The Beginning of Model Theory in the Algebra of Logic

Abstract

Model Theory is commonly closely connected to the work of Alfred Tarski. The main thesis developed in the present paper is that basic ideas of Model Theory, in particular as regards its structural and semantical respects, were anticipated in the work of Ernst Schröder (1844–1902), the main German representative of nineteenth century Algebra of Logic.¹ The second section is devoted to the clarification of the notion “Algebra of Logic”. In the third section Schröder’s programme of an Absolute Algebra is described in order to show that this programme has some features in common with modern Model Theory. According to Wilfried Hodges “[…] in a broader sense,model theory is the study of the interpretation of any language, formal or natural, by means of set-theoretic structures, with Alfred Tarski’s truth definition as a paradigm.”² The relation between notation, interpretation, and modelling will be discussed in the fourth section. The paper is concluded with some observations about Schröder’s notion of modality. An algebraic notation which is claimed to be suitable for all of logic should be able to express modalities as well. Schröder’s work contains only some preliminary epistemological remarks for such algebraic theory of modalities.