Sunday, August 13, 2006

Paper: Metaphysical Disputation Concerning Haecceitism and the Principle of the Identity of Indiscernibles

Metaphysical Disputation on Haecceitism and the Principle of the Identity of Indiscernibles

I. Introduction

The present disputation will be concerned with providing a clear and concise exposition of the logical status of differing forms of the Principle of the Identity of Indiscernibles (PII) with respect to differing notions of what constitutes an individual. First I will briefly consider historical formulations of the PII. This will show the fundamental role played by the concept of individual unity in making sense of the different formulations of the PII. It will be shown that a consideration of the principle requires first discussing the concept of an individual. The principle is only true or false with respect to these differing concepts and its truth values change according to the concept of the individual thus considered. Therefore, I will first consider two conceptions of an individual. The first of these conceptions will be categorized as the “primitive haecceity” approach, as typified by John Duns Scotus, Henry of Ghent, and, for the purposes of this paper, Robert Merrihew Adams (and my own additions to his theory). The second of these conceptions will be categorized as the “whole-entity” approach, as typified by William of Ockham, Francisco Suarez, and, for the purposes of this paper, Gottfried Wilhelm Leibniz. After considering these competing theses regarding individual unity, I will pursue the implications that follow from an acceptance of either of these views with respect to the PII.

II. Formulations of the PII: An Exposition of Several Views

Gottfried Wilhelm Leibniz maintained the validity of a metaphysical principle known as the Principle of the Identity of Indiscernibles (PII). He states the principle in different ways at different times. For example, in a letter to Antoine Arnauld, dated May 1686, Leibniz says: “…it is not possible for there to be two individuals entirely alike, or differing only numerically” (Philosophical Essays, 73). In “Primary Truths,” written in either 1686 or 1689, Leibniz states: “…in nature, there cannot be two individual things that differ in number alone. For it certainly must be possible to explain why they are different, and that explanation must derive from some difference[1] they contain” (Philosophical Essays, 32). In the “Monadology,” written in 1714, Leibniz writes: “For there are never two beings in nature that are perfectly alike, two beings in which it is not possible to discover an internal difference, that is, one founded on an intrinsic denomination” (Philosophical Essays, 214). Furthermore, in his correspondence with Samuel Clarke, Leibniz succinctly states in his letter dated June 2, 1716: “There is no such thing as two individuals indiscernible from each other” (Correspondence, 22). To summarize the force of each of these formulations of the PII, let us say that Leibniz’s version of the PII holds:

PII: In nature there will never be two individuals that are exactly the same.

This principle, held by Leibniz, holds that it will never be the case that we can find two different individuals to which we may predicate the exact same exhaustive set of properties and no other properties in addition. This principle has been met with strong criticism from the very beginning. In the course of this criticism, it has been re-formulated in different ways, each trying to capture the different things that it might imply. The most common way to distinguish between possible formulations of the principle is to consider it as applied to either all properties, including identity (presupposing that individuals have distinct identities), or only to properties other than identity. For example, in the course of Max Black’s dialogue “The Identity of Indiscernibles,” speaker B stipulates: “If you want to have an interesting principle to defend, you must interpret “property” more narrowly––enough so, at any rate, for “identity” and “difference” not to count as properties” (Black, 155). Here we see an acknowledgment of the importance of first considering the relationship between an individual and its properties before considering the truth value of the PII. The undesirable formulation of the PII, the one that B finds to be uninteresting, is what is commonly called the trivial version of the PII. This version states:

PII´: In nature there will never be two individuals that are exactly the same, where “exactly the same” means sharing all the same properties, including those related to identity.

This formulation is termed the trivial version since it seems prima facie true and uninteresting that no two things having different identities will ever be the same thing. B would prefer to investigate whether or not a more interesting formulation of the PII is true or false. For, if we are already taking ourselves to be considering two things, it seems trivial to say that if they have the same identity then they are the same individual and if they have different identities then they are different individuals. Following B’s stipulation, A says: “Will you at least allow me to include among ‘properties’ what are sometimes called ‘relational characteristics’––like being married to Caesar or being at a distance from London?” (Black 155). The version that A proposes to discuss instead is the following:

PII´´: In nature there will never be two individuals that share all the same properties (other than those related to identity), either relational or non-relational.

