Consistency, mechanicalness, and the logic of the mind

Synthese 90 (1):145-79 (1992)
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 Consistency  Formalism  Human  Logic  Mind
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DOI 10.1007/BF00485195
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References found in this work BETA
Hilary Putnam (1960). Minds and Machines. In Sidney Hook (ed.), Journal of Symbolic Logic. New York University Press 57-80.
Alonzo Church (1944). Introduction to Mathematical Logic. London, H. Milford, Oxford University Press.
Graham Priest (1979). The Logic of Paradox. Journal of Philosophical Logic 8 (1):219 - 241.

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Citations of this work BETA
Graham Priest (1993). Yu and Your Mind. Synthese 95 (3):459 - 460.

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