Physicalism and the Identity of Identity Theories


It is often said that there are two varieties of identity theory. Type-identity theorists interpret physicalism as the claim that every property is identical to a physical property, while token-identity theorists interpret it as the claim that every particular is identical to a physical particular. The aim of this paper is to undermine the distinction between the two. Drawing on recent work connecting generalized identity to truth-maker semantics, I demonstrate that these interpretations are logically equivalent. I then argue that each has the resources to resolve problems facing the other.

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  1. 1.

    There is even debate over the extent to which there is an interpretive question—see, e.g., Crane and Mellor (1990). I will not do justice to this challenge, but endeavor to address the aspect most relevant to my claim.

  2. 2.

    For the canonical defense of type-identity theory, see Smart (1959). For the purposes of this paper, I disregard the distinction between properties, types and kinds. I do not believe my claim turns on which of these we select.

  3. 3.

    For the canonical defense of token-identity theory, see Davidson (1970). As with properties, types and kinds, I ignore any distinction between particulars, instances and tokens.

  4. 4.

    For other metaphysically sensitive takes on this issue, see, e.g., Boyd (1980), Pereboom (2002).

  5. 5.

    For an application of this view to the interpretation of physicalism, see Schroer (2010).

  6. 6.

    By his own admission, Heil’s view relies on controversial assumptions. At one point, he states, “It will be difficult to find common ground here, difficult to occupy an uncontroversial perspective from which to assess competing theses. I am going to offer what strike me as plausible comments on the ontology of powers, but I admit that a philosopher with a theory can respond to what I have to say with a shrug” (Heil 2011, p. 40). I have a theory and am happy to supply the shrug.

  7. 7.

    There are more banal reasons to be suspicious of their account of property identity. Many maintain that propositions are 0-ary properties—i.e., that while ‘is next to’ is a binary property and ‘is next to Jill’ is a unary property, ‘Jack is next to Jill’ is a 0-ary property. It is not at all obvious how to extend Heil and Robb’s account to propositions, as it crucially relies upon them being located at the objects that bear them. Indeed, the identity conditions for properties are partially determined by the location of the objects that bear them. How, in this case, are we to understand identity conditions for 0-ary properties, which are not borne by anything?

  8. 8.

    For example, see Moore (1952, pp. 660–667), Carnap (1947, p. 91). This view remains viable; see Correia (2017).

  9. 9.

    One potential example of scientific reduction is the reduction of thermodynamics to statistical mechanics. The flow of heat is both identical to and reducible to statistical variations of particle movement. Indeed, some philosophers remain optimistic for reductions not only to physics in general but to statistical mechanics in particular (e.g., Albert (2003, pp. 35–71)).

  10. 10.

    See Smart (1959). However, for a contemporary philosopher who embraces the possibility of nomological danglers, see Cartwright (1999, pp. 23–34).

  11. 11.

    As with the interpretation of physicalism, the interpretation of the multiple realizability objection remains contentious. See Heil (1999), Gillett (2003), Polger (2004, pp. 1–39), Morris (Forthcoming) for some recent discussions on the issue.

  12. 12.

    See Fodor (1974) for the original discussion of this point, and Rosen (2015) for a related, more recent discussion.

  13. 13.

    See, e.g., Lewis (1986, pp. 192–193), Dorr (2016). For a reply see (Fine 2016b).

  14. 14.

    For a discussion of this point, see Morris (2011).

  15. 15.

    For an appeal to contingent identity in this context, see Smart (1959).

  16. 16.

    However, for a recent defense of contingent identities, see Kocurek (2018).

  17. 17.

    It has sometimes been claimed that supervenience physicalism is ‘minimal physicalism’: a core set of commitments that all physicalists ought to agree upon (see Lewis (1983)). This has been disputed. On the one hand, there are plausible interpretations of physicalism that are arguably uncommitted to supervenience (see, e.g., Block (1980)). On the other, supervenience may be too weak to genuinely count as physicalism. Stoljar (2010, pp. 127–163), for example, presents the possibility of a ‘polluted base.’ Suppose that mental properties were necessarily connected to physical properties, but were emergent: they existed independently from physical properties and possessed their own distinctive causal powers. In this case, supervenience physicalism would be true, but, intuitively, physicalism would be false. After all, the mental exists semi-autonomously from the physical. For a response on behalf of supervenience physicalism, see Morris (2014).

  18. 18.

