Dispositions and
essences.
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Université Paris XII et Institut Jean-Nicod (CNRS-UMR
8129).
(Colloque “Dispositions et pouvoirs causaux”, Paris
X-ENS Ulm, septembre 2002)
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From some time
now, dispositions have no longer been viewed as ethereal or occult powers that
have a pre-scientific status, threats or ghostly forces in need of redemption,
mere promissory notes, some lazy or inaccurate way of talking that no
self-respecting scientist should ever use. The pregnant spinsters have now
acquired the respectable status of unmarried mothers, up to the point that they
do lead a life of their own. Indeed,
not only are they viewed as possible accidental
properties of things: they are taken as essential
properties of things in nature. Even more, for some philosophers, all things in nature are essentially dispositional. I have tried
elsewhere[1] to sketch the historical and philosophical reasons
why there might have been such a revolution from pure elimination (as may be
found under various forms in Boyle[2], Quine[3], Goodman[4], or Ryle[5]) to inflation (Ian Thompson[6], Rom Harré[7], Nancy Cartwright[8], Karl Popper[9], Hugh Mellor[10], Simon Blackburn[11]) as regards dispositions, powers or capacities (with,
in some cases, their idealistic consequences[12]). In what follows, I would like to concentrate on
some less extreme versions of dispositional essentialism such as have been
proposed by some authors, especially Brian Ellis, and in an even less extreme
version, I think, by Stephen Mumford. I shall begin by presenting Ellis’s main
lines of argument and then try to see whether some of the difficulties raised
by his account and the answers suggested by Mumford are satisfactory,
especially as far as a dispositionalist account of laws is concerned. Favoring myself
some form of dispositional realism[13] rather than essentialism, I shall finally less
present here some arguments in favor of such a position than merely make some
suggestions as to what seem to me the major difficulties which any kind of
dispositionalism should be ready to face.
1. Brian Ellis’s conception of dispositional
essentialism : the main arguments[14].
Ellis’s
conception of dispositional essentialism (which he first exposed in an article
written with Caroline Lierse in 1994) is part and parcel of the more general
view he now entitles scientific essentialism, which can be summarized in three
basic theses[15] :
1) Scientific essentialism deals with natural kinds
such as events and processes and not only with objects and substances. According to Ellis, “the world is structured into hierarchies of natural
kinds of objects and processes : it
is not an amorphous world on which we must somehow impose our own system of
categories. There is a pre-existing grid of objective categories, and it is the
aim of natural science to reveal and describe them”[16]. Scientific essentialism is concerned with natural
kinds which range over events and processes as well as with the more
traditional sorts which range only over objects or substances[17]. According to scientific essentialism, the most
general laws of nature describe the essential properties of these global kinds,
and therefore hold necessarily of all objects, events and processes: “The law
of conservation of energy, for example, states that every event or process of this
global kind is one that is intrinsically conservative of energy. Hence, any
event which was not intrinsically conservative of energy could not be one of a
kind that would occur in our world. The laws we think of as causal laws are
generally more specific in their direct application. The laws of
electromagnetism, for example, apply directly to all electromagnetic radiation,
and hold necessarily of all such radiation. Therefore, if there is any
radiation which is not propagated according to these laws, it cannot possibly
be electromagnetic”[18].
2) Secondly,
scientific essentialism claims that “the essential properties of the most
fundamental kinds of things are not just the passive primary qualities of
classical mechanism, but also include a number of causal powers, capacities and
propensities — powers to act, and powers to interact”[19], namely properties which are essentially
dispositional in nature, implying dispositions to act and react in various
ways, depending on the circumstances. Traditionally, such properties have been
thought to be ontologically dependent on underlying categorical (i.e. non
dispositional) properties and on the laws of nature. According to the new
essentialism, however, at least some of these dispositional properties are
fundamental, and not dependent upon any other properties In other words (one
will note the Aristotelian and/or Leibnizian flavor), the basic things in the
world are essentially active and dynamic. “They are not just passive objects
obeying blindly the commands of God, as most seventeenth and eigtheenth Century
philosophers believed, a world of things having only the attributes of
extension and impenetrability, as Descartes’s and Locke’s worlds were; rather
it is a world in which things have their own internal dynamics, which are
essential to their natures, and which are determinative of their behaviour”[20]. In that respect, “all things are essentially active
and reactive: at the most basic level, what they are intrinsically disposed
to do is what makes them the kinds of things they are. Things of given
kinds must always be disposed to behave in certain kinds of ways, just by
virtue of being things of these kinds. Their identities as members of these
kinds depend on their being so disposed to act”[21]. Hence,” the real defining characteristics of the
most fundamental kinds of things that we know about, namely, thing like protons
and electrons, would all appear to lie in their laws of interaction. Things of
these kinds would appear to have no real defining characteristics at all apart
from their causal roles. A proton, for example, might be defined (by way of
real definition) as any particle which behaves as protons do. For no proton
could possibly fail to behave in these ways, and no particle other than a
proton could possibly imitate this behaviour. Its identity, qua proton,
might thus be defined by its causal role. Similarly, one might say that an
electron is, by real definition, any particle for which the laws of interaction
are precisely those of electrons. Nothing other than an electron could possibly
behave in such a way, and whatever does behave in this way has to be an
electron”[22].
3) Hence a third
thesis: the laws concerning the behaviour of protons, and their interactions
cannot be just accidental, i.e. laws which could well have been otherwise. On
the contrary, it is essential to the nature of the proton that it should be
disposed to interact with things of various kinds precisely as it does. The
protons’s causal powers, capacities and propensities are not just amongst the
accidental properties of protons, which depend on what the laws of nature
happen to be, but amongst their essential properties, without which there would
be no protons, and which protons could not lose without ceasing to exist[23].
Accordingly, “the
traditional view that the laws of particle physics are imposed on intrinsically
passive things which have kind identities which are independent of the laws of
their behaviour is thus implausible from the point of view of modern science.
Essentialism is a much more plausible position to take”[24].
