The paper explores the philosophical motivations that led to the emergence of the modern axiomatic model introduced by Hilbert and illustrates the meaning and scope of the Entscheidungsproblem, in this context having become “the main problem of mathematical logic” [Hilbert & Ackermann, 1950]. It is then analyzed how Turing's diagonal argument [1936] offers a negative answer to this problem, highlighting the inherent limitations of axiomatic formalization. Finally, the role of non-Turing-computable sequences and the implications of Turing's theoretical theorem for the theoretical foundations of computer engineering and with respect to the debate on the irreducibility of human thought are addressed.
Macchine e pensiero. Assiomatizzazione e limiti della computabilità a partire da Turing
CALEMi F. F.
In corso di stampa
Abstract
The paper explores the philosophical motivations that led to the emergence of the modern axiomatic model introduced by Hilbert and illustrates the meaning and scope of the Entscheidungsproblem, in this context having become “the main problem of mathematical logic” [Hilbert & Ackermann, 1950]. It is then analyzed how Turing's diagonal argument [1936] offers a negative answer to this problem, highlighting the inherent limitations of axiomatic formalization. Finally, the role of non-Turing-computable sequences and the implications of Turing's theoretical theorem for the theoretical foundations of computer engineering and with respect to the debate on the irreducibility of human thought are addressed.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.