Element contents
Series: Elements in Metaphysics
Identity
Published online by Cambridge University Press: 29 August 2022
Summary
Identity criteria are powerful tools for the metaphysician. They tell us when items are identical or distinct. Some varieties of identity criteria also try to explain in virtue of what items are identical or distinct. This Element has two objectives: to discuss formulations of identity criteria and to take a closer look at one notorious criterion of object identity, Leibniz's Law. The first section concerns the form of identity criteria. The second section concerns the better-regarded half of Leibniz's Law, the indiscernibility of identicals. The third section turns to the more controversial half of Leibniz's Law, the identity of indiscernibles. The author considers alternatives to Leibniz's Law as well as the possibility that there are no adequate identity criteria to be found.
- Type
- Element
- Information
- Series: Elements in MetaphysicsOnline ISBN: 9781009004671Publisher: Cambridge University PressPrint publication: 15 September 2022
References
Adams, M. M. (1976). “Ockham on Identity and Distinction.” Franciscan Studies 36 (1):5–74.Google Scholar
Adams, R. M. (1979). “Primitive Thisness and Primitive Identity.” Journal of Philosophy 76 (1):5–26.Google Scholar
Bacon, A. & Russell, J. S. (2019). “The Logic of Opacity.” Philosophy and Phenomenological Research 99 (1):81–114.Google Scholar
Baker, L. R. (1997). “Why Constitution Is Not Identity.” Journal of Philosophy 94 (12):599–621.Google Scholar
Baxter, D. L. M. (1988). “Many-One Identity.” Philosophical Papers 17 (3):193–216.CrossRefGoogle Scholar
Baxter, D. L. M. (2018). “Self‐Differing, Aspects, and Leibniz’s Law.” Noûs 52:900–20.Google Scholar
Bennett, K. (2004). “Spatio-Temporal Coincidence and the Grounding Problem.” Philosophical Studies 118 (3):339–71.Google Scholar
Boolos, G. (1997). “Is Hume’s Principle Analytic?” In Heck, R. G. (ed.), Language, Thought, and Logic: Essays in Honour of Michael Dummett. Oxford University Press. pp. 245–62.Google Scholar
Bricker, P. (2008). “Concrete Possible Worlds.” In Sider, T., Hawthorne, J. & Zimmerman, D. W. (eds.), Contemporary Debates in Metaphysics. Blackwell. pp. 111–34.Google Scholar
Bricker, P. (2021). “Composition as Identity, Leibniz’s Law, and Slice-Sensitive Emergent Properties.” Synthese: 4389–409.Google Scholar
Bueno, O. (2014). Why Identity Is Fundamental. American Philosophical Quarterly 51 (4):325–32.Google Scholar
Burgess, A. (2012). “A Puzzle about Identity.” Thought: A Journal of Philosophy 1 (2):90–99.Google Scholar
Caie, M., Goodman, J., & Lederman, H. (2020). “Classical Opacity.” Philosophy and Phenomenological Research 101 (3):524–66.Google Scholar
Caplan, B. & Muller, C. (2015). “Brutal Identity.” In S. Brook & A. Everett (eds.), Fictional Objects. Oxford University Press. pp. 174–207.Google Scholar
Carmichael, C. (2016). Deep Platonism. Philosophy and Phenomenological Research 92 (2):307–28.Google Scholar
Caulton, A. & Butterfield, J. (2012). “On Kinds of Indiscernibility in Logic and Metaphysics.” British Journal for the Philosophy of Science 63 (1):27–84.Google Scholar
Cotnoir, A. J. (2013). “Composition as General Identity.” In Bennett, K. & Zimmerman, D. W. (eds.), Oxford Studies in Metaphysics. Oxford University Press. pp. 294–322.Google Scholar
