Max Kistler
The Causal Criterion
of Reality and the Necessity of Laws of Nature
Metaphysica, vol. 3 (2002), No. 1, p. 57-86.
I propose an argument for the thesis
that laws of nature are necessary in the sense of holding in all worlds sharing
the properties of the actual world, 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 here is that the capacity to interact
causally - or to contribute to determining causal interactions - is not only
the ultimate metaphysical ground 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, which 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. The Causal Criterion of Reality
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. One version 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 the acceptance of the 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 not, in principle,
interact. Accepting the CCR forbids the postulation of particulars that 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 for this is that, in an analogous
manner to the case of particulars, it would contradict the CCR 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 that 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[8]. 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. Is it possible 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. It is metaphysically possible
because its existence would be a scientifically legitimate hypothesis which can
be evaluated in accordance with the CCR (our leading principle is the
generalisation of the domain of legitimate application of the CCR, from science
to metaphysics): 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
acceptance of the CCR gives us a fresh look on the traditional divide between
"Aristotelian" and "Platonist" 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, a universal U exists 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 certain other universals V such that the probability that instantiations
of V contribute to causally provoking instantiations of U is also non-zero.
2. Quiddity and haecceity
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, which 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, what I
argue for is that 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) 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
particulars and 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 "haecceity" in the case of
particulars and "quiddity" in the case of universals - which is the
metaphysical ground for their individual identity. Armstrong himself examines
in detail only the question of haecceity 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).
2.1. Haecceitism and anti-haecceitism
The affirmative answer to the
question whether there exists a metaphysical ground for the individual identity
of a particular, over and above the set of its properties, may be called
“haecceitism”, the negative answer “anti-haecceitism”. Let me briefly discuss
haecceitism and anti-haecceitism, with the help of an example of Armstrong's
(1989). This may then facilitate our inquiry into the analogous question for
universals. Take an extremely contracted possible world which contains only two
particulars, a and b. Each instantiates one and only one
property, in one case F, in the other G, so that this world consists in the
following conjunctive state of affairs:
I Fa Gb.
Now the different positions with
respect to haecceitism diverge in the replies they give to the question of which
worlds are possible that contain the same particulars and universals as (I).
One possible response is haecceitist: Each of the seven state-descriptions (in
Carnap's[10] terms) generated by combining F and
G with a and b, corresponds to a different possibility:
I Fa Gb. III Fa Fb Ga V
Fa Ga Gb
II Ga Fb IV
Fa Fb Gb VI
Fb Ga Gb
VII Fa Fb Ga Gb.
Consider pair I/II. In both of these
possible states of affairs (or possible worlds) there is exactly one individual
that is F and exactly one that is G[11]. Haecceitism is characterised by
the thesis that nevertheless, I and II express different possibilities. (The
fact that the two individuals existing in our contracted world are named by
different individual constants "a"
and "b" might already
suggest the haecceitist position. But the mere difference of names of the individual which has F
respectively in world I and world II is no proof that these are really
different possibilities. After all, it often happens within the actual world
that the same individual has different names. We would be misled in following
the suggestion that difference of name entails difference of identity.)
Both haecceitism and
anti-haecceitism come in a weak and a strong form. According to strong
haecceitism, a and b have an individual essence
distinguishing them and making worlds I and II different. This doctrine can be
motivated by the strong intuition that it makes a difference whether it is this (pointing to it) thing which is F
and not G or whether it is rather that
(pointing to it) thing which is F and not G (where the second particular is G
and not F). Strong haecceitism can indicate a clear ground for the intuition
that I and II are different possibilities. It could be seen as resulting from a
generalisation of Kripke's (1972) position with respect to macroscopic objects
such as tables and persons, extending it to cover all particulars, even
elementary particles. What makes such a position controversial is that the
notion of the essence of a particular used here by the haecceitist seems to be
an elusive and obscure notion, for it does not consist of some subset of its
properties. Moreover, it is doubtful whether Kripke's intuitions regarding macroscopic
objects have any plausibility regarding elementary particles.
Armstrong (1997) adopts weak haecceitism: as a form of
haecceitism it holds that I and II are different possibilities although they do
not differ with respect to properties. However, contrary to strong haecceitism
it rejects individual essences, to recognise only what is minimally required to
ground the difference between two particulars that are indistinguishable
according to their properties. Arguing for this position, Armstrong (1997, p.