As Brian Ellis
observes, the claim that the world is structured into hierarchies of natural
kinds of objects and so on, could in principle be accepted by philosophers who
were otherwise sympathetic to mechanism[25] : things of different natural kinds, they might say,
are just things made up of different basic ingredients, or of the same
ingredients, but put together in different ways, although there is nothing in
their natures which requires that they should behave in one way rather than
another. How they are disposed to behave depends on what the laws of nature
happen to be. Now it is precisely such a contingency thesis or Humean view of
the laws of nature that Ellis denies[26]. First, the relationship of dependence between the
causal powers and the laws of nature is the other way round: the laws depend on
the properties, not the properties on the laws; second implication: the laws of
nature are metaphysically necessary, and hence true in all possible worlds[27]. That is, “it must be metaphysically impossible for
things, constitued as they are, to behave other than in accordance with the
laws of nature. Even God (assuming Him to exist and be all powerful) couldn’t
make them behave contrary to their natures. He might change their natures,
perhaps, so that they might become, or be replaced by, different kinds of
things. But there is no possible world in which things, constituted as they
are, could behave any differently. For them to behave differently, they would
have to be or become things of different kinds, or be made up of things of
different kinds”[28]. Hence laws of nature are both descriptive and
prescriptive: “What science observes and codifies are the manifestations of
these dispositions. Hence, laws which describe how dispositional properties act
will, at the same time, tell us what things which have these properties
essentially must do in virtue of
being the kinds of things they are”[29].
The natural dispositions
are the truthmakers for these laws.
2. Mumford’s dispositional essentialism.
Even if Mumford characterizes his own
position as being mainly a functionalist[30] view of dispositions coupled with a neutral monistic
ontology, at several places, especially in his comment on Ellis & Lierse’s
paper[31] as well as in the
last chapter of his book Dispositions[32], he admits that he endorses dispositional
essentialism for certain basic kinds and agrees with many points raised by
Ellis and Lierse: only, he takes them to task for the ontology they deem
necessary for their position.
So,
let me try to spell out what are the main arguments Mumford advances in favor
of such dispositional essentialism:
1.
First of all, Mumford thinks that “the explanatory value of appeal to
dispositions typically resides in them being
causally efficacious and being properties”[33]. It means that they cannot be reduced, for example,
to a different class of entities such as events or occurrences, and that their
criterion of existence is the causal criterion which can be defined in the
following way :
“The
causal criterion of property existence: for any intrinsic abstract property P, P exists if
and only if there are circumstances C in which the instantiations of P have
causal consequences”[34].
2. Ellis and
Lierse, at least in their 1994 paper, were very clear that they did not seek to
“restore the reputation of dispositions by attacking the status of categorical
properties, or by arguing that all
properties are basically dispositional, as some philosophers have done”[35], but mainly to show that “their lowly status was a
consequence of their traditional affiliation with an inadequate ontology based
on a Humean metaphysic, and a flawed semantics of dispositional terms”(ibid.). So, what they sought to provide
was “a more adequate semantics, and an ontologically more satisfactory theory
of dispositions – one which allows at least some dispositions to be counted as
genuine properties existing in their own right”(ibid.).
Mumford, together
with most philosophers trying to rescue dispositions, agrees with the first
part of the program: a new semantics for disposition is needed, which in
particular should provide an adequate analysis of the relation (which is not
one of equivalence, but of irreducibility[36], between disposition ascriptions and subjunctive
conditionals.
3. Again, as
Ellis and Lierse, and unlike, for example, Hugh Mellor, who thinks that such
properties as triangularity which at first sight look categorical, may be
viewed as dispositional[37], Mumford does not so much attack the
Categorical-Dispositional distinction as he tries 1. to explain why it is
relevant only as a conceptual (though not a real[38]) distinction between ascriptions (chap. 4), 2. to
clarify the confusions attached to the concept “categorical”[39], 3. to fix some criterion for the distinction, namely
the following: both dispositional and categorical properties have causal roles.
But “disposition ascriptions are
ascriptions of properties that occupy a particular functional role as a matter
of conceptual necessity and have
particular shape or structure characterizations only a posteriori” whereas
“categorical ascriptions are ascriptions
of shapes and structures which have particular functional roles only a posteriori”, namely as part of scientific
investigation[40]. Indeed, “what is crucial to property monism (the
position Mumford adopts) is a justification of the claim that dispositions and
their categorical bases are actually the same states of particular things,
characterized in two different ways, rather than distinct states in the world”[41]. Which, incidentally means that “the identity
conditions for properties are separated from the identity conditions for
predicates”[42]. Hence “I can
know what it is for x to be soluble
though I need not know what it is for x
to have the particular molecular structure which is a categorical base of
solubility, say, xyz. I need not know
which molecular structure is involved or even what a molecular structure is,
even though ‘x is soluble’ may be true in virtue of the possession of the same
state that makes ‘x has molecular structure xyz’
true”[43].
4. Again, another
argument by which Mumford seems to agree with Ellis’s version of dispositional
essentialism is his rejection of the Continuing existence argument
raised by categorical realists to justify the need of categorical bases for
dispositions. Now the continuing existence is the claim that dispositions have
existence in between their manifestations only if they are grounded in
categorical properties. Indeed, as Ellis and Lierse hold, dispositions need to
be based in reality: “They must at least be properties of real things.
Moreover, it is often the case that things have the dispositions they do
because of their internal structures; and in all such cases, we may say that
the dispositions are grounded in these structures. However, it is not clear
that the basis of any given disposition must, or must, ultimately be
non-dispositional. For, without begging the question against non-Humeans, it
cannot be assumed that the basis of a disposition does not, or does not
ultimately, include other dispositions. For example, the dispositions of an
object might well depend on the causal powers of its parts, as well as on how
these parts are arranged”[44]. So a power could well be grounded in a further
power: not all powers need categorical properties. Nevertheless, Mumford is
very cautious to distinguish “ordinary” from “ultimate” dispositions. First, because “most dispositions are of the
ordinary variety”[45], so that ultimate dispositions are “limited’
(examples of which would be the dispositions of subatomic particles which
apparently have no internal constitution that could explain their behaviour).
Second, because the history of science shows that mistakes are possible in this
respect: “We cannot be sure, for any putative ungrounded position, whether it
is genuinely ungrounded or actually just an ordinary disposition and only
thought to be ultimate because of the incomplete state of our physics”[46]. Nonetheless, in terms of explanatory requirements
and sound methodology we cannot either rule out their existence a priori[47]. Even more: “The nature of explanation is such that
ungrounded dispositions will always have to be posited in order to avoid a regress of explanation and, further,
we have every reason, as part of the atomist strategy, to assume that there are
genuine ungrounded dispositions. So the function of ungrounded dispositions is
to ‘fill the space’ of our process of explanation”(ibid.).
