"A statue and the lump of clay of which it is made are two different objects
existing at the same place and time."


Most people would say that a statue is identical to the lump of clay from which it is made.  This is not an unreasonable thing to say.  After all, most people when asked how many things are located on the pedestal would agree that there is only one object there - a statue or a lump of clay depending on their aesthetic sensibilities (one person's work of art being another person's lump of clay).  The statue and the lump of clay are spatially coincident and neither has a physical part the other doesn't have.  There is no part of the statue that is not part of the lump of clay, and vice versa.  So it sure looks as if the statue and lump of clay are one - "numerically identical" - and hence a single object.  "Common sense" philosophy would therefore suggest that the essay title's quote is quite false.

But philosophers like to be clearer as to just what "identity" and "an object" amount to.  And that is where the scenario of the statue and the lump of clay come in.  The scenario goes something like this (variations in the minor details abound) -

On Monday, a sculptor acquires a lump of clay, and places it on her pedestal.  Let's call that lump "Lump" for identification.  On Tuesday, the sculptor shapes that lump of clay into a model of Michelangelo's David.  Let's call the clay model of David "Statue" for identification.  On Wednesday the sculptor and her friends admire Statue as it sits atop its pedestal.  On Thursday, tiring of her model of David, the sculptor squishes the lump of clay back into a ball in preparation for creating some other work.  On Friday, the sculptor sits and ponders her lump of clay, wondering what she should create with it.  So, on the pedestal, on Monday and the early part of Tuesday, there rests Lump.  On the latter part of Tuesday, all day Wednesday, and the early part of Thursday, rests Statue.  On the latter part of Thursday, and all day Friday, rests a lump of clay which may or may not be Lump.

The questions that philosophers pose with this scenario in mind are all related to the meaning of "identity" and about what constitutes "an object".  When and under what conditions is Lump identical with/to Statue?   By stipulation, Statue exists on Wednesday, when everyone is admiring it on the pedestal.  But does it also exist on Monday and Friday, when all that is perceptually there is a lump of clay?  Also by stipulation, Lump exists on Monday.  But does it also exist on Wednesday, when all that is perceptually there is Statue?   And does it also exist on Friday, when the clay has been squished back into a lump?

The philosophical literature on this issue can be roughly divided into six different approaches to these questions:
                      (a) the Constitution view (Wiggins(1), Wasserman(2));
                      (b) the Temporal Parts theory (Lewis(3));
                      (c) the Dominant Kind view (Burke(4));
                      (d) the Eliminativist view (Unger(5), van Inwagen(6), and Chisholm(7));
                      (e) the Deflationist view (Carnap(8), Putnam(9)); and
                      (f) the Relative Identity theory (Geach(10)).
The quoted statement in the essay title comes from the first of these approaches.  I'll discuss each of these different views in turn to see what, if anything, it can contribute to our understanding of this quote.

To start, consider this argument:

1.  Statue did not exist on Monday (but does exist on Wednesday).
2.  Lump did exist on Monday (and also exists on Wednesday and Friday)
3.  For any x and y, if x is identical to y then x and y have all the same properties,
                        if they don't then they are not identical. (Leibniz' Law:- If a=b then (F)(Fa <-> Fb) )
4.  Therefore Statue is not identical with Lump (from 1, 2, and 3)
5.  Therefore there are two objects (Lump and Statue) that exist
                      at the same time place and time (on the pedestal on Wednesday).

The essay's title quote is the conclusion of this Constitutionist argument.  Lump and Statue exist at the same place and the same time, but differ in many of their properties. Statute is aesthetically pleasing, while lump is an aluminum silicate amalgam.  Constitutionists accept that it is possible for there to be two objects in the same place at the same time.  The statue is said to be constituted by the clay that is Lump.  Constitution is not identity.  Constitution is a dependence relation.  The statue is constituted by clay, but not vice versa.  Statue and Lump share the same matter and the same parts, and it is thus that the two objects are able to occupy the same spatio-temporal location.  Spatial coincidence (the sharing of place) is explained by material coincidence (the sharing of parts).  But what explains material coincidence?  