108) develops the following thought experiment. He considers a possible world
consisting of two indistinguishable regions both of which contain parts
resembling our own Earth. At some point, one of the regions ceases to exist.
Weak haecceitism (as well as strong haecceitism, of course) can justify the
intuition that, for the people living in one of these regions, it makes a
difference whether it is them or the people on the other Earth who cease to
exist. However, the fact that the particulars' haecceity it postulates is at
least as obscure as the richer notion of individual essence of strong
haecceitism pleads against weak haecceitism. I shall come back to Armstrong's
thought experiment in a moment, to challenge its premise.
We can find arguments in favour of
the alternative position, anti-haecceitism, in Armstrong (1989) where he
adopted it. Armstrong conceives of "thin" particulars as perfectly
bare and only numerically different from each other[12]. He calls particulars in the
ordinary sense - particulars with all their properties - "thick"
particulars and analyses them as (conjunctive) states of affairs: the state of
affairs of the thin particular possessing its non-relational properties. The
thin particular does not have any individual essence; it acts only as an
anchor, which permits the instantiation of universals. If this is so, no
difference whatsoever corresponds to the difference in name between a and b. Therefore, the anti-haecceitist concludes, the descriptions I
and II do not express genuinely different possibilities, but rather describe
the same possibility in different ways.
As haecceitism, anti-haecceitism
also comes in a weak and a strong form. The strong form follows from the thesis
that particularity is reducible, either by arguing that particulars are bundles
of universals (Russell 1948, chap. 8) or of tropes (Williams 1953; Campbell
1990). Now, if the nature of a particular is exhausted by its properties, then
the Identity of Indiscernibles must hold: there can be no "mere numerical"
difference which would not be a difference with respect to some property or
other. This means, in our example, that world VII would contain, contrary to
the appearance of its description, only one individual. In the description of
VII, this unique individual is named twice by two different names.
However, the existence of
indistinguishable yet numerically different elementary particles gives a
powerful argument against this view. Contemporary quantum physics tells us that
there are systems of interacting bosons in which all particles share all
properties, including spatial localisation. Nevertheless, these particles can
be counted. Weak anti-haecceitism recognises (contrary to strong
anti-haecceitism) the possibility that world VII contains two numerically
different particulars. But it doesn't go any further than recognising this
possibility of numerical difference. Without attributing particulars a
haecceity that would make them metaphysically distinguishable (even though they
are physically perfectly indistinguishable) it provides a metaphysical
grounding for the denial of the Identity of Indiscernibles, more precisely for
the physical fact that there can be numerically different particulars sharing
all properties. (Recall however what both weak and strong anti-haecceitism
share - against haecceitism - the thesis that I and II express the same
possibility.)
It seems to me that the only
defensible positions are weak haecceitism and weak anti-haecceitism. Against
strong anti-haecceitism, it is reasonable (on physical grounds) to say that
world VII may contain two particles not one, and against strong haecceitism,
parsimony dictates to postulate as few obscure metaphysical entities as
necessary, and thus to try to do without a rich individual essence, especially
with respect to elementary particles.
Among the weak positions, I think we
should prefer weak anti-haecceitism: world VII contains two particles, but I
and II are the same possibility counted twice. The reason is the obscurity of
the notion of haecceity even in its minimal form. As there is a sensible option
doing without haecceity, it is preferable. Let us return for a moment to the
thought experiment mentioned above that Armstrong (1997) uses to argue against
weak anti-haecceitism. What makes weak anti-haecceitism implausible according
to Armstrong is that its advocate must say that there is no objective (not even
metaphysical) difference between its being the one or the other Earth-like
region which is destroyed. So when one of them ceases to exist there can be no
question as to which: sharing all their properties, they don't have enough
individuality to make this into a sensible question. I think that this argument
overlooks the difference between two macrophysical objects (the two Earth-like
regions in the thought experiment) and two interacting bosons, which in each
case, by hypothesis, share all properties.
The difference is that macrophysical
objects must, again for physical reasons, differ with respect to spatial
localisation. The set-up of Armstrong's thought experiment is physically
impossible. As such, it should not constitute a sufficient motivation to
postulate a general metaphysical principle granting them haecceity over and
above their numerical difference. We do not need to postulate haecceitism to be
able to account for the intuition that it makes a difference on which of those
two Earths you live, because the different spatial localisation of the two
Earth-like regions, by making them different individuals, suffices to ground
that difference. The macroscopic size of the Earth-like regions is essential to
the argument: if a and b were elementary particles, e.g. indistinguishable
bosons, there would be no analogous intuition showing that I and II should be
counted as different possibilities. To sum up, in the microscopic case, the
intuition needed for the argument is not available, and in the macroscopic
case, we have the clear intuition that I and II are different possibilities,
but we don't need to postulate an individual haecceity for a and b to give that
difference a metaphysical grounding.
