Question two was handled here indirectly in the interpretation of GURU’s principles of reasoning, and gets most obvious, possibly when examining the situations where GURU is supposed to lie. One might want to program GURU in such a way that, out of principle, it doesn’t lie. As a result, GURU wouldn’t be a Gödelian machine any more, but this would clearly be on the deontologists’ side of the philosophical spectrum.

Question one is answered by Gödel himself quite clearly. In his posthumously published Philosophical Essays [ 3] he states:

I am under the impression that [. . .] the Platonistic view is the only one tenable. Thereby I mean the view that mathematics describes a non-sensual reality, which exists independently both of the acts and the dispositions of the human mind and is only perceived, and probably perceived very incompletely, by the human mind [ 3].

References

1. Encyclopedia Britannica ME. 1999. CD-ROM. Normative Ethics.

2. Gödel, K. 1931. Über formal unentscheidbare sätze der principia mathematica und Verwandter Systeme I. Collected Works, vol. 3. S. Feferman, Ed. Oxford University Press.

3. Gödel, K. 1995. Some basic theorems on the foundations of mathematics
and their philosophical implications. Unpublished Philosophical Essays,
F. A. Rodríguez-Consuegra, Ed., chap. 2. Birkhäuser Verlag. 144-147.

4. Guerrerio, G. 2002. Kurt Gödel, Logische Paradoxien und Mathematis-che Wahrheit. Spektrum der Wissenschaft Verlagsgesellschaft.

5. Hofstadter, D. R. 1999. Gödel Escher Bach: An Eternal Golden Braid. Basic Books, Inc.

6. Laudon, K. C. 1995. Ethical concepts and information technology. Comm. of the ACM 38, 12. 33-39.

7. Nash, J. F. 1950. The bargaining problem. Econometrica 18.

8. Smullyan, R. 1987. Forever Undecided. Oxford University Press.

Biography Richard Bergmair ( rbergmair@acm.org) is a final-year undergraduate student of Computer Science at the University of Derby in Austria. He completed a five-year program in Computer Science at the level of secondary education and has been doing Software Engineering for IBM since he was 14. His primary research interests are Computational Linguistics and logic programming.