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Giorgio Venturi
University of Campinas
  1.  54
    Reflexive-Insensitive Modal Logics.David R. Gilbert & Giorgio Venturi - 2016 - Review of Symbolic Logic 9 (1):167-180.
  2. On Forms of Justification in Set Theory.Neil Barton, Claudio Ternullo & Giorgio Venturi - 2020 - Australasian Journal of Logic 17 (4):158-200.
    In the contemporary philosophy of set theory, discussion of new axioms that purport to resolve independence necessitates an explanation of how they come to be justified. Ordinarily, justification is divided into two broad kinds: intrinsic justification relates to how `intuitively plausible' an axiom is, whereas extrinsic justification supports an axiom by identifying certain `desirable' consequences. This paper puts pressure on how this distinction is formulated and construed. In particular, we argue that the distinction as often presented is neither well-demarcated nor (...)
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  3.  34
    A Note on Logics of Essence and Accident.David R. Gilbert & Giorgio Venturi - 2020 - Logic Journal of the IGPL 28 (5):881-891.
    In this paper, we examine the logics of essence and accident and attempt to ascertain the extent to which those logics are genuinely formalizing the concepts in which we are interested. We suggest that they are not completely successful as they stand. We diagnose some of the problems and make a suggestion for improvement. We also discuss some issues concerning definability in the formal language.
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  4.  41
    Speech Acts in Mathematics.Marco Ruffino, Luca San Mauro & Giorgio Venturi - 2020 - Synthese 198 (10):10063-10087.
    We offer a novel picture of mathematical language from the perspective of speech act theory. There are distinct speech acts within mathematics, and, as we intend to show, distinct illocutionary force indicators as well. Even mathematics in its most formalized version cannot do without some such indicators. This goes against a certain orthodoxy both in contemporary philosophy of mathematics and in speech act theory. As we will comment, the recognition of distinct illocutionary acts within logic and mathematics and the incorporation (...)
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  5.  13
    Independence Proofs in Non-Classical Set Theories.Sourav Tarafder & Giorgio Venturi - forthcoming - Review of Symbolic Logic:1-32.
  6.  19
    Neighborhood Semantics for Logics of Unknown Truths and False Beliefs.David Gilbert & Giorgio Venturi - 2017 - Australasian Journal of Logic 14 (1).
    This article outlines a semantic approach to the logics of unknown truths, and the logic of false beliefs, using neighborhood structures, giving results on soundness, completeness, and expressivity. Relational semantics for the logics of unknown truths are also addressed, specically the conditions under which sound axiomatizations of these logics might be obtained from their normal counterparts, and the relationship between refexive insensitive logics and logics containing the provability operator as the primary modal operator.
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  7.  11
    $$\mathrm {ZF}$$ ZF Between Classicality and Non-classicality.Sourav Tarafder & Giorgio Venturi - 2022 - Studia Logica 110 (1):189-218.
    We present a generalization of the algebra-valued models of \ where the axioms of set theory are not necessarily mapped to the top element of an algebra, but may get intermediate values, in a set of designated values. Under this generalization there are many algebras which are neither Boolean, nor Heyting, but that still validate \.
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  8.  9
    Tableaux for Essence and Contingency.Giorgio Venturi & Pedro Teixeira Yago - 2020 - Logic Journal of the IGPL:Doi 10.1093/jigpal/jzaa016.
    We offer tableaux systems for logics of essence and accident and logics of non-contingency, showing their soundness and completeness for Kripke semantics. We also show an interesting parallel between these logics based on the semantic insensitivity of the two non-normal operators by which these logics are expressed.
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  9.  9
    A Non-Standard Kripke Semantics for the Minimal Deontic Logic.Edson Bezerra & Giorgio Venturi - forthcoming - Logic and Logical Philosophy:1.
    In this paper we study a new operator of strong modality ⊞, related to the non-contingency operator ∆. We then provide soundness and completeness theorems for the minimal logic of the ⊞-operator.
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  10.  22
    Thin Objects Are Not Transparent.Matteo Plebani, Luca San Mauro & Giorgio Venturi - forthcoming - Theoria.
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  11.  3
    Forcing, Multiverse and Realism.Giorgio Venturi - 2016 - In Francesca Boccuni & Andrea Sereni (eds.), Objectivity, Realism, and Proof. Filmat Studies in the Philosophy of Mathematics. Springer Verlag.
    In this article we analyze the method of forcing from a more philosophical perspective. After a brief presentation of this technique we outline some of its philosophical imports in connection with realism. We shall discuss some philosophical reactions to the invention of forcing, concentrating on Mostowski’s proposal of sharpening the notion of generic set. Then we will provide an overview of the notions of multiverse and the related philosophical debate on the foundations of set theory. In conclusion, we connect this (...)
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  12.  16
    Ideal Objects for Set Theory.Santiago Jockwich, Sourav Tarafder & Giorgio Venturi - 2022 - Journal of Philosophical Logic 51 (3):583-602.
    In this paper, we argue for an instrumental form of existence, inspired by Hilbert’s method of ideal elements. As a case study, we consider the existence of contradictory objects in models of non-classical set theories. Based on this discussion, we argue for a very liberal notion of existence in mathematics.
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  13.  4
    Second Order Arithmetic as the Model Companion of Set Theory.Giorgio Venturi & Matteo Viale - forthcoming - Archive for Mathematical Logic:1-25.