If we take the material coincidence seriously, then Lump and Statue share all the same parts on Wednesday, so Statue is (ie. is numerically identical with) Lump.  What then about Statue on Monday and Friday?   Does it still exist because Lump exists?  And what about the conclusion (4) above, that maintains that Statue and Lump are not, in fact, numerically identical?  If Statue and Lump share the same matter, then what accounts for the differences in the various diverse properties of Lump and Statue?  If Statue is admired and appreciated on Wednesday, what is it about Statue and not Lump that results in that admiration of Statue and not Lump?   And how does Statue acquire those properties, if Statue is the same matter as Lump.  Philosophers advocating the constitution view are not very clear, and very far from unanimous, on how to answer these questions.

Finally, if it is acceptable on the Constitution view for there to be two objects in the same place at the same time, there is an infinite regress lurking here.  Consider a potter at her wheel.  As the lump of clay spins, the potter shapes the lump into a series of many (an infinite continuum?) intermediate shapes before she stops with one that satisfies her.  We thus have a (possibly infinite?) series of objects (proto-pots) each of which is a concrete individual numerically distinct from the initial lump of clay yet is spatially coincident with it, and shares with it every momentary property.

Since common sense tells us that there is "really" only a single object on that pedestal on Wednesday (or on that potter's wheel), the philosopher(s) who maintain the constitution view are perhaps using the concept of "an object" in a different sense that what is normally meant by those words.  Is this new word ("object*") relevant to an understanding of "object"?  Since other interpretations have been offered of the Clay and Statue puzzle, it is worth investigating them briefly before we draw any conclusions about the essay title's quoted assertion.

Temporal Parts theorists like Lewis take a completely different approach to explaining the series of "objects" that seem to exist at the same place and time.  Whether one maintains an endurance or a perdurance theory of temporal persistence, temporal parts theorists maintain that the transition of the lump of clay into a statue and back to a lump of clay is very much like the transition of Interstate-95 across several states.  Segments of the highway exist in different states, and have different properties in each state according to the particular maintenance policies of each state.  (Although, of course, the perdurance theorist will talk in terms of temporal stages of the lump of clay, while the endurance theorist will talk in terms of temporal counterparts of the lump of clay.)  For the temporal parts theorist, there is no problem with Lump and Statue being both present at the same time and place.  It is just like I-95 (a North-South highway) sharing a road segment with I-64 (an East-West highway).

For endurance theorists, however, the challenge is that the counterpart relation is a similarity relation rather than an identity relation.  And as with all talk of counterparts, recognizing when one thing is a counterpart of another (ie, Lump and Statue) will involve vague and context sensitive criteria.  For perdurance theorists, similarly, the challenge is that the four-dimensional "worm" that is labelled as both "Lump" and "Statue" extends (perhaps infinitely) in both temporal directions.  If next week, she reshapes Lump into another copy of Michelangelo's David, is that new copy also Statue?  Establishing when one part of that temporal worm should be called Lump or Statue will involve vague and context sensitive criteria. 

Talk of temporal parts therefore usually involves talk of "kinds" or "essences" that supposedly delimit parts of a perdurant 4-dimensional worm, or establish the similarity of endurant counterparts.  Lump is thus essentially clay, while Statue is essentially a statue.

Essentialism is the view that, for any specific kind of existant (or any arbitrary sortal), there is a set of properties all of which any existant of that kind must possess.  Thus all things can be precisely labelled or identified.  Certain properties possessed by a group of existants (things, people, abstract ideas) are universal to the group, and not dependent on context.  A member of the group may have other properties ("contingently") that are neither necessary to establish membership nor preclude its membership.  Essences are in nature, and not in the mind.  Hence it follows from essentialism that those words that pick out "natural kinds" have a single correct definition and meaning. 

