Max Kistler
The Necessity of Laws,
Quiddity and the Causal Criterion of Reality
in : A. Beckermann et C. Nimtz (eds.), Argument und Analyse – Sektionsvorträge,
Paderborn, Mentis (internet :
http://www.gap-im-netz.de/gap4Konf/Proceedings4/Proc.htm), 2002, p. 461-473.
I propose an argument for the thesis
that laws of nature are necessary in a metaphysical sense, on the basis of a
principle I propose to call the Causal Criterion of Reality (CCR). The CCR
says: for an entity to be real it is necessary and sufficient that it is
capable to make a difference to causal interactions. The crucial idea is that
the capacity to interact causally - or to contribute to determining causal
interactions - is not only the ultimate justification for the existence of an entity, but it also
provides a criterion for determining the nature
of that entity, i.e. its properties.
The alternative is to conceive of
laws of nature as contingent[1]:
they could be different from what they are like in the actual world, where that
possibility is understood to be metaphysical, not only epistemic. For the sake
of this paper, I shall accept Armstrong's (1983; 1997) thesis that laws of
nature are relations between universals. I also follow Armstrong in the view
that both the existence and the properties of particulars are metaphysically independent of the existence and
identity of other particulars[2].
However, what is controversial and what I shall challenge is his thesis that universals are like particulars in the
following respect: according to Armstrong, each universal is a logically
distinct entity whose existence and identity is independent of the existence
and identity of other universals. My aim in this paper is to show that the
identity of a universal is entirely determined by its lawful relations to other
universals. The crucial premise I use is the thesis that the CCR is a universal
criterion that applies both to particulars and universals. From the thesis that
the identity of a universal is exclusively determined by laws, it follows that
laws are necessary in the sense that they cannot differ without the universals
they link also being different. This creates a difficulty for those authors
who, as Armstrong, accept the CCR but nevertheless defend the view that laws
are contingent.
1. Naturalism and the CCR
According to a traditional
metaphysical principle, all and only those entities exist which make a causal
difference. Armstrong has called it the "Eleatic principle" by
reference to its formulation by the Eleatic Stranger in Plato's Sophist[3].
In Armstrong's words, "everything that exists makes a difference to the
causal powers of something" (Armstrong 1997, p. 41), and conversely, I
should add, everything that makes a difference to the causal powers of
something, exists[4]. This Causal
Criterion of Reality can serve as a justification of the postulation of the
existence of both particulars and universals. It can be justified by the claim
that it is a central part of scientific methodology. The philosophical position
of scientific realism consists in extending its validity to cover even
metaphysics[5].
First, the postulation of the
existence of particulars has a causal
background: Particulars are needed to make the existence of universals
compatible with naturalism - as I shall call the position characterised by the
acceptation of CCR - for universals cannot interact causally by themselves but
only through their instantiation in particulars. Conversely, just as there
cannot be causal interactions without particulars that interact, there cannot
either be particulars that do in principle not interact. Naturalism (by which I
mean the position which consists of accepting the CCR and its consequences)
forbids the postulation of particulars which are absolutely causally idle - the
probability of a neutrino interacting causally with anything may be extremely
low, but if it were zero, we wouldn't be justified in postulating the existence
of the neutrino in the first place.
Second, and most important for us,
the ultimate justification for the existence of a universal is that the best explanation of the fact that a set of
(elementary) particulars exhibits a specific pattern of causal interaction is
that those particulars instantiate a specific universal responsible for that
type of interaction. For each primitive type of interaction, there is a simple
universal. The dependence goes both ways: just as there is no type of
interaction without its universal, similarly there is no universal without its
specific type of interaction. The reason being that, in an analogous manner to
the case of particulars, it would contradict naturalism to postulate a
universal whose instantiation by a particular does not make any difference at
all to the causal interactions of that particular[6].
Two general remarks before we put
the CCR to work. The first concerns the epistemological status of the CCR: Is
it purely conceptual or is it rather empirical notwithstanding its generality?
As a generalization from a principle derived from the criteria which science
uses to justify the postulation of entities, it might seem that the CCR is not
entirely a priori, and that it would have to be abandoned in its full
generality if it turned out not to be respected in science. Let us conceive a
situation in which physics would postulate, say for considerations of symmetry,
a perfectly idle universal whose instantiation by a particular would not change
at all that particular's capacity to interact. There are two reactions to such
a situation, which seem to be more plausible than to conclude that it refutes
the overall validity of the CCR. First, one might conclude that the fact that a
scientific theory leads to the postulation of an idle universal pleads against
the theory rather than against the universal validity of the CCR. Second and
more importantly, even if the theory is accepted, one can interpret the idle property
as a "mere Cambridge", or merely relational, property, just as the
property of being a widow: The acquisition by Xanthippe of the relational
property of being a widow right at the moment of Socrates' death, leaves her
unchanged from a causal point of view. Being a widow is a merely relational
property, and not a real universal. I conclude that if the CCR is not purely a
priori, it seems to be a principle that is more central to our conceptual
scheme (and in particular to the part of the scheme used in science) than the
most general empirical principles[7].
The second remark concerns the
reference to capacities or dispositions in the above formulation of the CCR.
For particulars, I think it is plausible to suppose that all of them interact
causally at least twice: when they come into existence and when they disappear.
These causal interactions affect even a particular neutrino that does not at
all interact with anything between the events of its creation and its
annihilation. Still, our formulation of the CCR would allow for the possibility
that the universe has neither a beginning nor an end in time and that there
exist eternal particulars that never interact. (This is not actually the case
if the big bang theory is true). Their existence is nevertheless in agreement
with the CCR as long as their probability of interaction differs from zero. For
universals, the reference to capacities is more important. Think of a universal
which is instantiated by very few particulars and which bestows a very low
probability of interaction on these particulars. Would it be a legitimate
hypothesis that the universal exists even if, by accident, it does in fact
never influence any actual causal relations at all? It seems to me that the
answer should be yes, for such an hypothesis can be evaluated in accordance
with the CCR: To confirm it, one would have to try to increase the rate of
instantiation of the hypothetical universal and the frequency of the
interactions in which the probability of its manifestation is non-zero, up to
the point where there is sufficient reason either to accept or to reject the
hypothesis of the existence of that universal.
This reasoning shows that the
acceptation of the CCR gives us a fresh look on the traditional divide between
"Aristotelian" and "Platonistic" conceptions of universals.
The former is characterised by what Armstrong calls the "Principle of
Instantiation" (Armstrong 1983, p. 82), which says that every universal
must be instantiated at least once, whereas the latter allows the possibility
of universals that are never instantiated. Rather than taking a general stand
on that question, on a priori grounds, the CCR suggests the following position:
What is illegitimate is the postulation of a universal for which the
probability, once it is instantiated, that it influences causal interactions is
strictly zero. It is however legitimate to make the hypothesis of the existence
of a universal whose probability of contributing to causal interactions is
non-zero, but which happens not to have been instantiated, on the condition of
obeying the following general rule of scientific methodology: the hypothesis
must in principle be able to be confirmed or refuted, meaning that there must
be a way to increase the rate of instantiation of the hypothetical universal U
which would in turn lead to the manifestation of the non-zero probability of
its exercising an influence on interactions. In brief, it is reasonable to
postulate the existence of U if and only if both the probability that
instantiations of U make a causal difference to the instantiation of other
universals is non-zero and if there exist still other universals V such that
the probability that instantiations of V contribute to causally provoking
instantiations of U is also non-zero.
2. Quidditism and anti-quidditism
My main thesis is that the adoption
of the CCR as a general methodological principle is incompatible with the view
- held by Armstrong and others - that the laws of nature are contingent rather
than necessary.
The conception of laws as contingent
is of a piece with a conception of universals that assimilates them to a
special type of particulars (Armstrong calls them indeed "second-order
particulars"): as entities whose existence and identity is independent of
the existence and identity of other entities of the same type (i.e. particulars
or universals, respectively). True, it is part of the concept of a particular that it is independent in
this way of the existence and identity of other particulars. However, there is
a fundamental difference between particulars and universals as to the grounds
of their respective identity: in the case of particulars, there are scientific
grounds for thinking that their identity is not exhausted by their properties
(two particulars can differ numerically while sharing all properties[8])
whereas there are no such grounds in the case of universals. The identity of a
universal is entirely determined by
its properties[9].
Following Armstrong's (1989)
terminology, we shall formulate the question whether the identity of universals
is exclusively or only partially determined by their properties, by asking
whether these entities have, over and above their properties, an individual
essence - called "quiddity" in the case of universals - which is the
metaphysical ground for their individual identity[10].
Armstrong himself examines in detail only the question of the individual
essence of particulars and contents himself, for the parallel question
regarding universals, with saying that "quidditism for universals seems
very plausible. Each universal must surely have its own nature" (Armstrong
1989, p. 59).
According to a naturalist
metaphysics of properties (or universals), the role science attributes to a
given property, is the only source of determination of its existence and identity.
First, existence: The postulate that certain properties are real (universals)
is justified by its explanatory value: it allows saying very easily why
different particulars resemble each other, why two particulars can both be
similar and dissimilar, namely in different respects, and why similar
particulars behave in a similar way[11].
This conception of what makes a property a universal goes hand in hand with the
CCR. But, second, the crucial and less obvious point concerns not the
existence, but the identity of
universals: naturalism leads to the view that it is not only the question of whether a certain property is real that
is decided by the interactions it induces, but those interactions also decide
the question of what is the identity of the property. The CCR also provides a
criterion for determining the nature, i.e. the second-order properties of
universals.
This follows from the role of the
CCR as a truly universal metaphysical principle characterising naturalism. For
let us see what it means to ask for the properties of a universal: what are the
properties of the universal M of, i.e., having a mass of 30 kg? (Later on we
shall ask whether those properties exhaust the identity of the universal or
whether it has quiddity over and above them.) According to the CCR, the
universal M has all and only those properties that make a causal difference to
its instantiations. Now what causal difference makes an instantiation of M?
Here we rely on the thesis of the nomological theory of causation (NTC) according
to which all causal relations are determined by laws of nature[12].
According to the CCR, the properties of M are what determines the causal
difference M's instantiation can make. But according to the NTC, what
determines this in turn are the laws in which M takes part (the M-laws).
Following the NTC, it is only the M-laws that determine M's contribution to the
determination of causal interactions and, following the CCR, only what M can
contribute to causal interactions determines its properties. Therefore, the
identity of M, the set of its properties, is exclusively determined by the set
of M-laws.
Take as an example this table's
having M. The fact that it instantiates M is what permits to explain all the
facets of its behaviour which are due to its massiveness, most importantly its
being heavy and its resisting acceleration. Such connections to gravitational
force and acceleration, i.e. connections with other properties which are at
least indirectly linked to observable properties, are the only features of mass
that are identified by science. Now the crucial question is this. Does M have
an individual essence or "quiddity" which goes beyond the set of its
properties? Or does it at least possess a numerical identity which would allow
the possibility that there be two perfectly indistinguishable yet numerically
different universals?
Let W0 be the actual
world and M be the property of having a mass of 30 kg. Having M leads to
mass-behaviour such as falling and resisting acceleration. Quidditism, which
holds that M has an individual quiddity over and above its properties, and
independent of them, implies that there is a possible world W1 in which M
exists although it has different properties from those it has in W0. According
to quidditism, there is a possible world W1 in which M switches its roles with
a property of electrical charge, say E, the property of having a charge of 30
Coulomb.
W0: MB(M) CB(E).
W1: MB(E) CB(M).
M: having a mass of 30 kg. E: Having
an electrical charge of 30 Coulomb. MB: Mass Behaviour, CB: Charge Behaviour.
In W0, having M leads to
mass-behaviour like falling, whereas having E leads to behaviour characteristic
of electrically charged bodies (or "charge-behaviour"), like being
attracted to bodies bearing the opposite charge, whereas in W1, it is the other
way round: in that world, it is having M that leads to charge-behaviour,
whereas it is having E that leads to mass-behaviour.
Now, it seems to me that quidditism
violates the criterion of identity for universals we have developed above. If
all the properties of a given universal are determined by the laws in which it
takes part, then there is no ground for identifying M in W0 with M in W1: these
universals differ with respect to their properties. In fact, according to our
causal criterion of identity for universals, it is simply E in W1 that is
identical to M in W0 (and M in W1 is identical to E in W0). The universals have
the same properties in each world in which they exist. When we consider
possible world W1, what we do, instead of switching the properties of the
universals M and E, while keeping their identity constant in spite of that
switch, is just switch their names. We can call M by E's name, but whether it
is identical to this world's M is determined by whether it bestows mass-like
behaviour to the particulars instantiating it.
If it is (ideal) science that not
only alone decides whether a property is real, but also what its nature is by
way of discovering its lawful contribution to causal interactions, then there
can be no metaphysical identity between two universals (M in W0 and M in W1)
which bestow a different pattern of resemblance and of regularities on the
things possessing them in W0 and W1. Individual quiddity, which would allow
such an identification of M in W0 with M in W1, does not pass the test of
causal contribution: Nothing causal is common to these universals, therefore
the CCR rules out the existence of quiddity. It turns out that W0 and W1 just
describe the same (second-order) state of affairs by calling the universals by
different names.
We have arrived at anti-quidditism
according to which the inter-world identification of universals is determined
exclusively by the universal's nomic properties. Let us briefly look at a
related question: Couldn't there be, within one world, two (numerically
different) indistinguishable universals sharing all their nomic properties? I
shall call the position resulting from an affirmative answer "weak
anti-quidditism", the position resulting from a negative answer
"strong anti-quidditism". It is not a trivial question to ask whether
the Principle of the Identity of Indiscernibles should be denied for universals
for science seems to require such a denial in the case of particulars. Weak
anti-haecceitism for particulars is backed by the physical fact that elementary
particles can be numerically distinct and yet indistinguishable. However, on
the level of properties no analogous fact can be found that would justify the
postulation of two purely numerically distinct properties that share all their properties, i.e. which are
nomically indistinguishable. It would once more go against our causal criterion
of identity to allow two different universals of having a mass of 30 kg, which
would be embedded in exactly the same laws. This would be a purely nominal
distinction without a real difference.
The acceptation of the CCR as a
general metaphysical criterion of existence and identity leads to strong
anti-quidditism with respect to universals. The identity of a universal is
exclusively determined by its properties, which are in turn determined by the
laws the universal participates in. It is only apparently (or epistemically)
but not metaphysically possible that the very same universal exists in two
different worlds while having different properties in each, i.e. while taking
part in different laws in each.
Can this result be reconciled with
the above-mentioned intuition (Cf. Armstrong 1989, p. 59) that each universal
has its own nature? In fact, taking this intuition into account does not
require attributing quiddity to universals. Instead, we can consider the nature
of a universal as something which is determined by its relations, and in
particular its nomic relations, to other universals, in other words by the laws
in which it takes part. Having a specific nature does not presuppose - nor does
it entail - having an essence independent of lawful dependencies. In this
respect, particulars are similar: the fact that particular a has a specific nature doesn't entail that anything in this nature
is essential to a. Without
postulating an essence, the specific nature of an individual simply consists in
its properties[13].
But, you might ask, doesn't our
reasoning lead to the conclusion that all of a universal's properties are
essential to it, rather than none? What we call an essential property of
something is a property without which the thing wouldn't be the thing it is. If
we follow Kripke (1972) in holding that its origin is essential to a thing, I
would not be the person I am if I'd had different parents. In an analogous
manner, we could call those properties of a universal essential to it without
which it would lose its identity. According to the conclusion we have just
drawn, this is the case for all of a
universal's properties. So we would be led to the view that all of a universal's properties are
essential to it. However, this seems absurd for the concept of essence contains
the idea of something that remains constant despite variation (within or across
worlds). Instead of saying that all properties are essential, it seems more
correct and less misleading to say that a universal has no essence at all, and
that its nature is determined by the set of its properties, which are
themselves determined by the universal's lawful links to other universals. A
given universal A exists in all and only those worlds in which there exists a
universal which possesses all and only A's properties, i.e. its lawful links to
other universals. Conversely, in all possible worlds where the universal A
exists, it is embedded in the same laws. If it took part in different laws, it
would not be A. In this sense the laws are necessary.
If our reasoning is correct, we are
forced to question the legitimacy (or the interpretation) of what we do when we
reason about possible situations that are not only counterfactual but also
counterlegal, i.e. in which the actual laws of nature do not hold. Worlds
containing our actual universals but in which the laws of nature differ from
the actual world are only doxastic but not metaphysical possibilities. The
description of a counterlegal (and doxastically possible) world does not
describe a metaphysical possibility because it contains a contradiction: A
counterlegal world is a world that contains a universal (or several universals)
which is strictly identical to an actual universal, but which is embedded in
different nomic links to other universals. Yet, if as naturalism requires,
nomic links determine the identity of a property, these constraints contradict
each other. In a possible world with different laws, those laws cannot link the
same properties that are instantiated in the actual world.
3 What kind of necessity is the necessity of laws? Are there alien
universals?
We have come to the conclusion that
insofar as we reason about possible worlds which contain the universals
existing in the actual world, it is not possible that the laws of nature
holding in these worlds be different from what they actually are. Does this
mean that the laws of nature are necessary in the metaphysical sense that the
laws are the same in all possible worlds?
