Abstract
This paper is about the Problem of Order, which is basically the problem how to account for both the distinctness of facts like a’s preceding b and b’s preceding a, and the identity of facts like a’s preceding b and b’s succeeding a. It has been shown that the Standard View fails to account for the second part and is therefore to be replaced. One of the contenders is Anti-Positionalism. As has recently been pointed out, however, Anti-Positionalism falls prey to a regress argument which is to prove its failure. In the paper we spell out this worry, show that the worry is a serious one, and distinguish four possible strategies for Anti-Positionalism to deal with it.
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Notes
Throughout the paper I speak of converses as regards relations and also as regards facts. E.g. loving and being loved by are converse relations, and a’s loving b and b’s being loved by a converse facts (note that this, crucially, does not make a’s loving b and b’s loving a converse facts).
Also: I am omitting the ‘Uniqueness’ assumption, i.e. that no two distinct relations can give rise to a single fact (Fine 2000: 5). For our purposes, we need not go into this.
Specifically, in that case the problem needs refinement on at least two points: concerning O2, we then also want to have the identity of certain facts of objects related by a polyadic non-symmetric relation; concerning O3, we then also want to have the non-identity of certain facts of objects related by a polyadic symmetric relation.
References
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Acknowledgements
Many thanks to Joop Leo for explaining Anti-Positionalism to me (see Leo 2008), to two anonymous referees and my MA examiners Dennis Schulting, Arianna Betti and Paul Dekker for helpful feedback, and to Fraser MacBride for attracting my attention to Russell’s text cited in §6. The author is PhD fellow of the Research Foundation Flanders at Ghent University.
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Wieland, J.W. Anti-Positionalism’s Regress. Axiomathes 20, 479–493 (2010). https://doi.org/10.1007/s10516-010-9097-9
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DOI: https://doi.org/10.1007/s10516-010-9097-9