The limits of Humeanism


ORIGINAL PAPER IN PHILOSOPHY OF SCIENCE

The limits of Humeanism

Jesse M. Mulder1

Received: 6 July 2017 /Accepted: 23 April 2018 /Published online: 16 May 2018
# The Author(s) 2018

Abstract Humeans take reality to be devoid of ‘necessary connections’: things
just happen. Laws of nature are to be understood in terms of what ‘just happens’,
not vice versa. Here the Humean needs some conception of what it is that ‘just
happens’ – a conception of the Humean mosaic. Lewis’s Humeanism incorporates
such a conception in the form of a Lewis-style metaphysics of objects, properties,
and modality. Newer versions of Humeanism about laws of nature, such as the
Better Best Systems approach (BBS), typically reject such a Lewisian metaphys-
ics, but it remains unclear what they can offer in its place. By exploring different
candidate conceptions, this paper sheds light on the limits of Humeanism about
laws of nature: not all conceptions of the Humean mosaic form a suitable basis for
a Humean theory of laws. In fact, only a metaphysics roughly in line with Lewis’s
will do. The paper ends with a tentative generalization of this result, thus pointing
to the ‘limit’ of Humeanism in general: taking the Humean way of thinking to its
limit results in a rejection of the whole idea of such a mosaic – and hence of
Humean mosaic-based accounts of anything.

Keywords Humeanism . Laws of nature . Metaphysics . Modality. Material objects

A Humean attitude towards topics such as causality and laws of nature starts with
strong suspicions about what Hume called Bnecessary connections^: Bthere are no
ideas, which occur in metaphysics, more obscure and uncertain^ (Hume 2007, VII.1,
p. 45). It ends with analyses of the relevant notions that do not rely on such necessary

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https://doi.org/10.1007/s13194-018-0205-9

* Jesse M. Mulder
j.m.mulder@uu.nl

1 Utrecht, The Netherlands

http://orcid.org/0000-0002-8142-2533
http://crossmark.crossref.org/dialog/?doi=10.1007/s13194-018-0205-9&domain=pdf
mailto:j.m.mulder@uu.nl


connections. In reality, it is thought, things just happen, there is no ‘causal glue’ that ties
different events together, no laws that ‘govern’ the behavior of objects.1 Rather,
causality and laws are to be accounted for in terms of the things that just happen, not
vice versa.

But what does it mean to say that ‘things just happen’? Arguably, one could read
Hume here epistemologically, i.e., such that what the senses provide us with ‘just
happens’, that they reveal to us no ‘necessary connections’ – all we have to go on is a
mere succession of impressions.2 However, here I want to focus on what is known
under the label of contemporary Humean (or neo-Humean) theories of, e.g., laws of
nature and causality, and these understand themselves not primarily as epistemological
doctrines in this way, but rather as theories that build on regularities among what
objectively happens in the ‘mind-independent world’.3

The most explicit formulation of this sort of ‘metaphysical’ Humeanism can be
found in David Lewis, who dubbed it ‘Humean Supervenience’:

Humean supervenience … is the doctrine that all there is to the world is a vast
mosaic4 of local matters of particular fact, just one little thing and then another. …
We have geometry: a system of external relations of spatiotemporal distance
between points. Maybe points of space-time itself, maybe point-sized bits of
matter or aether or fields, maybe both. And at those points we have local
qualities: perfectly natural intrinsic properties which need nothing bigger than a
point at which to be instantiated.5 For short: we have an arrangement of qualities.
And that is all. There is no difference without difference in the arrangement of
qualities. All else supervenes on that. (Lewis 1986b, pp. ix–x)

Lewis indeed analyses causality and laws of nature in terms of the Humean mosaic, as
he conceives of it here, i.e., in terms of the Barrangement of qualities^. In particular, for
him the laws depend only on the actual arrangement of qualities (viz., our world): they
provide the best summary of that arrangement. Causality, on Lewis’s counterfactual
approach, is then understood to depend on how the qualities are arranged not only in

1 An anonymous referee reminded me that Roberts (2008) claims to be able to marry Humeanism to
‘governing’ (see, esp., §10.5). His is, however, a rather peculiar type of governing – and I would submit that
it is questionable whether his basic notion of ‘legitimate measurement procedures’ is in the end consistent with
Humeanism. Showing this would of course require a detailed discussion of Roberts’s views, which I cannot
undertake in the context of this paper. So when I talk of Humeans and Humeanism, I intend to be talking about
mainstream or standard Humeans and Humeanism, and leave it open whether my considerations are relevant
for less ‘orthodox’ variants like Roberts’s.
2 This epistemological take on the Humean mosaic later became the guiding thought of phenomenalism and of
logical empiricism. Hume himself can be taken to have started that tradition – see esp. Hume (2010, Part IV);
but probably Mill (1865, chs. XI–XIII) contains the first thorough statement of phenomenalism.
3 Of course, this does not mean that contemporary Humeans have nothing to say on, e.g., mental causation.
That is to say, they will claim that among the mind-independent matters of fact there are those that are (or
constitute, or subvene) mental states and events.
4 I follow Lewis’s phrasing here in speaking of the BHumean mosaic^. Other labels can also be found in the
literature; Roberts, for instance, calls it the BHumean base^ (Roberts 2008, p. 353).
5 We should not misunderstand Lewis here: he is not defending the physics that seems to be presupposed by
his present formulation. In a later article he makes explicit that he defends ‘the philosophical tenability of
Humean Supervenience,’ and that his defense ‘can doubtless be adapted to whatever better supervenience
thesis may emerge from better physics’ (Lewis 1994, p. 226).

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our own world but also in relevant other possible worlds, where the relevance is
captured using the actual laws (amongst other things).

But not all Humeans agree with Lewis on the nature of the mosaic. This raises the
question: which conceptions of the Humean mosaic are suitable for a Humean project?
Answering this question may help identify certain limits of the Humean project – only a
certain limited range of conceptions of the Humean mosaic will be suitable for the sorts
of Humean views about laws of nature or causality that one finds in the contemporary
debate. Now, I can’t fully answer this question, and determine the relevant limits of
Humeanism, within the context of this article. But I do aim to take a first step. In
particular, I will focus in what follows on the possibility of conceptions of the mosaic
that differ from Lewis’s as suggested by defenders of the recent so-called ‘Better Best
Systems’ (BBS) theory of laws. Still, as I hope to make clear in the afterthoughts at the
end of this paper (§4), the results may be taken to point in the direction of a more
comprehensive estimation of the limits of Humeanism (in the mentioned sense).

Thus, I start in §1 below by looking more closely at Humeanism about laws of
nature, in particular at Lewis’s ‘orthodox’ Best Systems view, with an eye to identifying
the elements that are relevant for the underlying conception of the Humean mosaic. In
§2 I then focus on the Humean mosaic proper by considering the BBS variant of
Humeanism about laws, which explicitly departs from the Lewisian view, and suggests
to replace it with an ‘explosive realism’. I consider various conceptions of the Humean
mosaic along ‘explosive realist’ lines that might be thought to provide suitable bases for
this Humean theory. Having dismissed certain shapes this conception might take in §2,
I then turn in §3 to what one might call ‘moderately’ Better Best Systems – the one
variant conception of the mosaic that survived §2’s criticisms. This variant stays rather
close to Lewis’s views in the relevant respects (hence ‘moderately’). Finally, in §4, I
offer the promised afterthoughts concerning the limits of Humeanism on the basis of
the considerations so far. In particular, I sketch two such limits: first, that the Humean
will have to stay in the vicinity of a Lewis-like conception of the mosaic if his project is
to make sense at all; and second, that there is some pressure, when considering the
motivation for the Humean enterprise, to abandon the very idea of a Humean mosaic
exhibiting regularities, and thus to entirely abandon the orthodox Humean project of
accounting for laws (or for anything whatsoever, for that matter) in terms of such
regularities.

1 Humeanism about laws

The Humean approach to laws of nature attempts to account for laws using materials
Hume would find acceptable – viz., a Humean mosaic. A ‘naïve’ Humean takes laws to
be just regularities within the mosaic: it is a law that As are B just if As are always B.
This move, as has been frequently observed, reverses the order of explanation: whereas
intuitively, the laws are to explain the behavior of things, the Humean has to say that the
behavior of things, taken together, explains the laws. (Humeans would typically take
this not as a problem for, but rather as a statement of, their view.) This reversal creates
the single most important challenge for Humeanism: to distinguish those generaliza-
tions that are truly ‘lawlike’ from other, merely accidental generalizations. After all, the
non-Humean can simply start with laws and use them to single out the law-like

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generalizations (assuming she still wants to deal in terms of generalizations at all, which
is false for quite some non-Humean views – Cartwright (1984) being a case in point).
Accordingly, the history of Humeanism consists in large part in attempts to meet this
challenge (even if not in these precise words).6

As said, Lewis’s ‘Best Systems’ account appears to be the most promising candidate
Humean account of laws of nature at present. It is also known as the Mill-Ramsey-
Lewis (MRL) account.7 Here is a concise statement of its core thesis:

We can restate Ramsey’s 1928 theory of lawhood as follows: a contingent
generalization is a law of nature if and only if it appears as a theorem (or axiom)
in each of the true deductive systems that achieves a best combination of
simplicity and strength. (Lewis 1973, p. 73)

The proposal is to have all possible summaries of the Humean mosaic compete with
each other. Such summaries are assumed to take the shape of deductive systems with
certain axioms, and the systems that score best on the balance between simplicity and
strength come out as winners: they are the ‘Best Systems’. Simplicity is cashed out, for
example, in terms of some complexity metric, whereas strength is understood in terms
of the amount of information embodied in the axioms – stronger systems say more
about the entire mosaic.8

As Lewis observes, it is not even required, on the Best Systems approach, to restrict
the laws to general truths: if it improves the overall balance of strength and simplicity, a
truth about particular aspects of the entire mosaic may be regarded as a law as well.9

What Lewis does require, however, is that we run the Best Systems competition on
the basis of a predicate-logical language containing a certain privileged set of predi-
cates. Without that restriction, so he rightly thinks, the whole project becomes trivial:
we could simply choose a language, say, with a primitive predicate P which is
stipulated to apply to an object just if it is part of a world which is composed of matters

6 For instance, Braithwaite (1927, 1928) suggested to understand the laws to be those generalizations that are
‘believed for reasons that are not logically demonstrative’ (1927, p. 467), that is, not deductively derived from
particular matters of fact. A contemporary heir to this sort of suggestion is Swartz, who summarizes his
position as follows: ‘there are a number (an infinite number, perhaps) of true universal, material conditional
statements (propositions), all of whose terms are perfectly descriptive, that is, make no reference to any
particular time, place, person, or thing in the world. The Regularist is content to allow that all these true
universal, material conditionals are physical laws …’ (Swartz 1985, p. 101). For an excellent in-depth
discussion of the development of Humeanism over the past century, and the challenges it faces, see Stroud
(2011, Ch. 2).
7 Apart from Lewis himself, defenders of the Best Systems approach, in one or another version, include
Beebee (2000), Albert (2001), Earman and Roberts (2005a, b), Loewer (2012), Dunn (2011), Cohen and
Callender (2009), and Callender and Cohen (2010).
8 Of course, it will be crucial to the case for a Best Systems approach that principled accounts of simplicity and
strength, and their balance, can be given. However, for present purposes we can abstract away from those
details and the worries they may evoke. (Such as the well-known worry that these norms incorporate an
unwanted psychological aspect into what it is to be a law. Lewis thinks not, as long as ‘nature is kind enough’
to convincingly make one system the absolute best one – see Lewis (1994, p. 479).)
9 Lewis does not think that ‘there are laws that essentially mention Smith’s garden, the center of the earth or of
the universe, or even the Big Bang’, but still, ‘such laws ought not to be excluded a priori’ (Lewis 1986b, p.
123). Albert (2001) and Loewer (1996) make use of this option in arguing that we should include the ‘Past
Hypothesis’ (viz., that the universe started out with a very low entropy state) in the Best System. See Frisch
(2011) for critical discussion.