2.2. Quidditism and anti-quidditism
Let us now turn to the analogous
question about the identity of universals. 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[13]. 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: According to the CCR, 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.
Thus, the CCR also provides a criterion for determining the nature, i.e. the
second-order properties of universals.
This follows from the acceptance of
the CCR as a truly universal metaphysical principle. 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, in
analogy with our question with respect to particulars, 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[14]. 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 let us ask the crucial question:
Does M have an individual essence or "quiddity" which goes beyond the
set of its properties (as haecceitism claims in the case of particulars)? Or
does it at least possess a principle of numerical difference which would allow
(as weak anti-haecceitism allows in the case of particulars) the possibility
that there be two perfectly indistinguishable yet numerically different
universals?
Let us try to reason in an analogous
way as we have done before in the case of particulars, to examine the
plausibility of quidditism and anti-quidditism. 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.
As we have seen, for
haecceitism there is a difference between I and II: it makes sense to ask which
of the two particles has F and not G, and which has G and not F. Each
particular having its individual haecceity, switching all properties results in
a different possible state of affairs. Similarly 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) Ù CB(E).
W1: MB(E) Ù 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 behaviour characteristic
of electrically charged bodies, like being attracted to bodies bearing the
opposite charge, whereas it is having E that leads to mass-behaviour like
falling.
Now, it seems to me that this
position - 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 share no property. 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.
But, one might object, how it is
possible to draw a modal conclusion about the essential nature of a universal
from premises bearing only on its actual nature? Such conclusions are clearly
not valid for particulars. David Lewis is a philosopher, but the fact that he
actually has this property is not sufficient for concluding that he has it
essentially: He might have been a plumber. However, the conceptual independence
between a particular and its accidental properties rests on the fact that we do
not conceive of particulars as of entities whose identity is determined by the
set of their actual properties. This is possible because we are particulars
ourselves. I can form a concept of myself independently of my actual
properties, and this allows me to think that I could have had other properties.
Through ostension, I can form a concept of this
thing, conceiving of it in complete independence of all its properties. Such a
conception of the thing independently of its properties allows us to judge that
it, thus conceived, might have had
other than its actual properties[15]. But universals are different. We
cannot conceive of them independently of their properties, in any of the ways
in which this is possible for particulars. We are no universals, and therefore
do not have the direct access to their identity that we have to the identity of
the particulars that we are ourselves. We cannot point to them, and therefore
do not have to universals the perceptual access we have to particulars because
we are particulars ourselves. Therefore, in virtue of the radically different
ontological status of universals and particulars, there is no legitimate ground
for the postulation of a non-qualitative quiddity independent of the actual
properties of a universal, which would parallel the ground we have for such a
postulate in the case of particulars.
As we have rejected haecceitism and concluded that I and II do not express genuinely different possibilities, but only different ways to describe the same possibility, so we must conclude here that W0 and W1 just describe the same (second-order) state of affairs by calling the universals by different names. Furthermore, no intuition similar to Armstrong's (1997) seems to be available here to argue at least in favour of weak quidditism.
We are left with the choice between
weak and strong anti-quidditism. Remember that weak anti-haecceitism has turned
out to be the position that best corresponded both to intuition and scientific
facts with respect to particulars. Weak anti-haecceitism denies that I and II
are different possibilities, but allows a numerical difference between
indistinguishable particulars, and thus denies the Principle of Identity of
Indiscernibles. It allows world VII to contain two not just one particle.
At this point I think that the
situation is different for universals than for particulars. To justify the
denial of the Principle of the Identity of Indiscernibles for a given category
of entities, it is necessary to give a strong argument. We found such a strong
scientific argument in the case of particulars, but none seems to be available
in the case of universals. Weak anti-haecceitism is backed by the physical fact
that elementary particles can be numerically different and still share all of
their properties. 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 acceptance 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[16].
