=Paper=
{{Paper
|id=Vol-2969/paper39-FOUST
|storemode=property
|title=Copies and Dependence
|pdfUrl=https://ceur-ws.org/Vol-2969/paper39-FOUST.pdf
|volume=Vol-2969
|authors=Massimiliano Carrara,Vittorio Morato
|dblpUrl=https://dblp.org/rec/conf/jowo/CarraraM21
}}
==Copies and Dependence==
https://ceur-ws.org/Vol-2969/paper39-FOUST.pdf
Copies and Dependence
Massimiliano Carrara1 , Vittorio Morato1
1
Department of Philosophy, Sociology, Education and Applied Psychology, University of Padua, P.zza Capitaniato 3,
Padua, Italy
Abstract
It seems natural to define the relation of "being a copy of" by means of the notion of similarity. While
similarity is essential in the characterisation of the copying relation, a simple similarity account of such
a relation does not seem to work. Counterexamples are easy to find. In this paper, we defend the idea
that the copying relation should also be characterised by means of a dependence relation. It is not
easy, however, to understand what kind of dependence relation is the right one. We will show that
ontological and counterfactual forms of dependence are modally too strong and we, provisionally, try
to use the modally weaker notion of historical dependence. Ontological, counterfactual and historical
dependence share the common feature of being rigid notions of dependence. In the final section of the
paper, we briefly discuss the idea that there might be non-rigid kinds of copying that therefore need to
be characterised by means of non-rigid kinds of dependence.
Keywords
copies, similarity, ontological dependence, counterfactual dependence, historical dependence, artifacts
1. Introduction
According to N. Goodman [1, p. 111], the relation of “being a copy of”, i.e. the relation between
two distinct objects such as the second is a “reproduction” of the first, is “unexpectedly complex”.
On a first try, one could in effect be tempted to simply define the copying relation by means
of the relation of similarity, treating “being a copy of” as a case of perfect similarity:
(C0) 𝑥 is a copy of 𝑦 iff 𝑥 is perfectly similar to 𝑦.1
A simple similarity approach to the copying relation, however, is problematic. The problems
are at least two.
FOUST 2021: 5th Workshop on Foundational Ontology, held at JOWO 2021: Episode VII The Bolzano Summer of
Knowledge, September 11–18, 2021, Bolzano, Italy
" massimiliano.carrara@unipd.it (M. Carrara); vittorio.morato@unipd.it (V. Morato)
0000-0002-3509-1585 (M. Carrara); 0000-0001-6332-0907 (V. Morato)
© 2021 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
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1
It is admittedly difficult to properly understand how perfect similarity should be characterised. For the aim of
this paper, we rest content with an intuitive sense of the notion, according to which two objects are perfectly similar
in case they share most, if not all, their quantitative/primary (size, matter, etc.) or qualitative/secondary (colour,
smell, etc.)) properties. From this rough characterisation, it follows, for example, that two objects of different size
cannot be copies of one another, even if they share all other properties. A referee suggests that one could model
the relation of copy in a relativised way: an object is not a copy of another in an absolute way (by being perfectly
similar to it), but only with respect to some class of "features". We prefer the absolute notion of copy; a relativised
notion would make the copying relation a sort of (imperfect) similarity relation, with the result of making too many
objects "copies" of one another.
The first one is that of accidental copies: it could happen that two completely ontologically
and historically independent objects end up being perfectly similar, without this implying that
the first is a copy of the second. For example: imagine two perfectly similar diamonds discovered
in two completely different and historically unrelated places. The two diamonds satisfy the
perfect similarity condition, but it would be strange, in such a situation, to claim that one is the
copy of the other. Similar cases could be imagined for artifactual objects too: there might be
two perfectly similar nails produced by different and unrelated firms, on the basis of different
and unrelated lines of production. The two would be perfectly similar, but none of the them
would be a copy of the other. In both cases, one might ask: which one of the twos is the copy of
the other? Which one is the original?
The second problem is that of the common original: assume that, from an original object, two
copies are made. The two copies are, by definition, perfectly similar to the original and thus
perfectly similar between themselves. But it would be strange to say that the two copies are
copies of one another. Again one might ask: which one is the copy? Which one is the original?
