Brendan McGrath
Is a statue the very same object as the statue-shaped hunk of stone located in the
same place?
A hunk of stone, going by the name of Stone, falls off a mountain, slides into a nearby
village, and is picked up by a budding sculptor. The sculptor nests in his house for days,
the neighbours hearing only the sounds of tools scraping. Finally, Stone is wheeled,
under a tarp, into the village centre. But when it is unveiled, the villagers are shocked to
see that not only has Stone changed shape, but that there is a whole new object on the
pedestal: a Statue.1 Naturally Statue was not present inside of Stone the whole time,
and once Stone crumbles into a different shape, it will persist while Statue ceases to
exist. Prodded as to whether the two have different life-spans, distinct histories,
diverging futures, and contrasting survival conditions, the villagers affirm that yes they
had. All the same, the villagers, when asked, estimate the number of objects standing
on the pedestal to be “one”. A singular issue emerges: whether we are justified in
saying that the material which makes something up is the very same thing as the thing
itself.
I will argue that although Statue and Stone appear to have some unshared properties in the broadest sense of the word ‘properties’ - these are such that their being unshared
does not constitute a violation of the identity relation which ‘being the very same object’
denotes. I will initially use Leibniz’s Law as a criterion of identity, but will show that
where the Statue and Stone seem to violate this Law, our relation of ‘sameness’ should
not be affected. This sameness will be put forward firstly with a positive argument, and
then by the consideration of potential objections to that argument. While I cannot hope
to conclusively defend this argument, I will at least attempt to show that many of the
objections put forth against it are unsatisfactory.
The form of Leibniz’s Law I will use as a starting point is the Indiscernibility of
Identicals.2 By this principle, if two things are identical, then each has all and only the
properties held by the other.3 It should be noted that, with this formulation, having the
1
The names Goliath and Lumpl, or Statue and Clay, are often used for similar problems
Using this to avoid the more controversial Identity of Indiscernibles
3
Inan, Ilhan, A Defense of the Indiscernibility of Identicals, Revue Roumaine de Philosophie, p.61-72,
Vol. 48, 2004
2
Brendan McGrath
same properties is necessary for identity, but not sufficient. It could be, theoretically,
that two things have identical properties and are distinct.4 However, whether this case
could manifest itself in reality is questionable, and in our case extremely doubtful. The
theoretical insufficiency of our principle, therefore, should have little bearing on how we
view the case of Statue and Stone. If the two have different properties, they cannot be
the very same, and if they have the same properties, we can almost unproblematically
consider them the very same.
Tentative criterion of identity in hand, we can assess whether Statue and Stone meet
this criterion. What follows attempts to demonstrate that the two meet this criterion
insofar as they share all properties. It seems true that all properties held by an object at
a particular time are either physical or supervenient on physical properties held by that
object at that time.5 Because Statue and Stone are, by definition, identical in physical
properties, they must be identical in all properties, and thus the very same object. Some
explanation is in order. If some set of properties is supervenient on a set of physical
properties, this means only that the former set must be grounded in physical properties,
and cannot change without a change in the physical.6 In less exact terms, these
properties arise out of physical properties. Our Statue could not change colour without a
difference in its physical composition, could not become smoother, sharper, more
beautiful without being physically altered.
The key premise here is the first: all properties are either physical or supervenient on
the physical. This may seem overly broad but has the backing of common sense: if
some properties did not ultimately consist in the physical, it is not clear in what they
would consist. But the premise as stated is open to easy refutation. The property of
being in a gallery does not arise solely from the physical properties of the statue, rather
from its relation to objects other than itself. This is plainly a property of the statue, and
not supervenient on its physical properties, thus giving a conclusive counterexample to
This is simply to say that one cannot infer ‘If P then Q’ from ‘If not P then not Q’
Paul, L.A, The Puzzles of Material Constitution, Blackwell Publishing Ltd., 2010
6
Orilia, Francesco and Swoyer, Chris, "Properties", The Stanford Encyclopedia of Philosophy (Spring
2016 Edition), Edward N. Zalta (ed.), URL =
<http://plato.stanford.edu/archives/spr2016/entries/properties/>.Accessed 1 June 2016
4
5
Brendan McGrath
the supervenience premise in its broadest form, and showing the above argument to be
unsound.