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of fact exactly similar to those that make up the actual mosaic. The generalization
‘Everything is P’ would then easily win the competition because it is maximally strong
and (arguably) maximally simple – but also very uninteresting. Now, Lewis’s way of
restricting the language for which we run the Best Systems machinery is by endorsing a
metaphysically privileged set of ‘perfectly natural properties’: those are the fundamen-
tal properties that are instantiated by the basic building blocks of the universe – Bmaybe
points of space-time itself, maybe point-sized bits of matter or aether or fields, maybe
both^, as I quoted Lewis above.10

In fact, the privileged set of natural properties is already required to arrive at a non-
trivial conception of the Humean mosaic in the first place: an abundant construal of
properties, on which any set of objects amounts to a property, trivializes the whole idea
of regularities within a mosaic. On such a construal it will be more appropriate to speak
of drawing patterns into the mosaic than of recognizing patterns in it.11

Hence, the (predicate-logical) language on which the Best Systems competition is to
be based should include primitive predicate symbols for just the ‘perfectly natural
properties’; contrived ones (like our P) are not allowed. In this way, the Best Systems
theory also avoids the allegedly impossible task of having to compare the balance of
simplicity and strength for systems couched in different vocabularies.12

Following Lewis, many have found it natural to identify this set of perfectly natural
properties with the fundamental properties of (future) physics.13 Yet this creates a
problem with regard to the laws of the other sciences (assuming that they trade in a
vocabulary different than that of physics), unless one is prepared to accept that only the
laws of physics are ‘true’ laws of nature. But not everyone is prepared to go that way,
and this is one of the motivations for the recently proposed amended version of the Best
Systems approach mentioned earlier: the so-called ‘Better Best Systems’ (BBS) ap-
proach.14 On this approach, each science has its own laws resulting from a Best
Systems competition based on the specific vocabulary of the science in question. It is
thought that this amendment to the Best Systems approach makes room for autono-
mous special sciences.15

2 The underlying Humean mosaic

I have introduced the Best Systems approach, and its recent ‘better’ variant, as a sort of
culmination of Humeanism about laws, i.e., as the most promising member of a family

10 See also Lewis (1983, pp. 366–8) and Lewis (1986b, pp. 123–4). Lewis envisages three options for
privileging natural properties: by means of a primitive predicate of naturalness; by providing a reductive
analysis in terms of universals; or in terms of tropes. But he does not take a stand: ‘the honors are roughly
even, and remain undecided’ (Lewis 1986a, p. 64).
11 But see Taylor (1993) for such a theory-relative (and hence anti-realist) construal of naturalness.
12 This point is developed in detail by Cohen and Callender (2009, pp. 5–8).
13 For a clear statement of just how Lewis intends this identification to be read, see Lewis (1994, esp. p. 474).
14 See Schrenk (2006) and Cohen and Callender (2009), Callender and Cohen (2010). The label ‘Better Best
Systems’ is Callender and Cohen’s.
15 Interesting questions can be asked about the proposal. For example, in biology most of the vocabulary from
physics is also used, but it seems possible that some law of physics, resulting from a physical vocabulary based
Best Systems competition, will not be a law in the Best System to which biology’s vocabulary gives rise (or
vice versa). I will not discuss these issues here, however.

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of views that does not take the laws to govern what happens, but rather takes them to
summarize what happens (either in simple regularities, or in the more complicated Best
Systems-fashion that Lewis made popular). This family of views thus builds on the idea
of a Humean mosaic: the mosaic is what is given, what needs to be adequately
summarized if we want to arrive at laws. Now, what does the mosaic have to look like
in order to provide a useful foundation for this type of approach? Most of the defenders
of a Humean theory of laws do not develop a detailed conception of this underlying
mosaic – except, of course, for Lewis, whose metaphysical views are developed in
considerable detail. Let us review his conception of the mosaic, so that we can then see
in which ways the BBS approach might diverge from that conception.

As we saw, Lewis’s conception of the mosaic is somewhat open still; it depends on
what the bearers of the most fundamental (perfectly natural) properties turn out to be.
Perhaps these are simply the space-time points themselves,16 perhaps they are indivis-
ible, point-sized bits of matter, maybe fields of some sort. For concreteness, let us
assume that the mosaic consists of point-sized bits of matter; and for convenience, let us
assume that every space-time point houses exactly one such point-sized ‘bit’. (Except
for the ease of exposition in what follows, nothing hangs on this.)

This gives us a basic conception of the mosaic. On Lewis’s view, composite objects
then come ‘for free’: they are simply mereological sums of such basic, point-sized bits.
Let us call such sums (Lewisian) material objects. To each region of space-time there
corresponds one and only one such object, and this means, for Lewis, that material
objects perdure (if their region is extended in time): they persist by having distinct
temporal parts at each time at which they exist. Material objects are thus individuated
by their spatiotemporal boundaries or, equivalently, by their (proper) parts.17 Different
region, different object.

For Lewis, this does not mean, however, that such objects could not have had
different spatiotemporal boundaries or that they could not have been composed by
different parts: these modal statements are to be analyzed using his counterpart-
theoretic framework, according to which it is possible for something to be larger than
it actually is (say) just if there is a possible world in which its counterpart is in fact
larger. In short, then, a thing’s non-modal qualities are determined by the distribution of
perfectly natural properties over the region of space-time it occupies, while a thing’s
modal features (including its dispositions etc.) depend on how things stand with its
counterparts in relevant possible worlds – where relevance is, again, determined in part
by what the laws are.18

So, on this Lewisian picture we must distinguish carefully between, on the one hand,
the modally ‘thin’ conception of objects as inhabiting his Humean mosaic by being
mereological sums of its basic, point-sized material ingredients, which in turn function

16 Some Lewisians take this to be the natural option, for reasons of parsimony: BThe identification of
spatiotemporal objects with the regions is just crying out to be made^ as Sider (2001, p. 110) writes, because
Botherwise we seem to gratuitously add a category of objects to our ontology.^
17 Lewis adopts classical extensional mereology – see, e.g., Lewis (1991, p. 81): BGiven a prior commitment
to cats, say, a commitment to cat-fusions [mereological sums of cats; JM] is not a further commitment. The
fusion is nothing over and above the cats that compose it. It just is them. They just are it. Take them together or
take them separately, the cats are the same portion of Reality either way.^
18 There is an apparent conflict here between the modal features to which Lewis’s principle of individuation
for objects gives rise (different region/parts, different object) and his counterpart-theoretic account of modality.
See Mulder (2013) for discussion.

