Giorgio Venturi

• Abstract

  This project aims to develop the new foundational approach to forcing which was initially proposed in "An Axiomatic Approach to Forcing and Generic Extensions", by Rodrigo Freire, covering cases that were left open. At the same time, in order to achieve this end goal, we will provide a conceptual analysis of the relevant notions as an attempt to illuminate forcing in a general setting.For…

  Axiomatic foundations of class forcing and symmetric extensions., AV.BR
• Speaking the unspeakable. Paradoxes Between Truth and Proof, AO.R

• Abstract

  We intend to develop the theory of models of non-classical set theories, in particular, paraconsistent set theories. In previous work, the visiting researcher developed a paraconsistent model of set theory in which the negation-free fragment of ZF is valid, but which does not satisfy Leibniz's law of indiscernibility of identicals. In this project, we aim to improve on these results by fi…

  Algebra-valued models of non-classical set theories, AV.EXT

(Only some records are available in English at this moment)

• Abstract

  The main goal of the proposed research is to account for the nature of the illocutionary force corresponding to hypotheses in logic and Mathematics, as well as to explain its role in the logical structure of mathematical language. Thus, it gives way to a convergence of central ideas of two research projects: Hypotheses, leaded by Prof. Peter Schroeder-Heister (Uni-Tübingen), and Genericit…

  Speech acts in Mathematics: hypothetical illocutions, BP.PD

• Abstract

  My goal in this project is to study the main proposed ontologies to deal with possible worlds and the modal logic framework used for philosophers in this field. Among the main ontologies that will be studied are the David Lewis's modal realism (1986), Plantinga and Stalnaker's atualism (1979), combinatorialism - famously defended by Cresswell (1979) -, and Rutley's meinongianism (1980). C…

  Modal logics and ontologies for possible worlds, BP.IC

• Abstract

  Many mathematicians work regularly on the study of mathematical objects, like sets, functions, matrix, etc. However, could we say that these entities exist? It seems a hard question even when we are dealing with the mathematics entities that might be the most fundamental, numbers. Furthermore, assuming one of the positions, that is, saying that such entities exist or not, raise new philos…

  A study on ontology of numbers, BP.IC

(Only some records are available in English at this moment)

• Abstract

  The student's research will focus on the metaontological dispute between neoquineans and neomeinongians, and intends to verify which is the best solution to the so-called paradox of negative existentials, which synthesizes the conflict between the two philosophical traditions under study. At the core of the dispute between neoquineans and neomeinongians is the thesis that quantifying over…

  Meinongian metaontology and the paradox of negative existentials, BE.EP.MS

• Abstract

  In this project I deepen the analysis of the internal logic of set theory - topic of my FAPESP project - proposing a logical analysis of the notion of consistency and its role in the set theoretical practice. This project has a multidisciplinary point of view and tries to combine the philosophical reflection about mathematical practice and the logical description of a mathematical structu…

  A logical analysis of the notion of consistency in set theoretical practice, BE.EP.PD