Yet this need not be a problem. The supervenience premise can be reformulated as
follows: all properties which must be shared in order to satisfy our criterion of identity
are either physical or supervenient on physical properties. At this stage you might retort
‘our criterion of identity is that two things share all properties; therefore this
reformulation refers to nothing less than all properties which must be shared in order
that all properties are shared’. Quite true: seen in this way, the reformulation is
synonymous with the original formulation and so is subject to the same refutation. But
this only indicates that our criterion requires clarification. Leibniz’s Law does not
concern itself with, or at least is not fit to concern itself with, every type of thing which
may be called ‘a property’. This is illustrated by the Masked Man fallacy: I know who my
father is; I do not know who the masked man in front of me is; therefore the masked
man is not my father. Alternatively:
1. My father has the property of being known by me
2. The masked man does not have the property of being known by me
3. If two things do not have the same properties, they are not identical (Leibniz’s
Law)
C. The masked man is not my father
Clearly there is something wrong: it could be that the masked man is my disguised
father. The argument must be unsound. The best explanation is that the set of
‘properties’ denoted by premise 3 is too broad, that some restriction must be put on the
scope of Leibniz’s Law. Otherwise, as seen above, it could not function as a valid
criterion of identity.
It remains, then, to determine which properties are not relevant to our criterion of
identity. An exhaustive list of all potential properties which need not supervene on the
physical would be unachievable and, thankfully, unnecessary for our purposes. All that
must be done is to identify which so-called properties are not shared by Stone and
Statue, and evaluate their significance on an ad hoc basis. If a convincing candidate
Brendan McGrath
can be found, our criterion of identity must include it and thus we would find that Statue
and Stone are not the very same. Three candidates will be proposed: essential
properties, tensed properties, and a less easily categorised property.
The first potential type of property has received much attention in the literature: the
essential property. Statue has the property of being essentially shaped in a certain way
(let’s say like a penguin), whereas Stone has the property of being accidentally penguinshaped. Where Statue would cease to be Statue if it changed shape7, Stone’s shape is
incidental to its continued existence. Stone could have been a penguin, or could have
been a dog, but Statue could only ever have been a penguin. The essential property is
thus a modal property, one characterised by necessity and conditionality. This modality
is clearly not supervenient on physical properties, and is not shared by Statue and
Stone. Is it necessary for our criterion of identity?
I contest, with Gibbard, that such modal properties are not possessed by an object
independently of how that object is described, or designated.8 Statue and Stone are
made of the same collection of atoms in the same arrangement; were they not
designated as Statue and Stone, neither would hold essential properties of any sort, as
they would not have the concepts of Statue and Stone to conform to. It seems
reasonable that a property must be held independently of designation in order to qualify
for our criterion of identity, therefore a difference in essential properties does not seem
to represent a genuine distinction between Statue and Stone.
However, Baker has attempted to provide counterexamples to the premise that modal
properties are dependent on designation.9 She points out that modal expressions
include not only ‘has the property of being essentially x’, but also conditional and
counterfactual expressions. The statements “that bullet could have killed you” and “Alice
can swim the English Channel”, she suggests, describe genuine properties of Alice and
the bullet which apply independently of the way we describe them. She further claims
7
It may continue to be a statue if it is not changed too radically, but it would no longer be Statue as we
have defined it
8
Gibbard, Allan, Contingent Identity, Journal of Philosophical Logic, p.187-221, Vol. 2, 1975
9
Baker, Lynne Rudder, Why Constitution is not Identity, The Journal of Philosophy, p599-621, Vol. 94,
No.12, 1997
Brendan McGrath
that scientific truths are often modal, as with “Mars could have been a site where
multicellular life developed”. To claim that modal expressions are only true or false
depending on how things are designated, she argues, is to claim that truth in science
can depend on how things are designated- an unacceptable conclusion.
I see this issue as arising from linguistic confusion. To say “Alice can swim the English
Channel” is really to say “Alice is in a physical (mental, spiritual, etc.) condition such that
she could swim the English Channel”. The sentence seems to have two parts, the
former describing her physical properties, and the latter an indication by the speaker
that these properties are sufficient to swim the English Channel. The confusion arises,
then, because the first segment ascribes genuine physical properties and the second
ascribes a modal property. Although the sentence is expressed in modal form, it is in
fact the non-modal subtext of the sentence which leads us to believe that “Alice can
swim the English Channel” refers to an Alice-intrinsic property. The modal aspect can
still be seen as only existing through designation. If this reading of the sentence is
convincing, we need not accept Baker’s as a decisive counterexample. Because, in
speech, the modal properties above cannot truly be ascribed without ascribing physical
properties as well, there is no need to suppose that it is the modal aspect which sparks
our intuition that “Alice can swim” is a designation-independent property of Alice.
This same reading should show that all of Baker’s supposed counterexamples can be
ignored. “Mars could have sustained life” cannot be asserted without implicitly asserting
certain life-sustaining properties of Mars - temperature, soil, atmosphere, and so on.
