This paper deals with conceptions of formality underlying 19th century symbolic logic, where notations and manipulation of signs played an important role. It is devoted specifically to the case of Ernst Schröder's "formal algebra", which extended with the algebra of relatives (as developed by C.S. Peirce) constituted the basis for a Pasigraphy as a universal notation system. The discussion will begin with the well-known distinction devised by Gottlob Frege between two sorts of formal theories. In the paper, both conceptions of formality will be connected with the corresponding attempts of constructing universal scientific notations (Schröder's Pasigraphy and Frege's Begriffsschrift). It will be shown that the Pasigraphy was an interpretation of that formal algebra. As a further conclusion, it will be suggested that each of the two conceptions of formality places logic in different levels and determines different conceptions of universality.