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 <a href="https://plato.stanford.edu/entries/square/">The Traditional Square of Opposition</a> 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 <i>not</i> of changing standards of rigor but of "shifting standard formalizations of preformal concepts" (in this case, the concepts of "every" and "some").