Mathematical Possibilities and Their Discovery

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


This Chapter attempts to answer the following questions: What is the ontological status of mathematical entities? What enables our epistemic access to such entities? Do we discover mathematical entities or simply invent them? Mathematical entities do not exist in space, time, or as links in a causal chain. Nor are they abstracted from actual-physical reality. Instead, mathematical entities are individual pure possibilities existing independently of our mind, of possible worlds, and of anything actual. Our intellect (by means of proofs, calculations, and the like) and imagination are reliable enough to give us sufficient epistemic access to such entities. Mathematical entities can be discovered; they cannot be invented. Nevertheless, truthful fictions may help us discover such entities as well as their general relations.

Original languageEnglish
Title of host publicationSynthese Library
PublisherSpringer Science and Business Media B.V.
Number of pages39
StatePublished - 2020

Publication series

NameSynthese Library
ISSN (Print)0166-6991
ISSN (Electronic)2542-8292

Bibliographical note

Publisher Copyright:
© 2020, Springer Nature Switzerland AG.

ASJC Scopus subject areas

  • History and Philosophy of Science
  • History
  • Language and Linguistics
  • Logic


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