This version is neither prima facie true nor false and seems to have more interesting implications than the trivial version.

In his “Primitive Thisness and Primitive Identity,” Robert Merrihew Adams takes into account the different ways of formulating the principle in terms of identity-related properties, non-identity-related properties, and non-relational, non-identity-related properties. His reasons for distinguishing between different formulations of the principle seem to be similar to those held by Black’s B. He says: “The Identity of Indiscernibles might be defined, in versions of increasing strength, as the doctrine that no two distinct individuals can share (1) all their properties, or (2) all their suchnesses, or (3) all their nonrelational suchnesses” (Adams, 11). Adams’ (1) corresponds to PII´. His (2) and (3) are similar to PII´´, except that he separates its last clause into two different versions of the PII. In order to better understand Adams’ three formulations of the principle, it will first be necessary to begin our discussion of the two competing notions of haecceity.

III. Concepts of an Individual: Several Expositions of Haecceity

In all three formulations of the principle, we find it concerned chiefly with the relationship between individuals and their properties. In order to understand what exactly is at stake in saying that two indiscernible things are identical, we must realize the primacy of the question of what makes something an individual. Different concepts of the individual will come to have differing implications on the truth and implications of the PII. Debates that fail to stipulate the variant of individual unity at hand will result in interlocutors talking past one another. It will be unclear whether or not some formulation of the PII is true or false if considered apart from any specific concept of individual identity. However, once we stipulate what specifically individuates things from each other, we will find ourselves in a much better position to discuss the principle. For these reasons, if we try to investigate the principle without first stipulating the notion of the individual under which we are considering it, not only will our efforts be fruitless but we will also come to entangle ourselves in unnecessary philosophical confusion.

One way of articulating the notion of an individual is by reference to a concept of haecceity. Haecceity is what allows a substance to be ‘this’ rather than ‘that’. That is, it is the notion that allows for the numerical differentiation of different individual substances. An individual substance is this individual substance rather than that individual substance in virtue of the distinct haecceity it possesses, which that individual substance lacks. While many different philosophers have accepted a notion of haecceity, the forms of haecceity they accept tend to be radically different. These differences will later be seen to play a strong role in the determination of the truth or falsity of different formulations of the PII.

Let us overly simplify the history of philosophy by distinguishing between two general ways in which philosophers have conceived of haecceities. We will speak first of those to whom haecceity is something nonqualitative that obtains to an individual distinct from the rest of their properties. Philosophers who subscribe to theories of this sort might be termed “primitive haecceitists,” insofar as they propose primitive, nonqualitative haecceities. A second group of philosophers who have maintained a concept of haecceity are those to whom haecceities are nothing but the conjunction of the entirety of some particular’s properties. Let us refer to these latter haecceitists as subscribing to a “whole-entity” conception of the notion. Out of consideration of the scope of this paper, we will further simplify by discussing one philosopher of each type. Of the primitive haecceitists, we will discuss Adams. Of the whole-entity haecceitists, we will discuss Leibniz.

Let us return then to Adams. We have already mentioned his concept of suchnesses. In the course of his paper, Adams distinguishes between properties of individuals that are “thisnesses” and properties that are “suchnesses”. First, he defines individuals as: “particulars such as persons, physical objects, and events” (Adams, 6). Adams then defines thisness as: “the property of being identical with a certain particular individual—not the property that we all share, of being identical with some individual or other, but my property of being identical with me, your property of being identical with you, etc” (Adams, 6). Each particular individual will have its own individual property of being identical with itself—its own thisness. Furthermore, he stipulates: “‘Thisness’ is intended to be a synonym or translation of the traditional term haecceity” (Adams, 6). Finally, he defines suchnesses as those purely qualitative properties that “…could be expressed, in a language sufficiently rich, without the aid of such referential devices as proper names, proper adjectives and verbs (such as ‘Leibnizian’ and ‘pegasizes’), indexical expressions, and referential uses of definite descriptions” (Adams, 7). Adams’ definitions of individuals and suchnesses remind us of Aristotle’s definitions of particulars and universals.[2] However, Adams distinguishes between individuals and the property of being that individual in addition to other qualitative properties capable of obtaining to many different individuals.