If the essence of the object on the pedestal is that of clay, then what is on the pedestal is Lump.  But if the essence of the object on the pedestal is that of a statue, then what is on the pedestal is Statue.  Of course, the difficulty in this case, is determining just what is the essence of whatever is on the pedestal.  Because on Wednesday, the thing(s) on the pedestal have both the properties of clay and the properties of a statue. 

The problem with essentialism is that many of the distinctions we make between objects are determined by our cognitive interests, and not vice versa.  A single grain of sand is not a heap.  Nor is two grains right next to each other. But ten thousand grains all together are a heap.  At which precise number of grains of sand does a collection of sand grains acquire the essence of a "heap"?   The collection of individual sand grains comes to be described as a heap when there are too many all piled together for us care about the specific number.  So if the essence of a heap exists at all, it is in the mind, not the sand.  Similarly, and famously, some distinctions between colours differ from one language to another(11).  Anyone who accepts a distinction between the conceptual and the factual must admit that "essences" are more verbal than natural.  So the Temporal Parts theory does not appear to contribute much to our understanding of the title quote, other than to offer an argument to the effect that the constitutionist view may be wrong.

Burke's Dominant Kind theory is very similar to an essentialist theory.  Although in Burke's case, he is dealing with a more specific set of properties.  Burke identifies an object with its persistence conditions.  The lump of clay and the statue have different persistence conditions, hence they are not the same object.  Yet he does not accept the Constitutionist's conclusion that there are two objects on the pedestal on Wednesday.  The thing on the pedestal (on Wednesday) is both a lump of clay and a statue, but only has the persistence conditions of one of these.  Burke's theory maintains that an object has the persistence conditions of its "dominant kind" (a concept very similar to a thing's essence).  An object's dominant kind is the kind that "entails possession of the widest range of properties"(12).  Since the statue has aesthetic as well as physical properties, while the clay has only physical properties, the statue has the wider range of properties and is thus the dominant kind.  Burke therefore concludes that Lump exists on Monday and Friday, but not on Wednesday.  Whereas Statue exist only on part of Tuesday, all of Wednesday, and part of Thursday.

But this means, of course, that the sculptor destroyed Lump when she reshaped the lump of clay into the image of Michelangelo's David, created the new object of Statue in that process, and destroyed Statue to recreate Lump when she squashed the clay back into a lump.  This is certainly counter intuitive, and would appear to run counter to the generally accepted principle that matter can be neither created nor destroyed (allowing for E=MC2, and so forth).

The other major problem with the Dominant Kind view is that it is not equipped to handle all of the problematic puzzles of identity.  In the Ship of Theseus scenario, for example, it would seem that all of the candidate objects are "Ships".  Since there is only a single "kind" involved, how do we establish the "dominant kind"?

So the Dominant Kind theory provides another alternative to the two objects thesis claimed in the essay's title, but the theory has some serous flaws that recommend continuing to examine the other alternatives.

Eliminativism, or "mereological nihilism", is the position that there are no composite objects (objects with parts).  Or at least, since there are a number of variations of this approach, none of the concrete objects that we normally accept as the regular furniture of the world are acceptable eliminativist objects.  There are only mereological simples (objects with no parts).  The eliminativist denys, therefore, that there are lumps of clay or statues, or any other macroscopic material objects.  There are only atoms (or molecules, or sub-atomic particles, depending on the variation) in the void.

For the rest of us, of course, there are material objects like lumps of clay and statues.  To deny our obvious perceptions is to place one's metaphysical position clearly at odds with common sense.  Whatever concept the eliminativist labels as "identity" or as "an object", it is not the same concept as is generally meant by those words.  Obviously, therefore, the Eliminativist is talking a different language than the rest of us.

