Andrzej Ehrenfeucht:

I knew Prof. Mostowski much less than some people think. Our contacts
were strictly professional. We never talked about private or personal
matters. The late fifties and early sixties were years of development of
mathematical methods in Logic. But informal discussions very often
centered on philosophical problems of the foundation of mathematics,
such as, "Which logic can be better justified, Classical or
Intuitionistic?", or "What are limitations of the axiomatic method?"
Many logicians had very definite opinions about such topics so the
discussion were quite lively. Prof. Mostowski could discuss each
philosophical stand in minute detail, but he rarely presented his own
opinions. Once when directly asked: "In what sense do mathematical
proofs exist?", he answered, "As a state of mind of a few
mathematicians." But his answer wasn't meant to be serious. But at some
occasions he explain his views on such matters, which I'll try to
summarize: "The goal of science is not to find the truth, but to provide
an understanding. So a scientist should know all explanations but he
should also be sceptical about all of them". And that was the most
valuable lesson I learned from Professor Mostowski.