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Towards a Formal Account of Identity Criteria

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Part of the book series: Logic, Epistemology, and the Unity of Science ((LEUS,volume 25))

Abstract

Identity criteria are used to confer ontological respectability: Only entities with clearly determined identity criteria are ontologically acceptable. From a logical point of view, identity criteria should mirror the identity relation in being reflexive, symmetrical, and transitive. However, this logical constraint is only rarely met. More precisely, in some cases, the relation representing the identity condition fails to be transitive. We consider the proposals given so far to give logical adequacy to inadequate identity conditions. We focus on the most refined proposal and expand its formal framework by taking into account two further aspects that we consider essential in the application of identity criteria to obtain logical adequacy: contexts and granular levels.

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Notes

  1. 1.

    Brand [1] has given a different characterization for the logical form of ICs in terms of second order modal logic: \(\exists F \forall x \forall y\)(if x and y are ϕs then \(\square (x = y \leftrightarrow F(x,y)))\)

  2. 2.

    It is debatable if there is a real distinction between two-level and one-level ICs . J. Lowe has suggested that a two-level IC can be recast as one-level. For example (O) can be so reformulated:

    $$\forall x \forall y((Direction(x) \land Direction(y)) \rightarrow (x = y \leftrightarrow \exists w \exists z (L(w) \land L(z) \land Of(x, w) \land Of(y, z) \land P(w,z))))$$

    where “Direction” is “to be a direction”, “L” “to be a line”, and “Of” “to be of” (Lowe discusses one-level and two-level identity criteria in [10, 11]).

  3. 3.

    If you prefer to maintain Williamson’s approaches, instead of R ± you can get R + or R −.

  4. 4.

    Note that the domain \({\mathcal D}\) remains fixed in all the granular structures, and so the set of contexts O. The relation R also is the same—for example, perceptual indiscriminability—but its interpretation can differ along the grain size of the structure, as we see in the example.

References

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Author information

Authors and Affiliations

  1. Department of Philosophy, University of Padua, Padua, Italy

    Massimiliano Carrara & Silvia Gaio

Authors
  1. Massimiliano Carrara
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  2. Silvia Gaio
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Corresponding author

Correspondence to Massimiliano Carrara .

Editor information

Editors and Affiliations

  1. , Faculty of Philosophy, University of Rijeka, Slavka Krautzeka bb, Rijeka, HR-51000, Croatia

    Majda Trobok

  2. , Department of Philosophy, University of Maribor, Koroška cesta 160, Maribor, 2000, Slovenia

    Nenad Miščević

  3. , Faculty of Philosophy, University of Split, Teslina 12, Split, 21000, Croatia

    Berislav Žarnić

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Carrara, M., Gaio, S. (2012). Towards a Formal Account of Identity Criteria. In: Trobok, M., Miščević, N., Žarnić, B. (eds) Between Logic and Reality. Logic, Epistemology, and the Unity of Science, vol 25. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-2390-0_12

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