In discussing his concept of thisnesses as the property held by an individual of being identical with itself, Adams is quick to note that by postulating a thisness property, he does not intend to postulate either that there exist “substrata without qualities of their own, which would be what was left of the individual when all its qualitative properties were subtracted” or that “individuals are nothing but bundles of qualities” (Adams, 7). It is neither the case that suchnesses in some sense obtain to a basic thisness nor that there is not any sense of an individual aside from the compilation of their thisness and suchnesses.

I am prepared to accept Adams’ concept of the individual, with one friendly amendment that will allow for a more nuanced understanding of the relationship between certain qualitative properties and the individual to come forth. I would like to take Adams’ concept of qualitative properties and subdivide it into two different kinds. Of the qualitative properties that pertain to an individual, I should like to differentiate between whatnesses and suchnesses. Whatness is intended to be a translation of the medieval term quiddity. The concept of an individual’s whatness should be taken to refer to those qualitative properties that necessarily obtain to an individual in virtue of his thisness. Given any instantiation of that individual, at any time in any world, his set of whatnesses will remain the same. For example, the whatnesses necessarily obtaining to Aristotle would include ‘being the son of Nicomachus and Phaestis’[3] and ‘being a human’[4], among others. There is no possible world in which these properties could not obtain to the individual Aristotle. The concepts of an individual’s suchness should then be taken to refer to those qualitative properties that only contingently obtain to an individual. For example, the suchnesses obtaining to Aristotle in our world would include ‘being named ‘Aristotle’’, ‘being the teacher of Alexander the Great’, etc. We may, however, posit a possible world in which the suchnesses obtaining to Aristotle would include ‘being named Schmaristotle’, ‘being one of Alexander the Great’s tax collectors’, etc. While both whatnesses and suchnesses are in some sense reminiscent of universals (insofar as it makes sense to speak of them applying to multiple individuals and their not requiring a subject in their iteration), I believe that it will serve us well to note the distinction. For, while we might wish to speak for example of Aristotle not having been the teacher of Alexander, we do not seem to be in any position to speak of his not having been a human. Similarly, while we may want to talk about the individual Bucephalus as necessarily having the whatnesses of ‘being a horse’ and ‘being the son of horse x and horse y’, we might also want to speak about his not having the suchnesses ‘being named ‘Bucephalus’’ or ‘being Alexander the Great’s horse’, it would make little sense to speak of the individual Bucephalus as having the whatnesses of ‘being a human’ or ‘being the son of Nicomachus and Phaestis’. There seems to be a correspondence between an individual’s haecceity, his whatness, and the suchnesses that may possibly obtain to him. An individual’s haecceity, in the form of thisness, is what differentiates it as this particular individual that has some qualitative whatnesses and suchnesses rather than that individual that has some qualitative whatnesses and suchnesses. For, while qualitative whatnesses and suchnesses may possibly obtain to multiple individuals, each of these individuals will necessarily have their own private thisness.

Let us now consider the position of whole-entity haecceitists, who, for the purposes of our paper, will be represented by Leibniz. One might at first object to referring to Leibniz as a haecceitist due to his vehement opposition to the Scotists. However, given an exposition of his metaphysics of individuality, we will see that, while he does not accept a Scotist account of haecceity, he does in fact defend his own distinct notion of haecceity.

Leibniz’s conception of haecceity differs in one key way from Adams’. While for Adams an individual’s haecceity is a non-qualitative property (thisness) that obtains to an individual along with a set of qualitative suchnesses while not being a function of them (or qualitative whatnesses and suchnesses according to my additions), for Leibniz, an individual entity’s haecceity is nothing but the result of the compilation of the entirety of that individual entity’s properties. Therefore, let us refer to Leibniz’s account as being “whole-entity” haecceitism. Furthermore, while Adams proposes that we may speak of the possibility of different qualitative suchnesses (or just suchnesses according to my distinction) pertaining to an individual along with his thisness, Leibniz holds that for every individual, there exists only one set of properties that may possibly pertain to him. This doctrine of the necessity of the entirety of an individual’s properties to his essence has come to be known as superessentialism.

