``The true'' in Gottlob Frege's ``Über die Grundlagen der Geometrie'' (Q1060202)

In this essay the author examines the metaphysical and metalogical ramifications of Gottlob Frege's controversy with David Hilbert and Alwin Korselt, over Hilbert's ''Grundlagen der Geometrie''. In this respect Frege's position was rather the conviction of a ''monistic notion of truth'', according to which theoretical sense and reference (mathematical and other) ''must'' be ''uniquely solvable''. ''No one can serve two masters. One cannot serve truth and untruth. If Euclidean geometry is true non-Euclidean geometry is false, and if non-Euclidean [geometry] is true, Euclidean geometry if false.'' In contrast with this position stands Hilbert's belief, ''puzzling'' according to the author, that whatever is consistent in some sense ''exists''. In opposition to Frege, Hilbert's, as well as Korselt's attitude was rather the position of a ''logical relativism''. This is not the place where a detailed discussion (according to the author's views) of the entire metatheoretical ''Neuland'' (''unexplored territory'') opened at that past time could be performed. Recent opinions of Michael Resnick, Michael Dummet and Friedrich Kambartel are also discussed, which emphasize some constructive aspects of Frege's argument, but according to the author ''pass over in silence the ways in which the monism undermines them''. The author concludes against the ''pervasively dogmatic presumption'' contained in Frege's conception and finishes with observations we give summarized here: ''The exploration of the Neuland in the two stages or levels, as it were: FREGE opened up the object- theoretical level: the still-unexplored structure of quantification over numbers. it remained for his successors to codify the structures of genuine metatheoretic quantification over theories about quantification over numbers'', etc.