This is a preprint of an article whose final and definitive form will be published in the Australasian Journal of Philosophy [year of publication unknown]; the Australasian Journal of Philosophy is available online at:




Alexander R. Pruss


Abstract: Substantive theories of diachronic identity have been offered for different kinds of entities.  The kind of entity whose diachronic identity has received the most attention in the literature is person, where such theories as the psychological theory, the body theory, the soul theory and animalism have been defended.  At the same time, Wittgenstein’s remark that ‘to say of two things that they are identical is nonsense, and to say of one thing that it is identical with itself is to say nothing at all’ suggests that the idea of further analyzing identity is mistaken at root.  I shall offer a simple, deflationary theory that reduces diachronic identity to quantification, synchronic identity and existence at a spacetime point (or at a time, for non-spatial entities).  On logical grounds, the theory is guaranteed to have no counterexamples.  Because the theory is guaranteed to have no counterexamples, all the imaginative examples offered as intuitive support for theories of personal identity are going to either be incorrect or compatible with the theory.  I shall argue that the deflationary theory is preferable on simplicity grounds to typical substantive theories, and that various problems that are commonly thought to concern diachronic identity are better seen as about something else. 


Keywords: identity, personal identity, time

1. Introduction

            A theory of diachronic identity is an attempt to explain what it is that makes an entity existing at one time be identical with an entity existing at another time.  Typically this is done by giving necessary and sufficient conditions that are both informative and constitutively explanatory of the identity.  For instance, one might say that a person x at t1 is identical with a person y at t2 if and only if (and if so, then because[1]) there is a chain of quasimemories running between x and y and there is no branching [Shoemaker 1970], or one might say that the identity holds if and only if there is a bodily continuity [Williams 1970] between x and y with no branching.  It is normal in the literature for the conditions to be specific to the kind of entity in question, as in the above examples that are specialized to persons.

            Yet, there is something strange about the idea of giving a substantive account of diachronic identity.  Diachronic identity is a species of identity, and identity seems to be one of the most basic concepts we have, more basic than such concepts as memory or soul.  The strangeness is captured by Wittgenstein’s remark:

Roughly speaking, to say of two things that they are identical is nonsense, and to say of one thing that it is identical with itself is to say nothing at all. [Wittgenstein 1921: 5.5303]

            But I will not go all the way with Wittgenstein.  Instead, I will give a simple deflationary[2] account of diachronic identity in terms of synchronic identity and some unproblematic conceptual ingredients.  The account is simple and extensionally correct.  The account will show that certain questions that are often thought to be about diachronic identity are, in fact, about something else.

            I do not fully endorse the deflationary account.  It is superior to the substantive accounts, but it may be that there is an account that is superior to the deflationary account: the view that all identity, whether diachronic or synchronic, is primitive.  Be that as it may, the availability of the deflationary account is a sufficient reason to reject the substantive accounts, and it is this rejection that is the main point of the paper.

            Furthermore, many of the major substantive accounts of diachronic personal identity have consequences that prima facie seem absurd.  Memory theories imply the strange consequence that temporary total amnesia (including of non-biographical memories) is as good from a self-interested point of view as anaesthesia.  Bodily continuity theories imply that it is logically impossible for my consciousness to be transferred into another body.  Brain theories face puzzles about what happens in brain splitting cases, with no answer being plausible.  Animalism implies that if your cerebrum were moved into another body you would stay behind.  We don’t generally start off by accepting the implausible consequences, but we are tempted to accept them because what seems to be the best theory in fact implies them.

            It is a merit of the deflationary account that it will have no such consequences.  It is compatible with the thesis that total amnesia is as good as anaesthesia and with its denial.  It is compatible with the claim that you always survive fission and with the claim that you never do and with the claim that you sometimes do and sometimes do not. 

            Before giving the full deflationary account of diachronic identity, as a warm-up I will give a simplified account of some diachronic identity sentences. 

            Throughout the paper, I shall use the example of personal identity, as that provides the best worked-out case of substantive theories of diachronic identity.

2. A simplified account

            Suppose that spatiotemporal location x2 is later than spatiotemporal location x1 (in a relativistic setting, this means that x2 is in the forward light cone of x1).  Let K be a non-phase kind.[3]  The question now is what fact it is in virtue of which the following holds:

(1)         Some K that is at spatiotemporal location x1 is identical with some K that is at spatiotemporal location x2?[4]

This formulation allows that there may be more than one K at these locations, and we are asking why it is that at least one K at x1 is identical with at least one K at x2.   It is often more natural to have ‘the K’ in place of ‘some K’, but that would involve us in the more complex analysis in the next section.

            The question of what it is in virtue of which a proposition holds is sometimes answered by specifying a truthmaker.  But unless Truthmaker Maximalism holds, it will sometimes be answered instead by giving another proposition.  Thus, when we ask what it is in virtue of which a piece of iron is hot, we answer that it is in virtue of the fact that its molecules have a high kinetic energy.  For simplicity and stipulatively, I shall identify facts with the true propositions that express them.  We might call a proposition q in virtue of which a proposition p holds an ‘ontological explanation’ or ‘account’ of p.

            The person who offers a substantive theory of personal identity—the criterialist, to borrow Merricks’ phrase with a slightly different meaning[5]—then answers the question of what it is in virtue of which (1) is true as follows:

(2)         $u$v(Ku & Kv & u is at x1 & v is at x2 & CK(u,x1,v,x2)),

where CK is the diachronic identity relation for Ks. 

            However, there is a much simpler deflationary answer to the question of what makes (1) hold:

(3)         $u(Ku & u is at x1 & u is at x2).

Of course, here, as in all similar expressions, the ‘is’ is tenseless.

