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  1. Le projet husserlien de réforme de al logique et ses prolongements chez Gian-Carlo Rota.Carlos Lobo - 2017 - Revue de Synthèse 138 (1-4):105-150.
    RésuméGian-Carlo Rota est l’un des rares grands mathématiciens de la deuxième moitié du XX e siècle dont l’intérêt pour la logique formelle soit aussi ouvertement déclaré et ne se soit jamais démenti, depuis sa formation d’étudiant à Princeton jusqu’à ses derniers écrits. Plus exceptionnel encore, il fait partie des rares lecteurs assidus de Husserl à s’être aperçu que la phé-noménologie poursuivait un projet de réforme de la logique formelle. L’article propose d’attester l’existence d’un tel projet chez Husserl ; d’en examiner (...)
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  • The Transcendental Source of Logic by Way of Phenomenology.Stathis Livadas - 2018 - Axiomathes 28 (3):325-344.
    In this article I am going to argue for the possibility of a transcendental source of logic based on a phenomenologically motivated approach. My aim will be essentially carried out in two succeeding steps of reduction: the first one will be the indication of existence of an inherent temporal factor conditioning formal predicative discourse and the second one, based on a supplementary reduction of objective temporality, will be a recourse to a time-constituting origin which has to be assumed as a (...)
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  • Talking About Models: The Inherent Constraints of Mathematics.Stathis Livadas - 2020 - Axiomathes 30 (1):13-36.
    In this article my primary intention is to engage in a discussion on the inherent constraints of models, taken as models of theories, that reaches beyond the epistemological level. Naturally the paper takes into account the ongoing debate between proponents of the syntactic and the semantic view of theories and that between proponents of the various versions of scientific realism, reaching down to the most fundamental, subjective level of discourse. In this approach, while allowing for a limited discussion of physical (...)
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  • Is There an Ontology of Infinity?Stathis Livadas - 2020 - Foundations of Science 25 (3):519-540.
    In this article I try to articulate a defensible argumentation against the idea of an ontology of infinity. My position is phenomenologically motivated and in this virtue strongly influenced by the Husserlian reduction of the ontological being to a process of subjective constitution within the immanence of consciousness. However taking into account the historical charge and the depth of the question of infinity over the centuries I also include a brief review of the platonic and aristotelian views and also those (...)
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  • Extending the Non-extendible: Shades of Infinity in Large Cardinals and Forcing Theories.Stathis Livadas - 2018 - Axiomathes 28 (5):565-586.
    This is an article whose intended scope is to deal with the question of infinity in formal mathematics, mainly in the context of the theory of large cardinals as it has developed over time since Cantor’s introduction of the theory of transfinite numbers in the late nineteenth century. A special focus has been given to this theory’s interrelation with the forcing theory, introduced by P. Cohen in his lectures of 1963 and further extended and deepened since then, which leads to (...)
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