In some legal documents, we read, "this page is intentionally left blank." Since this text is written on this page, the page is not really blank.
Is there a mathematical formulation for this paradox? I thought this was similar to Russell's paradox, but it doesn't seem so.
I admit I am not going to add much to the answers already in the comments, but typing this out helped me to clarify my own thoughts on the matter and might help OP as well. Any comment and correction is more than welcome.
In order to give an answer one should first define what paradox really means. Etymologically, a paradox is any sentence that goes against common belief. Quite literally anything that is somewhat unexpected or surprising. This is a tremendously informal definition which serves only to capture the broadest usage and meaning of the word paradox. A different and - in my opinion - more precise word to use in this context, is antinomy.
Antinomy: An antinomy is a proposition which leads to a conclusion of the form $A \iff \neg A$.
An example of antinomy is: $A$: "$A$ is false". That is, a sentence which states its own falsehood. If $A$ is true, then it is true that "$A$ is false". Thus $A$ should be false. If $A$ is false, then it is false that "$ A$ is false". Thus, $A$ should be true. Therefore, we have deduced that $A$ is true if and only if it is false; i.e., $A \iff \neg A$. An antinomy.
Perhaps the most famous antinomy of mathematics is Russell's paradox. Although this is conventionally identified as a paradox, there is nothing wrong, under our terminology, to call it an antinomy. More or less formally, this can derived as follows. Consider the set $S$ of all sets which do not contain themselves; i.e., $S = \{x \mid x \notin x\}$. If $S \in S$, then by definition of $S$ one should have $S \notin S$. If $S \notin S$, then by definition of $S$ again, one should have $S \in S$. Therefore, $S \in S \iff S \notin S$. An antinomy.
Now for the question. The proposition $B$: "This page is blank" could be surprising to some extent as it seems to clash with reality, but it is not an antinomy by our definitions and it is quite distinct from Russell's paradox. Assuming $B$ is true, leads to the belief that the page should be blank. The actual state of the world in this moment is such that the page is not blank. Thus, $B$ should be false. However, assuming $B$ is false leads to the belief that the page should have some text on it. As the world states right now this is perfectly true and $B$ remains false. Thus, although assuming that $B$ is true, leads to the conclusion that $B$ is false, the converse is not true. Assuming that $B$ is false is consistent with the state of the world.
