1965, pp. 408, 419; page-reference to the first edition):
[...] for full generality a complete analysis would have to be made of all the possible ways in which the human mind could set up finite processes for generating sequences. [...] we have to do with a certain activity of the human mind as situated in the universe. As activity, this logico-mathematical process has certain temporal properties; as situated in the universe it has certain spatial properties.
Post maintained that (CT) should be interpreted as a natural law and insisted on its empirical confirmation (similarly DeLong 1970, p. 195). However, one should be very careful with such claims. In fact, we have no general and commonly accepted psychological theory of human mental activities, even as far as the matter concerns ←55 | 56→the scope of computation. Hence, it is very difficult to think about (CT) as an empirical hypothesis about the human mind and its abilities. Eventually (CT) can be considered as related to mechanism in the philosophy of mind (see above) and even as confirming this view. Although we do not deny that (CT) has an application in philosophy, we do not think that this thesis as a tool for a philosophical analysis of the mind body problem functions as a genuine empirical hypothesis. We think that the use of (CT) for supporting mechanism in the philosophy of mind is very similar to deriving (or not) indeterminism from the principle of indeterminacy. We have to abstain from further remarks concerning this interpretation of (CT), because it would require a longer metaphilosophical discussion.
Ad. (B) One should distinguish two understandings of axioms or theorems. Firstly, axioms can be considered as principal metatheoretical assumptions. When Kreisel (1970) considers (CT) as a kind of reducibility axiom for constructive mathematics, he uses the concept of axiom in this sense. Yet, we are inclined to think that his comparison of (CT) with “hypothesis” ofV = L in set theory is rather misleading. In the case of V = L, there is no need to use quotes and say “hypothesis”, because we have to do with a set-theoretical axiom, whereas Kreisel’s analysis does not result in an axiomatic system of set theory. This leads to the second use of the term "axiom", referring to an element of an axiomatic system. A similar problem arises with respect to the category of being a theorem. Mendelson (1990, p. 230) writes:
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