Let us examine some quotations that support this reading of Leibniz. Leibniz asserts that every property obtaining to (that will ever obtain to) someone must be contained in the notion of that person. He says: “…the notion of an individual substance includes once and for all everything that can ever happen to it and [that], by considering this notion, one can see there everything that can truly be said of it, just as we can see in the nature of a circle all the properties that can be deduced from it” (Leibniz, Discourse on Metaphysics, §13). His conception of the complete notion of an individual includes the entirety of that individual’s properties across time. If we could conceptualize an individual’s “notion”, or, haecceity, then we would be able to deduce all the properties that will ever obtain to it. For, every predicate that will ever obtain to a person is contained in the notion of that person. However, if we only conceive of some incomplete set of an individual’s properties, we will not be able to conceive of that individual’s haecceity. Leibniz says:

“[Thus], taken in abstraction from the subject, the quality of being a king which belongs to Alexander the Great is not determinate enough to constitute an individual and does not include the other qualities of the same subject, nor does it include everything that the notion of this prince includes. On the other hand, God, seeing Alexander’s individual notion or haecceity, sees in it at the same time the basis and reason for all the predicates which can be said truly of him, for example, that he vanquished Darius and Porus…” (Leibniz, Discourse on Metaphysics, §8).

While human beings might not be able to conceive of persons so completely, due to the fact that they tend to form only confused and incomplete ideas of things, an idea of this fundamental haecceity exists in God’s idea. That is, considered properly, the individuality of any individual substance can be conceived of distinct from that of any other. While our confused notions of things, composed mainly of the products of the sensory perception of only some of a thing’s qualitative properties, may be such that we inadvertently see two actually discernible things (considered properly) as indiscernible, that does not mean that they are indiscernible or identical in principle. For, according to Leibniz, it is impossible for two individuals to have the same haecceity (individual concept) and still be numerically two individuals. We may err and believe, e.g., that two seemingly qualitatively identical (but actually different) things are one and the same.

IV. Implications of the Different Concepts of Haecceity for the PII

It makes little sense to argue that one is logically obligated to accept one or another metaphysical concept of the individual. We are in no position to obtain verification that either of the above positions is true or false in principle. Such is metaphysics. The choice of a theory of the individual is up to the reader. However, it is possible to understand what exactly the implications of an adherence to such views are. An understanding of the scope and implications of the available views will hopefully influence one’s choice. As we have come to understand two different ways of formulating the concept of an individual in terms of haecceity, it will now be fruitful to see the precise logical implications entailed by an adherence to either.[5] The implications to be presently considered will pertain to the truth value of the PII, transtemporal identity, and transworld identity. An exposition of these implications will come to bear on which metaphysical concept of the individual the reader will come to accept.

Let us now consider the implications of an adherence to the Leibnizian whole-entity conception of haecceity. In this case an individual is a complete set of world-indexed properties. As an individual’s haecceity persists across time in virtue of its perpetual constitution of the entirety of that individual’s transtemporal properties, we are in a position to grant the individual transtemporal identity with itself. Since at every point in time the individual will be conceived of most properly in terms of its whole-entity haecceity, it will make sense to speak of transtemporal persisting self-identity. All this is true in spite of the fact that we may observe an individual as exhibiting different qualitative properties at different points in time. However, insofar as an individual may only exist under one complete notion, it will be impossible to consider some given particular individual as possibly existing in some other world. For, not only might the qualitative properties possessed there differ, but as each property is in some sense world-indexed even the satisfaction of a seemingly identical set of properties will in fact lead to an entirely distinct haecceity. Therefore, to accept the Leibnizian whole-entity haecceitism is to be granted transtemporal but not transworld identity. The Leibnizian conception of the individual also necessitates an identification of PII´ and PII´´. For, as the entirety of an individual’s properties will determine its identity, there is no reason to distinguish between the two formulations of the PII. Thus, in this case, the PII is trivially true. For, no two things that possess all of the same properties, including those related to identity, will ever succeed in remaining two distinct individuals. Any two things that are indiscernible (in principle) with respect to properties will be identical.

