Vincenzo Ciccarelli’s research while affiliated with University of São Paulo and other places

In this paper I attempt a formalization of Descartes’ causal argument for the existence of God presented in the Third Meditation. By taking into account the philosophical setting of Descartes’ Meditations, I argue that the best logical theory to carry out the formalization is quantified modal logic where free logic is used for the first-order axioms. This fact is related to Descartes’ distinction between formal and objective reality which — to my mind — suggests both the adoption of modality (e.g. true in formal vs true in objective reality) and the possibility of using empty names (i.e. names which lack reference in “formal reality”). After presenting the formal system and the reconstruction of Descartes’ proof, I will discuss some issues related to the philosophical import of the formalization, such as the understanding of rigid designation and lack of reference. I will argue that the formalization of Descartes’ argument has an intrinsic philosophical value for it sheds light on the structure of argument, its implicit difficulties, and the use of logic itself to understand the philosophical tradition.

In this paper, I present two crucial problems for Wolff’s metaphysics of quantities: 1) The structural identification problem and 2) the Pythagorean problem. The former is the problem of uniquely defining a general algebraic structure for all quantities; the latter is the problem of distinguishing physical quantitative structure from mathematical quantities. While Wolff seems to have a consistent and elegant solution to the first problem, the second problem may put in jeopardy his metaphysical view on quantities as spaces. After drawing a parallelism between Wolff’s treatment of quantitative structures and Frege’s conception of quantitative domain, I propose a solution to the Pythagorean problem based on the idea that mathematical structures are the result of applying an abstraction principle on physical quantitative structures. In particular, I propose the view that abstraction may be seen as the operation of structure determination which transforms concrete physical quantities (i.e. undetermined structures) into abstract mathematical quantities (fully determined structures of thin and shallow objects). Keywords: Metaphysics of Quantities, Abstraction Principles, Locationism.

A famous passage in Section 64 of Frege’s Grundlagen may be seen as a justification for the truth of abstraction principles. The justification is grounded in the procedure of content recarving which Frege describes in the passage. In this paper I argue that Frege’s procedure of content recarving while possibly correct in the case of first-order equivalence relations is insufficient to grant the truth of second-order abstractions. Moreover, I propose a possible way of justifying second-order abstractions by referring to the operation of content recarving and I show that the proposal relies to a certain extent on the Basic Law V. Therefore, if we are to justify the truth of second-order abstractions by invoking the content recarving procedure we are committed to a special status of some instances of the Basic Law V and thus to a special status of extensions of concepts as abstract objects.

Este artigo é uma nota editorial de introdução ao dossiê temático ‘1892-2022: 130 anos de Über Sinn und Bedeutung de Frege’. Por meio do exame dos artigos publicados no dossiê, defendemos a tese de que o projeto fundacional do artigo de Frege de 1892 é mais amplo que o projeto logicista em filosofia da matemática e que se desenvolve ao longo de quatro dimensões fundamentais: 1) o desenvolvimento de uma teoria semântica geral; 2) a fundação filosófica de uma linguagem formal e dos principais modos de inferência; 3) a fundação do discurso científico; 4) o esboço de uma semântica para a linguagem natural.

Segundo a objeção da Má Companhia, o fato de que a infame Lei Básica V de Frege proporciona o padrão de definição geral dos princípios de abstração superior é uma boa razão para duvidar da validade deste tipo de definições. Neste artigo, eu argumento contra esta objeção, mostrando que o padrão de definição dos princípios de abstração — como extrapolados a partir do §64 do Grunlagen de Frege — inclui um requisito adicional (que denomino como a condição de especificidade) que não é satisfeito pela Lei Básica V, embora seja satisfeito por outras abstrações de ordem superior, tal como o Princípio de Hume. Mostro também que a falha deste requisito adicional no caso da Lei Básica V é engendrada por uma característica essencial da concepção de Frege da lógica, e que, assim, o próprio Frege não deveria ter tomado a Lei Básica V como uma definição por abstração.

Abstract The present work is a review of Imaguire's book 'Priority Nominalism'. In the first part I present the fundamental idea of the book along general lines; successively, I report a resume of each chapter and I present in more details the view of the author and the dialectic of his arguments. In the final part, I highlight some strong points of the book and I attempt a formulation of a possible difficulty arising from Imaguire's proposal.

In this article I offer an explicating interpretation of the procedure of content recarving as described by Frege in §64 of the Foundations of Arithmetic. I argue that the procedure of content recarving may be interpreted as an operation that while restricting the subject matter of a sentence, performs a generalization on what the sentence says about its subject matter. The characterization of the recarving operation is given in the setting of Yablo’s theory of subject matter and it is based on the relation of determination between properties. The main advantage of the proposal is its generality, for it is applicable not just to the case of abstraction principles

Review of the book 'Paraconsistent Logic: Consistency, Contradiction and Negation' (2016), by Walter Carnielli and Marcelo Coniglio