            While almost all instances of (2) offered in the literature have been counterexampled as a set of necessary and sufficient conditions for (1), it is obvious that (3) as an account of (1) has no counterexamples.  For, in fact, it is an easy theorem of first order logic that (1) holds if and only if (3) does.[6]

            Observe also that every ‘conceptual ingredient’ in (3) is also found in (2), namely: existential quantification (at least over Ks), predication of spatiotemporal location (at least to Ks) and conjunction.  Thus, the criterialist who offers (2) as an account of (1) cannot complain that (3) uses some undefined primitive.  The deflationary account of (1) uses no primitives besides those which the criterialist herself is committed to, and is a simpler general account than the criterialist’s answers.

            Moreover, the criterialist cannot worry that (3) presupposes diachronic identity in some hidden way.  For if something in (3) presupposes diachronic identity, so does something in (2).  Indeed, (2) is a much better candidate for such worry.  It may very well be that particular proposed cases of CK presuppose diachronic identity of Ks.  For instance, one might worry that there is no viable concept of quasimemory that does not presuppose diachronic identity that could be used in memory theories of personal identity.

            There is, however, a general account of identity that may seem almost as simple as the one offered above and is apparently fully general:

(4)         x and y are identical if and only if they have the same properties [e.g., Brody 1981].

But such a property-quantification account is subject to objections.  Either the properties the account quantifies over are all what one might call purely qualitative properties that do not make de re reference to any particular individual, like negatively charged, loved by someone, etc., or they include such properties as being taller than Jones.  If they do include the latter properties, the account trivializes, since among the properties there will be properties of the form being identical with x

            In the case where the properties quantified over are purely qualitative, the property account has the liability of being committed to the identity of indiscernibles, which is widely thought to be unlikely to be a necessary truth (for instance, it has been noted that current physics allows bosons like photons to have the same physical state).  Moreover, the account quantifies over properties and hence appears to be committed to their existence, and since it is supposed to be a fully general account of the identity of entities, it should apply also to the properties themselves, so that what makes two properties identical is that they have the same purely qualitative higher order properties.  But it is not clear that purely qualitative higher order properties are sufficient to distinguish properties.  For instance, imagine a world with an empty, flat spacetime, and where the laws are much like those in our world, except that instead of involving charge, they involve some analogous quantity charge* and the laws are symmetric under charge*-reversal: every situation allowed by the laws will also be allowed if we swap positive and negative charges*.  In that world, it does not appear possible to distinguish being positively charged* and being negatively charged* in terms of purely qualitative higher order properties without cheating.  Here is an illustrative way of cheating: being positively charged* has the higher order property of being such that everything that exemplifies it is positively charged*.  This cheats because to be positively charged* is to exemplify the property being positively charged*, and hence the property makes de re reference to a property and thus is not purely qualitative. 

3. Removing a limitation

            The above deflationary account works only for some diachronic identity sentences, but it does so with a particular simplicity.  But we would also like a general deflationary replacement for the well-formed formula (wff):

(5)         u at x1 is the same K as v at x2,

where x1 and x2 are at different times. 

            The criterialist gives an account of (5) in the following form:

(6)         Ku & Kv & u is at x1 & v is at x2 & CK(u,x1,v,x2).

            I will shortly offer a deflationary analysis of (5).  However, it is worth arguing that even if the deflationary theory were limited to the analysis of (1), the existence of that analysis would make criterialism implausible, and might still provide a viable theory of at least personal identity.

            The criterialist is committed to seeing (2) as that in virtue of which (1) is true.  But this is puzzling in the light of the obvious logical equivalence between (3) and (1).  Clearly, (3) is a much simpler account of (1) and does not mention identity, and so Ockham’s Razor highly recommends it.

            Perhaps, though, the criterialist can say that (2) is a ‘deeper’ analysis than (3) is. For example, it is a deeper analysis of <the piece of iron is hot> to say that the molecules have high molecular kinetic energy than it is to say that heat is present.  The ‘deeper’ analysis, then, is the one that is more fundamental.  But how can (2) be more fundamental than (3)?  All the fundamental concepts used in (3) also enter into (2), and none of them receive an explanation in (2).  It is surely not the case that (2) ontologically explains (3).  To explain (3) ontologically, we would have to either explain one of its conceptual ingredients or explain how these ingredients are put together.  But (2) does nothing like that—it simply uses the ingredients of (3) plus the ingredients of the CK term. 

            Thus, rather than (2) being a deeper account than (3), the right statement of their relationship is this.  Either, (2) is or is not necessary and sufficient for (3).  If it is not, then it is not necessary and sufficient for (1) either, as (1) and (3) are provably equivalent.  But if it is, then it is not an explanation of (3), but an expansion or obfuscation of it.

            Hence, even if the deflationary theory ended with (2), it would suffice to provide an argument against criterialism.  Moreover, it could still perhaps count as a theory of personal identity.  Compare, for instance, Horwich’s deflationary theory of truth [Horwich 1998].  Just as the deflationary theory give so far does not give necessary and sufficient conditions for (5), so too Horwich eschews giving a plug-in replacement for the well-formed formula ‘p is true’.  Instead, Horwich gives axioms—an infinite set of them—of the form <s> is true if and only if s that are supposed to fully characterize the concept of truth, at least when combined with the axiom that only propositions are true.  Somewhat similarly, I can offer a deflationary theory according to which diachronic identity for beings in spacetime is characterized by all biconditionals of the form:

(7)         Some K that exists at spatiotemporal location x1 is identical with some K that exists at spatiotemporal location x2 if and only if $u(Ku & u is at x1 & u is at x2).

This one might call a minimalist deflationary theory of diachronic identity.  But it is not the theory I will be defending in the rest of the paper.

            It may also be the case that there are some Ks for which it is plausible that distinct Ks cannot occupy the same spatiotemporal location.  For those Ks, the task of giving a drop-in replacement for the diachronic identity wff (5) is easy.  We can just say:

(8)         Ku & Kv & u is at x1 & v is at x2 & u is at x2.