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[17], 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
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 the CCR 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) and Freddoso (1986) they have, it seems to me, overlooked possible
worlds that differ from the actual world both with respect to universals and to
laws[18]. 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.
4 Some objections
Let us now consider some important
objections. To begin with, Mellor and Oliver contest the inference from the
premise that "a property like mass may well be identified, i.e.
distinguished from all others, by the laws (of motion, gravity, etc.) that link
it to other properties and thereby fix its powers" (Mellor and Oliver
1997, p. 30) to the conclusion that the laws are necessary. According to them,
such a relational identification of a property does not force us to abandon the
intuition that it is possible for mass to "figure in slightly, if not
entirely, different laws" (ibid.).
Whether this inference is valid depends indeed on the crucial point whether
universals have quiddity. Only that would make it possible to refer to them
rigidly, as it is possible with particulars, and to reason counterlegally about
them, as it is possible to reason counterfactually about a rigidly designated
particular. But universals are entities whose existence is hypothesized
theoretically by an inference to the best explanation, and that inference is
well justified only insofar as the identity of the hypothesized universal is
determined by their lawful connections to other properties. If the universal
whose existence we are justified in hypothesizing lacks quiddity, the possible
world considered by Mellor and Oliver in which mass figures in slightly
different laws, is an "alien" world in which not only the laws but
also the universals are, however slightly, different from our actual
universals. Having different properties from our mass and in the absence of a
common quiddity, that otherworldly "mass" is not our mass. What
Mellor and Oliver's case shows is that an alien possible world may be quite similar
to the actual world, and an alien universal quite similar to an actual
universal; but not that it is possible to change the laws without changing the
properties the laws relate.
Armstrong (1983, p. 162f.; 2000, p.
8f.) raises the following objection against Shoemaker's (1980) causal theory of
properties according to which "what makes a property the property it is,
what determines its identity, is its potential for contributing to the causal
powers of the things that have it" (Shoemaker 1980, p. 212). Although we
have been led to the conclusion that the identity of a property is determined
by its lawful relations, not its relations to causal powers, Armstrong's
argument is also an objection to our own proposal for it is generally directed
at theories which conceive of the identity of properties as determined by
relations. According to Armstrong, any theory that considers that the identity
of a universal is exhaustively determined by its second order-properties has
the unacceptable consequence that it reduces properties to mere potentialities,
which means that "act, so far as it occurs, is just shifting around of
potencies" (Armstrong 2000, p. 14). In other words, if the identity of a
property is entirely determined by its relations to other properties whose
identities are themselves also exclusively determined by relations to still
other properties, the theory faces a regress[19]. As P.J. Holt has put it, such a
theory makes us "lose the substance of the world" (Holt 1976, p. 23).
I think this objection can be overcome by conceiving of the determination of
the identity of properties along the lines of the Ramsey-Lewis account of the
implicit definition of theoretical terms[20]. If we had an ideal theory
explicitly stating all the actual laws of nature then we could implicitly
define all the natural properties. From the realist point of view, the fact
that we can't actually so define them for want of knowledge of the laws, is no
obstacle to our conceiving properties in this way. This consideration shows
that the relational determination of their identity doesn't make "pure
potentialities" of real properties, just as the fact that the meaning of
the theoretical concept of an electron is exhausted by its relations to other
concepts in physical theory does not make it a concept of a pure potentiality.
If one tries to state the identity of properties one by one, one is indeed led
into a circle; but a circle that is so big as to include all laws of nature, is
a virtuous one.
Another objection Armstrong raises
against theories that, like ours, let the identity of properties be determined
by (nomic) relations, is that it makes indistinguishable properties impossible.
However, Armstrong suggests that "it seems possible that a system both of
causal properties, and of nomic properties, might have a symmetrical structure
so that every property had its 'opposite' in the net, and that such opposite
properties should perfectly image each other in their causal/nomic position in
the property-net" (Armstrong 2000, p. 9). The idea seems to be that
Leibniz' law of the identity of indiscernibles might be violated on the level
of properties, just as it appears to be violated on the level of particulars
which can be - as quantum physics teaches us for the case of interacting bosons
- numerically different although they share all properties, even their spatial
localisation. He suggests that it might be the case in an analogous way that
there be two numerically different universals which share all their
(second-order) properties. This, or so goes the argument, pleads against
relational theories of universals for they are built on the validity of the
principle of the identity of indiscernibles in the case of universals, and
therefore cannot acknowledge the possibility described by Armstrong. Now, it seems
to me that any denial of Leibniz' law needs to be motivated on independent
grounds. Physics gives us such grounds for the case of particulars: It tells us
that some elementary particles in interaction constitute a counterexample to
Leibniz' law which is thus shown not to be generally valid for particulars. But
in the case of universals, there seems to be no independent ground for
postulating two numerically distinct though qualitatively indistinguishable
universals, and thus Armstrong's argument only begs the question against
relational theories of the identity of properties. Armstrong gives no
independent argument against the analysis which the relational theory of
properties would give of the situation described in the quote above: There is
just one net of properties which is counted twice.