Finally let us consider the implications of an adherence to an Adamsian primitive thisness haecceitism. In this case an individual is primarily constituted by a nonqualitative thisness. Secondly an individual exhibits or possesses both whatnesses that will persist across time and worlds and sets of suchnesses that may come to change across either time or worlds without fundamentally altering the individual. If the individual comes to satisfy different suchnesses over either time or worlds, he will nevertheless remain the same individual in virtue of his transtemporal and transworld thisness. For an individual to remain the same individual requires merely that he persist in satisfying the same primitive thisness. Purely qualitative properties have no bearing on the concept of the individual. Therefore, according to the Adamsian, PII´ is true. If any two things have the same haecceity, they are the same individual. For example, our Aristotle at birth is the same as our Aristotle under the tutelage of Plato. Furthermore, our philosophizing Aristotle is the same as another world’s taxcollecting “Schmaristotle”. The PII only applies to haecceities, not to any other qualitative properties. Furthermore, PII´´ is false. We may easily posit a case in which two distinct individuals, that is, two things possessing different Adamsian thisnesses, could come to satisfy the same set of qualitative properties. To suppose a possible world in which something different happens to an individual is not to suppose an entirely new individual. Rather, it is to consider what it would have been like had some person come to possess different qualitative properties than those possessed in some other world, such as the actual. It is in virtue of the direct reference of the name, e.g. “Aristotle”, to the thing (person) so named in the actual world that we may succeed in referring to him in other worlds, even in one in which he was not named e.g. “Aristotle”. We may therefore speak of the same thing possibly satisfying one set of qualititative suchnesses (φ1) in one world (w1) and another set of qualitative suchnesses (φ2) in another world (w2).

Let us now take this possibility a step further. Since we may reasonably consider one individual coming to satisfy different sets of qualitative suchnesses in different worlds, it is certainly reasonable to consider that two individuals could come to satisfy different sets of qualitative suchnesses in different worlds. Furthermore, why not consider these two individuals in the same two possible worlds. Now, suppose that in the second of these worlds, the second individual (of course to call him the second individual is purely arbitrary) satisfies the set of qualitative suchnesses satisfied by the first individual in the first world. Moreover, in the second world the first individual satisfies the set of qualitative suchnesses satisfied by the second individual in the first world. That is, they switch. Finally, let us make these individuals identical twins.

If we then suppose two monozygotic twins (a, b) we may suppose that one twin (a) satisfies a set of qualitative suchnesses (φ1) in w1 that the other twin (b) satisfies in w2 and that the set of qualitative suchnesses (φ2) satisfied by the second twin (b) in w1 be precisely that set satisfied by the first twin (a) in w2. It may help to give a table illustrating the possibilities being considered:









Let’s consider an example. In the actual world (w1), assuming for the sake of argument the literal truth of scripture, a satisfies the set of qualitative suchnesses (φ1) containing, e.g., ‘was born second’, ‘was named Jacob’, ‘acquired the birthright’, etc. Additionally, b satisfies the set of qualitative suchnesses (φ2) containing, e.g., ‘was born first’, ‘was named Esau’, ‘gave up the birthright’, etc. We may now consider a possible world (w2) in which a was born first, named Esau, gave up the birthright, etc, while b was born second, named Jacob, acquired the birthright, etc.

Here is what the Leibnizian would have to say about this case: What is called “a” in w1 is only identical with what is called “a” in w1. What is called “a” in w2 is only identical with what is called “a” in w2. What is called “b” in w1 is only identical with what is called “b” in w1. What is called “b” in w2 is only identical with what is called “b” in w2. That is, what we have here are four different individuals, only two of which are actual.