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as the basis for his Humean account of laws, and, on the other hand, a subsequent
modally ‘thick’ conception of those objects as, for instance, rabbits, stars, electrons, and
water molecules (I will give more content to this idea of modal ‘thickness’ below, and
defend it further in §3). This is to say that Lewis’s system embodies a reduction of those
modally ‘thick’ objects to the modally ‘thin’ ones: rabbits, for instance, just are material
objects satisfying certain qualitative and modal conditions. This assumes that the
qualitative and modal conditions can be fully separated in the final analysis.19 And
so in the end it doesn’t matter for Lewis whether we say that the mosaic is inhabited by
modally thick rabbits and the like, or rather by the modally thin material objects (since
the former are reduced to the latter anyway). But it does matter at the beginning, so to
speak. For, the reduction of (modally ‘thick’) rabbits etc. to (modally ‘thin’) material
objects only works (if it works at all) if the mosaic, and the laws, can be specified in
‘rabbit-free’ terms. Thus it transpires that the modally thin conception of the basic
elements of the mosaic (point-sized bits of matter) is fundamental: it provides the basis
for the reduction.20 Finally, this reduction crucially rests on the laws of nature: these
determine which worlds are relevant for settling the modal features of things. – I will
return to this intricate structure of Lewis’s Humeanism below, where we will see that
this clean separation of the qualitative from the modal has important consequences for
the space of Humeanly acceptable conceptions of the mosaic.

Now, as I said, not everyone accepts such a Lewisian construal of the Humean
mosaic. Callender and Cohen, for instance, regard it to be a virtue of their Better Best
Systems view that it is not committed to Lewisian metaphysics across the board.
Instead, they propose ‘explosive realism’:

[T]he world permits possibly infinitely many distinct carvings up into kinds, each
equally good from the perspective of nature itself, but differentially congenial and
significant to us given the kinds of creatures we are, perceptual apparatus we
have, and (potentially variable) matters we care about. (Cohen and Callender
2009, p. 22)21

The thought seems to be that ‘the world’, that is, the Humean mosaic, simply does not
settle the question which predicates we should start with when we want to look for
laws. Pace Lewis, there is no metaphysically privileged set of allegedly ‘perfectly
natural’ properties. By thus allowing to run Best Systems competitions based on many
different sets of properties, this proposal makes room for the special sciences to each,
autonomously, run its own Best Systems competition without having to worry about
how this enterprise relates to the supposed ‘perfectly natural properties’.

19 This assumption mirrors, of course, Hume’s famous distinction between matters of fact and relations of
ideas.
20 In Mulder (2013), I develop an account of the notion of fundamentality I am using here, and of the related
notion of reduction. (Following an anonymous referee’s advice, I have abstained from using the term
Bsupervenience^ here: it invites difficult questions that I don’t want to go into. Still, I think that what Lewis
aimed to capture with his label BHumean Supervenience^ comes very close to what I here sketch in terms of
reduction and fundamentality.)
21 Cohen and Callender borrow explosive realism from Sosa (1993, 1999), Dorr (2005), and Eklund (2008),
amongst others.

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However, by focusing solely on the properties that are or are not ‘allowed’, this way
of thinking leaves out one important issue: the objects that occupy the mosaic.22 What
are the implications of explosive realism for the conception of the objects that inhabit
the underlying mosaic?

This question is especially important if one wants to replace Lewis’s conception of
the mosaic, in terms of point-sized bits of matter displaying patterns of perfectly natural
properties, by a conception in terms of the various vocabularies of the various sciences,
as Cohen and Callender seem to propose. For it is not to be expected that these various
sciences conceive of the bearers of the various properties they are working with as
Lewisian material objects. Their conception of these objects may well be what I call
modally ‘thick’. I will gradually develop this point, and the complications it gives rise
to with respect to the conception of the mosaic, in what follows, and I will attempt a
further defense of the idea of modal ‘thickness’ in §3.

So let us start our inquiry into alternative (non-Lewisian) conceptions of the mosaic
by taking up Cohen and Callender’s suggestion: explosive realism. We will have to
distinguish between different ways in which one might intend to ‘explode’ reality in
order to arrive at an ‘explosive realism’. Initially, two such ways suggest themselves.
The first, which I will call substantial explosive realism, replaces the fundamental
conception of the mosaic in terms of a modally thin notion akin to Lewis’s point-sized
bits of matter with a fundamental conception of the mosaic in much less austere terms.
In fact, no limit whatsoever is placed on the terms in which the objects inhabiting the
mosaic are to be fundamentally understood – that’s the ‘explosion’. The second reading
of explosive realism, which I will call deflationary explosive realism, keeps the
fundamental conception of the mosaic in terms of a modally thin notion akin to Lewis’s
point-sized bits of matter intact, but stresses that this mosaic ‘permits’ (as Cohen and
Callender put it) a wide range of ‘carvings’ into various kinds of objects. So here the
explosion takes place not at the fundamental level but rather at the level of our ‘carving
operations’.