            Formula (8) does not use any conceptual resources beyond those also found in the criterialist account (6)—it just replaces the CK conjunct with two predications of locational properties.  Granted, the assumption that distinct Ks cannot occupy the same place is a strong one, but that assumption is widely (though perhaps mistakenly) accepted for many different kinds K, including for material persons.  In those cases, (8) could be a deflationary account of (5) superior to typical instances of (6). 

            Nonetheless, we shall not take this route, because it is better not to depend on the assumption that distinct Ks cannot be in the same place.  After all, plausibly, it is metaphysically possible that two ghosts occupy the same place.

            We are looking for an account of diachronic identity.  In this pursuit, it is licit to presuppose the concept of synchronic identity as relatively fundamental.  I shall write IK(x,y,t) for the claim that x and y are synchronically identical at t.  Now, given synchronic identity, it is easy to give a replacement for the diachronic identity wff (5):

(9)          Ku & Kv & u is at x1 & v is at x2 & u is at x2 & IK(u,v,T(x2)).

where T(x) is the time of the spatiotemporal location x.[7]

            I will take (9) to be the full deflationary theory of the diachronic identity of Ks that exist in spacetime (see the discussion of Objection 3 in the next section for a discussion of beings in time but not in space).  It is clear that there are no counterexamples.  Moreover, while the account presupposes synchronic identity, it does not presuppose diachronic identity.  The conceptual ingredients are: predication, location, existential quantification, the time of a spatiotemporal location, and synchronic identity.  The criterialist’s account makes use of all of these except perhaps the time of a spatiotemporal location and synchronic identity, but we need synchronic identity anyway, and the time of a spatiotemporal location is unproblematic (see also the response to Objection 2 in the next section).  The present account is simple and is guaranteed to have no counterexamples.  What more could one ask?

4. Objections

            Objection 1: ‘Some criterialist accounts have an added advantage.  The account they offer of diachronic identity also works synchronically.  For instance, on a soul theory of personal identity, a person u at t1 is identical with a person v at t2 if and only if there is an s such that s ensouls u at t1 and s ensouls v at t2.  This works just as well in the case where t1=t2.  Likewise, a bodily continuity theory might imply that u at t1 is identical with v at t1 if and only if u and v share all of their bodily parts.  Granted, not all theories of diachronic identity work synchronically.  I do not at t1 quasiremember what happens at t1, and indeed there is no chain of quasimemories here, so the memory theory may need a separate story synchronically.  But some do work synchronically, and these are superior to the deflationary theory.’

            Now, first of all, many soul-theorists do not see themselves as giving an account of synchronic identity but of the constitution of the human person.[8]  Such soul-theorists will not be offering this objection, and such soul-theories are compatible with the present deflationism. 

            Second, even if a criterialist theory of diachronic identity does work to give the extensionally right answer synchronically, there is something prima facie implausible about the idea that the theory is in fact telling us what synchronic identity consists in.  It doesn’t seem to be the case that I am now self-identical because there is a soul that now ensouls me and now ensouls me.

            Moreover, a deflationist might also be able to give a fairly simple account of synchronic identity, such as:

(10)     u is synchronically identical with v at t if and only if u is a part of v and v is a part of u.

This is extensionally correct if improper parts are parts and two things can’t each be a part of the other.  This is no more complex, and perhaps simpler, than the soul account of synchronic personal identity, and definitely simpler than the bodily continuity account.  Moreover, this account neatly works equally well for all kinds of things, while the criterialist accounts must be one per kind. 

            Objection 2: ‘The deflationary account is just a paraphrase: (3) and (9) are simply restatements of (1) and (7), respectively, rather than genuine philosophical accounts of (1) and (7).’[9]

            If ‘paraphrase’ and ‘restatement’ here means a cognitive equivalence, then the objection is simply that the deflationary account is too good.  But by definition there is no such thing as being too good.  It is a desideratum for a philosophical account of a concept to provide a cognitively equivalent definition.  This desideratum cannot always be met—sometimes we can only give partial analyses, and sometimes we need to modify the concept by giving a Carnapian explication.  But when the desideratum can be met, that is a good thing.

            Perhaps, though, the objection is that the restatement is too similar to the original, as if we were to explain <x is a container of gasoline> by <x is a vessel of petrol>.  On its face, this version of the objection fails.  I have not simply replaced words in the explicandum with synonyms in the explicans.  For if I had so done, then the explicans would contain a synonym for ‘diachronic identity’, which it does not.

            But suppose that some version of this objection is pressing.  Then, what I have done must be this: by cleverly rewording the explicandum, I have hidden the characteristic philosophical problems of diachronic identity, which will all return when I ask for a philosophical account of the terms in the explicans.  For instance, if I had defined ‘omnipotence’ as ‘having all power’, the problem of what omnipotence is would return as soon as I asked what the domain of quantification of ‘all’ was, and the answers available would be direct analogues of the standard substantive accounts of omnipotence.

            If this objection holds, then if it is asked what the truth of, say, (9) consists in, I have to answer in analogues to the ways that the criterialists answered the original question.  But that is not what happens.  Formula (9) is conjunctive and hence we need only give account of its conjuncts, and hence of four kinds of states of affairs:

(a) something’s being a K,

(b) something’s being at spatiotemporal location x,

(c) t being the time of a spatiotemporal location x, and

(d) synchronic identity. 

If the objection holds, then analyzing at least one of these concepts will force me to make use of analogues to theories of diachronic identity.  If I am not forced to do so, then the objection fails.

            Now, first of all, it certainly does not seem that diachronic identity is prior to synchronic identity.  As we saw in the discussion of Objection 1, it is not necessary to refer to diachronic identity to explain synchronic identity.  Moreover, an account of t’s being the time of a spatiotemporal location x can be given pretty explicitly without talking at all about diachronic identity: for instance, we can let t be the hypersurface containing x in the contextually-appropriate foliation of spacetime.  Thus, (c) and (d) are not a problem.

