In my previous post Sapir-Whorf Revisited I cited Lakoff's theories on metaphor. A much simpler critique of Pinker can be made, based only on Pinker. He says
"...the famous Sapir-Whorf hypothesis of linguistic determinism, stating that people's thoughts are determined by the categories made available by their language, and its weaker version, linguistic relativity, stating that differences among languages cause differences in the thoughts of their speakers". (The Language Insinct, p. 57)
Now simply substitute "culture" for "language":
"...the Revised S-W hypothesis of cultural determinism, stating that people's thoughts are determined by the categories made available by their culture, and its weaker version, cultural relativity, stating that differences among cultures cause differences in the thoughts of their members."
Sound more reasonable? Most of Pinker's critique in his chapter on "Mentalese" would not apply.
Mentalese also appears to have numerous flaws. On a small scale, what is mentalese for our modern word 'telephone'? On a larger scale, for 'cell doctrine'? For 'plate techtonics'? For 'Standard Social Science Model'? For 'physical symbol system hypothesis / computational theory of mind'? All of these concepts are uniquely made available to us by our culture. They were not hard-wired by evolution. They provide categories which determine (or at least cause differences in) our thoughts.
I also doubt human cognition is based on Predicate Logic. We aren't very good at it, and systems actually based on it normally fall apart on the first inconsistency encountered in the real-world (see Carl Hewitt's heroic attempts to fix this in Common sense for concurrency and strong paraconsistency using unstratified inference and reflection).