When I turned doctor in 1932, I was still wholly under the spell
of Principia M atheJllatica. To me this great work, by my teacher
Whitehead and his pupil Russell, was the datum plane of mathematical
logic. Improvement upon Principia was what I thought progress in
mathematical logic consisted in. Progress in that sense was indeed no
great challenge. The confusion of use and mention cried out for correction,
along with the resulting muddles over propositional functions,
implication, and ramified types. Uneconomical definitions and notations
lay open for pruning. Great pioneer works are proverbially easy
to improve. All these things I appreciated at the time. I t was only in
the following year, however, in Prague and Warsaw, that my perspective
was widened by Carnap, Tarski, and others to take in what had
been happening to logic in foreign climes.