Towards a Property Theoretic
Account of Counterfactuals
W.
In his classic Fact, Fiction and Forecast (1955), Nelson Goodman presents two
problems of counterfactuals. One is the
problem of determining what conditions are supposed to obtain under
counterfactual antecedents. The other is
the problem of providing an account of laws that is adequate for ensuring that
the consequents of counterfactuals would be true had the relevant conditions
held in conjunction with the counterfactual’s antecedent. What is explicitly given in the antecedents
of counterfactual sentences typically do not entail their consequents. For instance, the antecedent of
(1) If match m were struck, then it would have lit.
does not guarantee the truth of its consequent. When we accept a counterfactual like (1) as
true, we do so on the grounds that certain conditions obtain which, in
conjunction with those explicitly stated in the antecedent, would provide for
the truth of the consequent. For
instance, in asserting (1) we suppose that were match m struck it would also be dry, there would be oxygen present, there
would be no strong drafts, etc. The
first of Goodman's problems of counterfactuals is that of identifying the
relevant conditions supposed to obtain were the antecedent of the
counterfactual true. But, even assuming
that we have settled what relevant conditions are presumed to obtain under the
antecedents of counterfactuals, the truth of the counterfactual’s consequent is
only assured if we also have grounds for thinking the laws of nature would
still obtain under the relevant counterfactual circumstances. Were the laws different, then match m's being struck might fail to issue in
its lighting even if all of the relevant conditions pertaining to the first
problem of counterfactuals obtained.
Hence, Goodman's second problem of counterfactuals is that of giving an
account of laws such that given the relevant conditions, the truth of the
counterfactual’s antecedent would assure the truth of its consequent.
I will argue that a view of laws as metaphysical
necessities provides the best answer to Goodman's second problem. Such views have been advanced by authors
including Shoemaker (1980), Swoyer (1982), and Ellis
and Leirse (1994).
But advocates of necessary laws have yet to provide an account of
counterfactuals that adequately treats both of Goodman's problems of
counterfactuals. The aim of this paper
is to advance that cause, if only by a few small steps. I propose a property theoretic account of
counterfactuals. The leading idea of the
proposed account is that counterfactual conditionals, when true, are made true
in part by complexes of properties, the joint instantiation of which would
metaphysically necessitate the truth of the counterfactual’s consequent. The account of counterfactuals to be
developed here is motivated by consideration of the role of laws in supporting
counterfactuals. I will start with a
discussion of the problem of law for supporting counterfactuals. This will lead us to a view of laws as metaphysically
necessary accounts of the essential and dispositional nature of
properties. We will then employ this
conception of essentially dispositional properties as the central component of
an account of causal counterfactuals.
It was regularity theories of laws
that were initially subjected to criticism for failing to support
counterfactuals[1].
On a simple regularity view of laws, to say that it's a law that copper
expands when heated is say nothing more than
(2)
("x) (x is copper and x is heated É x
expands)
But (2) is consistent with the truth of either of the
following counterfactual conditionals.
(3) If this piece of
copper had been heated at time t, then it would have expanded at t'.
(4) If this piece of
copper had been heated at time t, then it would have shrank at t'.
The mere truth of the generalization (2) gives us no grounds
for favoring the truth of (3) over the truth of (4). But in asking that laws support
counterfactuals, we expect an account of laws to play an important role in
accounting for the truth of (3) and the falsity of (4).
The available alternatives to the
regularity theories of laws propose to handle the problem of supporting
counterfactuals by modally strengthening the laws in certain ways. Armstrong (1983), Dretske
(1977) and Tooley (1977) offer an alternative to
regularity theories of laws in their view that laws are nomic
relations that hold among universals (henceforth, the ADT view). On the ADT view, laws are not general facts
but second order singular facts about universals. On this view, "laws issue in
regularities but are not exhausted by regularities" (Armstrong, 1983). With the exception of Swoyer (1982), adherents of this view of laws have
taken nomic relations to hold between universals
contingently. A nomic
relation N (F,G) holds between the universals F and G contingently, but its
holding between F and G necessitates that all Fs are Gs and, further, is
alleged to support our claims that non-Fs would be Gs if they were F. The difficulty for this view is specifying
just how we should understand the nomic relation N so
that counterfactuals will be adequately supported. We might try to understand contingent nomic necessitation as holding no more than that universals
standing in a nomic relation necessitates a general
regularity. This much can be asserted as
follows:
(5) Necessarily, if N(F,G) holds,
then ("x) (Fx ÉGx).