Cotnoir, A. J. & Baxter, D. L. M. (eds.) (2014). Composition as Identity. Oxford University Press.Google Scholar
Curley, E. M. (1971). “Did Leibniz State ‘Leibniz’ Law’?” Philosophical Review 80 (4):497–501.Google Scholar
Della Rocca, M. (2005). “Two Spheres, Twenty Spheres, and the Identity of Indiscernibles.” Pacific Philosophical Quarterly 86:480–92.Google Scholar
Deutsch, H. & Garbacz, P. (2008). “Relative Identity.” In E. N. Zalta (ed.), Stanford Encyclopedia of Philosophy. https://plato.stanford.edu/entries/identity-relative.Google Scholar
Donaldson, T. (2017). “The (Metaphysical) Foundations of Arithmetic?” Noûs 51 (4):775–801.CrossRefGoogle Scholar
Dorr, C. (2014). “Transparency and the Context-Sensitivity of Attitude Reports.” In García-Carpintero, M. & Martí, G. (eds.), Empty Representations: Reference and Non-Existence. Oxford University Press. pp. 25–66.Google Scholar
Dorr, C. (2019). “Natural Properties.” In E. N. Zalta (ed.), Stanford Encyclopedia of Philosophy. https://plato.stanford.edu/entries/natural-properties.Google Scholar
Eddon, M. (2010). Three Arguments from Temporary Intrinsics. Philosophy and Phenomenological Research 81 (3):605–19.Google Scholar
Eddon, M. (2011). “Intrinsicality and Hyperintensionality.” Philosophy and Phenomenological Research 82 (2):314–36.Google Scholar
Epstein, B. (2015). The Ant Trap: Rebuilding the Foundations of the Social Sciences. Oxford University Press.CrossRefGoogle Scholar
Fine, K. (1983). “A Defence of Arbitrary Objects.” Proceedings of the Aristotelian Society, Supplementary Volume 57:55–77.Google Scholar
Fine, K. (1985a). “Natural Deduction and Arbitrary Objects.” Journal of Philosophical Logic 14:57–107.CrossRefGoogle Scholar
Fine, K. (2003). “The Non‐identity of a Material Thing and Its Matter.” Mind 112 (446):195–234.CrossRefGoogle Scholar
Fine, K. (2012). “A Guide to Ground.” In Correia, F. & Schnieder, B. (eds.), Metaphysical Grounding. Cambridge University Press. pp. 37–80.Google Scholar
Frege, G. (1879). Begriffsschrift, eine der arithmetischen nachgebildete Formelsprache des reinen Denkens. Louis Nebert.Google Scholar
Frege, G (1892). “Über Sinn und Bedeutung.” Zeitschrift für Philosophie Und Philosophische Kritik 100 (1):25–50.Google Scholar
Frege, G (1980 [1884]). The Foundations of Arithmetic: A Logico-mathematical Enquiry into the Concept of Number [Die Grundlagen der Arithmetik: eine logisch mathematische Untersuchung über den Begriff der Zahl], trans. J. L. Austin, 2nd rev. ed. Northwestern University Press.Google Scholar
Frege, G (2013 [1893]). Gottlob Frege: Basic Laws of Arithmetic [Grundgesetze der Arithmetik], trans. and ed. P. A. Ebert & M. Rossberg. Oxford University Press.Google Scholar
French, S. (1989). “Why the Principle of the Identity of Indiscernibles Is Not Contingently True Either.” Synthese 78 (2):141–66.Google Scholar
French, S. (2015). “Identity and Individuality in Quantum Theory.” In E. N. Zalta (ed.), Stanford Encyclopedia of Philosophy. https://plato.stanford.edu/entries/qt-idind/.Google Scholar
French, S. & Krause, D. (2006). Identity in Physics: A Historical, Philosophical, and Formal Analysis. Oxford University Press.Google Scholar
