FOM: 2nd-order logic

[Alasdair Urquhart]

I think Marcin Mostowski must be right in identifying
the logic mentioned by Vann McGee as the logic of
branching quantifiers.

I found some comments of Quine in "Philosophy of Logic"
on the subject of this logic, that are quoted on p. 50
of Boolos's "Logic, Logic and Logic."  In these comments
from pp. 90 and 91 of his book, Quine argues that
branching quantifier logic is not logic but mathematics,
on the grounds that it does not admit a complete proof
procedure for validity.