> Also many classical mathematicians appreciate this as an example > showing that the extensional notion 'Turing computable' is a slight > distortion of the intuitive notion 'computable'.
Possibly, but I don't think this is quite the right diagnosis. The issue is more subtle.
It's a well known phenomenon that many classically minded mathematicians who have had little practice in constructive thinking are unwittingly inconsistent in their reading of intuitionistic quantifiers. It's an equally striking phenomenon that classically minded mathematicians in certain contexts naturally adopt an intuitionistic reading of classical quantifiers. In addition to the example provided by Virgil it's not uncommon for people to mistakenly think, in a classical context, that countable sets come equipped with a designated bijection witnessing their countability.
-- Aatu Koskensilta (firstname.lastname@example.org)
"Wovon man nicht sprechan kann, darüber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus