Reduction and Elimination in Philosophy and the Sciences

Two Problems for NonHumean Views of Laws of Nature
Noa Latham, Calgary, Canada
Humeans and nonHumeans offer dramatically different
world-views stemming from their different accounts of the
status of the laws of nature of our world. Humeans take the
laws to be material conditional facts, while nonHumeans
take them to be nonmaterial. And this can be shown to be
equivalent to another popular way of distinguishing
Humean and nonHumean views. Humeans claim, and
nonHumeans deny, that the laws metaphysically
supervene on the totality of particular facts—those
describing the distribution of properties somewhere in
spacetime—where fact A metaphysically supervenes on
fact B iff A exists in all possible worlds in which B exists.
I shall assume that there is a fundamental level of
reality, and I shall regard fundamental properties as those
characteristic of such a level. Humeans can be
characterised accordingly as claiming that the fundamental
laws of our universe metaphysically supervene on the
totality of its fundamental particular facts, and
nonHumeans as denying this. I am also provisionally
assuming a view of properties that treats them as
independent of the laws in which they feature.
My discussion henceforth is thus narrower than
familiar discussions of laws of nature. I shall not examine
nonfundamental laws such as special science laws, ceteris
paribus laws of physics and thermodynamic laws. I see it
as an advantage of the account I am offering that it does
not run together what I take to be very different kinds of
laws in quest of a unified account.
A popular idea, which I think captures the intuitive
understanding of the role of fundamental laws in our
universe, is to think of them as analogous to rules of a
computer programme that changes an array of pixels on a
screen from one moment to the next. The way I like to put
it is to say that fundamental laws of nature are derivable
from a single fundamental law, analogous to the computer
programme, that (i) provides an instruction, given the
existence of a time-slice, as to what the next time-slice is
to be and (ii) makes it the case that this next time-slice
comes into existence. I call this the generative conception
of fundamental laws.
Humeans typically point to the absence of the
category of nomic facts on their view as a huge gain in
simplicity and as greatly favouring their view. In opposition
to this, it can be claimed that the advantage of simplicity
goes instead to the view that the universe is generated by
a fundamental law from an initial slice, as this provides a
sense in which only the fundamental particular facts of the
initial slice and the fundamental law are
causally/explanatorily basic. The regularities observed in
subsequent fundamental particular facts are all
explainable, while the Humean must treat them as a
cosmic coincidence. Humeans typically respond that their
view attributes a causally/explanatorily basic status to the
initial conditions and fundamental laws too. I think the best
reply to this is to say that what is compelling about this
nonHumean view is that laws and initial conditions provide
a mind-independent causal/explanatory basis for the
universe. By contrast, the laws are essentially minddependent
on the best worked out Humean account, David
Lewis’s, and it does not appear that any alternative
Humean account could escape this. The Humean cannot
offer a mind-independent sense in which anything is
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causally basic, or a mind-independent sense in which
anything less than the totality of fundamental particular
facts is explanatorily basic.
I believe almost all nonHumean views of laws are
committed to such fundamental generative laws. (Nancy
Cartwright’s view, if coherent, is one that is not.) These
include views that take fundamental properties to be
dispositional and to entail laws. Such views of properties
presuppose victory over the Humean view of laws, and
compete with other nonHumean views. I shall not dwell
here on these differences among nonHumeans as my
concern in this paper is to examine two problems that I
think almost all nonHumean views face.
The idea that the observed world is driven to unfold,
i.e. generated, over time by fundamental laws or
fundamental dispositional properties is I think the natural
way people have understood the workings of nature. This
appears to be a purely metaphysical view in the sense that
it is independent of scientific facts about our universe that
were unavailable to our ancestors and may be unavailable
to us today. In this respect the nonHumean view of laws
resembles the view with which it is often compared that
there is a physical reality independent of our sense
perceptions. What I will be arguing in the remainder of this
paper, however, is that the thesis that our universe is
generated may be empirically false and thus cannot be
defended as a purely metaphysical thesis. I think this
empirical sensitivity detracts greatly from the plausibility of
the generative view. But all the alternatives I have
encountered strike me as nonstarters.
The first problem is that generative laws appear to
be possible only for universes generated from a single
initial slice. This precludes backwardly infinite universes
such as a Steady State or oscillating universe, and
backwardly finite but open universes if these are coherent.
It also excludes universes for which the notion of a linear
temporal ordering of events doesn’t make sense in the part
of the universe where one would need an initial slice to be.
Why is an initial slice required? Well, some
particular fact is needed in addition to fundamental laws in
order for there to be a universe. And the only alternative to
the fundamental facts of a single slice appears to be the
fundamental facts of an infinite sequence of slices. This
reintroduces the Humean view with its problems in
characterising this infinite sequence as explanatorily basic
when it appears to be partly generated. Furthermore there
would be an implausible arbitrariness to the cutoff point
between this infinite sequence and the generated part of
the universe. So an initial slice is the only plausible option
from which a universe could be generated.
But why should there be a problem in generating a
temporally dense backwardly finite universe? Assuming for
the moment an absolute conception of time, then there is
either a last moment at which there is nothing and no first
moment at which there is something (a backwardly open
universe), or no last moment at which there is nothing and
a first moment at which there is something (a backwardly
closed universe). And perhaps both open and closed
options for the temporal topology of a backwardly finite
universe are also coherent if one rejects an absolute