•  2
    In Principii di Geometria (1889b) and ‘Sui fondamenti della Geometria’ (1894) Peano offers axiomatic presentations of projective geometry. There seems to be a tension in Peano's construction of geometry in these two works: on the one hand, Peano insists that the basic components of geometry must be founded on intuition, and, on the other, he advocates the axiomatic method and an abstract understanding of the axioms. By studying Peano’s empiricist remarks and his conception of the notion of mathe…Read more
  •  17
    Recent historical studies have investigated the first proponents of methodological structuralism in late nineteenth-century mathematics. In this paper, I shall attempt to answer the question of whether Peano can be counted amongst the early structuralists. I shall focus on Peano’s understanding of the primitive notions and axioms of geometry and arithmetic. First, I shall argue that the undefinability of the primitive notions of geometry and arithmetic led Peano to the study of the relational fe…Read more
  •  20
    Frege, Peano and the construction of a logical calculus
    Logique Et Analyse 253 3-22. 2021.
    In contemporary historical studies Peano is usually linked to the logical tradition pioneered by Frege. In this paper I question this association. Specifically, I claim that Frege and Peano developed significantly different conceptions of a logical calculus. First, I clam that while Frege put the systematisation of the notion of inference at the forefront of his construction of an axiomatic logical system, Peano modelled his early logical systems as mathematical calculi and did not really attemp…Read more
  •  17
    Frege, Peano and the Interplay between Logic and Mathematics
    Philosophia Scientiae 25 (1): 15-34. 2021.
    In contemporary historical studies, Peano is usually included in the logical tradition pioneered by Frege. In this paper, I shall first demonstrate that Frege and Peano independently developed a similar way of using logic for the rigorous expression and proof of mathematical laws. However, I shall then suggest that Peano also used his mathematical logic in such a way that anticipated a formalisation of mathematical theories which was incompatible with Frege’s conception of logic.
  •  157
    La Lógica de Gottlob Frege: 1879-1903
    Dissertation, Universitat de Barcelona. 2016.
    In this dissertation I offer a global and detailed reconstruction of the logic developed by Gottlob Frege throughout his career. Even though Frege's logic suffered profound modifications from his initial formulation in Begriffsschrift to its revised version in Grundgesetze, the significant differences between these two works have been rarely taken at face value. I not only argue that these differences exist, but I also explain how they should be understood in the light of the evolution of Frege'…Read more
  •  176
    Frege's Intellectual Life As a Logicist Project (review)
    Teorema: International Journal of Philosophy 39 127-138. 2020.
    I critically discuss Dale Jacquette’s Frege: A Philosophical Biography. First, I provide a short overview of Jacquette’s book. Second, I evaluate Jacquette’s interpretation of Frege’s three major works, Begriffsschrift, Grundlagen der Arithmetik and Grundgesetze der Arithmetik; and conclude that the author does not faithfully represent their content. Finally, I offer some technical and general remarks.
  •  67
    Begriffsschrift’s Logic
    Notre Dame Journal of Formal Logic 61 (3): 409-440. 2020.
    In Begriffsschrift, Frege presented a formal system and used it to formulate logical definitions of arithmetical notions and to deduce some noteworthy theorems by means of logical axioms and inference rules. From a contemporary perspective, Begriffsschrift’s deductions are, in general, straightforward; it is assumed that all of them can be reproduced in a second-order formal system. Some deductions in this work present—according to this perspective—oddities that have led many scholars to conside…Read more
  •  42
    After the publication of Begriffsschrift, a conflict erupted between Frege and Schröder regarding their respective logical systems which emerged around the Leibnizian notions of lingua characterica and calculus ratiocinator. Both of them claimed their own logic to be a better realisation of Leibniz’s ideal language and considered the rival system a mere calculus ratiocinator. Inspired by this polemic, van Heijenoort (1967b) distinguished two conceptions of logic—logic as language and logic as ca…Read more
  •  71
    Function and Argument in Begriffsschrift
    History and Philosophy of Logic 38 (4): 316-341. 2017.
    It is well known that the formal system developed by Frege in Begriffsschrift is based upon the distinction between function and argument—as opposed to the traditional distinction between subject and predicate. Almost all of the modern commentaries on Frege's work suggest a semantic interpretation of this distinction, and identify it with the ontological structure of function and object, upon which Grundgesetze is based. Those commentaries agree that the system proposed by Frege in Begriffsschri…Read more