The other challenge the eliminativist must deal with is the selection of "mereological simples".  Molecules are a useful candidate since they represent the smallest entity that retains chemical (ie. physical) properties.  But molecules have parts - atoms.  And atoms have parts - neutrons, protons, and electrons.  And protons have parts - quarks and gluons.  Do quarks or gluons have parts?   We don't know, but it is in principle possible.

Hence the eliminativist view is not going to be of any help in understanding the essay's title quote.  The eliminativist is going to argue that neither the statue nor the clay constitute an object at all.  But it seem reasonably clear that the eliminativist is not talking the same language as the rest of us, so the eliminativist argument is of dubious assistance.

Next is the Deflationist view.  A number of philosophers have suggested that the advocates of the various views of the statue and clay puzzle actually agree on all the underlying facts of the scenario, and that their dispute is merely verbal.  The deflationist would argue that each party to the dispute is using "locally specialized language" that, if clarified and paraphrased in terms that all parties would agree with, would evaporate the dispute.  The deflationist program is based on the premise that the Constitutionist argument provided above, can be rephrased into language that would be accepted by (say) an Eliminativist.  But this translation program would involve some very complex linguistic manipulations, and it is not at all obvious that either party to the dispute would accept the rephrasing.  Since examples of this work have yet to be accomplished, it is quite debateable whether it could be completed, even in principle.

In any event, even if true, the Deflationist's view of the issues presented by the Statue and Clay scenario would contribute nothing to our understanding of the essay's title quote.  The deflationist is arguing that the language used in the quote is not necessarily English, without offering a suitable English translation.

Finally, let's consider the Relative Identity view.  The Constitutionist argument presented above to justify the conclusion that there are two objects that exist at the same place and time, is based on Leibniz' Law (premise 3).  Leibniz' Law, also known as the principle of the Identity of Indiscernibles, is a principle of analytic ontology first explicitly formulated by Wilhelm Gottfried Leibniz in his Discourse on Metaphysics in 1686(13).  It states that no two distinct things exactly resemble each other.  This is typically understood to mean that any two objects that have exactly the same properties are actually the same object.  The Constitutionist uses this principle to argue that since Lump and Statue do in fact have different properties, they cannot be the same object.

However, a Relative Identity theorist will argue that Leibniz' Law in incomplete.  The relative identity theory maintains that there is no such relation as absolute identity - there are only relations of relative identity.  One cannot properly assert that "A is the same as B".  One must specify (overtly, or by context) a sortal - "A is the same K as B".  Leibniz' Law is thus seen as incomplete because it does not include a sortal.  The "corrected" version of Leibniz' Law is -
                                              For any x and y, if (x is the same K as y) and
                                                                      (x and y have all the same properties),
                                                                      then x is identical to y.

From the perspective of this theory, how we choose to describe the thing on the pedestal will determine whether it is the same from Monday through Friday.  If we choose to regard it as a lump of clay, then we can say that Lump exists throughout the week.  If we choose to regard it as a statue then we can say that Statue exists on Wednesday.  This is not to say that both Lump and Statue exist on the pedestal on Wednesday.  Because a sortal must be provided.  Lump exists as a lump of clay on Wednesday.  And Statue exists as a statue on Wednesday.

The advantages of the relativity thesis is that it nicely syncs with our common sense view of things.  Whatever it is that we wish to regard, what we call it, how we identify it, will depend on how we are thinking about it - the sortal we choose to apply.  It also means that how we view an object can change according to the context of our discussion, and our changing cognitive interests.  The Relative Identity theory would thus argue, with most of the other theories outlined above, that the essay's title quote is false. 

The oft referenced criticism of the relative identity theory is that its denial of both absolute identity and the unmodified form of Leibniz' Law jeopardizes the foundation of Logic and Set Theory.  But this is not in fact the case.  It is relatively easy to provide the necessary sortals to validate both Logic and Set Theory.  As one possible example, the ontological assumption of set theory is that set membership ranges over all ontologically possible existents.  So all we need to do is adopt that premise formally to re-establish Set Theory within the Relative Identity theory.