Consider the first option, which is, to be fair, not likely to coincide with what Cohen
and Callender have in mind. The mosaic is, on this proposal, not to be conceived,
fundamentally, in terms of Lewis-style point-sized bits of matter only. Rather, the
proposal is to ‘explode’ the fundamental conception of the mosaic, so that it includes
also modally ‘thick’ things like rabbits, tables, water molecules, mountains, oak trees –
and many, many unheard-of things.23 – Of course, as I said, Lewis’s mosaic can be said
to contain all of these as well. But it bears emphasizing that they do not play a role in
Lewis’s fundamental conception of the mosaic: there are rabbits in the mosaic because
there are suitable material objects (in his sense) that display a leporine distribution of
qualities and stand in appropriate relations to their counterparts in certain other possible
worlds. For Lewis the sortal concept rabbit is not fundamental in the way his concept

22 Stroud diagnoses this ‘blind spot’ in what he calls the ‘more or less standard picture’ underlying much
contemporary Humean thought as a result of adopting ‘first-order quantification theory’: this logical theory
makes it seem as if we can have a domain of objects without having to bother about how we conceive of those
objects – see, esp., Stroud (2011, p. 27).
23 An anonymous referee made it clear to me that a Humean is likely to reject this rendering of the position out
of hand by stating that it assumes without argument that things like rabbits, tables, water molecules etc. really
are modally ‘thick’, and that it would be much more plausible to start with a less ‘inflated’ conception of those
things. I briefly consider this option further down, and return to it once more in §3.

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of point-sized bits of matter is: to be a rabbit just is to be a sum of such bits of matter
(viz., a material object) satisfying certain qualitative and modal conditions. Hence,
fundamentally speaking, the Lewisian mosaic is not composed of things like rabbits. It
rather ‘permits’ them by providing suitable reductive bases. In other words: the
Lewisian mosaic has room for rabbits only if the sketched reductive analysis can be
pulled off; the fundamental conception of the mosaic is to provide the basis for that
reduction. Substantial explosive realism is radically different: it is fundamentally
composed of rabbits and the like; reduction is then out of the question.

So, asserting that the mosaic itself is, fundamentally, composed of such modally
‘thick’ things as rabbits etc., thus giving up on a reductive approach to all of these
kinds, elevates all of them to the status of fundamental sortal concepts – the status
point-sized bit of matter enjoys in Lewis’s framework. For, as soon as we reductively
explain the presence of, say, rabbits in terms of more basic things’ fulfilling certain
conditions, as on the Lewisian view, we have thereby removed them from our
fundamental conception of the mosaic – we are, then, using a (perhaps tacitly)
preformed conception of the mosaic to reductively account for the presence of rab-
bits.24 Thus, taking the mosaic itself to include the full ‘explosion’ results in an
incredibly wealthy catalogue of fundamental kinds of things (a maximally wealthy
catalogue, in fact). That is not all by itself a problem, of course (unless one is biased
toward desert landscapes), but it does create a tension with the very idea of a Humean
mosaic, which is supposed to be free of necessary connections. Let us see why.

The concept of a rabbit, I said, is modally ‘thick’. For instance, rabbits don’t simply
pop into existence; they come from their parents. A rabbit only stays alive as long as it
takes in suitable nourishment, meaning that in its past there has to have been enough
such nourishment in its proximity. Rabbits don’t turn into butterflies, meaning that in
the future it will not suddenly transform into one. It is clear, then, that if something
here-now is a rabbit, this has lots of implications for how things are at other places and
times: there have to have been parents, nourishment, absence of conditions too extreme
for rabbits to survive, etc. In other words, if something here-now in the mosaic is a
rabbit, and rabbit is a fundamental sortal concept, then the mosaic contains ‘necessary
connections’. (Note that this only holds because the modally thick concepts are taken to
be fundamental!) Nor does it make a difference to change the example to one drawn
from physics, rather than biology: electrons, like rabbits, don’t pop into existence
either; they don’t suddenly change from being negatively charged to being positively
charged (or to being 20 m in diameter); when shot into (regular) cloud chambers they
do not trace out the word ‘electron’, etc. These necessary connections threaten to make
the Humean, regularity-based approach to laws of nature superfluous: we can simply
list the necessary connections that we already have within the mosaic.25 In short, this
conception of the mosaic is quite substantial indeed; hence substantial explosive
realism. (There is an apparent way out here for the Humean; I discuss it in the next
section.)

The problem lies with the conceptual connections that I have boldly claimed to be
inherent in the concept rabbit (or electron). By elevating such concepts to fundamental

24 Here my notion of fundamentality is crucial – again, see Mulder (2013) for more detailed discussion.
25 We may of course go on to systematize these connections in a way much like the Best Systems approach
proposes, but it is clear that this does not even come close to being a Humean approach to laws of nature.

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concepts, these conceptual connections are turned into necessary connections – reduc-
tion (or elimination) is out of the question. So, one might think, the remedy is easy: we
just strip our concept of a rabbit (or electron) from all of these conceptual connections,
which leaves us with a purely qualitative residue of rabbithood (or electronhood –
though one might doubt whether anything at all is left over in this case). And then we
can say that the mosaic contains rabbits (or electrons) in this watered-down sense. On
reflection, however, this proposal really comes down to a reduction of rabbits and
electrons to something ontologically more fundamental, much like the Lewisian claim
that they reduce to material objects in his sense (i.e., to sums of point-sized bits of
matter). In other words, we thereby leave substantial explosive realism behind, in favor
of a more deflationary version of that theory.

So let us now consider that deflationary version of explosive realism. The mosaic,
on this view, does not fundamentally contain all the different objects, as in substantial
explosive realism, but rather permits being carved up into all those different kinds of
objects (as Callender and Cohen indeed put it). One very straightforward way of giving
meat to this idea is Lewis’s: his mosaic contains just material objects (in his sense), and
these indeed permit to be ‘carved up’ in myriad different ways. One may define a kind
of object K by just listing random qualitative and modal criteria; and if there are any
material objects (in Lewis’s sense) fulfilling these criteria, then there are K’s. This
works for rabbits (as Lewis thinks of them) just as well as it works for less familiar
kinds of things. As long as a reductive story along the sketched lines can be told,
anything can be claimed to be present in the mosaic, however modally ‘thick’ it may
be. – But, now explosive realism seems to be nothing new: we are back where we
started, with Lewisian metaphysics. The explosion thus doesn’t really add anything – it
is indeed, in that respect, a rather deflationary sort of explosion.

