There are cognitive differences between equalities “a=b” and “a=a”. What is the source of these differences? Frege tried to interpret it semantically in his On Sense and Reference. Afterwards this problem was called “Freges Puzzle”. Other Philosophers tried to answer it. They either treated it semantically by inheriting Frege’s method, or treated it syntactically. But so far none of them solved Freges puzzle. If there were some semantic theories which were able in solving Freges puzzle, their intrinsic “higher-order” Freges puzzles would still be insoluble, or it would force that distinct symbols would never be used on equalities. On the other hand, solving Freges puzzle syntactically is not better than merely demanding “these two expressions are cognitively different”. On this sense, Freges puzzle is insoluble.