pp 1–16 | Cite as

Quantity Tropes and Internal Relations

  • Markku KeinänenEmail author
  • Antti Keskinen
  • Jani Hakkarainen


In this article, we present a new conception of internal relations between quantity tropes falling under determinates and determinables. We begin by providing a novel characterization of the necessary relations between these tropes as basic internal relations. The core ideas here are that the existence of the relata is sufficient for their being internally related, and that their being related does not require the existence of any specific entities distinct from the relata. We argue that quantity tropes are, as determinate particular natures, internally related by certain relations of proportion and order. By being determined by the nature of tropes, the relations of proportion and order remain invariant in conventional choice of unit for any quantity and give rise to natural divisions among tropes. As a consequence, tropes fall under distinct determinables and determinates. Our conception provides an accurate account of quantitative distances between tropes but avoids commitment to determinable universals. In this important respect, it compares favorably with the standard conception taking exact similarity and quantitative distances as primitive internal relations. Moreover, we argue for the superiority of our approach in comparison with two additional recent accounts of the similarity of quantity tropes.



We wish to thank Gonzalo Rodriguez-Pereyra, Tuomas Tahko, and two referees of Erkenntnis for helpful comments on earlier versions of this paper. Moreover, we thank Finnish Cultural Foundation for funding this research.


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© Springer Science+Business Media B.V., part of Springer Nature 2017

Authors and Affiliations

  • Markku Keinänen
    • 1
    Email author
  • Antti Keskinen
    • 2
  • Jani Hakkarainen
    • 2
  1. 1.Faculty of Social Sciences (Philosophy)University of TampereTampereFinland
  2. 2.University of TampereTampereFinland

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