Notice that both the substantial and the deflationary option seemingly provide the
basics for the story about laws that Cohen and Callender are interested in: depending on
our interests etc. we can approach nature (the mosaic) with a certain set of concepts
(each science is warmly invited to bring its own set), and we will find that we can work
with those concepts, do science with them (with more or less useful results). Armed
with the concept rabbit, for instance, nature will show us all sorts of rabbit-related
matters of fact. The difference between the two versions of explosive realism is that on
the substantial view, objects corresponding to those concepts are among the funda-
mental ingredients of the mosaic, so that the rabbit-related matters of fact are irreduc-
ibly rabbit-involving, while on the deflationary view, such objects can (in principle) be
reduced to the fundamental ingredients of the mosaic. And the latter is true also for
Lewis’s own view. Deflationary explosive realism thus merely highlights a feature of
the Lewisian view; it does not significantly depart from that view – at least, not insofar
as the conception of the mosaic is concerned. (I consider whether this is enough for a
‘moderately’ Better Best Systems view in §3 below.)

Now, a genuinely new option is in the offing if we take the explosive realist idea in a
radically different direction, i.e., if we decide to treat Lewis’s material objects, which
form the reductive base that enables all the different carvings, as itself just the result of a
carving operation. That is to say, we stop thinking in terms of a fundamental conception
of the mosaic, providing a certain range of bottom-level, fundamental kinds of things
(viz., Lewis’s point-sized bits of matter), to which everything reduces. By doing so, we
suddenly find ourselves having left the camp of realism (at least, in one good sense of

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that slippery term): we stop asking for an account of the Humean mosaic, of what is
ontologically fundamental, we simply say that every carving is the result of our
applying concepts to something which also permits being carved up differently. – What
is this ‘something’? To what exactly can we apply all those various sets of concepts?
Well, there is no answer to this question, since every answer results from applying
certain concepts. The view in question rejects the very idea of a fundamental concep-
tion of the mosaic: no carving is ontologically fundamental. And in that sense it is anti-
realist. This view indeed really differs from Lewis’s account, which departs from the
ontologically fundamental notion of point-sized bits of matter (in spatiotemporal
arrangement).

It might be rather surprising that explosive realism, on this third reading, leads us
straight to anti-realism. What is called ‘explosive realism’ turns out to be, at least on
one reading of it, realism only by name.26 But what is more worrying, especially for
proponents of a Humean theory of laws, is that the entire project now starts to break
down. That is because the mosaic as it is independently of our carving it up has now
become intractable – in contrast to Lewis’s view, on which there is a way of considering
the mosaic independently from our way of carving it up, viz., in terms of the
distribution of perfectly natural properties over the point-sized bits of matter. There is
nothing to be said about the mosaic independently from our carving; the only way of
saying something about it – for instance, that it exhibits certain regularities – is by first
applying carving tools. So on this view it is, again, more appropriate to speak of
drawing patterns into the mosaic than of recognizing patterns in it.27 Put differently:
whereas in the previous options our choice between different vocabularies was a choice
between focusing our attention on different aspects of the very same underlying reality,
so to say, on this new, anti-realist view choosing between different vocabularies is more
akin to choosing between different worlds – in Goodman’s words, it is choosing
between different ‘ways of world-making’.

In order to see more clearly why this makes the Humean approach to laws of
nature break down, we need to return to Lewis’s view on rabbits once more. We
saw that he assumes that rabbits reduce to his material objects: a material object is
a rabbit just if it displays a suitable arrangement of qualities and also has the right
modal properties, which are spelled out in terms of its counterparts. Now, as I
mentioned earlier, the counterpart relation itself depends on laws of nature, on
Lewis’s view: the worlds in which our laws of nature are true are closer than the
other worlds. They form the ‘inner sphere’. Hence the basis on which the laws of
nature are determined cannot involve rabbits, or any other modally ‘thick’ objects
– that would be circular; these modal features are to be understood in terms of the
laws, after all. Again, the fundamental conception of the mosaic is in terms of the

26 I have been sloppy here with regard to how we should understand Brealism^. I do not think my argument
requires that I be more specific, but it may be helpful to point out that in the present context, there is at least a
clear distinction to be drawn between a regularity-based account of laws that takes the regularities to be Bthere
anyway ,̂ whether or not we single them out, and a regularity-based account that takes the regularities to
depend on us. The former is an ingredient in Lewis’s realism; the ‘new option’ I am considering here rejects
this and insofar can be considered an ‘anti-realism’.
27 These considerations have taken us in the direction of a ‘conventionalist’ view on material objects like
Sidelle’s, who calls what exists independently of our carving Bpure, non-individuated stuff^. See Sidelle
(1998, 2010). I seriously doubt whether this view is coherent, but that is beside the current point.

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distribution of qualities over the modally ‘thin’ point-sized bits of matter. So
Lewis’s conception of point-sized bits of matter, together with his array of purely
categorical, perfectly natural properties, ensures that there is a decent basis for the
Best Systems machinery to operate on. The freedom we may be said to enjoy as to
how we want to ‘carve up’ nature can only be understood against the background
of a fundamental conception of the mosaic that already provides the laws of
nature. Such is the order of metaphysical dependence in Lewis’s system.

By contrast, our anti-realist reading of explosive realism leaves no room for
such bootstrapping procedures. Given that no way of carving is ontologically
fundamental, it is simply arbitrary to first carve into spatiotemporally individu-
ated material objects (or point-sized bits of matter), then run a Best Systems
machinery, and then do the rest of the carving. We could just as well simply
carve directly into (modally thick) rabbits and the like, and then have the
necessary connections we thus introduce play the role of laws of nature. The
resulting view would be congenial to that more radical understanding of laws,
which also derives from Hume: the projectivist approach that Nelson Goodman
and others promoted.28 But of course, the point of the orthodox Humean,
regularity-based account was that the regularities that are to be elevated to the
status of laws are objective, mind-independent, and the resulting account of laws
of nature therefore ‘admirably realist when compared against projectivism’
(Cohen and Callender 2009, p. 2).