This problem reveals that the relation of perfect similarity and that of copying have different
formal properties. (Perfect) similarity is euclidean: if 𝑥 and 𝑦 are in the relation 𝑅 of perfect
similarity to 𝑧, then 𝑥 and 𝑦 are in the 𝑅 relation between themselves; the relation of copying
is instead not euclidean as it is revealed by the problem of the common original; two copies of
the same original are not between themselves in the relation of copying.
Notice that the problem of the common original is structurally similar and, in effect, named
after a similar problem arising for simple regularity accounts of causation; according to these
accounts (famously defended by D. Hume), 𝑐 causes 𝑒 if and only if 𝑒 regularly follows 𝑐. There
might be a case, however, where one cause 𝑐 might regularly produce two temporally distanced
effects: 𝑒1 at 𝑡1 and 𝑒2 at 𝑡2 ; in such a situation, 𝑒2 follows regularly 𝑒1 (assuming, of course,
that 𝑐 happens), but from this it does not follow that 𝑒1 would be the cause of 𝑒2 . As we will see,
there will be some connections between the relation of copy and that of causation and some
lessons from the causation debate could be applied to the case of the copying relation.
A simple way to fix the similarity approach might be that of adding intentionality to the
recipe. One can enrich (C0) in this way:
(C1) 𝑥 is a copy of 𝑦 iff (i) 𝑥 is perfectly similar to 𝑦 and (ii) 𝑥 is a product of intentional actions.
(C1) has the effect of limiting the domain of the copying relation to the products of (human)
intentionality. There are no natural copies, according to (C1). But limiting the relation of
copying might be problematic: after all, there are well-understood cases of copying in the
natural realm (e.g., DNA replication) and one might want one’s own theory of copying be able
to model also these natural cases.
Not only an appeal to intentionality is unduly restricting, but a simple appeal to intentionality
does not solve our problems: as we have seen for the case of nails, it is not difficult to imagine a
scenario where two perfectly similar objects are the product of two separate and independent
intentional actions and nonetheless are not in the relation of copy with one another.
Furthermore, (C1) (and thus an appeal to intentionality) is not able to solve the problem of
the common original: two copies of a common original are in fact the product of a single set of
intentional actions, they are perfectly similar to the original and thus between themselves, but,
again, one is not the copy of the other. Limiting the domain to the realm of intentional objects
does nothing to avoid the euclidicity of the similarity relation, so the countexamples remain
untouched by the new definition.
A way to solve the problem of the common original is by making explicit that the copying
relation gives rise to a form of dependence between a copy and its original:
(C2) 𝑥 is a copy of 𝑦 iff (i) 𝑦 is perfectly similar to 𝑥, (ii) 𝑦 depends on 𝑥.
According to (C2), an object which is a copy is a copy of something else on which, somehow,
depends. By means of (C2), we could solve the problem of the common original. Two copies of
a common original does not typically depend on each other, so, though perfectly similar, they
cannot be copies of one another. The appeal to dependence solves in a natural way also the
problem of accidental copies: two accidentally similar objects are not in a relation of copying,
because they typically do not depend on each other.
While dependence seems thus apparently essential to characterise the relation of copying, its
nature in (C2) should be better characterized, on pain of vagueness.
In current philosophical debate, the notion of dependence is hotly debated and discussed and
there are various kinds of dependence relations available on the market: from various forms
of ontological, conceptual, historic, counterfactual or causal dependence [2] to other kinds
of dependence relations such as grounding or supervenience[2]. What is the right notion of
dependence for the copying relation?
Aim of our short paper is, firstly, to show that it is not easy to select the right flavour of
dependence needed to define the copying relation. Secondly, we hope to made explicit some
constraints on an adequate characterization of the copying relation in terms of dependence.
2. Forms of Dependence and Copies
Let us consider, first, ontological or existential dependence. In general, an object 𝑥 is said to be
ontologically dependent on another object 𝑦 in case, necessarily, 𝑥 exists only if 𝑦 exists and it is
not the case that, necessarily, 𝑦 exists only if 𝑥 exists (Lowe [3], Correia [4]). A typical example
of ontological dependence is that between a set and its members: necessarily, a set exists only if
its members exist and it is the set that is ontological dependent on its members, not vice versa.
