Consistency,mechanicalness, and the logic of the mind

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.     

Verification, falsification, and the logic of enquiry

Our starting point is Michael Luntley's falsificationist semantics for the logical connectives and quantifiers: the details of his account are criticised but we provide an alternative falsificationist semantics that yields intuitionist logic, as Luntley surmises such a semantics ought. Next an account of the logical connectives and quantifiers that combines verificationist and falsificationist perspectives is proposed and evaluated. While the logic is again intuitionist there is, somewhat surprisingly, an unavoidable asymmetry between the verification and falsification conditions for negation, the conditional, and the universal quantifier. Lastly we are lead to a novel characterization of realism.     

Contingencies, logic, and learning

A logical analysis of operant learning is presented. In total, the analysis makes a number of predictions that are different from the predictions of any other theory. Individual predictions can be explained by other theories, but the pattern of predictions is unique. Some tests of the predictions of the analysis with human newborns are described. The analysis predicts increased variance in sucking with the introduction of continuous reinforcement. This does occur. The analysis predicts a decreased rate of sucking with a shift from continuous to partial reinforcement. This does occur. The analysis predicts an increased rate of sucking with a shift from continuous reinforcement to continuous plus noncontingent reinforcement. Due to methodological deficiencies, we have been unable to test this prediction. However, it has been confirmed by others. The most exciting prediction of the analysis is a rapid way of producing extinction. That has not been tested with newborns; however, there is confirmatory evidence in the literature.     

Language, truth and logic

Ohne Zusammenfassung

---

Language, truth and logic Alfred J. Ayer: 254 S. London 1936. Victor Gollancz Ltd.

     

Kant,wittgenstein and the limits of logic

This paper has two purposes. (1) To justify the claim that there is an important distinction underlying the saying/showing distinction of the Tractatus; the distinction which Kant characterises as that between historical and rational knowledge. (2) To argue that it is because the Tractatus accepts Frege/Russell logic as a complete representation of all thought according to laws, that what is shown cannot be recognised as knowledge. This is done by interpolating Frege's logical innovations between the views of Kant and Wittgenstein on logic and mathematics.