            The more difficult cases are (a) and (b).  Let’s start with (a).  One might worry that an account of what it is to be a K will have to presuppose diachronic identity for Ks.  The first answer to this is that, if so, then at least some criterialist analyses are equally in trouble.  For instance, suppose we are asked what it is for x at an earlier time to be the same person as y at a later time, and we answer that it is for x to be a person, and for y to have a chain of memories from the later time reaching back to x at the earlier time with no branching.  But in the answer, the first conjunct was that x is a person.  And indeed (2) and (6) reflect this, having attributions of Kness in them.  But if an account of what it is to be a person presupposes diachronic identity, then a circularity ensues just as much for the criterialist.

            Secondly, we might well be able to give an account of what it is to be a K simply in terms of the kind of structure that a K has at one time, for it might be that there is only one kind of entity instantiating that structure, and then we have given an account of K-hood without talking about diachronic identity.

            Thirdly, we can drop Khood from the deflationary account altogether, and instead of giving an account of what it is to be the same K, we simply give an account of what it is to be the same simpliciter, saying:

(11)     u at x1 is diachronically identical with v at x2 if and only if u is at x1 & v is at x2 & u is at x2 & I(u,v,T(x2)),

where I is synchronic identity.  Then Khood doesn’t enter into the explicandum or the explicans. 

            Next, consider whether analyzing states of affairs of type (b) forces one to presuppose diachronic identity.  Here there is some reason to think the answer is positive.  One might think, for instance, that my being in the year 2030 in Granada is to be analyzed in terms of my diachronic identity with someone in the year 2030 in Granada.

            One might think this, but one certainly one does not have to, and probably should not.  Suppose I began my existence at spatiotemporal location x.  Then it is very implausible to analyze the claim that I am (tenseless) at x in terms of any diachronic identity.  Plausibly, I could have been annihilated right after that moment, and then I would not have stood in any diachronic identity relations.  So probably one should not presuppose diachronic identity in analyzing locational states of affairs.

            To see that one does not have to, all we need to do is to consider the range of theories of location that are available.  Let’s briefly sketch three for definiteness.  Substantivalism: To be at a spatiotemporal location is to stand in a basic located-at (perdurantist substantivalism) or wholly-located-at (endurantist substantivalism) relation to that location, where a location is a concrete object (a region of spacetime, say).  Relationalism: Claims about u’s being at a spatiotemporal location are claims about u or a slice of u standing in certain spatiotemporal relations to other entities, and about their standing in a certain kind of nexus of spatiotemporal relations.  Property theory: Locations are special kinds of properties, and the set of this-worldly locations (which may be a subset of the set of all possible locations) has a metric structure; to be at a location L is simply to possess the property L.

            None of these theories analyze being at a spatiotemporal location in a way that presupposes diachronic identity.  Now, one might worry that each of them still presupposes diachronic identity somewhere.  But it is hard to see where.  Basically, each theory explains locatedness in terms of the predication of a certain kind of (possibly relational) predicate.  And predication does not appear to presuppose diachronic identity in general.  Or, at least, standard accounts of predication do not presuppose diachronic identity.  Platonism: You are R if and only if you exemplify Rness.  Trope theory: You are R if and only if a trope of your Rness exists;  or perhaps if and only if a trope of Rness is a part of you.  Nominalism: Predication as primitive.  None of the coherent combinations of these views of predication with the above views of location gives a view that presupposes diachronic identity.  So, for instance, a substantivalist perdurantist Platonist might say that u is at x if and only if <u, x> exemplifies locatedness-at.

            Therefore, not only is the deflationist account not a restatement that makes us come back to where we started, but by analyzing the deflationary explanation we are led to ask new questions, such as about Khood or about the nature of spatiotemporal locatedness. 

            Objection 3. ‘The deflationary theory explains not what makes u at time t­1 be identical with v at t2, but what makes u at spatiotemporal location x1 be identical with v at spatiotemporal location x2.’

            However, it is easy to go from the one to the other, in the case of spatiotemporal beings.  Thus, we can say that u at t1 is identical with v at t2 if and only if u exists at some spacetime position x1 which is at t1 and v exists at some spacetime position x2 which is at t2, and u at x1 is identical with v at x2

            We might worry about beings that are in time but not in space.  But for such beings, we can stipulate that spacetime is just one-dimensional—it’s just time. 

            Alternately, we can simply give an analogue of the original analysis:

(12)     u at t1 is the same K as v at t2 if and only if Ku & Kv & u is at t1 & v is at t2 & u is at t2 & I(u,v,t2).

This requires a relation of being at a time.  This relation can be accounted for in a variety of ways.  First, the substantivalist, relationalists and property accounts of what it is to be located at a spacetime locations all extend to being at a time.  Second, one might understand u’s being at t simply in terms of u existing at t, or its being the case at t that u exists (present tense).

            Objection 4. ‘The account (a) presupposes perdurantism (or endurantism or eternalism or B-theory).  But (b) perdurantism (or endurantism or eternalism or B-theory) is implausible (insert here one’s favourite argument against perdurantism or endurantism or eternalism or B-theory), and (c) an account of diachronic identity should not force a commitment to a particular answer about perdurantism (or endurantism or eternalism or B-theory).’

            We can begin by denying (c).  It would be entirely appropriate for an account of diachronic identity to have entailments for the philosophy of time

            But in fact the only temporal concept that the deflationary account makes use of is that of being-at a spatiotemporal location.  And some sentences attributing a spatiotemporal location are, in fact, true.  For instance, Napoleon is on Elba on June 3, 1815.  Thus if the attribution of spatiotemporal location requires perdurantism (or endurantism or eternalism or B-theory), then perdurantism (or endurantism or eternalism or B-theory) is true, and so the fact that the deflationary theory presupposes it is no objection to the deflationary theory.  But of course the opponents of perdurantism (or endurantism or eternalism or B-theory) will not concede that attributions of spatiotemporal location require the theory they reject, and if they are right, then (a) is false.  Thus, either (a) is false, or else it is true but not an objection.  It may be that the account highlights some difficulty (say, related to temporary intrinsics) with one of these theories, but it does not create the difficulty.

