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Synthese

, Volume 90, Issue 1, pp 145–179 | Cite as

Consistency, mechanicalness, and the logic of the mind

  • Qiuen Yu
Article

Abstract

G. Priest's anti-consistency argument (Priest 1979, 1984, 1987) and J. R. Lucas's anti-mechanist argument (Lucas 1961, 1968, 1970, 1984) both appeal to Gödel incompleteness. By way of refuting them, this paper defends the thesis of quartet compatibility, viz., that the logic of the mind can simultaneously be Gödel incomplete, consistent, mechanical, and recursion complete (capable of all means of recursion). A representational approach is pursued, which owes its origin to works by, among others, J. Myhill (1964), P. Benacerraf (1967), J. Webb (1980, 1983) and M. Arbib (1987). It is shown that the fallacy shared by the two arguments under discussion lies in misidentifying two systems, the one for which the Gödel sentence is constructable and to be proved, and the other in which the Gödel sentence in question is indeed provable. It follows that the logic of the mind can surpass its own Gödelian limitation not by being inconsistent or non-mechanistic, but by being capable of representing stronger systems in itself; and so can a proper machine. The concepts of representational provability, representational maximality, formal system capacity, etc., are discussed.

Keywords

Formal System System Capacity Strong System Representational Approach Proper Machine 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Kluwer Academic Publishers 1992

Authors and Affiliations

  • Qiuen Yu
    • 1
  1. 1.Dept. of Computer ScienceWayne State UniversityDetroitUSA

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