Does our theory of properties face
the "Meinongian problem" (Armstrong 2000, p. 10) that each of an
object's properties is necessarily related to non-existent lawful consequences
of non-actual but possible situations? In Armstrong's example, the possession
by an object of the property of "4 kilograms exact in rest-mass"
necessitates, in non-actual situations where a given non-actual force acts on
that object, a well-determined acceleration, according to the laws that are
essential to the property. It seems to me that it is not at all inevitable to
draw from this premise the Meinongian conclusion that "the object's having
that mass-property [...] is [...] related to [...] the non-existent"
(Armstrong 2000, p. 11). The relational theory is not committed to a dubious
ontology allowing for the presence of mere possibilia in the actual world. It
just makes a negative claim about which non-actual worlds are or are not
possible. What it says is that there is no possible world in which some object
having the property of 4 kilograms exact in rest mass is acted upon by a given
force and in which this action is not followed by the acceleration dictated by
the laws of nature of the actual world which govern that property in all possible
worlds in which it exists. No Meinongian consequences are forced on the
relational theory of properties.
Finally, the specification of the
truth conditions of counterfactuals makes it, according to David Lewis (1973),
necessary to consider possible worlds in which there occur "small
miracles" which are events violating the actual laws of nature. Otherwise,
says Lewis, one could not coherently conceive of a world which is very similar
to ours but in which the antecedent of the counterfactual is true. Without
miracles, at least in a deterministic world, even the slightest deviation from
the actual world concerning the fact mentioned in that antecedent would require
a huge divergence reaching back through the whole chain of causal ancestors of
that fact[21]. The relational theory of
properties implies indeed that there can be no miracles, no possible worlds
with the same properties as exist in the actual world but where the actual laws
governing those properties are not (always) followed. But this seems to plead
rather against Lewis' theory of the truth-conditions of counterfactuals than
against our theory of properties. For how reliable is the judgment one makes
about the truth-value of the consequent of a counterfactual by looking at the
possible world which is closest to the actual among those in which its
antecedent is true, if that world allows for miracles? By definition, just
anything can happen in such a world, the consequent can be true or false by a
miracle that is sufficiently small not to threaten the overall closeness to the
actual world.
5 Dispositional essences, causal powers, and natural kinds
Laws are second-order relations
between properties, and thus equivalent to second-order relational properties
of properties. At least some of these nomological properties of properties are
essential to them, in the sense that the property would not be the property it
is if it did not possess it. Thus the laws corresponding to these nomological
properties are necessary in a particular sense: although they do not hold in
all possible worlds - they are not logically necessary - they hold in all
worlds in which the property exists. This account is in some respects similar
to "dispositional essentialism" (DE), a position defended by Bigelow,
Ellis and Lierse (1992), Ellis and Lierse (1994), and Ellis (1999; 2000; 2001).
According to DE, "among the essential
properties of many different natural
kinds of things, we must include certain important dispositional properties" (Bigelow 1999, p. 45). As a
consequence, "The causal laws [...] are grounded in the intrinsic
properties and structures of the natural kinds. [...] [These properties]
include the causal powers, capacities and propensities which determine how the
various natural kinds of things are disposed to behave and interact with each
other." (Ellis 1999, p. 21/2). The position defended in the present paper
shares with DE the rejection of the Humean doctrine of the contingency of laws.
But there are several important differences between DE and the view defended
here.
1. Kinds vs. properties. According
to DE, laws are grounded in dispositions that are essential properties of natural kinds, which are primitive and
fundamental kinds of entities. "If K is a natural kind of thing, then
everything of that kind must have the appropriate structure and properties. The
general form of such a law is: For all x, if x is an instance of K, then Px"
(Ellis 1999, p. 28). On the view defended here, it is the essential nomological
properties of properties that provide
the grounding of laws. My main reason for holding that (natural) properties are
more fundamental than natural kinds is that kinds are complex types of
substances that share structural properties. But the constituents of such a
structural property are simpler properties which the laws holding for them bind
together in this. So it seems that the identity of a kind depends on the
identity of its constitutive properties, together with the relevant laws[22].