However, in terms of supporting counterfactuals, (5) offers
no advance over the regularity theory on which it holds trivially that
(6) Necessarily, if ("x)
(Fx ÉGx) then ("x)
(Fx ÉGx)
Supporting counterfactuals requires
that nomic relations have some "modal
weight" not enjoyed by other contingent facts. That is, our account of nomic
necessitation must give us good grounds to believe that the laws hold under the
antecedent suppositions of counterfactual conditionals. If nomic relations
hold contingently, their holding under counterfactual antecedents cannot be
taken for granted.[2]
To appreciate the force of this point,
we should consider more closely what truths hold and what truths fail to hold
under the suppositions of counterfactual antecedents. To employ the metaphor of possible worlds,
the closest possible world at which the antecedent of a counterfactual is true
must differ from the actual world in more respects than those specifically
cited in the antecedent. On a rainy day,
I might correctly hold that if my cat were outside, she'd be wet. At the closest possible world where my cat is
outside, the fact that my cat is sleeping by the fireplace presumably does not
hold. But other truths must also fail to
hold. The closest possible world where
my cat is outside must be one where, contrary to fact, either I opened certain
doors or windows this morning, or I neglected to let my cat in last night, or
the laws of nature differ in ways that allow my cat to pass through walls or
closed doors and windows. We are happy
to allow that were my cat outside I would have opened or failed to open doors
or windows at various times. But we do
not allow that had my cat been outside, the laws of nature would have
differed. The problem at hand for an
account of laws is that of explaining why we should expect the actual laws to
hold under counterfactual antecedents while other contingent truths do
not. Armstrong, Tooley
and Dretske each assert that laws are preserved under
the antecedents of non-counterlegal
counterfactuals. But none of these
authors gives an account of nomic necessitation that
would explain the privileged status of laws over other contingent truths.
The problem of law for supporting
counterfactuals apparently has a limited number of possible solutions. We can attempt to identify some special modal
status for nomic relations which is adequate for
supporting counterfactuals but falls short of metaphysical necessity or we can
accept laws as metaphysical necessities.
Perhaps most philosophers who endorse realist accounts of laws would
prefer the first of these options. But
the matter of supporting counterfactuals has been a standing problem for the
view that laws are contingent relations between universals for some while and
little headway has been made. Nor do the
prospects look good.
In recent literature, the view that
laws are metaphysical necessities found early support in the work of Sydney
Shoemaker (1980) and Chris Swoyer (1982) and has more
recently found favor in Ellis and Lierse (1994). Following Ellis and Lierse,
I will call the view of laws that has emerged in this literature “dispositional
essentialism.” Dispositional
essentialism is the view that laws are accounts of the dispositional nature of
fundamental properties. Dispositional
essentialism can be developed in a variety of ways depending on just what
properties are taken to be fundamental and determine laws. Ellis proposes that dispositions are
constitutive of natural kinds. So to be
a proton, for instance, is just to be a thing that has certain mass, charge and
spin dispositions. Since instantiation
of a disposition entails a counterfactual, it is clear that dispositional
essentialism about laws will adequately support at least some
counterfactuals. Consider, for instance,
(3) from above:
(3)
If this piece of copper had been heated at time t, then it would have
expanded at t'.
This counterfactual is adequately
supported because the disposition to expand when heated is essential to the
kind copper. But dispositional
essentialism faces an obstacle in providing a general solution to the problem of
law in the measures it must take to accommodate certain of our modal
intuitions.
Dispositional essentialism makes the
laws of nature metaphysically necessary.
An obvious objection to dispositional essentialism is that it appears to
violate a modal intuition that the laws are contingent. Intuitively, the speed of light might have
been a bit faster or a bit slower, gravity might have been a bit stronger or
weaker, and so forth. Accommodating
these intuitions appears to require that the laws of nature might have been
different. We might easily conclude that
the laws must then be contingent.
In fact I think this objection is
fairly easily dispatched. Dispositional
essentialists take the laws to follow necessarily from the dispositional
properties of things. This view allows
that the world might have been different in a variety of respects. It might have differed with respect to the
amount of matter/energy in the world, or the distribution of stuff in
space-time, or with respect to the fundamental dispositions had by that
stuff. What dispositional essentialists
ought to say about the alleged intuition that the laws are contingent is that
it is really just the intuition that things might have been differently
disposed. If things had different
dispositions, then events would have been governed by different necessary
laws.
