Conceptual Structuralism

Abstract This paper defends a conceptualistic version of structuralism as the most convincing way elaborating philosophical understanding in line with classical tradition. The argument begins revision tradition “conceptual mathematics”, incarnated key figures period 1850 to 1940 like Riemann, Dedekind, Hilbert or Noether, showing how it led structuralist methodology. Then tension between ‘presuppositionless’ approach those authors, and platonism some recent versions structuralism, is presented. In order resolve this tension, we argue for idea ‘logical objects’ form minimalist realism, again authors including Peirce Cassirer, introduce basic tenets conceptual structuralism. remainder devoted an open discussion assumptions behind and—most importantly—an show objectivity mathematics can be explained from adopted standpoint. includes that advanced builds on hypothetical (Riemann, Peirce, others), which presented discussed detail. Finally, ensuing notion interpreted particularly robust intersubjectivity, distinguished fictional social ontology.