5. Another
important point of agreement in both versions of essential dispositionalism has
to do with the indeterminate[48] character of most dispositions, either causal[49] or stochastic[50].
6. But most of
all, Mumford agrees with Ellis not only in letting disposition ascriptions play
an explanatory role and in conceiving dispositions as units of explanation, but
in favoring a dispositionalist account of laws, instead of what he labels the
“law view”, namely, the view that laws, conceived as constant conjunctions or
natural necessitations of events, are the basic building blocks of explanation[51]. Instead, “the dispositionalists attempts to dispense
with laws of nature by grounding natural necessities within the individual
instantiated properties themselves. This gives us the model of instantiated
properties as real powers to do things. It is also useful to speak of them as
enablements or affordances where this conveys the dispositional notion of
causal mediation between events. Thus we have natural necessities without
commitment to general laws ranging over classes of events. Instead of general
necessities, natural necessity occurs at the level of the particular. It is not
in virtue of a general law that sugar dissolves when in a liquid, for instance,
it is in virtue of a particular state or instantiated property possessed by
that sample that it does so”[52].
In various
places, Mumford has, quite convincingly, I think, outlined the advantages
offered by such a dispositionalist account of laws over both the Humean
supervenience view as most strongly defended by David Lewis[53] and the Dretske[54]-Tooley[55]-Armstrong[56] (DTA) view of laws, which, despite its challenging
the Humean view by taking laws to be real things in nature involving necessary
connections between properties, still retained some vestiges of the Humean
metaphysic.
Now, what are
indeed the advantages of seeing laws to be supervenient upon dispositions
instead of dispositions being supervenient upon laws?
The problems with
some laws (I do not deal here with statistic laws) (such as “all water boils at
one hundred degree centigrade or “all ducks have webbed feet”) are well
known: the identification of them with
universally quantified conditional statements is doomed to failure. The main
challenge to regularity accounts of law is to distinguish coïncidental from
genuinely lawlike regularities[57] and, secondly, virtually no statements of this form
are true[58]. As Nancy Cartwright has argued, laws of nature qua general statements are, for the most
part, idealizations and abstractions that should not be regarded as literally
true. And the ceteris paribus
strategy amounts to triviality.
Getting away from
the notion of the statements of laws being general truths, the DTA or “nomic necessitation” version, by
construing them as causal relations holding between universals constitutes a
progress in so far as it allows realist causal claims that go beyond empirical
evidence[59]. But the nomic necessitation view does not explain
how nomic necessitation entails the corresponding generalisations – it has to
stipulate that it does. Moreover, at least in the case of Armstrong’s
conception, according to Mumford, although it deals with exception cases (the
“oaken” laws as opposed to the “iron” laws), it too, like Hume’s and Lewis’s
accounts, is “committed to reading off the laws from the actual history of
events at a world”[60] and is caught up
in some form of actualism: “The only
existence of the laws is in what particular causal sequences occur, so the laws
are determined by the events” (ibid.). Causation holds between
universals but it can only do so if it has instantiations standing in the right
relation.
Mumford thinks
that a right account of laws must reside somewhere “twixt regularity and
regulation”, namely between the descriptive regularist view and the theological
view concentrating on regulation with laws as God’s prescriptions. In order to
qualify as the right interpretation of laws, both somewhat descriptive and
prescriptive, viewing these as that “which bind the possible and necessary but
not the actual in the natural world at which they apply”, a dispositionalist
standpoint seems the most appropriate. For example, instead of construing “all
ravens are black”, let us drop the
requirement that the conditionals associated with law statements must be
universally quantified: let us just say instead “ravens are black” without
quantification. Now there is no need for quantification if we understand such a
statement as being not explicitly about a numerable quantity of ravens but as
being about the normal dispositional colouring of the species. According to
Mumford, such a view fits with scientific practice: namely, the scientist finds
a typical representative of some species or kind of thing and then, in
carefully controlled conditions, finds out some natural dispositional property
of that thing. He is not concerned with amassing more and more cases of black
ravens, nor will be troubled by the existence of strange cases, such as an
albino (the equivalent of C.B. Martin’s electro fink-case)[61]. Thus, such a
notion of “the natural behaviour of things” supplies us with as much description and regulation as we need for
our laws, it gives us a sense of objects having natural governing principles
without obliging us to give up contingency. Indeed, Mumford contends, “because
of the dispositional force of such governing principles, these dispositions
need not be manifested: whether or not they are manifested depends on the
contingencies of the world’s history; for instance, on whether the right
stimulus conditions are ever realized and whether the correct background
conditions are in place”. In the second place, “what the laws are best
understood as descriptive of is not actual or possible events but the
capacities of things. Thus, the truth of the claim that a fair coin has a 50/50
chance of landing a head or a tail is true not in virtue of the result of any
toss or sequence of tosses, but in virtue of the 50/50 propensity the coin has
to land head or tail.…The probabilistic law can thus be explained by it being
descriptive of an actual disposition and the account also explains the
possibility of unrealized laws. The disposition ascription is true of the coin
if it is never tested and thus there can be two true but different ascriptions
in two worlds that coïncide in all their events”[62]. In the third place, “there is plenty of contingency
in these laws: one needs not even appeal to another possible world to
illustrate this : the laws of nature could change, gradually or
instantaneously. The laws are fixed only by what things (can) do at present.
Thus ravens are black now, meaning that it is true of the raven kind that its
normal members are dispostionally black, but tomorrow, through a divine
intervention, normal ravens may become dispositionally pink. More naturally,
over a period of time normal ravens may become grey through evolutionary
processes. So such an account leaves open the possibility that even the
fundamental laws could change”(ibid.).
So far so good.
But are such arguments wholly convincing?
3. Some suggestions about the main difficulties
dispositional realism should be ready to face.
Mumford as well
as Ellis or other proponents of the redemption of dispositions intend to confer
them a real and not merely fictional status. But what kind of reality have
dispositions actually gained? In other words, are their respective versions of
dispositional essentialim or functionalism realistic enough?
There are a lot
of convincing aspects in Mumford’s account but some are also somewhat puzzling.
I shall take them in turn.
