Bach C.P.E or J.C.?

[jagruys]

In the List of works by Carl Philipp Emanuel Bach, I find some fifty times Notes like: "J. C. Bach's authorship uncertain" or "J. C. Bach's authorship doubtful". Is that really what is intended, or should "J.C. Bach's" be corrected into "C.P.E. Bach's"?

http://imslp.org/wiki/List_of_works_by_ ... anuel_Bach