Garland, C. (2020). “Grief and Composition as Identity.” Philosophical Quarterly 70 (280):464–79.Google Scholar
Geach, P. T. (1973). “Ontological Relativity and Relative Identity.” In Munitz, M. K. (ed.), Logic and Ontology. New York University Press. pp. 287–302.Google Scholar
Glazier, M. (2020). “Explanation.” In Michael J. Raven (ed.), Routledge Handbook of Metaphysical Grounding. Routledge. pp. 121–32.Google Scholar
Goodman, J. “Consequences of Conditional Excluded Middle.” Unpublished manuscript. https://jeremy-goodman.com/ConsequencesCEM.pdf.Google Scholar
Hacking, I. (1975). “The Identity of Indiscernibles.” Journal of Philosophy 72 (9):249–56.Google Scholar
Hawthorne, J. (2003). “Identity.” In Loux, M. J. & Zimmerman, D. W. (eds.), The Oxford Handbook of Metaphysics. Oxford University Press. pp. 99–130.Google Scholar
Heck, R. (1997). “The Julius Caesar Objection.” In Heck, R. G. (ed.), Language, Thought, and Logic: Essays in Honour of Michael Dummett. Oxford University Press. pp. 273–308.Google Scholar
Heller, M. (1990). The Ontology of Physical Objects: Four-Dimensional Hunks of Matter. Cambridge University Press.Google Scholar
Hoffmann-Kolss, V. (2019). “Defining Qualitative Properties.” Erkenntnis 84 (5):995–1010.Google Scholar
Horsten, L. (2019). The Metaphysics and Mathematics of Arbitrary Objects. Cambridge University Press.Google Scholar
Huggett, N. & Norton, J. (2014). “Weak Discernibility for Quanta, the Right Way.” British Journal for the Philosophy of Science 65 (1):39–58.Google Scholar
Hume, D. (2007). A Treatise of Human Nature: Volume 1, ed. M. Norton & J. Norton. Clarendon Press.Google Scholar
Hume, D. & Macnabb, D. G. C. (eds.) (1738). A Treatise of Human Nature: Being an Attempt to Introduce the Experimental Method of Reasoning Into Moral Subjects. Collins.Google Scholar
Jauernig, A. (2008). “The Modal Strength of Leibniz’s Principle of the Identity of Indiscernibles.” Oxford Studies in Early Modern Philosophy 4:191–225.Google Scholar
Koslicki, K. (2004). “Constitution and Similarity”. Philosophical Studies 117 (3):327–63.Google Scholar
Koslicki, K. (2015). “The Coarse-Grainedness of Grounding.” In Bennett, K. & Zimmerman, D. W. (eds.), Oxford Studies in Metaphysics, vol. 9. Oxford University Press. pp. 306–42.Google Scholar
Krämer, S. (2020). “The Logical Puzzles of Ground.” In Raven, M. J. (ed.), Routledge Handbook of Metaphysical Grounding. Routledge. pp. 413–24.Google Scholar
Kripke, S. A. (1980). Naming and Necessity: Lectures Given to the Princeton University Philosophy Colloquium. Harvard University Press.Google Scholar
Langton, R. & Lewis, D. K. (1998). “Defining ‘Intrinsic’.” Philosophy and Phenomenological Research 58 (2):333–45.Google Scholar
Leibniz, G. W. (1973 [1696]). “On the Principle of Indiscernibles.” In Philosophical Writings, ed. G. H. R. Parkinson, trans. M. Morris & G. H. R. Parkinson. J. M. Dent and Sons Ltd. pp. 133–35.Google Scholar
Leibniz, G. W. (1996). New Essays on Human Understanding, trans. and ed. Remnant, P. and Bennett, J.. Cambridge University Press.Google Scholar
Lewis, D. K. (1983). “New Work for a Theory of Universals.” Australasian Journal of Philosophy 61 (4):343–77.Google Scholar
Lewis, E. (1995). “The Stoics on Identity and Individuation.” Phronesis 40 (1):89–108.Google Scholar
