Center for Philosophy of Sciences of the University of Lisbon

Funder

Organizational Unit

Publications

Peano’s structuralism and the birth of formal languages

Publication . Bertran-San-Millán, Joan

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 features of the systems of objects that compose these theories. Second, I shall claim that, in the context of independence arguments, Peano developed a schematic understanding of the axioms which, despite diverging in some respects from Dedekind’s construction of arithmetic, should be considered structuralist. From this stance I shall argue that this schematic understanding of the axioms anticipates the basic components of a formal language.

2022Journal article

Open access

Peano’s Geometry: From Empirical Foundations to Abstract Development

Publication . Bertran San-Millán, Joan

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 mathematical proof, and by discussing his critique of Segre’s foundation of hyperspace geometry, I will argue that the tension can be dissolved if these two seemingly contradictory positions are understood as compatible stages of a single process of construction rather than conflicting options.

2023Book part

Embargoed access

On Creativity and Generative-AI Aesthetics: some thoughts and concerns

Publication . Corrêa, Graça P.

This article starts by approaching categorizations of value in art, as well as different concepts of art, to discuss how they may apply to generative AI aesthetics. Drawing on Peirce’s seminal concepts of abductive creativity and agapism, in addition to notions of embodiment from neuroscience and phenomenology, it argues that creativity in art entails embodied and environed living agents. Keywords: art and technology, artificial intelligence, generative AI (GAI), Artificial Intelligence Generated Content (AIGC), Peirce agapism.

2023-12Journal article

Open access

Longing and belonging through migration: Otherness and empathy in theatre and philosophy

Publication . Corrêa, Graça P.

This article examines how theatre and philosophy may critically contribute to discussing empathy towards otherness in the context of the ongoing massive surge of migration across the globe. Drawing on concepts from philosophical works by Baruch Spinoza, Henri Bergson and Jacques Derrida, it investigates how different dramaturgical techniques and aesthetics ‐ namely in Euripedes' Children of Heracles (c.430 BCE), Roland Schimmelpfennig's The Golden Dragon (2009) and Nikos Kazantzakis and Graça P. Corrêa's Christ Recrucified (1954/2018) ‐ address ethical-affective percepts such as empathy and hospitality in a theatre dealing with migration experiences.

2019-11-01Journal article

Open access

The Multi-Causal Basis of Developmental Potential Construction

Publication . Vecchi, Davide; Santos, Gil

In this article we analyse the issue of what accounts for developmental potential, i.e., the possible phenotypes a developing organism can manifest during ontogeny. We shall argue in favour of two theses. First, although the developing organism is the unit of development, the complete causal basis for its potential to develop does neither lie entirely in itself as a whole nor in any specific part of itself (such as its genome). Thus, the extra-organismal environment must be counted as one of the three necessary, partial and complementary causal bases for development potential. Secondly, we shall defend a constructivist view of the developmental process. If the genome, the developing organism and the extra-organismal environment are to be counted as proper elements of the causal basis for an organism’s developmental potential, the latter is not a given. Rather, it is the result of an interaction-based construction, a process sometimes generating genuine developmental novelty. We will thus argue for an interactionist multi-causal basis view of developmental potential construction. We contend that our view provides a biologically tenable and metaphysically coherent account of developmental dynamics.

2023-01-30Journal article

Open access