Full Idea
Turing showed that any formal process can be specified computationally, and captured by a Turing Machine. Hence logical rules (and arithmetic) could be obeyed not by someone representing and following them, but by causal organisation of the brain.
Gist of Idea
Turing showed that logical rules can be specified computationally and mechanically
Source
report of Alan Turing (works [1935]) by Georges Rey - Contemporary Philosophy of Mind 8.2
Book Reference
Rey,Georges: 'Contemporary Philosophy of Mind' [Blackwell 1997], p.212
A Reaction
It is questionable whether logic is an entirely formal process, if it involves truth. You would need an entirely formal notion of truth for that. But a brain can do whatever a flow diagram can do.