In this article, Lucas maintains the falseness of Mechanism - the attempt to explain minds as machines - by means of Incompleteness Theorem of Gödel. Gödel’s theorem shows that in any system consistent and adequate for simple arithmetic there are formulae which cannot be proved in the system but that human minds can recognize as true; Lucas points out in his turn that Gödel’s theorem applies to machines because a machine is the concrete instantiation of a formal system: therefore, for (...) every machine consistent and able of doing simple arithmetic, there is a formula that it can’t produce as true but that we can see to be true, and so human minds and machines have to be different. Lucas considers as well in this article some possible objections to his argument: for any Gödelian formula we could, for instance, construct a machine able to produce it or we could put the Gödelian formulae that we had proved as axioms of a further machine. However - as Lucas underlines - for every of such machines we could again formulate another Gödelian formula, the Gödelian formula of these machines, that they are not able to proof but that we can recognize as true. More general arguments, such as the possibility to escape Gödelian argument by suggesting that Gödel’s theorem applies to consistent systems while we could be inconsistent ones, are moreover refuted by Lucas by maintaining that our inconsistency corresponds to occasional malfunctioning of a machine and not to his normal inconsistency; indeed, a inconsistent machine is characterized by producing any statement, on the contrary human being are selective and not disposed to assert anything. (shrink)

A survey of more philosophical applications of Gödel's incompleteness results.

This paper presents a defense of Epistemic Arithmetic as used for a formalization of intuitionistic arithmetic and of certain informal mathematical principles. First, objections by Allen Hazen and Craig Smorynski against Epistemic Arithmetic are discussed and found wanting. Second, positive support is given for the research program by showing that Epistemic Arithmetic can give interesting formulations of Church's Thesis.