Gödel's incompleteness theorems and their suite, including the undecidability theorems of Church, have figured essentially in numerous attempts of uneven quality to refute mechanism.¹ Most of these attempts have met with various equally uneven criticisms which have in turn stimulated refined, though still inconclusive, further attempts.² Professor Lucas, who himself is the author of several such attempts, frankly admits that "the application of Gödel's theorem to the problem of minds and machines is difficult" ([52], p. 145). He even concedes, in a rejoinder to my own uneven criticism of his position [82],