The aim of this study is to elucidate the notion of propositional function as exposed by Russell within the no class theory of Principia Mathematica. According to the realistic interpretation, propositional functions are metaphysical objects consisting of individuals, objectual variables and attributes. According to the nominalistic interpretation, however, they are linguistic expressions. I attempt to show that the best accessible interpretation is the linguistic realistic one. Unlike the nominalistic version of the linguistic interpretation – which treats propositional functions as mere sequences of letters – it explains propositional functions as linguistic expressions with their meanings, so to speak, assuming also that abstract objects such as properties do exist.
Financed by the National Centre for Research and Development under grant No. SP/I/1/77065/10 by the strategic scientific research and experimental development program:
SYNAT - “Interdisciplinary System for Interactive Scientific and Scientific-Technical Information”.