Locke, J. (1979 [1689]). An Essay Concerning Human Understanding, ed. P. Nidditch, rev. ed. Oxford University Press.Google Scholar
Lowe, E. J. (1989). “What Is a Criterion of Identity?” Philosophical Quarterly 39 (154):1–21.Google Scholar
Lowe, E. J. (1995). “Coinciding Objects: In Defence of the ‘Standard Account’.” Analysis 55 (3):171–78.Google Scholar
Magidor, O. (2011). “Arguments by Leibniz’s Law in Metaphysics.” Philosophy Compass 6 (3):180–95.Google Scholar
Maurin, A.-S. (2019). “Grounding and Metaphysical Explanation: It’s Complicated.” Philosophical Studies 176 (6):1573–94.Google Scholar
McSweeney, M. (2020). “Logic.” In Raven, Michael J. (ed.), The Routledge Handbook of Metaphysical Grounding. Routledge. pp. 449–59.Google Scholar
Merricks, T. (1998). “There Are No Criteria of Identity Over Time.” Noûs 32 (1):106–24.Google Scholar
Mooney, J. (2022). “Criteria of Identity Without Sortals.” Noûs 00:1–18 https://doi.org/10.1111/nous.12419.Google Scholar
Muller, F. A. & Seevinck, M. P. (2009). “Discerning Elementary Particles. Philosophy of Science 76 (2):179–200.CrossRefGoogle Scholar
Nelson, M. (2019) “Propositional Attitude Reports.” In E. N. Zalta (ed.), Stanford Encyclopedia of Philosophy. https://plato.stanford.edu/entries/prop-attitude-reports.Google Scholar
O’Leary-Hawthorne, J. (1995). “The Bundle Theory of Substance and the Identity of Indiscernibles.” Analysis 55 (3):191–96.Google Scholar
Parfit, D. (1971). “Personal Identity.” Philosophical Review 80 (January):3–27.CrossRefGoogle Scholar
Plate, J. (in press). “Qualitative Properties and Relations.” Philosophical Studies: 1–26.Google Scholar
Parsons, C. (1965). “Frege’s Theory of Numbers.” In Black, M. (ed.), Philosophy in America. Cornell University Press. pp. 180–203.Google Scholar
Paul, L. (2010). “The Puzzles of Material Constitution.” Philosophy Compass 5 (7):579–90.Google Scholar
Poggiolesi, F. (2020). “Logics of Ground.” In Raven, Michael J. (ed.), Routledge Handbook of Metaphysical Grounding. Routledge. pp. 413–24.Google Scholar
Quine, W. V. (1976). “Grades of Discriminability.” Journal of Philosophy 73 (5):113–16.Google Scholar
Raven, M. J. (2013). “Is Ground a Strict Partial Order?” American Philosophical Quarterly, 50 (2):191–99.Google Scholar
Raven, M. J. (2020) “Kit Fine.” The Internet Encyclopedia of Philosophy. https://iep.utm.edu/fine-k/#:~:text=Kit%20Fine%20is%20an%20English,turn%20within%20contemporary%20analytic%20philosophy.Google Scholar
Rodriguez-Pereyra, G. (2006). “How Not to Trivialise the Identity of Indiscernibles.” In Strawson, P. F. & Chakrabarti, A. (eds.), Concepts, Properties and Qualities. Ashgate.Google Scholar
Rodriguez-Pereyra, G. (2014). Leibniz’s Principle of Identity of Indiscernibles. Oxford University Press.Google Scholar
Rodriguez-Pereyra, G. (2017). “Indiscernible Universals.” Inquiry: An Interdisciplinary Journal of Philosophy 60 (6):604–24.Google Scholar
Rosen, G. (2010). “Metaphysical Dependence: Grounding and Reduction.” In Hale, B. & Hoffman, A. (eds.), Modality: Metaphysics, Logic, and Epistemology. Oxford University Press. pp. 109–36.Google Scholar
Salmon, N. (2010). “Lambda in Sentences with Designators: An Ode to Complex Predication.” Journal of Philosophy 107 (9):445–68.Google Scholar
Saunders, S. & Muller, F. A. (2008). “Discerning Fermions.” British Journal for the Philosophy of Science 59 (3):499–548.Google Scholar
