I am still not 100% sure I understand what the question is asking for, but it occurred to me today that one example might be the following statement:

$(*)$ If every S is P then some S is P.

Today, we would say that $(*)$ is not valid, because if S is vacuous then "every S is P" is true but "some S is P" is false. However, for most of the history of Western civilization, $(*)$ was considered valid. This is usually explained by saying that the "classical" statement that "every S is P" really means, in modern language, "there exists some S and every S is P." This point is discussed in detail in the article on The Traditional Square of Opposition in the Stanford Encyclopedia of Philosophy, where it is also pointed out that if we additionally translate "some S is not P" into modern language as "if there exists some S then some S is not P" then we can recover the entire traditional square of opposition.

This seems to meet Sridhar Ramesh's request for an example not of changing standards of rigor but of "shifting standard formalizations of preformal concepts" (in this case, the concepts of "every" and "some").