The Adamsian, however, would be committed to a different interpretation of the case. Despite their having satisfied the same sets of qualitative suchnesses in the two different worlds, a is still a regardless of the world and set of qualitative suchnesses that he satisfies therein. Additionally, b is still b despite the world and set of qualitative suchnesses that he satisfies therein. That is, insofar as a in w1 is indiscernible from a in w2 in terms of haecceity, they are the same thing. Similarly, insofar as b in w1 is indiscernible from b in w2 in terms of haecceity, they are the same thing. Furthermore, insofar as a in w1 is discernible from b in w2 in terms of haecceity, they are different things. Finally, insofar as b in w1 is discernible from a in w2 in terms of haecceity, they are different things. In this sense, as we may speak of the same individual satisfying the same thisness (at least) from conception to death (i.e., across time) and across different possible worlds, to accept Adamsian primitive thisness is to be granted the truth of PII´, the falsehood of PII´´, and the existence of transtemporal and transworld identity. Transtemporal and transworld identity may thus be reformulated as the identity of qualitatively (but not nonqualitatively, i.e. haecceitively) discernibles. Insofar as the truth of PII´ allows for transtemporal and transworld identity within an Adamsian concept of the individual, we must now admit that the PII, thus formulated, is not as trivial in its truth as we might previously have thought.

V. Concluding Comments

The reader is now aware of the necessary connection between one’s account of individuality and the variant of the PII that one is bound to. It is improper to attempt a discussion of the PII without first considering under what account of individual unity it is to be considered. Individual unity may be conceived of in terms of two versions of haecceity or distinct from any such notion whatsoever. While I leave it up to the reader to choose for himself whether or not he would like to allow haecceities into his metaphysics (and to choose whichever variant he likes if he does), I should like to confess that I (the self-same I who began writing this sentence approximately four seconds ago and who might not have ever written it) do accept haecceities, specifically the amended Adamsian account given above. I accept this formulation on the basis of its simplicity and its ability to account for transtemporal and transworld identity.


Adams, Robert Merrihew. “Primitive Thisness and Primitive Identity.” The Journal of Philosophy, Vol. 76, No. 1 (January, 1979), 5-26.

Black, Max. "The Identity of Indiscernibles", Mind, New Series, Vol. 61, No. 242, (April, 1952), 153-164.

Kripke, Saul. Naming and Necessity. Harvard University Press. Cambridge, 1980.

Leibniz, G. W. and Clarke, Samuel. Correspondence ed. Roger Ariew. Hackett. Indianapolis, 2000.

Leibniz, G. W. “Discourse on Metaphysics.” Philosophical Essays. Hackett. Indianapolis, 1989. 35-65.

Leibniz, G. W. “Letter to Arnauld [May 1686].” Philosophical Essays. Hackett. Indianapolis, 1989. 30-4.

Leibniz, G. W. “The Monadology.” Philosophical Essays. Hackett. Indianapolis, 1989. 213-25.

Leibniz, G. W. “Primary Truths.” Philosophical Essays. Hackett. Indianapolis, 1989. 30-4. Sprigge, Timothy. “Internal and External Properties.” Mind, New Series, Vol. 71, No. 282 (April, 1962), 197-212.

[1] Here it must be noted that the “difference they contain” must be a difference in things that may be predicated of them. It will become evident that this is the case when we discuss Leibniz’s notion of haecceity below.

[2] In Chapter 7 of De Interpretatione Aristotle remarks: “Now of actual things some are universal, others particular (I call universal that which is by its nature predicated of a number of things, and particular that which is not; man, for instance, is a universal, Callias a particular)” (Aristotle, 17a38).

[3] Recall Saul Kripke’s consideration of the fact that from an individual born of certain parents in one world cannot be born of others in a different world. That is, the sperm and egg out of which an individual is formed can only come from two specific people. (Naming and Necessity, 110-13).

[4] Consider Timothy Sprigge’s discussion of whether or not “the particular we call the Queen” could possibly have had the property of not being human. He says: “The internalist suggests that we cannot imagine that particular we call the Queen having the property of at no stage in her existence being human. If the antiinternalist admits this, admits that it is logically inconceivable that the Queen should have had the property of, say, always being a swan, then he admits that she has at least one internal property. If on the other hand he says that it is only a contingent fact that the Queen has ever been human, he says what it is hard to accept. Can we really consider it as conceivable that she should never have been human?” (“Internal and External Properties”, 203).

[5] For the sake of brevity, we will refrain from discussing bare substratum and trope theories of the individual.


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