It should be clear from the
preceding discussion that this is not the case. The laws are the same as those
of the actual world only in those worlds
that contain the same universals as our world. The CCR does not prevent the
existence of possible worlds with universals different from those of the actual
world or, in Lewis' (1986a) terms, "alien" universals. The CCR allows
- in fact predicts - that such alien worlds have laws that differ from all
actual laws. The possibility of alien worlds matches with the intuition that
there might have been other - or more - properties than there actually are. We
must distinguish between simple and structurally complex universals here.
First, complex universals: if we had different - or additional - sense organs,
e.g. organs like those that guide bats by detecting ultrasounds, it seems
plausible that we would have experiences of a phenomenologically different quality.
If there were a superheavy element of atomic number 130, it would have
different properties from all actual elements. Both the phenomenological
property of experiencing ultrasound and the physical properties of atoms of
atomic number 130 are complex properties resulting from the structural
combination of actual universals. They are either identical to, or at least
supervene on, combinations of actual properties. Such properties could exist
even if the laws of nature were unchanged. Therefore their possibility does not
yet establish that laws are not necessary in a strong metaphysical sense.
For this, we must consider the
metaphysical possibility that there be alien elementary particles with alien fundamental properties. Such fundamental
alien universals need non-actual laws to determine their identity.
Instantiating the alien universal A determines a certain lawful behaviour, for
the laws connecting it to other properties make it the property it is. But
these laws are different from all actual laws, for no actual law contains (by
definition of the concepts of alien
and actual) any alien universal like
A. Let us follow the implications of such a situation. If alien A-particles can
interact with B-particles, these latter must be alien too because no actual particle
has the property to interact in a certain way with A-particles. And so for all
types of particles with which A interacts: If a particle of type X interacts
with alien particles, it must itself be alien. The same reasoning applies to
all universals which are lawfully connected to some universal or other which is
lawfully connected to A. In the end, in a possible world with alien universals
and alien laws, there could be non-alien universals and laws only in the
following case: There might be, within an alien world, a set of universals
which are not lawfully linked at all to any of the alien universals. As a
matter of law, there could be no interaction that would depend both on alien
and non-alien properties. With the exception of such mixed worlds in which
there is no interaction between the alien and the non-alien part, worlds that
contain one alien universal will contain only
alien universals and, by consequence, only alien laws.
The following situation has emerged
from our investigation: with respect to universals, there are three different
types of possible worlds. The actual laws of nature are necessary in a sense
which is weaker than logical or metaphysical necessity: they hold in all and
only the possible worlds of the first two types: those which contain the same
universals as the actual word, either exclusively or in addition to alien ones.
However, our actual laws do not hold in completely alien worlds, which are the
worlds of the third type, which contain only alien universals and only alien
laws. Conversely, non-actual laws are not impossible in a strong metaphysical
sense because possible worlds of the second and third type contain such laws.
In the end, are the laws of nature
necessary or contingent? Constructing a possible world by recombining only
actual universals, forbids changing the laws, for changing the laws means
changing the properties. This means that the laws of nature are necessary
relatively to the actual universals. As far as one reasons about actual
universals, counterlegal worlds containing these properties are metaphysically
impossible. Thus, those authors as Shoemaker (1980; 1998), Swoyer (1982), Fales
(1993) and Ellis and Lierse (1994) who have argued that the laws of nature are
necessary in a metaphysical sense, are partly right. But with the exception of
Tweedale (1984) they have, it seems to me, overlooked possible worlds that
differ from the actual world both with respect to universals and to laws. If
nothing stands in the way of considering this as a genuine possibility, it
shows that laws are not absolutely necessary. In this respect, our conclusion
is compatible with the thesis held by Kneale (1949), Pargetter (1984) and von
Wright (1984) that nomic necessity can be reduced neither to metaphysical nor
to logical necessity.
5. Conclusion
The CCR has been the centrepiece of
our argument for the necessity of laws. We still have to meet the challenge
posed against our metaphysical use of that principle by Armstrong's thesis that
it is "not [...] a necessary truth, but merely good methodology"
(Armstrong 1984, p. 256). According to Armstrong, the CCR has only the status
of a methodological principle, which has no force to decide questions of
metaphysical possibility and necessity. There is no better way to find out
about the nature of a universal than to examine its causal powers, yet for
Armstrong these causal powers do not make up its identity. This allows him to
maintain the thesis that the laws of nature are contingent, and that universals
have an intrinsic nature, a quiddity, which is ontologically independent of the
causal powers associated with the universal (or, in other words, independent of
its nomic links to other universals).