    For a discussion of the way Kripke’s insights affected the interpretation of physicalism, see Boyd (1980).

  19. 19.

    See, again, Davidson (1970).

  20. 20.

    For an early discussion of this point, see Fodor (1974).

  21. 21.

    See Dorr 2016, Correia 2017, Correia and Skiles 2017, Rayo 2013.

  22. 22.

    E.g., Dorr (2016), Correia (2017).

  23. 23.

    Note that this approach commits us to the claim that states have proper parts; they are the kinds of things that are capable of mereological composition. This is an assumption I embrace. The state of a ball being both red and round, for example, might be the composite of the state of the ball being red with the state of it being round.

  24. 24.

    There are plausibly distinct notions of possibility (see Fine (2002).) As I mention in section 5, I take the most relevant notion of possibility to be nomological possibility The states I am concerned with are states that are physically possible.

  25. 25.

    Many have advanced interpretations of physicalism without taking a stand on what it takes to be physical. Davidson (1970), for example, interprets physicalism as the claim that every event is identical to a physical event without detailing what it takes for an event to be physical. Chalmers and Jackson (2001) argues that every truth is a priori knowable from the conjunction of the physical truths, indexical truths, phenomenal truths and a totality truth, without specifying what it takes for a truth to be a physical truth. Schaffer (2017) defends an interpretation according to which physicalism is the claim that chemical, biological and psychological entities are grounded in physical entities, without defining the notion of a physical entity.

  26. 26.

    I operate with a notion of improper parthood rather than proper parthood, so every state is a part of itself.

  27. 27.

    One might phrase this in terms of ‘physical predicates’—my hesitancy comes from my desire to not conflate a theory of predicates with a theory of to be F.

  28. 28.

    For related accounts, see Correia (2017), Correia and Skiles (2017).

  29. 29.

    A brief aside: the first formulation clarifies what it is for a predicate to be defined functionally. A predicate F is defined in functional terms just in case there is a predicate G that specifies the performance of a certain function such that ‘To be F is to be G’ is true. For example, if a heart is defined in functional terms, it may be that ‘To be a heart is to perform the function of pumping blood throughout the body’ is true.

  30. 30.

    The first argument that a state of affairs counts as a token that I am aware of occurs in Heil (2011). As I discuss below, the second formulation may most closely resemble what Morris (2018) calls ‘truth-maker physicalism.’

  31. 31.

    For the sake of brevity, I omit mention of falsifiers, but what I say about verifiers strictly applies to falsifiers as well.

  32. 32.

    The reflexivity of generalized identity serves only to guarantee that there exists some G or other such that to be F is to be G. Any G such that to be F is to be G is physical, since all verifiers of ‘Ga’ are physical verifiers according to the second formulation.

  33. 33.

    This predicate is not new. It was discussed most prominently by Lewis (1983) in his account of laws of nature. Lewis, drawing on Mill (1947, pp. 391), argues that a sentence expresses a law of nature just in case it strikes the optimal balance of simplicity and strength, where simplicity is given by the length of the sentence and strength is given by descriptive power. A potential worry is that, on this conception, ‘Fa’ is a law of nature. After all, it is maximally strong (in that it describes the entire history of the world) and is remarkably simple (in that it is two characters long). Lewis avoids this concern by employing a language that only possesses terms for perfectly natural predicates. However, my use for F is differs from his.

  34. 34.

    There may be issues arising from states that do not actually obtain. I discuss this in section five while addressing the modal scope of physicalism.

  35. 35.

    Or, more accurately, are not undermined by the presence of hearts.

  36. 36.

    Note that, on the current approach, this also requires F to be physical; I see no objection to F being both mental and physical.

  37. 37.

    Heil (2000) presents an additional concern for truth-making views. An adequate reply requires delving further into technical details of truth-maker semantics than I have space to do. Roughly, Heil defends a notion of truth-making in which truth-makers do not necessitate the claims they are truth-makers of. For example, it may be that the presence of five coins in my pockets is a truth-maker for ‘there are exactly five coins in my pocket,’ despite the fact that the presence of five coins is compatible with the presence of six. Although I am sympathetic to view on which truth-makers necessitate the claims they are truth-makers of, it is readily possible to modify the present semantics to accommodate Heil’s point. As Fine (2017); Elgin (forthcoming) note, this is achieved by omitting totality states in verifiers of ‘\(\forall x Fx\).’

  38. 38.

