In search of aleph-null: how infinity can be created

Research output: Contribution to journalArticleScientificpeer-review

Abstract

In this paper I develop a philosophical account of actual mathematical infinity that does not demand ontologically or epistemologically problematic assumptions. The account is based on a simple metaphor in which we think of indefinitely continuing processes as defining objects. It is shown that such a metaphor is valid in terms of mathematical practice, as well as in line with empirical data on arithmetical cognition.
Original languageEnglish
JournalSynthese
Volume192
Issue number8
Pages (from-to)2489-2511
Number of pages23
ISSN0039-7857
DOIs
Publication statusPublished - 2015
MoE publication typeA1 Journal article-refereed

Fields of Science

  • 611 Philosophy
  • infinity
  • philosophy of mathematics

Cite this

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title = "In search of aleph-null: how infinity can be created",
abstract = "In this paper I develop a philosophical account of actual mathematical infinity that does not demand ontologically or epistemologically problematic assumptions. The account is based on a simple metaphor in which we think of indefinitely continuing processes as defining objects. It is shown that such a metaphor is valid in terms of mathematical practice, as well as in line with empirical data on arithmetical cognition.",
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In search of aleph-null : how infinity can be created. / Pantsar, Markus.

In: Synthese, Vol. 192, No. 8, 2015, p. 2489-2511.

Research output: Contribution to journalArticleScientificpeer-review

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AB - In this paper I develop a philosophical account of actual mathematical infinity that does not demand ontologically or epistemologically problematic assumptions. The account is based on a simple metaphor in which we think of indefinitely continuing processes as defining objects. It is shown that such a metaphor is valid in terms of mathematical practice, as well as in line with empirical data on arithmetical cognition.

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KW - philosophy of mathematics

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