On the dispositional essentialist’s
account, if it is a law that all Fs are Gs, it is so due to the causal powers
essential to F-ness. The essential
nature of F-ness makes it metaphysically necessary that all Fs are Gs. If laws are taken to be metaphysical
necessities, then there is no question to be asked about whether they are true
at this world or that. They are simply
true at all worlds. But the actual Fs
might not have been Fs. They might
instead have been Hs where it is metaphysically necessary that Hs are Js but
not Gs. Dispositional essentialism does
not deny that things might have had different dispositions. So it looks like necessary laws can be
reconciled with our modal intuitions.
However, this raises a new issue of relevant conditions for supporting
counterfactuals. Given that things could
have been otherwise disposed, events might have been governed by other
necessarily true laws that analyze the different dispositions things might have
had. Given this, the problem of support
for counterfactuals re-occurs in a different form. We must now ask what grounds we have for
supposing that things are similarly disposed at the closest possible world
where the antecedents of counterfactuals are true.
The underlying stuff of which our piece of copper is constituted might
have constituted a thing of a different kind, having different
dispositions. The antecedent of (3)
specifies copper as the kind of thing that is heated. If the disposition to expand when heated is
essential to things of the kind copper, then (3) is adequately supported. But the following counterfactual isn't:
(7)
If this thing (which in fact is copper) were heated, then it would
expand.
The underlying stuff of which the
thing at issue is constituted might have belonged to some kind other than
copper, which lacks the disposition to expand when heated. Dispositional essentialism makes clear how
laws as accounts of fundamental dispositions can support a range of
counterfactuals whose antecedents invoke dispositional properties. But counterfactual antecedents don't always
specify such law grounding properties, the essential nature of which can
support the counterfactual.
At this point we should pause to notice that we are
no longer concerned with Goodman's second problem of counterfactuals. Here we are raising a concern about the role
of relevant accidental conditions in supporting counterfactuals. Dispositional essentialism resolves what
Goodman took to be two problems of counterfactuals into one: the problem of
relevant conditions. Possible worlds
semantics provides one framework for addressing this issue. In the remainder of this paper I will suggest
how the resources of dispositional essentialism can be developed into an
alternative to possible worlds semantics for counterfactuals.
The dispositional
essentialist’s ontology suggests a property theoretic account of
counterfactuals as an alternative to Lewis’s possible worlds semantics for
counterfactuals. On this account, what
makes a counterfactual true, and what is expressed or conveyed by a
counterfactual’s antecedent, is in part a complex of properties including a
disposition whose manifestation entails the counterfactual’s consequent. That metaphysically necessary laws are
entailed by the dispositional components in the property complexes we invoke
with counterfactuals explains the widely held notion that laws have a special
role to play in supporting counterfactuals.
But ultimately it is properties that do the work of making true
counterfactuals true.
The leading idea of
the proposed account is that true counterfactuals are made true in part by
relations of metaphysical necessitation holding between properties. That is, a counterfactual represents a
relation of metaphysical necessitation holding between those properties
expressed by its antecedent, and properties whose instantiation provides for
the truth of the counterfactual's consequent.
On the proposed
account, part of what is expressed by a counterfactual is a strict conditional
of the form
(8) Necessarily, (If P then Q)
The antecedent of
this strict conditional is a proposition that represents the instantiation of a
complex of properties. The consequent
follows from the antecedent as a matter of metaphysical necessity. In the case of causal counterfactuals, the
complex property given in P is an event type that includes dispositional
components and involves the obtaining of their precipitating conditions. The consequent is a proposition entailed by
the manifestation of those dispositional elements. So for instance, in
(9) Had I struck
match m, it would have lit.
the antecedent represents an event type
that involves match m being struck, flammable, dry, in the presence of
oxygen, etc. and the consequent represents an event that is metaphysically
necessitated by the event type (including its dispositional elements) that is
represented by the antecedent. But (9)
must express more than this strict conditional.
For the strict conditional is true whether or not match m is dry or wet, in the presence or
absence of oxygen, etc. In addition to
expressing the strict conditional, (9) affirms the instantiation of those
conditions relevant to a counterfactual’s support.