We can now see that in order to arrive at a suitable objective and mind-independent
(in short: realist) construal of the mosaic, one needs to endorse some kind of positive
conception of the fundamental sort(s) of things that inhabit the mosaic. I have used a
construal of the mosaic in terms of point-sized bits of matter displaying patterns of
perfectly natural properties as my paradigm example, but strictly speaking this is not
the only option. What matters is that the basic elements that occupy the mosaic (as well
as the properties that are instantiated by those elements) are construed in a modally thin
way – e.g., mereologically, spatiotemporally, or in some other way (if there is). We
have seen that this rules out both substantial explosive realism and the anti-realist view
just discussed. And I have indicated that the deflationary version of explosive realism
does not really depart from a Lewis-style metaphysical view. However, as indicated,
this may still seem to provide an entry point for the BBS theorist. In the next section,
we consider this option in more detail.

3 Moderately Better Best Systems?

Let us return to the question why the Humean should accept my assumption that
rabbits, tables, water molecules, electrons etc. are modally ‘thick’ in the first place.
Doesn’t this flagrantly beg the question against the Humean? Notice that I have
valiantly admitted, and even stressed, that Humeans can deal with this alleged ‘thick-
ness’ by offering a reductive account, for instance along the lines of Lewis’s story. (For
the record, I am not in the least convinced that such a reduction can be pulled off – it
will require, in Lewis’s version as well as in potential other versions, that we can fully

28 See, e.g., Goodman (1955) and Ward (2002).

682 Euro Jnl Phil Sci (2018) 8:671–687



separate off the modal from the qualitative, and I don’t think this is possible.29) But the
crucial point here is that the very thought that rabbits, tables, etc. can be thought of in a
modally thin way is nothing but a statement of Humeanism. To Humeans, this stripping
off of the modal features of things is likely to be a matter of course (or a habit of the
mind, if you like); if pressed, there will be allusions to arguments of a familiar Humean
style (Byou don’t see that this rabbit over here must have had parents, nourishment, etc.,
now do you?^). I will not discuss the credibility of these sorts of arguments here; it is
enough for my purposes to point out that this skeptical attitude towards the modal
features of things is not to be taken as the default understanding of objects in the world
in the various sciences. It is by thus not following the Humean in reconceiving
everything in modally ‘thin’ terms that I was able to point at possible conceptions of
the mosaic that really do differ from Lewis’s. For my question was: what conception of
the mosaic does this Humean stance require? It turned out that there is not much room
indeed for diversity at this point: a Lewis-style fundamental conception of the mosaic,
in terms of modally thin point-sized bits of matter, or something along those lines, is
going to be the standard for the Humean. So no adventurous explosion of reality will be
available, and the generous gesture towards special sciences, to simply bring their own
conceptual toolbox to the game, turned out to come under special conditions: the
conception of the objects that form the domain to which the predicates of the relevant
science are applicable must be ‘Humeanized’.

Now, the reader might at this point be left with a seemingly justified puzzlement: if
what I’ve been putting forward makes sense, there is no room for a substantial
departure from the Lewisian orthodoxy, but I also hinted that this orthodoxy comes
close to being simply a ‘statement of Humeanism’.30 So isn’t it enough, then, for a BBS
theory to simply stick to the Lewisian story, and merely insist that we give up the
doctrine of perfectly natural properties when it comes to running a Best Systems
competition? I even admitted that one could still justifiably characterize the change
in view thus proposed as a move towards ‘explosive realism’ – if one thereby means the
deflationary version of that doctrine explored above.

This points in the direction of the Humean option that my considerations in §2 left
open. It can be made precise as follows.31 Suppose that we do start with a set of sortal
concepts that may come with ‘thick’ modal profiles – for instance, suppose we start
with rabbits and the like. (Perhaps we are zoologists.) Now, I said, this threatens to
make the detour through a Best Systems machinery superfluous: we already have all
manner of ‘necessary connections’ built into those modally ‘thick’ concepts. But, so the
Humean might argue, we can understand these to be provisional. We can simply use
those concepts with all their modal thickness to merely fix their extensions, and then run
a Best Systems competition on the basis of those extensions. The laws resulting from

29 See, e.g., Millgram (2009, 2011) for powerful suspicions about this sort of reduction generally; and Mulder
(2016) for a defense of the irreducibility of the basic categories of biology in particular. – Also, as I noted
earlier, the presupposed separability of the qualitative and modal dimension of things resembles Hume’s
famous division between matters of fact and relations of ideas.
30 Thanks to an anonymous referee for insisting that I treat this option in more detail.
31 I owe awareness of this interesting further Humean move to an anonymous referee, who pointed out to me
that Markus Schrenk, one of the earliest defenders of a Better Best Systems view (see Schrenk 2006),
discussed it during a talk entitled BTrouble with Properties for Better Best Systems^ at LMU on 17 December
2012.

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this procedure might exactly mirror the modal connections we started out with, but they
need not. Perhaps they mirror them only partly, perhaps no laws are forthcoming
whatsoever, and perhaps unexpected new ones emerge.

Notice that in order to Bfix extensions^, we need to have a conception of the entities
that will make up those extensions – no entity without identity, as Quine famously
quipped. As the point of the extension fixing is to get rid of the modal ‘thickness’, the
conception of the elements in those extensions must be like Lewis’s: modally thin. In
other words, we are indeed back with deflationary explosive realism.

The proposal is, thus, to first ‘convert’ the set of concepts of a given science
(zoology, in our example) to Humeanly acceptable ones, and then run a Best Systems
competition on that basis. This conversion comes down to a reductive account of the
relevant modally thick kinds. Thus, rabbits are supposed to be reducible to material
objects in a suitably modally thin sense (e.g., sums of point-sized bits of matter)
displaying appropriate patterns of qualities, and standing in suitable modal relations.

