Constitution as a Relation within Mathematics
Johansson (Ingvar)
Source: The Monist, Vol. 96, No. 1, Constitution and Composition (January, 2013), pp. 87-100
Paper - Abstract

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Author’s Introduction

  1. Constitution is a relation that might be said to be situated between identity and separate existence. If a constitutes b, then a and b are separate entities, even though they are located in the same place, and b may not be able to exist in separation from a. Normally, when the existence of the relation is discussed, it is discussed as being a possible or impossible relation between spatiotemporally located individual entities. This state of affairs is reflected in the fact that the 2012 version of Stanford's online encyclopedia has no entry simply called 'Constitution', only one called 'Material Constitution' ("Wasserman (Ryan) - Material Constitution", 2009). In what follows, I will take it for granted that, really, there is a synchronic relation of material constitution that saves our everyday world from ontological reduction; a relation very much like the one argued for by Lynne Rudder Baker ("Baker (Lynne Rudder) - Persons and Bodies: A Constitution View" [2000] and "Baker (Lynne Rudder) - The Metaphysics of Everyday Life: An Essay in Practical Realism" [2007]) and Amie L. Thomasson (Ordinary Objects [2007]).
  2. What I will argue is that there is a relation of constitution within the realm of mathematical entities, too. For instance, I will claim that the mathematical points of a mathematical line are to the line what (to take the most common example of material constitution) the matter of a statue1 is to the statue2. The argumentation is intended to be of such a character that it can be followed, at least in principle, even by philosophers who have some knowledge of elementary mathematics but no special training in mathematics.
  3. The strong thesis of this paper, then, is that there are constitution relations within mathematics. Hopefully, however, readers who are not convinced may nonetheless accept that there is as much a problem around the relation of constitution within mathematics, as there is one within the realm of everyday life.
  4. In order to avoid all misunderstandings, let me at once say that I do not think that mathematicians as mathematicians have anything to learn from what I am saying, but this is no stranger than the fact that in everyday life people can talk about and discuss statues3 and their matter without any problems. In both cases, the constitution problem is a philosophical problem that is importantly related to the issue of ontological reduction versus nonreduction. In the last section, I will make some comments on the relationship between mathematical constitution and a neglected kind of material constitution, property constitution.

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