            Objection 5. ‘The memory and bodily identity theories of personal identity provide epistemically useful criteria of identity.  The deflationary account is also epistemologically useless, unlike criterial accounts which help to explain the reliability of our ordinary practices of diachronic reidentification.’

            The objection has two parts: the deflationary account does not provide useful criteria, and it does not explain the reliability of our epistemic practices.  These parts are distinct.  Indeed, deflationary accounts do not provide epistemically useful criteria—thus, the deflationary account of the truth of the proposition <Snow is white> does not give one any hints as to how one should check whether the sentence is true.  But that is not a problem for a deflationary account.  As Aristotle said, we proceed from the more evident to the less evident, and our epistemically useful criteria are often tied to the more evident, while the less evident is ontologically fundamental.  Similarly, the realist, trope and nominalist accounts of predication do not provide any epistemically useful criteria for when a particular predicate applies to a particular object, and this is no objection to these theories.

            Moreover, the deflationary theory applies to all kinds of beings, while a typical criterialist theory only applies to one kind, say persons or animals.  It is normal for a more general theory of what something consists in to be less useful epistemically than a theory crafted to a particular case.  Thus, a general theory of what speaking consists in would be less useful for recognizing when Socrates is speaking than a theory of what speaking Greek consists in would be.  But the generality is worth having.

            Furthermore, a given criterialist theory T of the diachronic identity of Ks either is or is not extensionally correct.  If T is extensionally correct, the deflationary theorist can use that theory as an epistemic criterion of the diachronic identity of Ks, since the deflationary account is compatible with the extensional correctness of substantive competitors.  In this regard, the deflationary theory carries less commitment than a typical criterialist theory.  While the bodily continuity theorist of personal identity is committed to the memory theory being extensionally incorrect, the deflationary theorist need not take a stance on which of these theories is correct.  On the other hand, if T is not extensionally correct, then it is inferior to the deflationary theory which is guaranteed to be extensionally correct.  But even then, the deflationist can accept T as providing a prima facie epistemic criterion for diachronic identity.

            As for the claim that substantive theories of identity help to explain the reliability our practices of diachronic reidentification, let us consider how that might work.  We have multiple epistemic criteria for recognizing the diachronic identity of persons, such as bodily continuity, memory, similarity of behaviour, and combinations of these.  No one substantive theory of the diachronic identity of persons will directly justify all of these practices.  Rather, a particular theory will explain the reliability of one of these practices, and then it will be combined with empirical facts to show that the other practices are also reliable.  For instance, the memory theory will directly explain the reliability of identifying persons on the basis of memories.  When the theory is combined with the plausible claim that memories are carried by brains and that brains rarely move between skulls, we get an explanation of the reliability of identifying persons on the basis of bodily continuity.  A particular substantive theory of identity, thus, only directly explains the reliability of one method, and the reliability of the other methods follows when additional data is added.

             There are multiple routes that a deflationist can take here, and I will only sketch one.  We observe, in a very broad sense of ‘observe’, all sorts of cases of property possession.  Something is a queen of England, something is human, something is a queen of Canada, something is a frog, something is born in 1926, something lays eggs, something exists in 2009, and something is obligated by a coronation oath.   We observe cases of relational property possession as well: something that is human hears something that croaks.  And then we try to form explanatory theories, which explanatory theories include theories about how the properties are to be apportioned to individuals, playing Ockham’s razor (minimizing the number of individuals) and explanatory fruitfulness off against each other.  In doing this, we apportion being queen of England, being human, being queen of Canada, being obligated by a coronation oath, being born in 1926, existing in 2009 and being a human who hears something that croaks to one individual, and being a frog, laying eggs and being something that croaks and is heard by a human to another.  And hence we come to accept that there is one and the same human who was born in 1926 and who exists in 2009.  It empirically turns out that an apportionment that balances Ockham’s razor against explanatory fruitfulness both makes chains of memories belong to one person and makes persons typically have continuous bodies, and so the memory and bodily continuity criteria are reliable.

            Objection 5. ‘Suppose that facts about Ks reduce without remainder to facts about the arrangement of the particles that are parts of Ks.  In that case, it is not clear that the deflationary account is conceptually any simpler than the criterial account.  For the deflationary account makes use of location facts—facts about a K being located at x—and such facts will reduce to facts about the arrangement of particles.  Likewise, facts about the obtaining of the criterion CK and about synchronic identity will reduce to facts about the arrangement of particles.  Given the reduction, it will no longer be clear that the deflationary account is conceptually simpler than the criterial ones, since both kinds of accounts are built in a complex way out of the conceptual ingredients of particle physics.’

            But it is controversial that there ever are successful non-eliminative reductions.  And we could run a modus tollens on the objection.  For non-reducible Ks, the deflationary account is correct.  But identity is a basic metaphysical and logical relation.  It would be implausible that identity should consist of something radically different in the case of different kinds of beings—something deflationary in the case of non-reducible beings and something substantive in the case of other beings.  Therefore, if the deflationary account does not hold for Ks, then Ks are not beings.  And hence if the deflationary account does not hold for reducible entities, there are no reducible entities—reduction is elimination.

            But the best answer may be this: The deflationary account is simpler for basic beings, ones that are not reducible.  The present objection only supports the claim that the deflationary account is no simpler than the criterial account for non-basic, reducible beings—it does not show that the deflationary account is more complex even in that case.  Therefore, overall theoretical simplicity still makes it plausible to say that the deflationary view is the right view in all cases.  In reducible cases, however, quantification over and predication of locations to Ks will be explained differently—and these explanations might make use of concepts such as memory or bodily continuity.

            If one does not like this solution, one might go for a view on which identity for more fundamental entities is different from identity for less fundamental ones, and insist that the deflationary view only applies to the fundamental entities.  Such an account would still have interesting implications for diachronic personal identity if persons are fundamental.

