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

  • Javier Legris
Part of the Studies in Universal Logic book series (SUL)

Abstract

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.

Keywords

History of logic Algebra of logic Formality Ernst Schröder 

Mathematics Subject Classification

01A55 0303 03A05 

Notes

Acknowledgements

It is a truism that the idea of universality is essential to Jean-Yves Beziau’s work. In some respect, Jean-Yves devotes his life to this idea. The following historical comments can be interesting in connection with it. This paper is a result of a research project supported by the Consejo Nacional de Investigaciones Científicas y Técnicas from Argentina (PIP 11220080101334, CONICET). It also benefited from the additional financial support of the Alexander von Humboldt Foundation. I wish to thank Volker Peckhaus for helpful and valuable comments on an earlier draft of this paper.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.IIEP-BAIRES, Facultad de Ciencias EconómicasUniversidad de Buenos AiresCiudad Autónoma de Buenos AiresArgentina

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