What Are Structural Properties?†
By Johannes Korbmacher, Georg Schiemer. Philosophia Mathematica, 2018
113 citations recorded by the source corpus.
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.
Subfields: Artificial Intelligence, Computational Theory and Mathematics, Experimental and Cognitive Psychology
View Paper: https://www.semanticscholar.org/paper/0a63717ce6ccec72d20045e6ddf4f0c382ae7ffe
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