If it seems
surprising that so much should be expressed by such a simple claim as (9),
consider in detail the propositional content of a
belief one might use (9) to express. It
is not a belief merely about a match being struck; without regard to the
presence or absence of gales, tidal waves or space suits. It is a belief about a flammable, well-made, dry match struck against an appropriately
abrasive surface in the presence of oxygen and in the absence of strong
breezes, etc. When we assemble all of
these conditions presumed in the contents of our beliefs it is not implausible
that the propositional content of our counterfactual
beliefs include strict conditionals.
I have proposed that, strict
conditionals are part of what we express with counterfactuals. In Counterfactuals
(1973), Lewis argues against the view that counterfactuals are strict, or
necessary, conditionals. Among the
challenges the proposed account of counterfactuals must meet is to answer
Lewis' argument for taking counterfactuals to be "variably strict",
rather than strict conditionals. Lewis'
grounds for denying that counterfactuals are strict conditionals involve series
of conditionals including the following:
(10) If Otto had come, it would have been a lively
party.
(11) But if Otto and Anna had come it would have
been a dreary party.
(12) But if Waldo had
come as well [as Otto and Anna], it would have been lively.
Given appropriate beliefs about Otto, Anna and
Waldo, we would want to endorse (10), (11) and (12). In (11), the antecedent of (10) is
strengthened and the consequent of (10) is denied. Likewise, in (12), the antecedent of (11) is
strengthened and the consequent of (11) is denied. But since the strengthened antecedent in (11)
entails the weaker antecedent in (10), (11) entails,
(13)
Had Otto come to the party, then it would have been dreary.
And (13) contradicts (10). A similar contradiction can be derived in the
case of (11) and (12). Lewis concludes
that (10) cannot be taken to assert the strict conditional,
(14)
Necessarily, if Otto comes to the party, then it is lively.
because (14) is contradicted by (13) which follows from
(11).
I think the way to answer this
argument is to accept counterfactual sentences
as "variably strict" in the specific sense that they can be used to
express (or perhaps we should say, "convey") different counterfactual
propositions on different occasions.
This strikes me as a natural and intuitive view to take of
counterfactual sentences like (10) through (12). When we accept (10), we take it as expressing
(or conveying) something more complex and specific than what is explicitly
stated in (10). We accept it as
expressing something about what would have been the case had Otto come to the
party, without Anna, and Otto is in good spirits, and not in a coma, and Otto's
friends still attended, and nobody called the police, etc. When we accept (11), with its negation of
(10)'s consequent, we accept it as expressing or conveying a strict conditional
antecedent which does not entail the antecedent of the counterfactual
proposition expressed (or conveyed) by (10), but contradicts it specifically
with regard to Anna's presence at the party.
I have presented
the property theoretic account of counterfactuals in terms of counterfactuals
whose antecedents are consistent with the laws that hold (those that analyze
the dispositions that in fact are had by things). Counterlegal
counterfactuals (counterfactuals whose antecedents are not consistent with the
laws that hold) present a challenge for the proposed view. We seem to have clear intuitions about
counterfactuals such as the following:
(15) Had there been a negatively charged proton in the
neighborhood of an electron these particles would experience a mutual repulsion
in accordance with Coulomb's law.
But according to the dispositional
essentialist, the antecedent of (15) is metaphysically impossible. One way to handle counterlegals
on the proposed treatment of counterfactuals is to take terms like "proton"
in counterlegal antecedents to have non-standard
referents. There may be good reasons to
deny that negatively charged but otherwise proton like particles are
protons. We can take this essentialist
view of protons and still make sense of counterfactual antecedents that use
"negatively charged proton" as really concerning negatively charged
but otherwise proton like entities. The
account proposed can be extended to cover counterlegals
by means of such re-interpretation of terms in counterlegal
antecedents. There is the concern that
in recognizing such non-standard usage in counterlegals,
we undermine the essentialist semantics we employ elsewhere. But I find nothing implausible in the view
that counterlegal antecedents are just semantically
peculiar. If I object to someone's use
of "negatively charged proton" in a counterfactual antecedent on the
grounds that a negatively charged particle would not really be a proton, I
think it likely that I will be accused of taking the speaker too literally and
that what they are really concerned with is not a proton but a negatively
charged and otherwise proton like particle.
The likelihood of hearing a defense of the possibility of negatively
charged protons is remote.
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