Applying this definition to the relation of copying we will obtain the following:
(C3) 𝑥 is a copy of 𝑦 iff (i) 𝑦 is perfectly similar to 𝑥, (ii) necessarily, 𝑥 cannot exist unless some
original object 𝑦 does and it is not the case that, necessarily, the original 𝑦 exists only if 𝑥
does.
The problem with (C3) is that two objects might be in a relation of copying without any
of them being in a relation of existential dependence with the other. In particular, the copied
object, once it is created, is an ontological independent object from the original. The original
could go out of existence, but the copied object would still continue to exist. The existence of a
copying relation between 𝑥 and 𝑦 does not force the necessary co-existence between 𝑥 and 𝑦.
One could copy a painting and then destroying the original: the copy would still be the copy of
the original painting and it can exist independently from it; thus, it would not be ontological
dependent on it. Ontological dependence seems to be too strong. Another form of dependence
is needed.
One might try with a weaker form of dependence. Let us consider, for example, counterfactual
dependence. An object 𝑥 counterfactually depends on 𝑦 just in case the following counterfactual
conditional is true: if 𝑦 had not existed, 𝑥 would not have existed. Counterfactual dependence is
often used to define causal forms of dependence. For Lewis, for example, 𝑐 is a cause of 𝑒 if and
only if there is a causal chain between 𝑐 and 𝑒 where a causal chain is a series of counterfactual
dependence relations connecting 𝑐 and 𝑒 (see Lewis [5]).
Applying the counterfactual dependence to the definition of copying we will obtain the
following:
(C4) 𝑥 is a copy of 𝑦 iff (i) 𝑦 is perfectly similar to 𝑥, (ii) had 𝑦 not existed, 𝑥 would not have
existed.
According to this definition a certain sword is a copy of, say, Alexander the Great original
sword in case, not only it is perfectly similar to the original, but also it is counterfactually
dependent on the original sword: had the original sword not existed, neither the copied sword
would have existed. This seems plausible, at least prima facie: a copied object would not have
existed, if the original object from which it is copied had not existed.
The advantage of counterfactual dependence over existential/ontological dependence lies in
that it does not require necessary co-existence to obtain. Of course, copy and original must exist
in the actual world, but then the only thing required is that, in all relevant worlds/possibilities,
the non-existence of the original brings with it the non-existence of the copy. All other cases
are admitted: there might worlds where the original ceases to exist, but the copy continues to
exist or even worlds where the original exists, but not the copy. The counterfactual approach to
copy basically captures the idea that a copy must be similar to the original and exists because
the original exists.
There is something to say about the restriction on "relevant" worlds whose mention is needed
to understand the relation of counterfactual dependence: in the standard, Lewis’s semantics
([6]) for counterfactuals (and thus in the analysis of counterfactual dependence used in (C4))
the restriction on relevant worlds has to be intended as a restriction over most similar worlds
to the actual world.
In (C4) there is thus a double commitment to similarity: there is the "perfect similarity"
mentioned in clause (i), which is a relation of similarity between objects, but there is another
kind of similarity, overall similarity among possible worlds, needed to make sense of the relation
of counterfactual dependence.
There are at least two possible problems for a counterfactual understanding of the copying
relation. The first is that the relation of counterfactual dependence tends to overgeneralise.
There might be two perfectly similar objects in a counterfactual dependence relation between
each other, but not because they are in a copying relation between each other. Consider, for
example, a mathematician, call him "Jack", who proves a certain theorem only because he comes
to know that another mathematician, call him "Jones", has proved it. Assume that Jones’s proof
is not yet published and nobody has ever seen the actual proof. The existence of Jack’s proof is
thus counterfactually dependent on the existence of Jones’s proof. The former would not have
existed, had the latter not existed. But as it happens and unbeknownst to both mathematicians,
Jack’s proof is perfectly similar (in an intuitive sense in which two proofs could be perfectly
similar) to Jones’s proof. In such a case, the similarity would be a matter of mere coincidence.