1)The merits
of ontological deflation or “neutrality”: from properties to predicates. It
is surely an interesting part of the neutral monistic understanding of
dispositions to show how the dispositionality or non dispositionality of a
property or state is not a question which is (mainly) grounded in ontology, but
is, rather, a matter relative to the predicate
with which the property or state is denoted and to the connection between this
predicate and the behaviour which is mediated[63]; or again that “it is not a truth of ontology whether
a property is dispositional or not; it can only be a truth about concept”[64]. All the same, as both Ellis and Mumford have
observed, such a conceptual reading of the issue does not prevent you from
being a realist, as Peirce once also noted, who was one of the first
philosophers to attach a particular importance to the reality of dispositions:
“Anybody may happen to opine that ‘the’ is a real
English word; but that will not
constitue him a realist. But if he finds that, whether the word ‘hard’,
itself be real or not, the property, the character, the predicate hardness is not invented by men, as the
word is, but is really and truly in the hard things and is one in them all, as
a description of habit, or behaviour, then, he is a realist”[65].
So indeed, any correct account of the role
and nature of dispositions should start with a semantic account of
dispositional predicates, as Hugh Mellor also reminded us[66], and, in particular, should try to deal with the
reasons why dispositional ascriptions might be meaningless (for example, due to
finkish, antidote or mimic cases), or why reduction sentences may or may not
tell us what “all” dispositional predicates mean. Suppose, for example, that we
know all the manifestations of courage: are we going to be able to say what
“courageous” means by summing up all the reduction sentences that say what
those manifestations are? Or course not: as Peirce insisted on, a disposition
is, by essence, irreducibly general and indeterminate, and cannot be reduced to
the mere conjunction of its occurrences.
2) Dispositions
as properties or how should one understand the Categorical-Dispositional distinction?
But, as Mellor,
Ellis or Mumford also insist on, properties are not (or are not given) simply
by the meaning of our predicates[67]. Nobody would ever think that the planet Mars is, or
is part of, or is defined by the meaning of the “word” Mars which we use to
refer to it. On the contrary, what gives consistency to the referential
capacity of our predicate , when we use it, is that it takes for granted the
existence and the identity of planet Mars. In other words, we want a
conditional and non verifunctional statement such as “if x was dropped,
it would break” to have a truthmaker. This is why Mellor, following Armstrong[68], rejects the Rylean and counter intuitive view
according to which when a fragile thing a and a non fragile thing b are
not dropped, there need not be a factual difference between them[69]. On the contrary, one should say that if a is
fragile and b is not, then a and b, whether dropped or
not, must differ in some respect, the most obvious difference consisting in the
fact that a has the property of being fragile, which b has not.
But how should
one explain what that property consists in? To a certain extent, Mumford
refuses to commit himself too far.
“The
functionalist theory of dispositions states that nature consists of
hierarchically ordered levels where at each level there are entities or
properties than can be characterized either dispositionally or structurally and
whether they are dispositional or structural characterizations depends on their
explanatory relations to other entities or properties within the whole of which
they are a part”
Hence:
“Relative to the functional role of causing
dissolving when in liquid, a denotation of a property P that has that
causal role by conceptual necessity - solubility- is dispositional. Denoted in
such a way that does not conceptually necessitate that causal role, perhaps in
terms of molecular structure, that same property comes out as
non-dispositional. By the argument from the identity of causal role, however,
these two denotations are of the same state or property instance”[70].
In a similar vein, Mellor suggests that
properties are neither categorical nor dispositional: they just are.
But this is a bit
unsatisfactory. To a certain extent, Avicenna had a similar formula when he
said that equinitas est equinitas tantum.
Now everybody knows that the whole problem of universals started from the
questions raised by grounding the objective indeterminacy of such a “tantum”.
It seems too easy, or a way to have one’s cake and eat it, to deny a real
distinction between the Categorical and the Dispositional while agreeing that a
conceptual distinction is needed, meaning by this that it must have some
objective foundation, or that it is more than a distinction of reason, namely,
more like what Duns Scotus would have named a formal distinction, that
is “a distinction from the nature of the thing occurring between two or more
really identical formalities, of which one, before the operation of the
intellect, is conceivable without the others though inseparable from them even
by divine power”[71]. One way or other, some deep metaphysical issues will
have to be handled here with great care.
3.
Substantival or Relational Realism? Again, the “neutral” monism is in
danger of committing itself to more ontology than it would surely be prepared
to, at least in the following respect: In Hume’s ontology, there is a sharp
distinction between the way a thing is, and how it is disposed to behave: the
way it is depends on what its properties are. How it is disposed to behave
depends on what the laws of nature are. The two are supposed to be independent
of each other[72]. Mumford’s general view has the great advantage of
trying to account of the changes that occur in the world, from the inside: as he
somewhere says, a world described entirely in categorical terms is a static
world, and hence, not ours[73]. Again, the familiar Humean point that it is a
logically contingent matter what effect follows from any antecedent event, and
that laws of nature are what is added to animate, so to speak, the world, has
something unconvincing about it.
This is precisely
such a confusion which Peirce diagnosed in the scholastics’ treatment of
dispositions. As is well known, the scholastics (with the maxim operari sequitur esse) claimed that the
operations or activities reflected a corresponding perfection in that thing,
which could account for its ability to perform that sort of operation. It was
on the basis of this principe that they were able to specify natures and natural
classes. If a man performs an action that others animals cannot, such as
reasoning, then the man has a power that other animals do not possess. If such
a capacity is the distinguishing characteristic, it is dignified with the title
“nature”. But why did Peirce finally object to the scholastic operari sequitur esse, i.e. to the
substantial form as a dispositional character - aside from the question of how
scientific one is in determining distinguishing characters[74]? Because it failed to reveal the relational structure which is ultimately involved. That is, the
scholastics were right, as far as they went, but their limited logic did not
allow them to see that the nature, power, or disposition represented in these
monadic predicates was only a truncated image of a relational law. Apparently,
it was the old logic’s inability to handle abstractions properly that was
mainly at fault[75]. The scholastics did not realize that their most
important abstractions were really hypostatized relations, and therefore that real
abstractions indicated real relations - laws and not forms. I am not sure
whether Peirce’s substitution of a relational realism to a substantival
realism is necessarily the correct way of handling the problem of dispositions,
but at any rate, it is true that there is, from Mumford’s part, a very
unelaborated commitment to a view of what an object is in terms of a plain substance,
and not much elaboration either on the “something” which justifies or
constitues the truthmaker for a dispositional ascription: is it mere epistemic indeterminacy? Or is
this indeterminacy linked with some irreducible, metaphysical features of, for
instance, some Common Nature? Again, Mumford is obviouly committed to a trope
theory view of instantiated particulars but neither does he provide an account
of the process of instantiation or individuation nor does he present a
justification of the reasons why he should rather favor such a view instead of
another[76], while admitting that there are notorious
difficulties, raised by Russell for example, with a tropist account.
4) The generality objection: Contingency
or Necessity?
There are advantages in adopting a
dispositionalist view of laws, as Mumford has clearly outlined[77].
But the dispositionalist also faces problems: namely, how can he, without
general laws, explain why generalities in behaviour are true of kinds? For
example, all sugar dissolves in liquid and tastes sweet to the tongue. Is is
merely a cosmic coïncidence that each sample of the kind carries the same set
of capacities? Could we have rogue samples that possessed different
dispositions? Here we face a very serious issue with which I am not sure I
clearly understand Mumford’s position or whether he provides a satisfactory
answer to it: this has to do, it seems to me, with the contingency he wants to
maintain in his dispositionalist account of laws.
In the last
chapter of Dispositions, Mumford
clarifies the charge he had adressed in a previous article, namely that Ellis
and Lierse argued that dispositional essentialism entailed “a definite answer
to this debate: that dispositions were ultimate, rather than laws. This
involved them making a number of controversial (and poorly justified) claims,
such as the laws of nature were logically necessary instead of contingent as
the Humean tradition takes them to be”. But, Mumford contends, dispositional
essentialism could be true even if it were laws rather than dispositions that
were in the relevant sense ultimate or basic. Which does not mean, he hastens
to adds, “that the basic laws view is
proved” or that he was
offering a proof, even though in places he “pushed that view for dialectical
purposes”[78]. Further, “although basic dispositions as truthmakers
of laws are not necessary for the claim of dispositional essentialism about
certain fundamental kinds in science, as Ellis and Lierse suggested,
…dispositional essentialism may be required for the credibility of the basic
dispositions view because it suggests a solution to the generality problem that
exists for the basic dispositions view. Hence, basic dispositions are not
required by dispositional essentialism but dispositional essentialism may be
required for basic dispositions” (Ibid.).
Intricate (or
dialectical) as it may sound, such a formulation points to some difficulties I
have in understanding Mumford’s exact position as far as the status of laws is
concerned, as well as regards the explanatory role he wishes himself to confer
to “basic” dispositions. In particular, is Mumford really subscribing to the
contingency thesis (CT : the laws of
nature are logically contingent) about laws?
In Dispositions, he explicitly says he
endorses it: “Although dispositions bring natural necessity in the world there
still exists the kind of logical contingency that is required. The replacement
of laws with real dispositions is no threat to the view that the way nature
behaves could have been otherwise but it does mean that CT will have to be
revised accordingly”. Indeed, “a
modified version of the CT can be given that is framed in terms of the
contingency of a particular’s capacities, rather than the contingency of laws”.
And he pursues: “There exist relevant conceptual necessities of dispositional
essentialism, such as that described above where an electron must,
conceptually, have certain dispositions if it is to be an electron. Such
conceptual necessities do not threaten natural contingency in the sense that
the only logical necessities are conceptual. Hence it is logically contingent
that a particular entity is a particular with the capacities it actually has.
That particular could have had different dispositions to the ones it actually
has, even though this would entail that the particular belonged to a different
kind in virtue of that fact. Such contingency does not threaten the identities
for such entities across possible worlds however, for our disposition
ascriptions are actual-world relative”[79].
Hence Mumford
denies Ellis and Lierse’s move according to which dispositional essentialism
requires the logical necessity of physical laws. “While it is certainly true
that an electron would not be an electron if its behaviour were different from
the behaviour it has in the actual world, this necessity is purely conceptual.
That it is in virtue of behaviour B that a particular x is
classified within a kind K does not entail that x necessarily has behaviour B”(ibid.).
According to Mumford, this involves a misunderstanding of the scope of the
logical necessity involved. “That a particular possesses any disposition is
logically contingent even though some particulars, such as electrons, would not
have been classes as such if they had a different behaviour. To deny this would
be to claim that an electron’s behaviour is dictated by logic, and, presumably,
physics is a trivially analytic human folly” (ibid.).
But I do not think that such a criticism is
justified, at least, as far as Ellis’s dispositional essentialism is concerned,
which indeed does imply some necessitarist account of dispositions, if it aims
at presenting kinds of processes as discovered principles active in nature and
not as invented classifications. But to a certain extent too, I do not see how
Mumford can maintain, even in a reformulated way, the CT about a particular’s
capacities. What he may maintain at most (and in fact, it seems to be mainly
what he provides as a further account of laws in the paper given at the
Grenoble Conference) are some contingent elements understood as changes or
departures from the law. At all events, I doubt that one could go so far as
admitting such contingency as the one Mumford alludes too: “Thus ravens are
black now, meaning that it is true of the raven kind that its normal members
are dispositionally black, but tomorrow, through a divine intervention, normal
ravens may become dispositionally pink”. Indeed this is making fun of physics
or of the laws of evolution. It seems
that the contingency Mumford wants to introduce has more to do with what Peirce
called “conditional necessity”[80], in order to account both of the both descriptive and
regulative “would-be” (which was not merely a may be or a will be) character of
dispositional laws and the tychistic or chance elements he deemed necessary to
introduce in his both synechistic and evolutionary metaphysics[81].
Anyway, should that really be an advantage
for the dispositionalist account of laws to try, by all means, to avoid any
kind of necessity? For one thing, as we know from Kripke’s and Putnam’s works,
a point also recently emphasized by F. Jackson[82], many necessary facts can be known to be true by a
posteriori means only: certain identity statements, including identity
statements concerning scientific and natural kinds, express propositions that
are necessarily true, but that can be known only a posteriori. Hence, in
general, as A. Bird has shown in a recent paper[83], the thought that laws might be necessary but
knowable only a posteriori is not objectionable and should be familiar
from other cases. Furthermore, it can be shown that some laws are necessary but
have every appearance of contingency:
“Let us for sake of argument grant that the basic laws
of nature are contingent. Let a non-fundamental law, say, a law of chemistry,
assert that the substance S has some property D. We shall call this law L (S,
D). This law may supervene some underlying, more fundamental (contingent) law
C. So C entails (L(S,D)(i.e. necessarily, C implies L (S,D). Substances
themselves exist as a result of the laws of nature. And it might be that in
order for the substance S to exist, some fundamental laws must be true. In
particular the existence of S might require the truth of C. Hence S exists
entails C. So we have L entails C entails L(S,D). Hence the very existence of S
necessitates the truth of the law L (S,D). Hence there is no world where S
exists but the law L (S, D) fails to hold. Precisely this relationship can be
shown to hold between the existence of salt (sodium chloride) and the law that
salt dissolves in water. The underlying law in this case is Coulomb’s law which
governs both the electrostatic attraction required for salt to exist and also
is sufficient to encure that salt dissolves in water. Clearly the law that salt
dissolves in water is a posteriori and at first sight it seems entirely
contingent. But it can be shown to be necessary, even if we assume that the
underlying laws are contingent”[84].
Whatever we decide in favour of contingent or
necessary laws, it remains that one should be careful, when adopting such and
such form of dispositional essentialism or realism, not to indulge in what
Popper thought was the major defect of essentialism: to aim at providing an ultimate
explanation of what reality consists in. While Mumford’s recourse to
“ungrounded” dispositions may sometimes sound a little bit like a virtus dormitiva, I prefer to view it
less as a quietist (or Wittgensteinian) invitation (something like:
justification must end somewhere) than as a principle of sound, fallibilistic
methodological procedure.
[1]. « Sur la réalité des
propriétés dispositionnelle », Actes du Colloque de l’université de
Caen (janvier-février 2000), à paraître en 2003.
[2]. “The Origins and Forms of
Qualities”, in M. A. Stewart (ed.), Selected Philosophical Papers of Robert
Boyle, Manchester, Manchester University Press, 23, 1979, 1-96.
[3].
Cf. for ex. The Roots of Reference, La Salle, Ill., 1974, p. 11,
or The Ways of Paradox, 1966, Harvard University Press, p. 71-72.
[4]. N. Goodman, Fact, Fiction and
Forecast, Indianapolis, 1955.
[5]. G. Ryle, The Concept of Mind,
London, Hutchinson, 1949.
[6]. Ian .J.Thompson, “Real
Dispositions in the Physical World”, British Journal for the Philosophy of
Science, 1988, 39, 67-79, p. 76-77.
[7]. Rom Harré, “Powers”, British Journal for the Philosophy of
Science, 2, 1970, 55-101; R. Harré & E.H. Madden, “Natural Powers and
Powerful Natures”, Philosophy 48, 1973, 209-230 ; R. Harré & E.H.
Madden Causal Powers: A Theory of Natural Necessity, Oxford,
Blackwell, 1975.
[8]. Nature’s Capacitie and their Measurement, Oxford, Clarendon Press, 1989: “It is not the laws that
are fundamental, but rather the capacities”(p. 181); also see The Dappled World, Cambridge, Cambridge
University Press, 1999.
[9]. A World of Propensities,
Bristol, Thoemes Press, 1990.
[10]. D.H. Mellor, especially “In
Defense of Dispositions”, Philosophical Review, 83, 1974, 157-181;
“Counting Corners Correctly”, Analysis, 42, 1974, 96-97 and “The
Semantics and Ontology of Dispositions”, Mind, vol. 109, 436, oct. 2000,
757-779.
[11]. For Blackburn, science finds
dispositions “all the way down”, “Filling in Space”, Analysis,
50, 1990, 62-5.
[12]. Cf. S. Blackburn, ibid.
[13] . I have tried to spell out some arguments in favor of such a position in « Sur la réalité des propriétés dispositionnelles », art.cit.
[14]. B. D. Ellis & C. E. Lierse,
“Dispositional Essentialism”, Australasian
Journal of Philosophy 72, 1994, 27-45 ; “Natural Kinds and Natural
Kind Reasoning”, in Natural Kinds, Laws
of Nature and Scientific methodology, P. Riggs (ed.), Kluwer Academic
Publishers, Dordrecht, 1996, 11-28 ; “Causal Powers and the Laws of
Nature”, in Causation and Laws of Nature,
H. Sankey (ed.), Kluwer Academic Publishers, Dordrecht, 1999, 21-42 ;
“Bigelow’s Worries about Scientific Essentialism”, ibid., 77-97 ; “Response to D. Armstrong”, ibid., 49-55 ; Scientific Essentialism, Cambridge
University Press, 2001 ; and for a good summary of his position, see “The New Essentialism and the Scientific
Image of Mankind” (NESIM),
http://www.rescogitans.it/ita/scenari/tilgher/Ellis.htm.
[15]. Cf. NESIM, 3 “Scientific
essentialism”.
[16] . NESIM, 3.
[17]. Ibid., and Scientific Essentialism, op.cit., p.3.
[18]. NESIM, 3 and Scientific Essentialism, op.cit., p. 6.
[19]. NESIM, 3. Cf. Scientific
Essentialism, op.cit., p. 106-144. This is what D. Armstrong objects to.
See his “Reply to Ellis”, in Causation and Laws of Nature, op.cit., 43-48. He argues
that such intrinsic causal powers are Meinongian properties, and thus
objectionable. In principle, he says, there could be causal powers which happen
never to be exercised. If such properties have no categorical bases, as Ellis
allows is possible, then such powers can be defined only by relationships
between non-existent objects, i.e. between the kind of circumstances which
would trigger them and the kind of display which would then result. For Ellis’s answer see op.cit., p.
133-135.
[20]. NESIM, 3. Ellis claims that it is this second tenet of scientific essentialism which sets it apart most strongly from other theories of the nature of reality.
[21]. Ibid.
[22]. NESIM, 4.
[23] . Scientific Essentialism, op.cit., p. 2.
[24]. NESIM, 4.
[25]. Op.cit., p. 107 ff.
[26]. See Scientific Essentia lism, op.cit., p. 4, p. 7, and p. 44 ff, p. 211 ff., p. 229 ff., p. 261 ff.
[27]. Op.cit.,part four, chaps. 6 and 7, p. 203 ff.
[28]. “The most elementary kinds of
things all have fixed causal powers, i.e. their dispositional properties are
all fixed by their essential natures. A copper atom, for example, has the same
dispositional properties wherever or whenever it might occur. The same is true
of a proton or an electron. They are things which belong to what might be
termed “fixed natural kinds”.Their distinguishing feature is that you cannot
change any of their dispositional properties. They do what things of these
kinds always do, and you cannot teach them any new tricks. There can be no
question of a copper atom, for example, being disposed to behave in one way at
one time, but in a different way at another time. Nothing with such variable
powers could possibly be a copper atom”. NESIM, 5.
