Giorgio Venturi
Biographic Data
| ID | 3591928 |
|---|---|
| NAME | Giorgio Venturi |
| GIVEN NAMES | Giorgio |
| FAMILY NAME | Venturi |
| SIGNATURE | VENTURI G |
| AFFILIATIONS | Universidade Estadual de Campinas (UNICAMP) |
| ORCID | 0000-0001-9089-4340 |
| VERIFIED | Yes |
| TOTAL WORKS | 9 |
| TOTAL CITATIONS | 3 |
| WORKS AS AUTHOR | 8 |
| WORKS AS EDITOR | 1 |
| FIRST PUBLICATION YEAR | 2014 |
| LATEST PUBLICATION YEAR | 2026 |
| H-INDEX | 1 |
Generic Sets and Arbitrary Objects
In this paper, I investigate whether generic sets, in the context of the theory of forcing, can be understood as arbitrary objects in the sense of Fine or Horsten. I will provide a partially positive and partially negative answer. Specifically, the answer will depend on whether I will consider generic sets as objects or as names. I also compare our perspective with Horsten's view on Boolean‐valued sets as arbitrary objects. I conclude by suggesti…
Axioms and Postulates as Speech Acts
We analyze axioms and postulates as speech acts. After a brief historical appraisal of the concept of axiom in Euclid, Frege, and Hilbert, we evaluate contemporary axiomatics from a linguistic perspective. Our reading is inspired by Hilbert and is meant to account for the assertive, directive, and declarative components of modern axiomatics. We will do this by describing the constitutive and regulative roles that axioms possess with respect to th…
Thin Objects Are Not Transparent
In this short paper, we analyse whether assuming that mathematical objects are “thin” in Linnebo's sense simplifies the epistemology of mathematics. Towards this end, we introduce the notion of transparency and show that not all thin objects are transparent. We end by arguing that, far from being a weakness of thin objects, the lack of transparency of some thin objects is a fruitful characteristic mark of abstract mathematics
How to make (mathematical) assertions with directives
It is prima facie uncontroversial that the justification of an assertion amounts to a collection of other (inferentially related) assertions. In this paper, we point at a class of assertions, i.e. mathematical assertions, that appear to systematically flout this principle. To justify a mathematical assertion (e.g. a theorem) is to provide a proof—and proofs are sequences of directives. The claim is backed up by linguistic data on the use of imper…
Fine’s Postulationism, Objectivity, and Mathematical Creation
We analyse Kit Fine’s proposal of a procedural Postulationism for mathematics. From a linguistic perspective, we argue that Postulationism is better understood in terms of declarative speech acts. Based on this observation, we argue in favor of a form of Declarationism able to account for both the objectivity of mathematics and its creative dimension
Speech acts in mathematics
From Plato to Weil and beyond
At the end of the 19th century, genericity took an important step toward mathematical analysis, due to the developments promoted by the Italian school of algebraic geometry. However, its origins can be traced back to ancient mathematics in the work of prominent philosophers and mathematicians, such as Plato and Euclid. In this article, we will try to show how a key notion in the structuralist turn of algebraic geometry evolved from a vague lingui…
At least one black sheep
From Logic to Practice
From Logic to Practice
From Plato to Weil and beyond
At the end of the 19th century, genericity took an important step toward mathematical analysis, due to the developments promoted by the Italian school of algebraic geometry. However, its origins can be traced back to ancient mathematics in the work of prominent philosophers and mathematicians, such as Plato and Euclid. In this article, we will try to show how a key notion in the structuralist turn of algebraic geometry evolved from a vague lingui…
At least one black sheep
Speech acts in mathematics
Fine’s Postulationism, Objectivity, and Mathematical Creation
We analyse Kit Fine’s proposal of a procedural Postulationism for mathematics. From a linguistic perspective, we argue that Postulationism is better understood in terms of declarative speech acts. Based on this observation, we argue in favor of a form of Declarationism able to account for both the objectivity of mathematics and its creative dimension
Thin Objects Are Not Transparent
In this short paper, we analyse whether assuming that mathematical objects are “thin” in Linnebo's sense simplifies the epistemology of mathematics. Towards this end, we introduce the notion of transparency and show that not all thin objects are transparent. We end by arguing that, far from being a weakness of thin objects, the lack of transparency of some thin objects is a fruitful characteristic mark of abstract mathematics
How to make (mathematical) assertions with directives
It is prima facie uncontroversial that the justification of an assertion amounts to a collection of other (inferentially related) assertions. In this paper, we point at a class of assertions, i.e. mathematical assertions, that appear to systematically flout this principle. To justify a mathematical assertion (e.g. a theorem) is to provide a proof—and proofs are sequences of directives. The claim is backed up by linguistic data on the use of imper…
Axioms and Postulates as Speech Acts
We analyze axioms and postulates as speech acts. After a brief historical appraisal of the concept of axiom in Euclid, Frege, and Hilbert, we evaluate contemporary axiomatics from a linguistic perspective. Our reading is inspired by Hilbert and is meant to account for the assertive, directive, and declarative components of modern axiomatics. We will do this by describing the constitutive and regulative roles that axioms possess with respect to th…
Generic Sets and Arbitrary Objects
In this paper, I investigate whether generic sets, in the context of the theory of forcing, can be understood as arbitrary objects in the sense of Fine or Horsten. I will provide a partially positive and partially negative answer. Specifically, the answer will depend on whether I will consider generic sets as objects or as names. I also compare our perspective with Horsten's view on Boolean‐valued sets as arbitrary objects. I conclude by suggesti…
Epistemology (8 works) · Philosophy (8 works) · Computer Science (7 works) · Philosophy and Theoretical Science (6 works) · Mathematics (5 works) · History and Theory of Mathematics (4 works) · Computability, Logic, AI Algorithms (3 works) · Linguistics (3 works) · Algebra over a field (2 works) · Artificial Intelligence (2 works)