            Objection 6. ‘Nobody seriously thinks that the criterialist theories say what the diachronic identity consists in.  The only claim made is that the criteria provide necessary and sufficient conditions for identity.’[10]

            If this objection is right, then I have no need to convince anyone that criterialist theories fail to say what diachronic identity consists in, though it is still worth producing an argument for this failure.

            But the objection is not right.  I will give only one example, from a standard reference work.  Eric Olson writes:

The question is what is necessary and sufficient for a past or future being to be you. If we point to you now, and then describe someone or something existing at another time, we can ask whether we are referring to one thing twice, or referring once to each of two things. (There are precisely analogous questions about the persistence of other objects, such as dogs.)  The Persistence Question asks what determines the answer to such questions, or makes possible answers true or false. [Olson 2008]

While Olson starts with the question of what is necessary and sufficient for persistence, his expansion on the question shows that he is looking for what ‘makes’ an answer be correct. 

            Objection 7. ‘The criterialist’s analysis (2) of (1) makes use of the formula Ku & Kv & u is at x1 & v is at x2 & CK(u,x1,v,x2), quantified over u and v.  In this formula, each of the variables u and v occurs three times, and it is essential to understanding the formula that all the occurrences of u be taken as co-referring, and all the occurrence of v be taken as co-referring.  This co-referringness presupposes an identity, but only a synchronic one.  If ti is the time coordinate of xi, then in “Ku” and in “u is at x1”, we are talking of the object u at t1, and because CK(u,x1,v,x2) expresses a relation that takes place between u at t1 and v at t2, the third occurrence of the variable u is also assumed to be merely synchronically identical with the first two.  However, in the proposed deflationary analysis (3), we have a problem with the conjunctive formula Ku & u is at x1 & u is at x2.  If the first occurrence of u is taken to refer to the object at t1, then “u is at x2” presupposes a diachronic identity between something at t1 and something at t2.  And if the first occurrence of u is taken to refer to the object at t2, then “u is at x1” presupposes a diachronic identity between something at t2 and something at t1.  Thus, the criterialist analysis of (1) presupposes only synchronic identity, while the deflationary analysis circularly employs diachronic identity.’[11]

            The objection holds that in a formula in which a variable x occurs freely more than once, it is implicitly presupposed that ‘the same x’ is being talked about.  But if there is an implicit presupposition, it should be possible to make that presupposition explicit. 

            Consider, for instance, the formula Fx & Gx.  How could we make explicit the alleged implicit sameness of x?  Maybe: Fx & Gx & x=x?  But that surely does not help: it only multiplies from two to four the instances of x that are allegedly implicitly said to be identical, and embarks one on a vicious regress the next step of which is the no more illuminating Fx & Gx & x=x & x=x.  Or perhaps we can make the implicit identity explicit by a second quantification: Fx & $y(y=x & Gy).  But this alleged explicitation does nothing helpful, since we still have x occurring freely in two places in the resulting formula, and once again we would have a regress the next step of which is: Fx & $z(z=x & $y(y=z & Gy)).

            The above suggestions make it implausible that one could make the allegedly implicit assumption of sameness explicit in First Order Logic (FOL).  Perhaps, though, the objection is that the quantification apparatus of FOL does not correctly represent logical structure.  As an example of such a view, maybe we could think that a quantification of the form $x(Fx & Gx) is more perspicuously rendered in English as

(13)     There is an F, and that very F is a G,

and the use of ‘that very’ implicitly smuggles in identity.  Thus, the deflationary formula (3) would be rendered more perspicuously as

(14)     There is a K, and that very K is at x1 and that very K is at x2.

            This version of the objection requires two claims.  First, that something like (13) and (14) best captures the logical form of quantification, and, second, that the ‘that very’ implicitly smuggles in an identity.  Whether the first claim is correct, I do not know.  That one has discovered a better way to express quantification than in FOL would be a bold claim.  But in any case, the second claim is implausible.  For if identity is implicitly smuggled in, we should once be able to make that explicit.  Perhaps, then, (13) when made explicit says:

(15)     There is an F, and something identical with that very F is a G.

Here we do indeed have explicit identity, but once again we have a regress problem, since (15) also has the form ‘There is an F, and that very F is a G*’, where x is a G* if and only if something identical with x is a G, and this is the same form as (13).  I do not have an argument that there is no other way to make explicit the allegedly implicit identity, but the prospects appear bleak.

            Furthermore, the suggestion that formulae in which a free variable occurs more than once presuppose an identity claim do not appear to make any sense in the case of disjunctive formulae.  Consider FxÚGx.  Is there any presupposed identity?  We are not saying that the same x that is F is also G.  I suppose we could be taken to be saying that ‘the same x is F or G’, but here ‘the same’ can be dropped, and we can just say: ‘x is F or G’.  But it does not appear likely that the functioning of quantificational mechanisms differs depending on whether the formula within the quantifier is conjunctive or disjunctive.  To understand FxÚGx you need only need to understand the use of quantificational variables, as well as to understand the predicates ‘F’ and ‘G’ and the connective ‘Ú‘.  By the same token, then, to understand Fx & Gx, you only need to understand the use of quantificational variables, as well as ‘F’, ‘G’ and ‘&’.  Now, if the use of quantificational variables or of conjunction requires an understanding of diachronic identity, then it seems that substantive identity theorists are equally in trouble, in that typical substantive accounts also make use of quantificational variables (e.g., in quantifying over souls or quasi-memories) and conjunction. 

            Maybe, though, the worry is simpler.  It is simply that when we quantify in (3), we are treating the very same object, u, as existing at two different times.  And indeed we are.  But there is a trivial conjunctive analysis of the claim that ‘the very same object, u, exists at two different times’: u exists at one time and u exists at the other time.  And this is, further, to be analyzed not in terms of diachronic identity, but in terms of whatever it is that spatiotemporal location is to be analyzed in terms of—say, primitive located-at-x relations.  And it is not the business of an account of diachronic identity to explain spatiotemporal locatedness.