    Morris suggests that this worry need not apply to every version of truth-maker interpretations of physicalism when discussing a proposal by Schulte (2014).

  39. 39.

    Or, if it does, it presumably does so because it denies the existence of impossible states.

  40. 40.

    This paraphrases the third formulation. On this restriction, the first formulation is unaltered, but exact equivalence is defined in terms of the identity of actual verifiers and falsifiers.

  41. 41.

    See Kim (1993, p. 90) for the first discussion of this example.

  42. 42.

    For a precise definition of compatibility on the truth-maker approach, see Fine (2017).


  1. Albert, D. (2003). Time and chance. Cambridge: Harvard University Press.

    Google Scholar 

  2. Block, N. (1980). Troubles with functionalism. In N. Block (Ed.), Readings in the philosophy of psychology (Vol. 1). Cambridge: Harvard University Press.

    Google Scholar 

  3. Boyd, R. (1980). Materialism without reductionism: What physicalism does not entail. In N. Block (Ed.), Readings in the Philosophy of Psychology (Vol. 1, pp. 1–67). Cambridge: Harvard University Press.

    Google Scholar 

  4. Cameron, R. (2008). Truthmakers and ontological commitment: Or how to deal with complex objects and mathematical ontology without getting intro trouble. Philosophical Studies, 140, 1–18.

    Article  Google Scholar 

  5. Cameron, R. (2010). How to have a radically minimal ontology. Philosophical Studies, 151, 249–64.

    Article  Google Scholar 

  6. Carnap, R. (1947). Meaning and necessity: A study in semantics and modal logic. Chicago: University of Chicago Press.

    Google Scholar 

  7. Cartwright, N. (1999). The dappled world. Cambridge: Cambridge University Press.

    Google Scholar 

  8. Chalmers, D., & Jackson, F. (2001). Conceptual analysis and reductive explanation. The Philosophical Review, 110(3), 315–61.

    Article  Google Scholar 

  9. Correia, F., & Skiles, A. (2017). Grounding, essence and identity. Philosophy and Phenomenological Research.

  10. Correia, F. (2017). Real definitions. Philosophical Issues, 27(1), 52–73.

    Article  Google Scholar 

  11. Crane, T., & Mellor, D. H. (1990). There is no question of physicalism. Mind, 99(394), 185–206.

    Article  Google Scholar 

  12. Davidson, D. (1970). Mental events. In L. Foster & J. W. Swanson (Eds.), Essays on actions and events (pp. 207–24). Oxford: Clarendon Press.

    Google Scholar 

  13. Della Rocca, M. (2014). Razing structures to the ground. Analytic Philosophy, 55(3), 276–94.

    Article  Google Scholar 

  14. Dorr, C. (2016). To Be F Is To Be G. Philosophical Perspectives, 30(1), 39–134.

    Article  Google Scholar 

  15. Elgin, S. (forthcoming). The semantic foundations of philosophical analysis.

  16. Fine, K. (2002). Varieties of necessity. In T. Gendler & J. Hawthorne (Eds.), Conceivability and possibility. Oxford: Oxford University Press.

    Google Scholar 

  17. Fine K (2016a). Angellic content. Journal of Philosophical Logic45(2), 199–226.

    Article  Google Scholar 

  18. Fine, K. (2016b). Identity criteria and ground. Philosophical Studies, 173, 1–19.

    Article  Google Scholar 

  19. Fine, K. (2017). Truthmaker semantics. In B. Hale, C. Wright, & A. Miller (Eds.), Companion to the philosophy of language (pp. 556–77). Oxford: Blackwell.

    Google Scholar 

  20. Fodor, J. (1974). Special sciences: Or the disunity of science as a working hypothesis. Synthese, 28(2), 97–115.

    Article  Google Scholar 

  21. Gillett, C. (2003). The metaphysics of realization, multiple realization and the special sciences. The Journal of Philosophy, 100, 591–603.