Schaffer, J. (2009). “On What Grounds What.” In Chalmers, D., Manley, D. & Wasserman, R. (eds.), Metametaphysics: New Essays on the Foundations of Ontology. Oxford University Press. pp. 347–83.Google Scholar
Schaffer, J. (2012). “Grounding, Transitivity, and Contrastivity.” In Correia, F. & Schnieder, B. (eds.), Metaphysical Grounding: Understanding the Structure of Reality. Cambridge University Press. pp. 122–38.Google Scholar
Schiffer, S. “The Mode-of-Presentation Problem.” In C. Anthony Anderson & J. Owens (eds.), Propositional Attitudes: The Role of Content in Logic, Language, and Mind. CSLI. pp. 249–68.Google Scholar
Shoemaker, S. (1999). “I–Sydney Shoemaker: Self, Body, and Coincidence.” Aristotelian Society Supplementary Volume 73 (1):287–306.Google Scholar
Shumener, E. (2020a). “Explaining Identity and Distinctness.” Philosophical Studies 177 (7):2073–96.Google Scholar
Shumener, E. (2020b). “Identity.” In Raven, M. J. (ed.), Routledge Handbook of Metaphysical Grounding. Routledge. pp. 413–24.Google Scholar
Sider, T. (2001). Four Dimensionalism: An Ontology of Persistence and Time. Oxford University Press.Google Scholar
Sider, T. (2007). “Neo-fregeanism and Quantifier Variance.” Aristotelian Society Supplementary Volume 81 (1):201–32.Google Scholar
Thompson, N. (2016). “Grounding and Metaphysical Explanation.” Proceedings of the Aristotelian Society, 116 (3):395–402Google Scholar
Thomson, J. J. (1983). “Parthood and Identity Across Time.” Journal of Philosophy 80 (4):201–20.Google Scholar
Trogdon, K. (2013). “An Introduction to Grounding.” In Hoeltje, M., Schnieder, B. & Steinberg, A. (eds.), Varieties of Dependence. Philosophia Verlag. pp. 97–122.Google Scholar
van Inwagen, P. (1994). “Composition as Identity.” Philosophical Perspectives 8:207–20.Google Scholar
Wallace, M. (2011a). “Composition as Identity: Part 1.” Philosophy Compass 6 (11):804–16.Google Scholar
Wallace, M. (2011b). “Composition as Identity: Part 2.” Philosophy Compass 6 (11):817–27.Google Scholar
Wehmeier, K. F. (2012). “How to Live Without Identity – And Why.” Australasian Journal of Philosophy 90 (4):76–777.Google Scholar
Whiting, J. (1999). “Back to ‘The Self and the Future’.” Philosophical Topics 26 (1–2):441–77.Google Scholar
Wilhelm, I. (2021). “The Counteridentical Account of Explanatory Identities.” Journal of Philosophy 118 (2):57–78.CrossRefGoogle Scholar
Williamson, T. (2001). “Vagueness, Identity and Leibniz’s Law.” In Giaretta, P., Bottani, A. & Carrara, M. (eds.), Individuals, Essence and Identity. Kluwer Academic Publishers.Google Scholar
Wittgenstein, L., Colombo, G. C. M., & Russell, Bertrand (1922). Tractatus Logico-Philosophicus. Fratelli Bocca.Google Scholar
Wörner, D. (2021). “On Making a Difference: Towards a Minimally Non-Trivial Version of the Identity of Indiscernibles.” Philosophical Studies 178 (12):4261–78.Google Scholar
Wright, C. (1983). Frege’s Conception of Numbers as Objects. Aberdeen University Press.Google Scholar
Wright, C. & Hale, B. (2001). The Reason’s Proper Study: Essays Towards a Neo-Fregean Philosophy of Mathematics. Clarendon Press.Google Scholar
Yablo, S. (1987). “Identity, Essence, and Indiscernibility.” Journal of Philosophy 84 (6):293–314.Google Scholar