            The anonymous reader who offered Objection 7 has also offered me a simpler response to the objection.  Sentences like ‘Fa & Ga’ that contain multiple occurrences of ‘a’ are governed by a convention about repeated use of a symbol that requires them to be understood in such a way that both occurrences of ‘a’ refer to the same thing.  However, it is not a vicious circularity that a sentence S giving an analysis of a concept C is such that one must employ C to understand S.  (We might offer this example: one might have to employ some grammatical concept—say, that of a subordinate clause—to be able to parse a certain particularly complicated sentence, and yet that sentence can be non-circularly giving an analysis of that concept.)

            Objection 8. ‘In the deflationary account, but not in substantive theories, one needs to quantify over entities that persist over time.’ 

            This objection would be pressing if there were a way, in general, to reduce quantification over persisting entities to quantification over momentary entities, and the substantive theorist performed such a reduction.  For if there is no reduction, then the substantive theorist herself makes use of quantification over persisting entities when she states that for all x and y, x is diachronically identical with y if and only if her criterion holds.  After all, the only interesting case of this is where x and y are persisting entities.  (Diachronic identity for non-persisting entities is trivial—it never holds.)  But to claim that quantification over persisting entities is to be reduced to quantification over momentary entities is to take all persisting entities to be non-fundamental.  That is a very controversial claim.

            Now, granted, some stage theorists may make such a claim.  However, such stage theorists are not simply giving an account of diachronic identity—they are giving a complete reductive account of quantification over persisting entities.  But to reduce quantification over persisting entities to quantification over non-persisting entities is, plausibly, to reduce persisting entities to non-persisting ones (according to some appropriate version of the Quinean account of ontological commitment).  If moving to such a reductive account turns out to be the only way to defend a substantive account of diachronic identity, then we once have the very interesting result that substantive accounts of diachronic identity are only plausible given the non-fundamentality of the persisting entities.  We do, however, have grounds to be antecedently sceptical of the prospects for a reductive account of all persisting entities because of the history of failure in the business of giving reductive accounts in general.

5.  ‘Problems of diachronic identity’

            It is commonly thought that there are problems of diachronic identity which have wider implications.  One might well like to know whether a certain foetus in my past is me, whether the human lying on a bed in a nursing home is Terri Schiavo[12], or whether the ship of Theseus is in one dock or another or neither at the end of the rebuilding.  In the human cases, such knowledge can have bioethical consequences, whereas the case of the ship will matter to insurance companies.

            The deflationary account is quite compatible with there being answers to these questions.  Just as the deflationary view of truth does not deny that there is an objective matter of fact whether <Snow is white> is true, so too the deflationary view of personal identity does not deny that there is an objective matter of fact about what exists at what spatiotemporal locations.

            Nor does the deflationary view deny that there are useful epistemic criteria for when a K at x1 is identical with a K at x2.  These criteria might even be in the form of necessary and sufficient conditions.  The deflationist’s only claim here is that the fulfilment of the criteria does not explain what the diachronic identity claim consists in.

             Nonetheless, if a deflationary view of the diachronic identity of Ks is correct, it would be surprising if there were a useful necessary and sufficient philosophical condition for that diachronic identity, beyond the deflationary one.  The question about diachronic identity is simply a question about when something that has one spatiotemporal location has another.  But we do not expect interesting and elegant metaphysical answers to co-instantiation questions like: ‘When does something that has positive charge also have spin up?’  Metaphysics answers the latter by something epistemically unhelpful like: ‘When there is something that has both a positive charge trope and a spin up trope as parts of itself’ or ‘When something exemplifies being positively charged and having spin up.’ 

            Of course if facts about electrons, charge and/or spin were to supervene on facts about more basic entities, then the question of when something that has positive charge also has spin up would in principle have a substantive answer.  Similarly, Zimmerman [1998] is right that if Ks supervene on Ms, then there will be necessary and sufficient criteria for diachronic identity of Ks in terms of facts about Ms.  But even if there are such criteria, we have little reason to think that in the case of highly complex Ks such criteria will be at all useful.  They may, for instance, be infinitely long, or at least very long (certainly any criterion for the identity of persons in terms of the arrangement of fundamental particles will be extremely complex). 

            As an example of what a deflationist may say about particular substantive questions, consider the question whether when a person u undergoes total amnesia, the post-amnesiac person v with the same body b as u is identical with u.  Deflating, and letting x be the spatiotemporal location of b after the accident and assuming that nobody else is located at x, our question is simply:

(16)     Is u located at x?

            Now, normally questions like that are not metaphysical questions.  It is not a metaphysical but a historical question to ask:

(17)     Is Napoleon in Paris on Christmas Eve, 1803? 

However, (17) is a little different from this historical question in that even given all the relevant empirical facts after the accident, any answer to (17) will still be controversial, while the answer to (18) will be clear given the empirical facts.  The reason for that is that in the case of (17) we have a conflict between our usual methods of resolving ‘Is u located at x?’ questions.  One way is to track u’s body from some point in spacetime where reference to u was fixed (e.g., if u is a name, this might be the point where u is baptized with that name) and see if we get to x.  This leads to an affirmative answer in the amnesia case.  Another way is to see whether the individual at x remembers being u, or at least remembers being someone who remembers being someone … who remembers being u, or stands in some more complicated memory relation to being u.  This route leads to a negative answer.  Or one might combine these criteria, play them off against each other, try to find a closest match, etc., and thereby arrive at an answer.  The criterialist theorist then argues that one of these answers is guaranteed correct, if the facts are as described.

            The deflationist is less likely to take the route of arguing that one of these answers is guaranteed to be correct.  For when we no longer think that facts about memory or bodily continuity or closest matches constitute identity, our reasons for thinking that they are necessary and sufficient for identity are weakened.  In the special case of psychological continuity, this is particularly plausible.  After all, why should there be a metaphysically necessary coincidence between the obtaining of locational properties of persons and the existence of chains of quasimemories?  Why, for instance, should v’s having the property of first-person quasiremembering something that happened to a person at spatiotemporal location x1, together with the satisfaction of a no-branching condition, entail that v also has the property of being located at x1?