Similarly, it is difficult to imagine any ostensibly genuine modal property which does not
depend on properties physical or supervenient on the physical.10 Of course, the modal
properties of Statue and Stone - namely their essential properties - cannot convincingly
be seen as asserting non-modal properties, but this is irrelevant as their essential
properties are not the ones which threatened Gibbard’s argument. On this grounding,
we can consider Gibbard’s argument sound and see essential properties as not held by
objects independently of how they are designated. The distinct essential properties of
Statue and Stone must not, then, establish them as distinct objects.
10
Baker provides further examples, all of which implicitly assert non-modal properties
Brendan McGrath
But another property presents itself as distinct: the tensed property.11 Whereas Stone
has the ‘property’ having been part of a mountain yesterday, Statue has no such
property (it only just came into existence). The property is not supervenient on the
current physical state of Stone, rather on its past state. Should we worry about this?
There seems reason to: an object’s history does in some cases inform the properties we
ascribe to it. Hamlet is a tragic hero12 not because of his physical properties at a given
time, but because of his having been incited to revenge and going on to die completing
his quest. His tragic hero-ness must come from properties across time, not from his
state at any one time. Because he is a tragic hero throughout, it must be that properties
to do with past and future apply at a given time. As Stone fell from his mountainside
home and was manipulated into the shape of a penguin, it is a tragic stone, where
Statue is no such thing.
However, it does not seem that being a tragic hero is something that can apply at any
particular time. The problem dissolves if we see Hamlet as a hero only when viewed
from a broader lens. This is not outlandish. Were Hamlet asked if he was a tragic hero,
he would look concerned and say “no”. The present moment does not seem an
appropriate time to ascribe such properties, giving little reason to resort to tensed
properties to explain them. The implications of this are that Statue and Stone should be
one and the same for every moment that Stone is appropriately shaped, but that viewed
from a broader time, they are distinct. This last point may sound odd, but only because
of the language we have used. Phrased as ‘Stone falls from a mountain, is sculpted,
and can now also be described as Statue’, their absolute distinctness does not seem so
troubling.
Finally, we must consider a nebulous sort of property. It makes sense to say of Statue
that it is lovingly crafted or widely admired, but to say the same of a lump of stone would
sound odd. Does this point to genuinely disparate properties? I think not. To say “the
evening star rises in the morning” sounds odd, while to say “the morning star rises in the
11
Orilia, Francesco and Swoyer, Chris, "Properties", The Stanford Encyclopedia of Philosophy (Spring
2016 Edition), Edward N. Zalta (ed.), URL =
<http://plato.stanford.edu/archives/spr2016/entries/properties/>. Accessed 1 June 2016
12
The example is fictional but the same principles should apply as to real stones and statues
Brendan McGrath
morning” sounds perfectly normal, even though both names refer to Venus. This
illustration reveals the problem to be merely linguistic. It is not that the different senses
used to refer to the one object have different properties, only that some properties are
relevant when certain senses, and not others, are used. It may sound strange, but “the
lump of granite is famous worldwide” is just as true as “the statue is famous worldwide”.
We need not suppose that Statue and Stone have distinct properties just because of the
different ways used to describe them.
I have come, then, to the unsurprising conclusion that a statue and the lump of stone in
the same place are indeed the very same object being referred to differently. But this
last point helps explain why the question may have been raised in the first place. The
tension between ‘Statue’ and ‘Stone’ is, in some ways, the tension between our
manifest image of the world and our scientific image: the way we view the world in our
everyday lives, and the way science encourages us to view the world. 13 Through a
metaphysical discussion of the grounding of properties, our working criterion of identity
was refined to establish that, at any given time, Statue and Stone are one and the
same. But even if they share all relevant properties, the wide difference in the way they
can be viewed suggests that our experiences with the same object can differ wildly.
They may be the same, but I experience them differently. I might be eager to demolish
this object if I view it as a lump of stone, but if I recognise it as the product of hours of
labour, a thing of monetary value, and a source of profound beauty, I might hesitate.
Word count excluding title, footnotes and bibliography: 2498
Bibliography
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599-621, Vol. 94, No.12, 1997
Gibbard, Allan, Contingent Identity, Journal of Philosophical Logic, pp.187-221, Vol. 2,
1975
13
Sellars, Wilfrid, Philosophy and the scientific image of man, Science, perception and reality 2 pp. 3578, 1963
Brendan McGrath
Inan, Ilhan, A Defense of the Indiscernibility of Identicals, Revue Roumaine de
Philosophie, pp.61-72, Vol. 48, 2004
Moyer, Mark, Statues and Lumps: A Strange Coincidence?, Synthese, Vol. 148, Issue
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<http://plato.stanford.edu/archives/spr2016/entries/properties/>.Accessed 1 June 2016
Paul, L.A, The Puzzles of Material Constitution, Blackwell Publishing Ltd., 2010
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reality 2 pp. 35-78, 1963
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