    This is an introductory paper to a series of results linking generic absoluteness results for second and third order number theory to the model theoretic notion of model companionship. Specifically we develop here a general framework linking Woodin’s generic absoluteness results for second order number theory and the theory of universally Baire sets to model companionship and show that a \-property formalized in an appropriate language for second order number theory is forcible from some \large cardinals if and only if (...)
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  14.  2
    At Least One Black Sheep: Pragmatics and the Language of Mathematics.Luca San Mauro, Marco Ruffino & Giorgio Venturi - 2020 - Journal of Pragmatics 1 (160):114-119.
    In this paper we argue, against a somewhat standard view, that pragmatic phenomena occur in mathematical language. We provide concrete examples supporting this thesis.
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  15.  19
    Infinite Forcing and the Generic Multiverse.Giorgio Venturi - 2020 - Studia Logica 108 (2):277-290.
    In this article we present a technique for selecting models of set theory that are complete in a model-theoretic sense. Specifically, we will apply Robinson infinite forcing to the collections of models of ZFC obtained by Cohen forcing. This technique will be used to suggest a unified perspective on generic absoluteness principles.
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  16.  8
    From Logic to Practice: Italian Studies in the Philosophy of Mathematics.Giorgio Venturi, Marco Panza & Gabriele Lolli (eds.) - 2014 - Springer International Publishing.
    In the Tractatus, it is stated that questions about logical formatting cannot be meaningfully formulated, since it is precisely the application of logical rules which enables the formulation of a question whatsoever; analogously, Wittgenstein’s celebrated infinite regress argument on rule-following seems to undermine any explanation of deduction, as relying on a logical argument. On the other hand, some recent mathematical developments of the Curry-Howard bridge between proof theory and type theory address the issue of describing the “subjective” side of logic, (...)
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  17.  3
    Many-Valued Logics and Bivalent Modalities.Edson Bezerra & Giorgio Venturi - forthcoming - Logic and Logical Philosophy:1-26.
    In this paper, we investigate the family LS0.5 of many-valued modal logics LS0.5's. We prove that the modalities of necessity and possibility of the logics LS0.5's capture well-defined bivalent concepts of logical validity and logical consistency. We also show that these modalities can be used as recovery operators.
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  18.  11
    Book Review: Linnebo, Ø., Philosophy of Mathematics. [REVIEW]Giorgio Venturi & Felipe Albarelli - 2019 - Manuscrito 42 (2):113-119.
    We review Linnebo's Philosophy of Mathematics, briefly describing the content of the book.
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  19.  16
    A Direct Proof of the Five Element Basis Theorem.Boban Veličković & Giorgio Venturi - 2017 - Mathematical Logic Quarterly 63 (3-4):289-298.
    We present a direct proof of the consistency of the existence of a five element basis for the uncountable linear orders. Our argument is based on the approach of König, Larson, Moore and Veličković and simplifies the original proof of Moore.
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  20.  18
    Foundation of Mathematics Between Theory and Practice.Giorgio Venturi - 2014 - Philosophia Scientiae 18 (1):45-80.
    Je me propose dans cet article de traiter de la théorie des ensembles, non seulement comme fondement des mathématiques au sens traditionnel, mais aussi comme fondement de la pratique mathématique. De ce point de vue, je marque une distinction entre un fondement ensembliste standard, d'une nature ontologique, grâce auquel tout objet mathématique peut trouver un succédané ensembliste, et un fondement pratique, qui vise à expliquer les phénomènes mathématiques, en donnant des conditions nécessaires et suffisantes pour prouver les propositions mathématiques. Je (...)
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  21.  1
    Thin Objects Are Not Transparent.Matteo Plebani, Luca San Mauro & Giorgio Venturi - forthcoming - Theoria.
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  22.  15
    Hilbert Between the Formal and the Informal Side of Mathematics.Giorgio Venturi - 2015 - Manuscrito 38 (2):5-38.
    : In this article we analyze the key concept of Hilbert's axiomatic method, namely that of axiom. We will find two different concepts: the first one from the period of Hilbert's foundation of geometry and the second one at the time of the development of his proof theory. Both conceptions are linked to two different notions of intuition and show how Hilbert's ideas are far from a purely formalist conception of mathematics. The principal thesis of this article is that one (...)
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  23.  12
    Preservation of Suslin Trees and Side Conditions.Giorgio Venturi - 2016 - Journal of Symbolic Logic 81 (2):483-492.
  24.  9
    Hilbert, Completeness and Geometry.Giorgio Venturi - 2011 - Rivista Italiana di Filosofia Analitica Junior 2 (2):80-102.
    This paper aims to show how the mathematical content of Hilbert's Axiom of Completeness consists in an attempt to solve the more general problem of the relationship between intuition and formalization. Hilbert found the accordance between these two sides of mathematical knowledge at a logical level, clarifying the necessary and sufficient conditions for a good formalization of geometry. We will tackle the problem of what is, for Hilbert, the definition of geometry. The solution of this problem will bring out how (...)
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  25.  11
    Foundation of Mathematics Between Theory and Practice.Giorgio Venturi - 2014 - Philosophia Scientae 18:4580.
  26.  3
    A Note on the Introduction of Hilbert’s Grundlagen der Geometrie.Giorgio Venturi - 2017 - Manuscrito 40 (2):5-17.
    ABSTRACT We present and discuss a change in the introduction of Hilbert’s Grundlagen der Geometrie between the first and the subsequent editions: the disappearance of the reference to the independence of the axioms. We briefly outline the theoretical relevance of the notion of independence in Hilbert’s work and we suggest that a possible reason for this disappearance is the discovery that Hilbert’s axioms were not, in fact, independent. In the end we show how this change gives textual evidence for the (...)
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