            Necessary substantive conditions for diachronic identity are, however, in better shape than sufficient substantive conditions.  The reason for this is that it may be an essential property of Ks that they have a certain diachronic causal structure.  Thus, plausibly, it is impossible that u be an organism and cease to exist and then come back into existence with no appropriate causal connection to its pre-destruction states[13], just as, plausibly, it is impossible that an ear e be a part of a horse h when h has a heart, lungs, brain, etc. that are not appropriately causally connected with e.

            Thus, many questions that are generally thought to concern diachronic identity, such as whether an organism could be resurrected, are in fact not about diachronic identity, but about the logical relations between predicates: e.g., are being located somewhere prior to t0, not being located anywhere between t0 and t1, being located somewhere after t0 and being an organism mutually compatible?

            Similarly, from a deflationary point of view, and modulo some uncontroversial claims, answering the question whether the comatose woman in the bed in the nursing home is Terri Schiavo depends not on an analysis of identity, but on asking whether personhood is an essential property, and, if it is, what level of mental capacities is compatible with personhood. 

6. Conclusions

            Certain claims apparently about diachronic identity, such as that something at x1 is identical with something at x2, can be very easily deflated into claims about quantification and the predication of locational properties.  This by itself is enough to show that there is something bogus about taking diachronic identity to be constituted by something substantive.  Other diachronic identity claims, such as ones involving variables or proper names, e.g., that Timmy at t0 is identical with Timothy at t1, require synchronic identity for their analysis, but it is legitimate to use synchronic identity to analyze diachronic identity.

            The deflationary approach is overall much simpler than any of the criterialist ones, and has the great advantage that it is guaranteed not to have counterexamples.  By itself, the deflationary account might be epistemically less useful than the criterialist ones.  But this is only true because the criterialists have made the dubious move of taking what seem to be defeasible epistemic criteria and making one or a combination of them into metaphysical criteria.  The deflationist can accept all the ‘necessary and sufficient’ claims of the criterialist if the criterialist can justify them—and the deflationist will simply say that these claims are not what diachronic identity consists in.[14]

Baylor University


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Horwich, Paul 1998. Truth (2nd edition), New York: Oxford University Press.

Lauinger, William 2009. Human Well-Being: The No Priority Theory, Ph.D. dissertation, Georgetown University.

Merricks, Trenton 1998. There Are No Criteria of Identity Over Time, Nous 32: 106-124.

Olson, Eric T. 2008. Personal Identity, The Stanford Encyclopedia of Philosophy (Spring 2010 Edition), ed. Edward N. Zalta, URL = <>.

Shoemaker, Sydney 1970. Persons and Their Pasts, American Philosophical Quarterly 7: 269-285.

Williams, Bernard 1970. The Self and the Future, Philosophical Review 79: 161-180.

Wittgenstein, Ludwig 1921 (1999). Tractatus Logico-Philosophicus, transl. C. K. Ogden, Trowbridge UK: Redwood Books.

Zimmerman, Dean 1998. Criteria of Identity and the ‘Identity Mystics’, Erkenntnis 48: 281-301.

[1] The “if and only if (and if so, then because)” connective is a variant on Lauinger’s “if and only if (and directly because)” [Lauinger 2009].

[2] I am grateful to Trent Dougherty for the insight that my basic theory is appropriately called “deflationary”.  This insight guided the development of the theory.

[3] A non-phase kind is a kind such that any entity that falls under it at one time must fall under it at all times.  The standard term to use here is “substance sortal”, but that is misleading, because the distinction also applies to spatiotemporal entities that are not substances, like tropes.  For instance, trope thought about by Quine is a phase kind and trope of roundness is a non-phase kind.

[4] One might more generally ask when some K1 at x1 is identical with a K2 at x2.  Answering this question would require a slight generalization of the analyses below.

[5] Merricks [1998] thinks that the necessary and sufficient conditions offered by the criterialist need not be explanatory.  But it is not a particularly interesting task to give informative necessary and sufficient conditions that are not explanatory.  Thus, the theist can say that x=y iff God believes the same things of x as he believes of y.  This is substantive and informative, but not explanatory, since presumably the reason God believes the same things of x as he believes of y is that he is omniscient and x=y.  Our definition of a criterialist is narrower than Merricks’.

[6] To see this, note that (1) in logical notation is: $u$v(Ku & Kv & u is at x1 & v is at x2 & u=v), and then use your favorite proof formalism for first order logic with equality.

[7] If one has a Galilean four-dimensional space-time, so that a location x can be represented by three spatial and one temporal coordinate, T(x) is just the value of the temporal coordinate.  In a relativistic setting, if a time is a spacelike hypersurface in some contextually fixed foliation F of spacetime (the foliation acting to fix the reference frame), then T(x) is the hypersurface in F that contains x.

[8] I am grateful to Steve Evans for a point like this.

[9] A number of philosophers I’ve talked to about this have offered a version of this objection.  In particular, Michael Gorman and Tim Pawl have done so.

[10] Robert Koons made this objection in correspondence, but the wording is mine.

[11] This objection was made by an anonymous reader, but the wording is largely mine.

[12] In the case of Terri Schiavo, following a cardiac arrest a vegetative state was diagnosed, and a feeding tube was required for the sustenance of life.  Eight years later, a prolonged legal battle between Schiavo’s husband and her parents ensued over the husband’s desire to remove the feeding tube. 

[13] I am grateful to Dean Zimmerman for this point.

[14] I am especially grateful to Michael Beaty, Todd Buras, Trent Dougherty, Steve Evans, Michael Gorman, Jonathan Jacobs, Daniel Johnson, Tim Pawl, Chris Tollefsen, Dean Zimmerman, and several anonymous readers of this paper for very helpful discussions and comments.