In the final analysis, the essay title's quoted assertion is both clearly counter-intuitive, and open to considerable debate from a number of sides.  The Constitutionist, whose argument this quote is from, will maintain its truth.  All of the other protagonists to the debate will maintain either that the assertion is simply wrong (the Temporal Parts view, the Dominant Kind view, the Eliminativist view, and the Relative Identity view) or employing "locally specialized language" so that it does not mean what it appears to mean (the Deflationist view).

Because I maintain a Conceptualist view of particulars and universals, I am drawn strongly to the Relative Identity view of the statement.  I would therefore maintain that the title quote is flatly wrong.  A statue and the lump of clay of which it is made are not two different objects.  There exists at one place and time only one object, that can none-the-less be regarded under any number of meaningful sortals.  As I mentioned at the beginning - "One man's work of art is another man's lump of clay".  It all depends on your point of view.  But as long as one is speaking English, there remains only one object being viewed.


Notes & References

(1)   Wiggins, D., Identity and Spatio-Temporal Continuity, Blackwell Publishing, Oxford England. 1967,

(2)   Wasserman, R., "The Constitution Question," NoÃ�'Â�s, Vol 38, 2004. Pg: 693-710.

(3)   Lewis, D., "Survival and Identity," in A. Rorty (ed.), The Identities of Persons, University of >California Press, Berkeley, 1976, Pgs 17-40.

(4)   Burke, M., "Copper Statues and Pieces of Copper: A Challenge to the Standard Account," Analysis, Vol 52, 1992. Pgs: 12-17.

(5)   Unger, P., "There are no Ordinary Things," Synthese, Vol 41, 1979. Pgs: 117-154.

(6)   van Inwagen, P., Material Beings, Cornell University Press, Ithaca, New York, 1990.

(7)   Chisholm, Roderick M., "Parts as Essential to their Wholes," Review of Metaphysics, Vol 26, 1973. Pgs: 581-603.

                      Person and Object, Allen and Unwin, London, England, 1976.

(8)   Carnap, R., "Empiricism, Semantics, Ontology," Revue Internationale de Philosophie, Vol 4, 1950. Pgs: 20-40.

(9)   Putnam, H., "Truth and Convention: On Davidson's Refutation of Conceptual Relativism," Dialectica, Vol 41, 1987. Pgs: 69-77

                      "The Question of Realism," in J. Conant (ed.), Words and Life, Harvard University Press, Cambridge, MA, 1994. Pgs: 295-312.

                      Ethics Without Ontology, >Harvard University Press, Cambridge, MA, 2004.

(10)   Geach, P., Reference and Generality, Cornell University Press, Ithaca, New York, 1962.

                      "Identity," Review of Metaphysics, Vol 21, 1967. Pgs: 3-12.

(11)   Wikipedia contributors, "Linguistic relativity and the color naming debate", Wikipedia, The Free Encyclopedia, 20 November 2010, URL=<http://en.wikipedia.org/w/index.php?title=Linguistic_relativity_and_the_color_naming_debate&oldid=397857105> [accessed 8 January 2011]

(12)   Burke, M., "Preserving the Principle of One Object to a Place: A Novel Account of the Relations among Objects, Sorts, Sortals and Persistence Conditions," Philosophy and Phenomenological Research, Vol 54, 1994. Pg: 607.

(13)   Forrest, Peter, "The Identity of Indiscernibles", The Stanford Encyclopedia of Philosophy(Fall 2010 Edition), Edward N. Zalta (ed.), URL=<http://plato.stanford.edu/archives/fall2010/entries/identity-indiscernible/>.


Wasserman, Ryan, "Material Constitution", The Stanford Encyclopedia of Philosophy(Spring 2009 Edition), Edward N. Zalta (ed.), URL=<http://plato.stanford.edu/archives/spr2009/entries/material-constitution/>.

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