Nominalism and constructivism in seventeenth-century mathematical philosophy

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This paper argues that the philosophical tradition of nominalism, as evident in the works of Pierre Gassendi, Thomas Hobbes, Isaac Barrow, and Isaac Newton, played an important role in the history of mathematics during the 17th century. I will argue that nominalist philosophy of mathematics offers new clarification of the development of a "constructivist" tradition in mathematical philosophy. This nominalist and constructivist tradition offered a way for contemporary mathematicians to discuss mathematical objects and magnitudes that did not assume these entities were real in a Platonic sense, and helped lay the groundwork for formalist and instrumentalist approaches in modern mathematics.

Original languageEnglish (US)
Pages (from-to)33-59
Number of pages27
JournalHistoria Mathematica
Issue number1
StatePublished - Feb 2005
Externally publishedYes


  • Constructivism
  • Isaac Newton
  • Nominalism
  • Pierre Gassendi

ASJC Scopus subject areas

  • Mathematics(all)
  • History


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