"The simple theory of types, T, and Zermelo set-theory, Z, are
two of the best-known ways of formalizing the foundations of
mathematics. For a long time it has been tacitly assumed that
anything that can be done in one system can also be done in the
other by a suitable "translation", or, at least, that one is
consistent if and only if the other is."
[He then goes on to refute that tacit assumption by showing that Z proves
the consistency of T.]
I have been looking for contemporary documentary evidence that for
"a long time" up till 1949, that assumption was indeed widely made.
All I have found so far is a paper (in the JSL XIII, 1948) of Turing on
Practical Forms of Type Theory, that begins "Russell's theory of
types, though probably not providing the soundest possible foundation
for mathematics, follows closely the outlook of most mathematicians.",
and Skolem's comment in his 1922 paper (van Heijenoort's Source Book,
page 291) that only Zermelo's system has found general acceptance whereas
mathematicians have taken but little interest in the Russell--Whitehead
system.
Neither of those seems exactly to support Kemeny's statement.
I should be glad to be told of any papers within the relevant period that
support or confute Kemeny's statement.
A. R. D. Mathias