Abstract
Are identity criteria grounding principles? A prima facie answer to this question is positive. Specifically, two-level identity criteria can be taken as principles related to issues of identity among objects of a given kind compared with objects of a more basic kind. Moreover, they are grounding metaphysical principles of some objects with regard to others. In the first part of the paper we criticise this prima facie natural reading of identity criteria. This result does not mean that identity criteria could not be taken as grounding principles. In the second part, we propose some basic steps towards a conceptual reading of grounding. Such a way of understanding it goes along with an epistemic reading of identity criteria.
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Notes
We will return on this point later.
Grounding is one of the most discussed notions in contemporary philosophy. Roughly, grounding is a type of non-causal, primitive relation (or operation) such that the grounded entities, usually facts, are somehow explained, determined or constituted by the grounding entities. The grounding revolution (Schaffer 2016, 91) contributed to clarifying the meaning of locutions such as “in virtue of” and “because”. The literature on grounding is massive. Some basic and introductory papers on it are: Fine (2002, 2012), Correia and Schnieder (2012), Clark and Liggins (2012), Raven (2015), Trogdon (2013) and Bliss and Trogdon (2016). An enlightening introduction to grounding and related notions is Chapter 5 of Tahko (2015).
We want to thank an anonymous referee for pointing out this issue.
For a discussion on the ontology of mathematics in the light of the grounding approach, see De Florio (2018).
We would like to thank an anonymous referee for emphasising this important point and, moreover, for suggesting some possible developments of the argument.
For a very useful overview on this topic with a focus on the reasons for which we might find reflexive instances of dependence unacceptable, see Bliss (2018).
The same problem has been observed by Shumener (2017, p. 6).
A new proposal on the above question is in Azzano and Carrara (2017).
The formal proof is in Carrara and Giaretta (2004, p. 223).
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Acknowledgements
Early versions of this paper have been read at the following conferences, workshops or seminars: Metaphysical and Mathematical Explanation II—Explanation, Grounding, and Dependence (Pavia, December 2017), ECAP9 (Munich, August 2017), IUC Conference in Metaphysics, (Dubrovnik, June 2017), From Foundations to Applications: Workshop in the Philosophy of Mathematics (Milan, June 2017), Ontoformat Seminar (Milan, April 2017), Grounding Grounding (Alghero, October 2016). We are indebted to the participants in events for stimulating discussions. Thanks also to the referees of Synthese for their useful and detailed comments. Finally, many thanks for criticisms, suggestions and encouragement to: Lorenzo Azzano, Mark Balaguer, Otávio Bueno, Daniele Chiffi, Ilaria Canavotto, Alessandro Giordani, Øystein Linnebo, Vittorio Morato, Elisa Paganini, Francesca Poggiolesi, Marco Panza, Andrea Sereni, Tuomas Tahko, Paolo Valore, and Luca Zanetti.
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Carrara, M., De Florio, C. Identity criteria: an epistemic path to conceptual grounding. Synthese 197, 3151–3169 (2020). https://doi.org/10.1007/s11229-018-1878-5
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DOI: https://doi.org/10.1007/s11229-018-1878-5