The two proofs are thus in a relation of perfect similarity and in a relation of counterfactual
dependence, yet we would not say that Jack has copied Jones’s proof and/or that Jack’s proof is
a copy of Jones’s proof.2
The other problem is the idea on which such an understanding of the copying relation is
based, namely that the copied object exists because the original exists. This might suggests the
idea that it is the identity of the copied object that depends on that of the original object, that
the copied object could not exist unless they are the copy of the original object. Being a copy
of does not seem to be an essential relation. From the fact that 𝑥 is a copy of 𝑦, it does not
follow that, in every world where 𝑥 exists, 𝑥 is a copy of 𝑦. It seems plausible to assume that the
sword that in this world is the copy of Alexander the Great original sword is not necessarily a
copy of that sword in every other world where it exists: there might be (relevant) worlds where
the sword is a copy of other swords (perfectly similar, but not identical to Alexander the Great
sword) or worlds where such a sword is not a copy of any sword.3
The existence of a relation of copying in this world between two objects does not seem to
imply any modal consequence for the objects involved, or at least not the modal consequences
required by counterfactual dependence.
Something even weaker than counterfactual dependence is thus needed. The kind of depen-
dence needed should make two entities dependent on each other (modulo perfect similarity),
but without imposing too much "modal force" on this kind of dependence. Historical dependence
might be of some help. According to A. Thomasson [7, p. 31]):
Historical dependence is at hand in cases in which one entity requires another in
order to come into existence initially, although it may be able to exist independently
of that entity once it has been created. This variety is weaker than constant
[ontological] dependence, because it does not require that the supporting entity be
present at all times that the dependent entity is.
From this rough characterisation, it emerges that historical dependence is a mundane kind of
dependence: two entities are in a relation of historical dependence in case there is an existential
2
We would like to warmly thank a referee for suggesting a counterexample to the counterfactual conception of
copying along the same lines. In our example, we have applied the notion of perfect similarity to abstract entities
such as proofs. Admittedly, it might be problematic to specify exactly what it means for two abstract entities to be
perfectly similar, but we think that, as far as our example is concerned and in the special case of proofs, the notion
is quite comprehensible.
3
A referee suggests that a sword, existing in 𝑤𝑖 which is not designed to be a copy of Alexander the Great’s
sword, could not be the same sword existing in the actual word 𝑤* which is instead designed to be a copy of
Alexander the Great’s sword. We do not share this intuition which is based, we think, on the wrong assumption that
the property of being designed to be the copy of Alexander the Great’s sword is an essential property of a certain sword.
In general, we think that, while some intentional properties might be fundamental for the identity of (artifactual)
objects, intentional properties like these should not be taken to determine their identity. If the sword in 𝑤𝑖 and the
sword in 𝑤* are made of the same material, have the same constituent parts and are designed to be swords, why
should not they be taken to be the same object?
dependence between them in the actual world. This kind of historical, existential dependence
does not necessarily have any modal consequences: in particular, it does not require that the two
entities necessarily co-exist, nor that they co-exist in the class of most relevant worlds. Notice,
however, that historical dependence is not incompatible with such kinds of modal-existential
forms of dependence. If 𝑥 is ontologically or counterfactually dependent on 𝑦, then 𝑥 also
historically depends on 𝑦, but the converse does not necessarily obtain: there might be totally
contingent relations of historical dependence that do not give rise to any kind of ontological or
counterfactual forms of dependence. The fact that an object has been contingently produced
(in case of artifacts) or has been generated (in case of natural objects) as a result of a copying
procedure in this world, does not force the conclusion that such an object could not have come
into existence or produced if not as a result of such a procedure.
The copying relation could thus be understood in terms of historical dependence by means
of the following definition:
(C5) 𝑥 is a copy of 𝑦 iff (i) 𝑦 is perfectly similar to 𝑥, (ii) 𝑥 historically depends on 𝑦.
3. The Problem of Copies without Originals
In all cases discussed so far, we have assumed that the copying relation should be treated as
a kind of object-to-object relation. A copied object is a copy of a specific original object. In
current terminology, this is expressed by saying that we have treated the copying relation as a
rigid relation. In general, a relation of dependence is rigid in case its relata are specific objects
(e.g., the relation between a non-empty sets and its members, the relation between a material
objects and its constituents parts).
However, the situation might be more complicated than this and, if it is, this could put some
pressure on the definitions we have given. The copying relation might be a non-rigid relation
or at least, not necessarily rigid (a dependence relation is not necessarily rigid in case there are
possible cases where the relata of such a relation are not objects).
