Search

In this article I propose to look at set theory not only as a founda­tion of mathematics in a traditional sense, but as a foundation for mathemat­ical practice. For this purpose I distinguish between a standard, ontological, set theoretical foundation that aims to find a set theoretical surrogate to every mathematical object, and a practical one that tries to explain mathematical phenomena, giving necessary and sufficient conditions for the proof of mathematical propositions. I will present some example of this use of set theoretical methods, in the context of mainstream mathematics, in terms of independence proofs, equiconsistency results and discussing some recent results that show how it is possible to “complete” the structures H(ℵ1) and H(ℵ2). Then I will argue that a set theoretical foundation of mathematics can be relevant also for the philosophy of mathematical practice, as long as some axioms of set theory can be seen as explanations of mathematical phenomena. In the end I will propose a more general distinction between two different kinds of foundation: a practical one and a theoretical one, drawing some examples from the history of the foundation of mathematics.

L’istituto della certificazione dei contratti (artt. 75 ss. d.lgs. 276/2003) viene analizzato partendo da un approccio di teoria della regolazione. La certificazione è rappresentabile come modello di autoregolazione rafforzata (“enforced self-regulation”), e viene descritta nel suo funzionamento presentandola come concreta modalità di attuazione normativa della funzione di controllo sui fini sociali della libera iniziativa economica (art. 41, comma 3, Cost.), di cui si propone una interpretazione evolutiva che richiama il principio di sussidiarietà orizzontale. / 𝑇ℎ𝑒 𝑝𝑎𝑝𝑒𝑟 𝑎𝑛𝑎𝑙𝑦𝑠𝑒𝑠, 𝑡ℎ𝑟𝑜𝑢𝑔ℎ 𝑎 𝑝𝑒𝑟𝑠𝑝𝑒𝑐𝑡𝑖𝑣𝑒 𝑜𝑓 𝑖𝑛𝑑𝑖𝑟𝑒𝑐𝑡 𝑟𝑒𝑔𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝑜𝑛 𝑡ℎ𝑒 𝑙𝑎𝑏𝑜𝑢𝑟 𝑚𝑎𝑟𝑘𝑒𝑡, 𝑡ℎ𝑒 𝐼𝑡𝑎𝑙𝑖𝑎𝑛 𝑙𝑒𝑔𝑎𝑙 𝑝𝑟𝑜𝑐𝑒𝑑𝑢𝑟𝑒 𝑐𝑎𝑙𝑙𝑒𝑑 ‘𝐶𝑒𝑟𝑡𝑖𝑓𝑖𝑐𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑐𝑜𝑛𝑡𝑟𝑎𝑐𝑡𝑠’ (𝑎𝑟𝑡. 75 𝑠𝑠. 𝐷.𝑙𝑔𝑠. 276/2003). 𝐶𝑒𝑟𝑡𝑖𝑓𝑖𝑐𝑎𝑡𝑖𝑜𝑛 𝑖𝑠 𝑟𝑒𝑔𝑎𝑟𝑑𝑒𝑑 𝑎𝑠 𝑎 𝑚𝑜𝑑𝑒𝑙 𝑜𝑓 “𝑒𝑛𝑓𝑜𝑟𝑐𝑒𝑑 𝑠𝑒𝑙𝑓-𝑟𝑒𝑔𝑢𝑙𝑎𝑡𝑖𝑜𝑛”. 𝐶𝑒𝑟𝑡𝑖𝑓𝑖𝑐𝑎𝑡𝑖𝑜𝑛’𝑠 𝑓𝑢𝑛𝑐𝑡𝑖𝑜𝑛𝑠 𝑎𝑛𝑑 𝑒𝑓𝑓𝑒𝑐𝑡𝑠 𝑎𝑟𝑒 𝑎𝑛𝑎𝑙𝑦𝑠𝑒𝑑 𝑖𝑛 𝑡ℎ𝑒 𝑝𝑎𝑝𝑒𝑟, 𝑠𝑜 𝑡ℎ𝑎𝑡 𝑖𝑡 𝑖𝑠 𝑎𝑑𝑑𝑟𝑒𝑠𝑠𝑒𝑑 𝑎𝑠 𝑎 𝑣𝑜𝑙𝑢𝑛𝑡𝑎𝑟𝑦 𝑡𝑜𝑜𝑙 𝑎𝑖𝑚𝑒𝑑 𝑎𝑡 𝑏𝑒𝑖𝑛𝑔 𝑝𝑎𝑟𝑡 𝑜𝑓 𝑡ℎ𝑒 𝐶𝑜𝑛𝑠𝑡𝑖𝑡𝑢𝑡𝑖𝑜𝑛𝑎𝑙 𝑠𝑦𝑠𝑡𝑒𝑚 𝑜𝑓 𝑐𝑜𝑛𝑡𝑟𝑜𝑙𝑠 𝑓𝑜𝑢𝑛𝑑𝑒𝑑 𝑜𝑛 𝑡ℎ𝑒 𝑟𝑢𝑙𝑒 𝑜𝑓 “𝑠𝑜𝑐𝑖𝑎𝑙 𝑝𝑢𝑟𝑝𝑜𝑠𝑒” 𝑑𝑒𝑙𝑖𝑚𝑖𝑡𝑖𝑛𝑔 𝑎𝑛𝑑 𝑑𝑒𝑓𝑖𝑛𝑖𝑛𝑔 𝑡ℎ𝑒 𝐶𝑜𝑛𝑠𝑡𝑖𝑡𝑢𝑡𝑖𝑜𝑛𝑎𝑙 𝑝𝑟𝑖𝑛𝑐𝑖𝑝𝑙𝑒 𝑜𝑓 𝑒𝑐𝑜𝑛𝑜𝑚𝑖𝑐 𝑓𝑟𝑒𝑒𝑑𝑜𝑚 (𝑎𝑟𝑡. 41.3 𝐶𝑜𝑛𝑠𝑡.), 𝑖𝑛 𝑎𝑛 𝑒𝑣𝑜𝑙𝑢𝑡𝑖𝑜𝑛𝑎𝑟𝑦 𝑝𝑒𝑟𝑠𝑝𝑒𝑐𝑡𝑖𝑣𝑒 𝑏𝑎𝑠𝑒𝑑 𝑜𝑛 𝑡ℎ𝑒 𝑝𝑟𝑖𝑛𝑐𝑖𝑝𝑙𝑒 𝑜𝑓 ℎ𝑜𝑟𝑖𝑧𝑜𝑛𝑡𝑎𝑙 𝑠𝑢𝑏𝑠𝑖𝑑𝑖𝑎𝑟𝑖𝑡𝑦.

Among the many archetypal figures that are hidden behind transhumanist thought, the myth of Prometheus is, without a doubt, the one with the greatest semantic force. In the arts, hybrid artistic forms, at the border of different disciplines such as sculpture, performance, dance, biotechnology, information technology, seem to approach this sensibility. How do transhumanist artists use this post-modern "new grammar"? Through which iconographic, technical, symbolic elements the man of the transhumanists is translated into artistic representations? Our analysis, transdisciplinary and cross-cultural, aims to answer these questions through the reading of some works by artists closely next to transhumanism: Orlan, shaper of her own body through plastic surgery, Neil Harbisson, known as the first cyborg, or the Fronte Vacuo’s artists who hybridize themselves with computer slags and artificial intelligences.