What are structural properties?

Johannes Korbmacher (Corresponding author), Georg Schiemer

Publications: Contribution to journalArticlePeer Reviewed


Informally, structural properties of mathematical objects are usually characterized in one of two ways: either as properties expressible purely in terms of the primitive relations of mathematical theories, or as the properties that hold of all structurally similar mathematical objects. We present two formal explications corresponding to these two informal characterizations of structural properties. Based on this, we discuss the relation between the two explications. As will be shown, the two characterizations do not determine the same class of mathematical properties. From this observation we draw some philosophical conclusions about the possibility of a 'correct' analysis of structural properties.

Original languageEnglish
Pages (from-to)295–323
Number of pages29
JournalPhilosophia Mathematica: philosophy of mathematics, its learning, and its application
Issue number3
Publication statusPublished - 18 Oct 2018

Austrian Fields of Science 2012

  • 603113 Philosophy

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