[29]. B. Ellis & C. Lierse, art.
cit., p. 40.
[30]. I have shown in « sur la réalité des propriétés dispositionnelles » (art.cit.), the difficulties raised by a « functionalist » account of dispositions. On the problems linked with « functions », see also J. Searle, The Construction of Social Reality, 1995, New Yok, éditions Free Press, p. 29 ff.
[31]. “Ellis and Lierse on Dispositional
Essentialism”, Australasian Journal of
Philosophy, 73, 1995, 606-612.
[32]. Clarendon Press, Oxford, 1998, p.
234 ff.
[33]. Op.cit., p. 14.
[34]. Op.cit., p. 122. This
means, in particular, that mere “Cambridge changes” are not allowed. S.
Shoemaker also agrees on that criterion; see his “Causality and Properties”, Time
and Cause, edited by P. van Inwagen (Dordrecht : D. Reidel, 1980), 109-35,
repr. in Properties, ed. by D. H. Mellor & Alex Oliver, Oxford:
Oxford Readings in Philosophy, 1997, 228-254, p. 232. cf. Evan Fales in Causation and Universals, p. xiii: “A
physical universal exists if and only if it is a member of the causal ‘web’ ;
if it is then it exists whether or not it is ever instantiated” quoted by
Mumford, op.cit., p. 123. Let us note
that some philosophers do no accept the idea that the causal criterion should
be a criterion for the existence of a property. For ex., Alex Oliver, “The
Metaphysics of Properties”, Mind, vol. 105, 417, jan. 1996, 1-80, p. 8..
[35]. Art.cit., p. 27. The philosophers
they cite are R. Harré and E.H. Madden, as well as Evan Fales, who “has argued
that the essential properties of the most fundamental natural kinds are their
monadic properties, and, in so far as these properties are dispositional,
things of these kinds must behave as these properties prescriube” (Evan Fales,
“Essentialism and the Elementary Constituents of Matter”, Midwest Studies in Philosophy, 11, 1986, 391-402, Causation and Universals, London,
Routledge, 1990). Nevertheless, Ellis and Lierse admit that “in the case of the
fundamental particles, the dispositional properties may indeed be all that we
have” (art.cit., p. 29). Mumford agrees with this. Not only does he admit the
possibility of “ungrounded dispositions”, but his functional analysis makes him
give importance to such functionalist systems as “thermostats” or thermometers
whose essence is clearly entirely dispositional (op.cit., p 8), i.e.
that “the exact mechanisms that equip a thermostat with the dispositions it has
are, in a significant way, irrelevant to the fact that it is a thermostat..
Roughly, for something to be a thermostat, it must be sensitive to changes in
temperature and be able to trigger a switch if a pre-calibrated temperature
threshold is crossed”(ibid.).
[36]. Dispositions, op.cit.,
p. 63. See chaps 3 and 4 for more details: “What I suggest is the rejection of
a solely conditional analysis of dispositions and that we treat them as real
instantiations of properties which afford possibilities rather than just being
shorthand ways of talking about certain combinations of events”.
[37]. “Counting Corners Correctly”,
art.cit., p. 97. Ellis & Lierse note that Mellor’s dispositional
foundationalism, which purports to tbe Humean, faces difficulties: “By
embracing the Contingency Thesis, Mellor, at the very least, has to subscribe
to the view that the laws in this world are only contingently related to the
entities that exist in it. Thus, the behaviour of an entity must be logically
distinct from the kind of thing it is. Now, if Mellor wants to 1) deny the
existence of categorical properties, 2) avoid embracing a behaviourist theory of dispositions, and
3) have an ontology of occurrent properties, then his only option is to identify a disposition with some
occurrent property or properties which are not dispositional. But what could
these be? Could they be, perhaps, those structural or other properties which
must exist if the disposition is to exist?” (art. cit., p. 35).
[38]. He is very careful to distinguish
the two levels. See for ex. p. 145: “The thesis of property dualism tries to
take this distinction (ie. C-D) further into ontology. Property Monism, on the
other hand, is the claim that the conceptual distinction is the only distinction because it denies that
there is an ontological division in reality which the conceptual division
maps”. “There are not distinct categorical and dispositional types of
properties but there are distinct categorical and dispositional ways of talking
about instantiated properties”.
[39]. “In particular, if ‘categorical’
means ‘unconditional’, dispositions are, in a very obvious way, categorical :
when I say that a particular sugar-cube is soluble, I am in no way making an
ascription conditionally for I am saying that it is actually soluble now, not
that it could be soluble if some other conditions obtained”(p. 64).
[40]. Dispositions, op.cit., p. 77.
[41]. Dispositions,
op.cit., p. 145. In particular this means that “the identity conditions
for properties are separated from the identity conditions for predicates”(p.
146). At the same time, it implies also, as Armstrong puts it, “the
emancipation of the theory of universals from the theory of semantics”, A Theory of Universals, Cambridge,
Cambridge University Press, 1978, p. 6. For Mumford this position has the
following consequence: “We can have property monism even if identification
between universals cannot be made. The only problem becomes, whether there is
some plausible notion of a property instance that can warrant our consent”(p.
160).
[42]. Op.cit., p. 146.
[43]. Op.cit., p. 148.
[44] . Ellis & Lierse, art.cit., p. 31.
[45] . Dispositions, op.cit., p. 229.
[46]. Ibid., p. 231.
[47]. Ibid., p. 233.
[48]. This indeterminacy in a
deterministic world is due to the linguistic vagueness. Hence, “To define
fragility, for example, we cannot do much better than say that a fragile object
is likely to break if dropped, or
otherwise handled roughly. Any more precise definition might capture some more
specific concept of fragility. But it would not be the broad but vague concept
with which we are familiar”. On the contrary, in an indeterministic world such
as ours, “the dispositions are causally interminate, not because of vagueness,
but because of the indeterminacy underlying phsycial processes. For example,
the probability that a radium atom existing at t will have decayed by t +
∂ is, for any given frame of reference, a precisely specifiable function
of ∂, and this probability is independent of the circumstances in which
the radium atom exists. Hence, we cannot, even in principle, eliminate this
causally indeterminate disposition in favour of any more precisely defined
dispositions which are causally determinate” (Ellis & Lierse, art.cit., p.
42).
