My question is if there is some concrete symbolic logic at the foundation of human reasoning -something very rudimentary, but still formal? Question may be seen in context of the article given below.
Refer to the following article by Wilfried Sieg : Godel on Computbility On Page 12 of 19, paragraph 2, author writes: "In a deep sense neither Church nor Godel recognized the genuinely distinctive character of Turing’s analysis, i.e., the move from arithmetically motivated calculations to general symbolic processes that underlie them. Most importantly in the given intellectual context, these processes have to be carried out programmatically by human beings: the Entscheidungsproblem had to be solved by us in a mechanical way; it was the normative demand of radical intersubjectivity between humans that motivated the step from axiomatic to formal systems. It is for this very reason that Turing most appropriately brings in human computers in a crucial way and exploits the limitations of their processing capacities, when proceeding mechanically".
Also, can somebody explain Sieg's claim that the move was from arithmetically motivated calculations to general symbolic processes that underlie them : It is clear Sieg is aware of μ-recursive functions, and their equivalence to Turing machines, then what exactly are these symbolic processes? And what is he trying to say by writing: "the Entscheidungsproblem had to be solved by us in a mechanical way"?