2. Causal power vs. nomic
dependency. The fundamental essences of DE are causal powers belonging to natural kinds. We have found that the
fundamental essences belong to properties, and that the essence of a property
consists more generally in the set of its nomic
dependencies, of which causal powers are only a special kind. It is, e.g.,
essential for Cu-atoms that crystals made up of them are good conductors of
electricity. However, the property of being a component of a crystal which is a
good conductor, is not a causal power of the Cu-atom, because there can be no
causal relation between different properties one object has at one time (the
properties of being a Cu-atom and of being a constituent of a good conductor).
To be a conductor of electricity is of course a causally powerful property, but
here we are talking about the nomic relation between being a Cu-atom and
forming (with other Cu-atoms) a conductor, and this relation though essential
for being a Cu-atom, is not causal[23].
3. DE says that laws depend on
dispositional essences[24], whereas I have defended the idea
that dispositions depend on laws. On the latter view, nomic relations are fundamental. However, DE
conceives of the dispositional essences as atomic and separate for each kind.
But then, how can an instance of an atomic essence necessitate the
instantiation of other properties by other individuals? The relational nature of
laws avoids this problem, because many laws link properties of one particular
to properties of other particulars. The presence of a massive body here
lawfully imposes on massive bodies there a tendency to move. How could one
reduce this relational lawful fact to an atomistic essence characterising one
massive body in itself?
4. Dispositional predicates must be
distinguished from dispositional properties or powers. Dispositional predicates
are defined by a conditional linking a test condition (in its antecedent) to a
manifest behaviour (in its consequent). The defenders of DE do not always take
this distinction seriously enough. Ellis says that, if P is a dispositional
property (a causal power), "necessarily, anything that has P must be
disposed to display P in some appropriate circumstances. [...] A causal law
identifies P by describing both the circumstances C and the display E. The
general form of a causal law is therefore: For all x, necessarily, if Px and Cx
then Ex." (Ellis 1999, p. 28). This characterization echoes the
verificationist definition of dispositional predicates, in terms of an
observable test condition C and an observable manifestation E of the
disposition[25]. The conditional truth condition
for (propositions involving) dispositional predicates
can only be used for characterising the essence of a dispositional property if it is qualified in two ways,
only the first of which is recognised by DE: first, the essence of the property
is constituted not by one conditional but many. Ellis (2001) now clearly
endorses Mellor's "principle of multiple manifestation" according to
which "a real property must manifest itself in more than one way"
(Ellis 2001, p. 122). It implies that a power cannot be exhaustively
characterised simply by one conditional linking a test condition to a
manifestation, in the same way in which one can define a dispositional
predicate. But Ellis' behavioural characterisation overlooks a second important
fact about dispositional properties: The lawful links essential to a property
do not necessarily link it to manifest, or observable properties, whereas in
Ellis characterisation of a dispositional property, the triggering and response
conditions must be observable. According to Ellis, if a disposition <C,E>
to have the effect E in circumstances C is "causally determinate"
then "an event of the kind E must occur to x [..] as a result of a C-type
event occurring to x at t" (Ellis 2001, p. 130). Ellis conceives of the
“law of action” of a causal power as relating categorical properties. The
causes and effects in which a causal power manifests itself, are “changes that
would occur in the relation between things, or in the structures of things”, but
these changes in relations “are not causal powers, or propensities or
liabilities, or anything of the sort.” (Ellis 2001, p. 137)[26]. However, perfectly deterministic
dispositions do not obey this condition because their effects are typically
themselves dispositional and do not always manifest themselves in a way that
only depends on C. For example, a negative electrical charge at point P has the
disposition (in virtue of a deterministic law) to create an electrical field
that has, at some point Q distant from P, the strength E. But if, as will
generally be the case, the charge is not the only one around, the total
electrical field strength at Q will not be E, as determined by the charge at P,
but the result of the superposition of many dispositions for an electrical
field at Q.
6 Conclusion
Let us return to the CCR, which 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 that 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[27].
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[27]I am grateful to my auditors at the
GAP4 conference 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.