Now, as I have stressed above, this assumed reduction is not a matter of course. In
particular, such a reduction is likely to require perfectly natural properties. For without
those, the reductive claim has little substance. If all sets of point-sized bits of matter (or
all sets of material objects, for that matter) are equal as regards their ‘naturalness’, there
is no such thing as the pattern of qualities corresponding to any particular rabbit, much
less anything like a pattern of qualities that is (somehow!) common to all rabbits. So we
would first need to isolate some set of relevant properties in terms of which the
reduction may proceed. And this set would in fact be available if the science in question
(zoology, we’re imagining) came with its own privileged set of fundamental properties
in terms of which the reduction is to be effected. But, again, this is simply incredible: no
special science comes pre-packaged with its own Humeanly acceptable reductive
apparatus.

Now, the Humean might simply hold that the qualitative aspect of, e.g., rabbits
requires no such reduction to patterns of more basic qualities, that we can treat rabbit,
when stripped of all modal elements, as simply an irreducible feature of certain material
objects considered as wholes, i.e., as a ‘perfectly natural property’ in its own right.32

Now, further doubts could be articulated about the feasibility of this proposal. For
instance, this is not likely to be faithful to the way rabbit is treated in zoology. And we
are still assuming that rabbits can be reductively conceived in such a way that their
modal dimension is disjoint from their qualitative dimension, yet this assumed disjoint
conception is likely to presuppose laws – laws are to determine which possible worlds
are relevant for the evaluation of the modal dimension, after all. Perhaps this can in turn
be solved by insisting that the reduction doesn’t require a full-blown analysis of the
modality involved, but merely a removal of that modality. Well, maybe; but notice that
this again adds to the list of demands the defender of a BBS approach is putting on the
sciences to be allowed into her game in the first place. Only if one assumes both a
modally flat conception of the underlying mosaic, and a reductive analysis of the
science’s basic vocabulary along Humean lines which does not already invoke laws of
any kind, is there any chance of getting the proposal off the ground.

32 An anonymous referee suggested that I discuss the view of rabbithood as a quiddity at this point. I won’t do
so, since I do not want to get involved in the metaphysical intricacies that this notion invites.

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I will not pursue this further as an argument against the BBS approach, but leave it to
the reader to judge whether there is reason for optimism. It was not my aim, after all, to
refute this view, but rather to explore what the conception of the underlying mosaic
must be like in order to be acceptable for such a Humean project. So let us zoom out a
bit and see what kind of answer our reflections suggest to that larger question.

4 Afterthoughts: the limits of Humeanism

Our explorations give rise to the following diagnosis. The misgivings about ‘necessary
connections’ that are more or less definitive of Humeanism are, in the end, symptoms
of a very deeply rooted suspicion towards conceptual connections in general: concep-
tual connections are, at best, mere relations between ideas, to put it in Humean
terminology; what could they possibly tell us about reality? To say that they capture
real ‘necessary connections’ out there is just to project what belongs within the mind to
the outside world. However, and this is what I have tried to bring out in the above, to
cash out this familiar Humean picture, the Humean needs to devise a conception of this
‘outside world’ that indeed lacks those necessary connections. Put briefly, the Humean
strategy of ‘disarming’ conceptual connections by showing that they amount to no
more than harmless, matter-of-factly regularities among the things ‘out there’ requires
that the fundamental conception of those things ‘out there’ be devoid of conceptual
connections. So the Humean project requires that the fundamental conception of the
mosaic be modally ‘thin’, in order to provide the basis in terms of which the more
troublesome conceptual connections can be disarmed. I took Lewis’s view as my stock
example in the above, and argued that something along those lines is what is required.

This diagnosis thus indicates a ‘limit of Humeanism’: the options for a credible
conception of the Humean mosaic are quite limited – e.g., a shift to an ‘explosive
realism’ can only be made within these limits (i.e., in the form of ‘deflationary’
explosive realism). But we can push this conclusion a little bit further, albeit tentatively,
to indicate a more troublesome ‘limit of Humeanism’: if it is reification of conceptual
connections that is bothering the Humean, there is considerable pressure for him to
resort to anti-realism. For even on as modally flat a conception of the Humean mosaic
as Lewis presents, there are still conceptual connections: his spatiotemporally (or
mereologically) individuated material objects come with their own humble but non-
empty modal profiles. For instance, no material object could be larger or smaller than it
is, since different spatiotemporal boundaries by definition means different material
object.33

Let me close by linking these observations to the traditional Humean argument
against necessary connections. Hume says that, if we look closely, we never see any
necessary connections – this is an expression of the mentioned suspicion towards
conceptual connections.34 By extension, however, we could argue that we never see
any succession in time or any contiguity in space; we only see the sensory qualities, the

33 See Mulder (2013) for a more elaborate defense of this claim, and for treatment of the obvious reply that
Lewis can solve this with the aid of his counterpart-theoretic analysis of modality.
34 Stroud (2011, p. 95) rightly remarks that this famous Humean line of thought is indeed not really an
argument for, but rather an expression of, his skepticism. See also Anscombe (1971).

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spatial and temporal relations between them are not themselves such qualities. Indeed,
even the difference and the resemblance between different sensory impressions are not
themselves impressions, nor is the conceptual determination of impressions as impres-
sions an impression.35 Thinking this traditional Humean argument through to the end,
then, leads to the conclusion that all of these determinations are the result of what the
mind does with ‘the given’, much like the mind, on Hume’s view, creates an expecta-
tion of the effect whenever the cause is present. At its limit, then, this type of suspicion
towards the conceptual leads to a form of anti-realism, on which no fundamental
conception of the mosaic can be given at all. At this limit, Humeanism entails rejection
of metaphysics tout court, and hence will not yield an ‘admirably realist’ account of
anything.

Funding Information Research leading to this article was supported by the Netherlands Organisation
for Scientific Research (NWO), grant number 275-20-068.

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0
International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use,
distribution, and reproduction in any medium, provided you give appropriate credit to the original
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http://www.elijahmillgram.net/publications/mrms.pdf
http://www.elijahmillgram.net/publications/mrms.pdf

	The limits of Humeanism
	Abstract
	Humeanism about laws
	The underlying Humean mosaic
	Moderately Better Best Systems?
	Afterthoughts: the limits of Humeanism
	References