Séminaire de Logiques Non Classiques : Marianna Antonutti
Nous avons le plaisir de vous annoncer la prochaine séance du séminaire "Logiques Non Classiques", qui aura lieu le jeudi 4 février à 16h, dans la salle des conférence à l'IHPST (13 rue du Four, 75006). Nous accueillerions Marianna Antonutti (IHPST), qui présentera une communication intitulée "Human Effective Computability".
Human Effective Computability
In a 1972 paper, Kreisel draws a distinction between 'machine-effective' or 'algorithmic' computability, and 'human-effective' computability. While he agrees that Turing gave a rigorous analysis of the former, he does not explain in much detail what is meant by the notion of 'human effective computability'. In this paper (joint work with Leon Horsten), we apply Kreisel's notion of 'informal rigour' to the notion of human effective computability. We follow Kreisel in relating this notion to a notion of 'absolute' or 'informal provability', and we elaborate on the idealisations involved in the notion of informal provability, in terms of which the notion of human effective computability is analysed. However, we disagree with Kreisel about the precise way in which this is best done. The two resulting ways of analysing human effective computability give rise to two variants of the Church-Turing Thesis, one of which, we will argue, is more plausible than the other. Ultimately, the hope is that a rigorous analysis of the notion of human effective computability might establish or refute the Church-Turing Thesis for human effective computability, thus giving us information about the scope and limitations of mathematical reasoning.