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1 results

  • Chapter 8 - The Character of Arithmetical Knowledge

  • from Part III - Epistemology and Ontology
  • Markus Pantsar, Aachen University of Technology
  • Book:
    Numerical Cognition and the Epistemology of Arithmetic
    Published online:
    15 March 2024
    Print publication:
    28 March 2024, pp 178-199

  • Summary

    In Chapter 8, I deal with the threat that the present account strips arithmetical knowledge of all the important characteristics traditionally associated with it: apriority, objectivity, necessity and universality. I argue that apriority can be saved in the strong sense of arithmetical knowledge being contextually a priori in the context set by our cognitive and physical capacities. Objectivity can be saved in the sense of maximal inter-subjectivity, while necessity can be saved in the sense of arithmetical theorems being true in all possible worlds where cognitive agents with proto-arithmetical abilities have developed. Finally, universality of arithmetical truths is saved through arithmetic being universally applicable and shared by all members of cultures that develop arithmetic based on proto-arithmetical abilities.