[49]. “Where we have a causal
disposition, there is typically a certain pattern of cause-and-effect or
stimulus-and-response which anything having the disposition would normally
display if it were appropriately caused or stimulated to do so” (Ellis &
Lierse, art.cit., p. 40).
[50]. “A Stochastic disposition is a
propensity of some kind, in which the antecedent condition is not strictly the
cause of its manifestation, but only a necessary condition for it. For example,
the disposition of a radium atom to decay in a certain way is a stochastic
disposition. If this species of radioactive decay is to occur, it is a necessary condition that radium atomes should exist. But
events of radioactive decay are not caused
by the existence if such atoms. Not, as far as they know, are they caused
by anything else. There is just a certain objective probability p that
within any given-time interval ∂ such an event will occur’ (ibid.,
p.40).
[51]. Dispositions, op.cit., p. 217.
[52]. Op.cit., p. 221.
[53]. Counterfactuals, Blackwell,
1973 and “Humean Supervenience Debugged”, Mind,
1994.
[54]. F. Dretske, “Laws of Nature”, Philosophy of Science, 1977,
248-268.
[55]. M. Tooley, “The Nature of Laws”, Canadian Journal of Philosophy, 1977,
667-698; Causation: a Realist Approach, Oxford, Clarendon Press, 1987.
[56]. What is a Law of Nature?
Cambridge, Cambridge University Press, 1983.
[57]. See A. Bird, “The Dispositionalist
Conception of Laws”, Foundations of
Science (forthcoming) 2003. The best of these is the systematic regularity
theory of Lewis (following from Ramsey), Counterfactuals, Cambridge,
Mass., Harvard University Press, 1973, p. 72-77: according to this view, a
generalisation states a law only if it is deducible from that axiomatic
systematisation of the facts that optimally combines strength and simplicity.
While this reduces the pressure of the objection from accidental regularities,
it does not, as Bird notes, remove it altogether. “For we could imagine a
system of laws that was itself rather complicated and weak but which generated
an accidental regularity, whose addition to the axiomatic sytem might in fact
add considerably to its strength without detracting much from its overall
simplicity”.
[58] . Dispositions, op.cit, p. 122 ff.
[59]. When the relation holds between
two universals it entails the corresponding generalisation but the reverse
entailment does not.
[60]. S. Mumford, « L’état des lois», paper from the Conference which
took place at the University of Grenoble (december 2000), in Objets,
propriétés, états de choses : le renouveau de la métaphysique australiene, Paris,
Vrin.
[61]. C. B. Martin,”Dispositions and
Conditionals”, The Philosophical Quarterly, 44, 1994, 1-8. Note that
C.S. Peirce makes a similar remark: “what the chemist is interested in is not
the particular sample, but the molecular structure”, The Collected Papers of
C.S. Peirce, Cambridge, Mass., Harvard University Press, (8 vols. 1939-1958),
vol. 4, § 530.
[62] . This is more than a counterfactual difference, Dispositions, op.cit., p. 231.
[63]. Dispositions, op.cit., p. 210.
[64]
. Ibid., p. 213.
[65]. Collected Papers, op.cit., vol.1. §27n1.
[66]. Mellor, 2000, art.cit., 757-779.
[67]. Mellor, Matters of Metaphysics,
Cambridge, Cambridge University Press, 1991, p. 171. See also B. Ellis, op.cit.,
p. 18, n.1.
[68]. 1997, A World of States of
Affairs, Cambridge, Cambridge University Press, chap. 6.6.
[69]. Ryle, 1949, chap. 5.
[70]. S. Mumford, op.cit., p. 215.
[71]. M. J. Grajewski, The Formal
Distinction of Duns Scotus, Washington, 1944, p. 93.
[72]. Cf. Ellis & Lierse, art.cit., p. 28.
[73]. Op.cit., p. 214.
[74]. Collected Papers, vol. 6 § 361.
[75]. Collected Papers, vol. 3 § 642.
[76]. He rejects’s Prior’s contention that
some identification of properties as universals is needed. Mumford claims that
he can have property monism even if identification between universals cannot be
made. The only problem becomes whether there is some plausible notion of a
property instance that can warrant our consent. One candidate notion is that of
trope, being an “abstract particular”(cf. K. Campbell, Abstract Particulars,
Oxford 1990, or J. Bacon,
Universals and Property Instances,
Oxford, 1996), such as the
redness of a particular apple or the squareness of a particuler window.
According to the ontology of tropes, squareness and redness in general do not
exist, but only as samples of particular rednesses and squarenesses of things.
But, as Mumford himself admits, the problem with such an account is notorious,
and was noted by B. Russell: the trope theorist cannot explain how a number of
tropes resemble each other. How is it that ten red things are all red, for
instance? Mumford has this formulation : “Unless we accept some notion of properties
being instantiated in particulars, then it seems difficult to sustain the
evident link between a thing’s properties and the causal transactions into
which it enters. It is difficult, in short, to see how, unless we allow that
there are particular property instances possessed wholly by objects and
substances, a thing’s properties can have causal effects. What causes a square
peg to fit a square hole? It is not a timeless universal that exists nowhere,
rather it is something about this hole and this peg, regardless of what else
exhibits a similar quality elsewhere”. (op.cit., p. 161). Indeed, but it
is precisely on the “something about” that we expect some explanation
[77]. Cf. op.cit., p. 221 ff.
[78] . Op.cit., p. 235-236.
[79]. Op.cit., p. 236-237.
[80]. Collected Papers, vol. 2 §
664. This is a point recently emphasized by A. Bird, “Necessarily Salt Dissolves in Water”, Analysis 61, 2001, 267-275, and “On whether some laws are necessary’, Analysis 62 (2002),
257-274.
[81]. Cf. C. Tiercelin, « C.S. Peirce et le projet d’une
métaphysique scientifique évolutionnaire »,
Publications de la Sorbonne, Philosophie 5, nov. 2000, 453-463.
[82]. From Metaphysics to Ethics: a
Defense of Conceptual Analysis, Oxford, Clarendon Press, 1998. I have
analysed and commented such views in C. Tiercelin, « La métaphysique et l’analyse
conceptuelle », Revue
de Métaphysique et de Morale, oct-déc. 2002, 559-584.
[83]. “The Dispositionalist Conception
of Laws”, forthcoming (2003). Available in PDF on A. Bird’s web page.
[84]. Cf A. Bird, ibid., p. 8, §
7.1; see also A. Bird, “On whether some laws are necessary”, Analysis
62, july 2002, 257-270.