    Google Scholar 

  22. Heil, J. (1999). Multiple realizability. American Philosophical Quarterly, 36(3), 189–208.

    Google Scholar 

  23. Heil, J. (2000). Truthmaking and entailment. Logique & Analyse, 169–70, 231–42.

    Google Scholar 

  24. Heil, J. (2003). From an ontological point of view. Oxford: Oxford University Press.

    Google Scholar 

  25. Heil, J. (2011). Powers and the realization relation. The Monist, 94(1), 34–53.

    Article  Google Scholar 

  26. Heil, J. (2012). The universe as we find it. Oxford: Oxford University Press.

    Google Scholar 

  27. Heil, J., & Robb, D. (2003). Mental properties. American Philosophical Quarterly, 40(3), 175–96.

    Google Scholar 

  28. Horgan, T. (1984). Functionalism and token physicalism. Synthese, 59(3), 321–38.

    Article  Google Scholar 

  29. Kim, J. (1993). Mind and supervenience. Cambridge: Cambridge University Press.

    Google Scholar 

  30. Kocurek, A. (2018). Counteridenticals. The Philosophical Review, 127(3), 323–69.

    Article  Google Scholar 

  31. Kripke, S. A. (1980). Naming and necessity. Cambridge: Harvard University Press.

    Google Scholar 

  32. Lewis, D. (1983). New work for a theory of universals. Australasian Journal of Philosophy, 64(4), 343–77.

    Article  Google Scholar 

  33. Lewis, D. (1986). On the plurality of worlds. Oxford: Oxford University Press.

    Google Scholar 

  34. Mill, J. S. (1947). A system of logic. Longmans: Green and Co.

    Google Scholar 

  35. Moore, G. E. (1952). The philosophy of G.E. Moore (pp. 660–667). New York: Tudor Pub Co.

    Google Scholar 

  36. Morris, K. (Forthcoming). Multiple realization and compositional variation. Synthese.

  37. Morris, K. (2011). Theoretical identities as explanatia and explananda. American Philosophical Quarterly, 48(4), 373–85.

    Google Scholar 

  38. Morris, K. (2014). Supervenience physicalism, emergentism, and the polluted supervenience base. Erkenntnis, 79, 351–65.

    Article  Google Scholar 

  39. Morris, K. (2018). Physicalism, truthmaking and levels of reality: Prospects and problems. Topoi, 37, 473–82.

    Article  Google Scholar 

  40. Pereboom, D. (2002). Robust nonreductive materialism. The Journal of Philosophy, 99(19), 499–531.

    Article  Google Scholar 

  41. Polger, T. (2004). Natural minds. Cambridge: MIT Press.

    Google Scholar 

  42. Rayo, A. (2013). The construction of logical space. Oxford: Oxford University Press.

    Google Scholar 

  43. Rosen, G. (2010). Metaphysical dependence: Grounding and reduction. In A. Hale & B. Hoffman (Eds.), Modality: Metaphysics, logic and epistemology. Oxford: Oxford University Press.

    Google Scholar 

  44. Rosen, G. (2015). Real definition. Analytic Philosophy, 56(3), 189–209.

    Article  Google Scholar 

  45. Schaffer, J. (2017). The ground between the gaps. Philosopher’s Imprint, 17(11), 1–26.

    Google Scholar 

  46. Schroer, R. (2010). How far can the physical sciences reach? American Philosophical Quarterly, 47(3), 253–66.

    Google Scholar 

  47. Schulte, P. (2014). Can truthmaker theorists claim ontological free lunches? European Journal of Philosophy, 22, 249–68.

    Article  Google Scholar 

  48. Shoemaker, S. (1994). Physical realization. Oxford: Oxford University Press.

    Google Scholar 

  49. Smart, J. J. C. (1959). Sensations and brain processes. The Philosophical Review, 68(2), 141–56.

    Article  Google Scholar 

  50. Stoljar, D. (2017). Physicalism. Stanford Encyclopedia of Philosophy (pp. 1–67).

  51. Stoljar, D. (2010). Physicalism. Abingdon: Routledge.

    Google Scholar 

  52. Wilson, J. (1999). How superduper does a physicalist supervenience need to be? The Philosophical Quarterly, 49(194), 33–52.

    Article  Google Scholar 

  53. Wilson, J. (2014). No work for a theory of grounding. Inquiry, 57(5–6), 535–79.

    Article  Google Scholar 

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I would like to thank the attendees of the 2018 workshop on the History and Metaphysics of the Concept of Laws of Nature at Central European University for their helpful feedback, as well as Shamik Dasgupta, Michael Della Rocca, Catherine Elgin, Kit Fine and Barry Loewer for their illuminating discussions and written comments on previous versions of this paper.

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Elgin, S.Z. Physicalism and the Identity of Identity Theories. Erkenn (2020).

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  • Physicalism
  • Generalized identities
  • Truth-maker semantics
  • Multiple realizability