In particular, there seems to be plausible cases of copied objects that are not copies of
some specific objects. Consider those particular instances of copies which are counterfeits. A
counterfeit is typically a copy of an original, specific, object, falsely presented as an original
object, but there seems to be counterfeits that are copies, but not copies of an object. Consider
the notorious case of the forged Vermeers made by Van Meegeren. As laid out in most art
history textbooks, Han van Meegeren was a Dutch painter who decided to prove his talent by
forging paintings of some of the most famous artists, including Johannes Vermeer. He replicated
so well the style and colours of the artist that the best critics and experts of the time regarded
his paintings as genuine Vermeers. The forged Vermeers made by Van Meegeren, however,
were not copies of some specific original painting made by Veermer, even though they quite
clearly count as copies of Veermer.4
4
We surely understand – and in part share – the qualms of one of the referees about the forged Vermeer’s case:
one could, in effect, claims that the Vermeer case is not a case of a copied object, because the forged Vermeer is
not a copy of anything. Our intuition in this case is that, while the forged Vermeer is surely not a copy of some
object, it could still be considered, in some sense – to be further specified – a "copied object": a counterfeit is usually
considered a copied object. Our proposal is that the sense in which an object could be copied without being the
If such cases are accepted, all rigid definitions of the copying relation become problematic, or,
at least, not able to cover all cases in which we wish to apply such a relation. A solution might
be to use a non-rigid notion of dependence; in general, non-rigid dependence might be defined
as a relation between an object and a sortal: in general, 𝑥 non-rigidly depends on 𝐹 if and only
if 𝑥 depends on the existence of some object that is 𝐹 .
By means of non-rigid dependence we may define a corresponding notion of historical, non-
rigid dependence by means of which we could solve the Van Meegeren cases. A painting by Van
Meegeren is a copied object not because there exists some specific object of which it is a copy
and with which is in a relation of historical dependence, but because there exist some paintings
that instatiate a sortal like "paintings in the style of Veermer" that the copied object somehow
"imitate". The notion of "imitation of an object instatiating a sortal 𝐹 " should substitute, in such
non-rigid characterisation of the copying relation, the notion of perfect similarity.
4. Conclusions
In this paper, we have defended the view that the copying relation should be defined also by
means of a dependence relation and not simply by means of similarity. The problem, however,
is to understand what kind of dependence is the right one. We have emphasised the difficulties
of using ontological or counterfactual dependence. The problem with them is that they seem to
have too much modal force. We have then defended, at least provisionally, the idea that a notion
of historical dependence might do the work needed. Ontological, counterfactual and historical
dependence, at least in the way in which we have characterised them, share a common element:
they all are rigid kinds of dependence. If the copying relation is defined in terms of them, it
becomes thus a rigid relation as well. In the final section of the paper, we have discussed the
idea that there might be non-rigid kinds of copying relation, where an object is not a copy of
some specific object, but of objects instantiating some sortal property.
References
[1] N. Goodman, Languages of Art, 2nd ed., Hackett, Indianapolis, 1976.
[2] T. Tahko, E. Lowe, Ontological dependence, in: E. N. Zalta (Ed.), Stanford Ency-
clopedia of Philosophy, 2020. URL: https://plato.stanford.edu/archives/fall2020/entries/
dependence-ontological/>.
[3] E. Lowe, The possibility of metaphysics, Clarendon Press, Oxford, 1998.
[4] F. Correia, Ontological dependence, Philosophy Compass 3 (2008) 1013–1032.
[5] D. K. Lewis, Causation, Journal of Philosophy 70 (1973) 556–567. Reprinted with a postscript
in Lewis [8, Ch. 21, pp. 159–213].
[6] D. K. Lewis, Counterfactuals, Blackwell, Oxford, 1973.
[7] A. L. Thomasson, Fictions and Metaphysics, Cambridge University Press, Cambridge, 2007.
[8] D. K. Lewis, Philosophical Papers, volume II, Oxford University Press, Oxford, 1986.
copy of some specific object could be captured, at least partially, by means of a non-rigid notion of dependence and
a corresponding non-rigid notion of copying. This would reinforce the main point of this short paper, according to
which there are interesting relations between copying and dependence.