A Brief Note on Gödel, Nagel, Minds, and Machines

  • Wilfried Sieg
Part of the Outstanding Contributions to Logic book series (OCTR, volume 13)


This note is a brief comment on Feferman’s Gödel, Nagel, Minds, and Machines. It emphasizes the need to expand proof theory and use its formal tools for the analysis of the informal proofs of mathematical practice. Natural formalization is seen as one important step toward providing what Feferman called for, namely, “an informative, systematic account at a theoretical level of how the mathematical mind works that squares with experience”.


Mechanist thesis Mechanism and mind Computability Natural formalization Theory of proofs 


  1. 1.
    Gentzen, G.: Die Widerspruchsfreiheit der reinen Zahlentheorie. Mathematische Annalen 112, pp. 493–565 (1936)Google Scholar
  2. 2.
    Gödel, K.: Some basic theorems on the foundations of mathematics and their implications; delivered as the 25\(^{th}\) Gibbs Lecture on 26 December 1951; published in volume III of Gödel’s Collected Works, pp. 304–323. Oxford University Press (1995)Google Scholar
  3. 3.
    Gowers, T.: Interview. Not. Am. Math. Soc. 63(9), pp. 1026–1028 (2016)Google Scholar
  4. 4.
    Lukas, J.R.: 1959 Minds, machines and Gödel; given in 1959 to the Oxford Philosophical Society; published in Philosophy XXXVI, pp. 112–127 (1961)Google Scholar
  5. 5.
    Nagel, E., Newman, J.R.: Gödel’s Proof. Scientific American CXCIV, pp. 71–86 (1956)Google Scholar
  6. 6.
    Nagel, E., Newman, J.R.: Gödel’s Proof. New York University Press, New York (1958)Google Scholar
  7. 7.
    Penrose, R.: The Emperor’s New Mind: Concerning Computers, Minds, and the Laws of Physics. Oxford University Press, Oxford (1989)Google Scholar
  8. 8.
    Sieg, W.: Searching for proofs (and uncovering capacities of the mathematical mind). In: Feferman, S., Sieg, W. (eds.) Proofs, Categories and Computations – Essays in Honor of Grigori Mints, pp. 189–215. College publication (2010)Google Scholar
  9. 9.
    Sieg, W.: Gödel’s philosophical challenge (to Turing). In: Copeland, B.J., Posy, C.J., Shagrir, O. (eds.) Computability – Turing, Gödel, Church, and Beyond, pp. 183–202. MIT Press (2013)Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Department of PhilosophyCarnegie Mellon UniversityPittsburghUSA

Personalised recommendations