The mind-body problem is one of the important topics in philosophy of mind and cognitive science. Following the analytical tradition of linguistic and logical analysis

we focus on two aspects of the mind- body problem: one is around Gödel's incompleteness theorem

and the other is on cognitive logic

especially on the question of whether Epistemological Arithmetic and machines are private. In the former case

in response to the popular view that the Gödel Incompleteness Theorem supports dualism in the mind-body problem

H. Putnam constructs a counter-argument that defends the computationalist agenda: the equivalence of mind and Turing machine. In this regard

the paper discusses Putnam's line of analysis and then argues that it is unsound. In the latter case

the paper examines in detail the cognitive form of the expression of privateness and concludes

together with recent results in EA

that the existence of privateness in Turing machines is logically untenable and

therefore

we argue that the mind is not equivalent to a machine in terms of cognitive ability and privateness

i.e.

the computationalist agenda is not valid.