On Universality and Formality in 19th Century Symbolic Logic: The Case of Schröder?s ?Absolute Algebra

JAVIER LEGRIS

The Road to Universal Logic. Festschrift for 50th Birthday of Jean-Yves Béziau Volume I

Birkhäuser

Lugar: Basel; Año: 2015; p. 351 - 359

This paper deals with conceptions of formalityunderlying 19th Century symbolic logic, where notations and manipulation ofsigns played an important role. It is devoted specifically to the case of ErnstSchröder?s ?formal algebra?, which extended with the algebra of relatives (asdeveloped by C. S. Peirce) constituted the basis for a Pasigraphy as a universal notation system. The discussion will beginwith the well-known distinction devised by Gottlob Frege between two sorts offormal theories. In the paper both conceptions of formality will be connectedwith the corresponding attempts of constructing universal scientific notations(Schröder?s Pasigraphy and Frege?s Begriffsschrift). It will be shown thatthe Pasigraphy was an interpretation of that formal algebra. As a furtherconclusion it will be suggested that each of the two conceptions of formalityplaces logic in different levels and determines different conceptions ofuniversality.Keywords: History of Logic - Algebra of Logic ?Formality ? Ernst SchröderMathematical Subject Classification: 01A55 ? 03 03 ?03A05