This is a very abstract issue - it
belongs to meta-metaphysics dealing with the question of which arguments are to
be used and accepted in metaphysical discussions and by which criteria to judge
the adequacy of those arguments. I have chosen to follow the lead of
naturalistic metaphysics, which consists in adopting the principle that it is (ideal)
science that should ultimately decide about the existence and identity of all
entities. Armstrong's alleged possibilities fall outside the framework of such
a metaphysics: the alleged identity between the universal M of the actual world
with a universal E of a different possible world where E does not share any
property at all with our actual M is by hypothesis inaccessible to science. The
quiddity, which Armstrong postulates in order to ground such a cross-world
identity, is no less obscure than the scholastic forms from which it takes its
name[14].
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[1]Cf. Armstrong (1983, chap. 11),
Armstrong (2000), Lewis (1986b, p. 163).
[2]Their existence and properties are
of course causally dependent on other
things, but it is metaphysically possible that they exist and have the
properties they actually have even if their actual particular causes and
effects don't exist. In other words, the causal relation between particular
events is an external relation.
[3]Plato, Sophist, 247d-e.
[4]Armstrong himself insists that the
CCR is only methodological but not metaphysical. See discussion below, in the
conclusion. Jaegwon Kim has called it "Alexander's Dictum" (Kim 1992,
p. 134), in honour of Samuel Alexander (1920) who has defended it as a
metaphysical principle: "To be real
is to have causal powers" (Kim 1992, p. 135; Kim's italics).
[5]According to scientific realism the
postulation of universals is justified by the need to explain the way things
interact with each other and, through perception and action, with us.
[6]It is important to note that the
acceptation of the CCR does not necessarily lead to denying the existence of
such entities as possible worlds, possible or necessary states of affairs, or
of such allegedly non spatio-temporal entities as numbers and classes. Rather,
in order that the type of entity in question can be acknowledged within the
overall metaphysical scheme, what has to be shown in each case is that these
entities are either identical or at least supervene on entities which obey the
CCR. On the condition that the subvenient entities obey the constraints of
naturalism, so do the supervenient, even in such a controversial case as that
of numbers.
[7]I assume that the distinction
between what is a priori or analytic and what is a posteriori or synthetic is
one which admits of degrees, and that this fact does not make the distinction
useless or meaningless.
[8]According to quantum mechanics this
is true within systems of so-called "identical particles".
[9]These properties are second order
properties. As we shall see, following the CCR, those second order properties
are determined by all and only the laws in which the universal takes part.
[10]In the case of particulars, such an
individual essence is generally called "thisness" or
"haecceity". Several terms have been used for the putative essence of
universals, in particular "haecceity", "suchness" and "quiddity".
Following Armstrong, I shall call the putative essence of a particular a
"haecceity" and the putative essence of a universal a
"quiddity".
[11]Which properties are universals is
decided by the roles those properties play according to ideal science.
Intuitions about which properties are universals are regularly over-ruled by
the adoption of scientific theories.
[12]See Davidson (1995) for the view
that this is a conceptual truth, Heathcote and Armstrong (1991) for the view
that it is only empirically true.
[13]Compare the reasoning Armstrong
offers in support of the thesis that the simplicity (or complexity) of a
universal belongs to its nature, in the sense that it could not change from one
world to another. If it could, universal F could be simple in W1, but complex
in W2, e.g., by being identical with the conjunction G&H in W2. His
argument against this possibility is that it is absurd to claim that
"simple F in W1 is identical with G&H in W2" (Armstrong 1989, p.
67). However, this is not an argument for quidditism although it has been interpreted
in this way (Forbes (1991, p. 352) takes the argument to show that "a
property's logical structure is essential to it"): to make the hypothesis
that a given universal is complex rather than simple, means to make a
hypothesis about laws. The hypothesis that F is identical to G&H has
content only if G and H have their own nature which means that they are
lawfully linked to still other universals or that they enter into the
constitution of other universals. In both cases, the hypothesis is equivalent
to attributing properties to F. Armstrong's argument establishes that if a
universal has such properties, it must have them in every possible world where
it exists. But this is just the opposite from quidditism: the essence or
quiddity of a universal would be something which would allow it to be identical
across worlds in spite of and
independently of its changing properties.
[14]I am grateful to my auditors in
Bielefeld and to David Armstrong for helpful comments and criticism on an
earlier version of this paper, as well as to Joan Cullen for linguistic advice.