIORGIO; YAGO, PEDRO TEIXEIRA. Tableaux for essence and contingency. LOGIC JOURNAL OF THE IGPL, v. 29, n. 5, p. 719-738, . (19/17407-2, 16/25891-3)
VENTURI, GIORGIO. GENERICITY AND ARBITRARINESS. LOGIQUE ET ANALYSE, v. N/A, n. 248, p. 18-pg., . (16/25891-3)
VENTURI, GIORGIO; VIALE, MATTEO. WHAT MODEL COMPANIONSHIP CAN SAY ABOUT THE CONTINUUM PROBLEM. Review of Symbolic Logic, v. N/A, p. 40-pg., . (16/25891-3)
TARAFDER, SOURAV. NON-CLASSICAL FOUNDATIONS OF SET THEORY. JOURNAL OF SYMBOLIC LOGIC, v. 87, n. 1, p. 30-pg., . (16/25891-3)
TARAFDER, SOURAV; VENTURI, GIORGIO. INDEPENDENCE PROOFS IN NON-CLASSICAL SET THEORIES. Review of Symbolic Logic, v. N/A, p. 32-pg., . (16/25891-3)
RUFFINO, MARCO; SAN MAURO, LUCA; VENTURI, GIORGIO. Speech acts in mathematics. SYNTHESE, v. 198, n. 10, p. 10063-10087, . (18/17011-9, 16/25891-3)
GILBERT, DAVID; KUBYSHKINA, EKATERINA; PETROLO, MATTIA; VENTURI, GIORGIO. Logics of Ignorance and Being Wrong. LOGIC JOURNAL OF THE IGPL, v. N/A, p. 16-pg., . (16/25891-3, 18/25501-6)
VENTURI, GIORGIO; VIALE, MATTEO. Second order arithmetic as the model companion of set theory. ARCHIVE FOR MATHEMATICAL LOGIC, v. N/A, p. 25-pg., . (16/25891-3)
JOCKWICH MARTINEZ, S.; VENTURI, G.. On Negation for Non-classical Set Theories. JOURNAL OF PHILOSOPHICAL LOGIC, v. 50, n. 3, p. 22-pg., . (17/23853-0, 16/25891-3)
GILBERT, DAVID R.; VENTURI, GIORGIO. Reflexive-Insensitive Logics, the Boxdot Translation, and the Modal Logic of Generic Absoluteness. NOTRE DAME JOURNAL OF FORMAL LOGIC, v. 62, n. 2, p. 269-283, . (16/25891-3)
PISTONE, PAOLO; TRANCHINI, LUCA; PETROLO, MATTIA. The Naturality of Natural Deduction (II): On Atomic Polymorphism and Generalized Propositional Connectives. STUDIA LOGICA, . (16/25891-3)
PLEBANI, MATTEO; SAN MAURO, LUCA; VENTURI, GIORGIO. Thin Objects Are Not Transparent. THEORIA-A SWEDISH JOURNAL OF PHILOSOPHY, . (16/25891-3)
VENTURI, GIORGIO. GENERICITY AND ARBITRARINESS. LOGIQUE ET ANALYSE, n. 248, p. 435-452, . (16/25891-3)
VENTURI, GIORGIO. Infinite Forcing and the Generic Multiverse. STUDIA LOGICA, v. 108, n. 2, p. 277-290, . (16/25891-3)
BEZERRA, E.; VENTURI, G.. Many-Valued Logics and Bivalent Modalities. LOGIC AND LOGICAL PHILOSOPHY, v. N/A, p. 26-pg., . (16/25891-3)
TARAFDER, SOURAV; VENTURI, GIORGIO. ZF Between Classicality and Non-classicality. STUDIA LOGICA, v. 110, n. 1, . (16/25891-3, 19/12527-0)

Please report errors in scientific publications list using this form.