Reduction and Elimination in Philosophy and the Sciences

Assessing Humean Supervenience
Amir Karbasizadeh, Tehran, Iran
1. Humean Supervenience:
Humean Supervenience is a central article of faith for
David Lewis, who defines it thus:
“Humean supervenience is named in honor of the
greater [sic] denier of necessary connections. It is
the thesis that all there is to the world is a vast mosaic
of local matters of fact, just one little thing and
then another…We have geometry: a system of external
relations of spatio-temporal distance between
points. Maybe points of spacetime itself, maybe
point-sized bits of matter or aether 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.
For short: we have an arrangement of qualities.
And that is all. All else supervenes on that.”
(Lewis 1986 p. x)
The "all else" includes nomic facts (laws, physical necessity,
causation, etc.). The gist of Lewis' suggestion is that
every contingent property instantiation supervenes on the
arrangement of perfectly natural properties. One may ask
what Lewis means by a “perfectly natural property.” Recall
that Lewis has a rather hybrid conception of properties,
being an amalgam of two very different property conceptions.
(1) On the one hand, Lewis has a conception of
properties according to which a property is just the set of
all of its instances, this-worldly and other-worldy. So the
property of being a donkey is the set of all donkeys, both
donkeys from our world and other-worldly donkeys. To
have this property is to be a member of the class of donkeys.
This conception of properties is abundant because
on this view, "any class of things, be it every so gerrymandered
and miscellaneous and indescribable in thought and
language, and be it ever so superfluous in characterizing
the world, is nevertheless a property (Ibid, p.192) Concerns
from many fronts (e.g., Lewis' desire to formulate
viable theories of laws, causation and events) require that
there be some way to distinguish the properties that
ground objective resemblances and which are causally
efficacious from those which are not. (2) In light of this,
Lewis has supplemented his abundant conception of properties
with a sparse conception of properties. Although his
hope is that a viable nominalistic sparse theory of properties
is formulable, Lewis would settle for, (roughly) Armstrongian
universals as well. With this contrast in mind, we
can finally grasp the conception of "perfectly natural properties"
operative in Lewis’ conception of Humean Supervenience.
Lewis gives the following sufficient condition for
a property being perfectly natural:
A property, F, is perfectly natural if its members are
all and only those things that share some one universal.
Properties like mass, charge and spin, at least at the present
point of scientific development, seem to be apt candidates
for being perfectly natural properties.
2. Humean supervenience: Two Independent
Theses
Although he does not mention it, Lewis's Humean supervenience
has two logically independent theses. The first,
which we may call Separability, claims that spatio-temporal
relations are the only fundamental external physical relations.
To be precise:
Thesis 1 (Separability): The complete physical state
of a non-alien world is determined by (supervenes
on) the intrinsic physical state of each spacetime
point (or each pointlike object) and the spatiotemporal
relations between those points.
Separability posits, in essence, that we can chop up
space-time into arbitrarily small bits, each of which has its
own physical state, much as we can chop up a newspaper
photograph into individual pixels, each of which has a particular
hue and intensity. As the whole picture is determined
by nothing more than the values of the individual
pixels plus their spatial disposition relative to one another,
so the world as a whole is supposed to be decomposible
into small bits laid out in space and time.
The thesis of Separability concerns only how the
total physical state of the universe depends on the
physical state of localized bits of the universe. The second
component of Lewis's Physical determination takes care of
everything else:
Thesis 2 (Physical Determination): All facts about a
non-alien world, including modal and nomological
facts, are determined by its total physical state.
I have employed the new terminology “Physical determination”
to distinguish Thesis 2 from Physicalism. Physicalism
holds that two worlds which agree in all physical respects
(i.e. with respect to all items which would be mentioned in
a perfected physics) agree in all respects. Thesis 2 essentially
adds to Physicalism the further requirement that all
physical facts about the world are determined by its total
physical state, by the disposition of physical properties. If
one holds 1 , for example, that the laws of nature do not
supervene on the total physical state of the world (at least
so far as that state can be specified independently of the
laws), then one can be a Physicalist while denying Physical
determination. One can hold that worlds which agree
on both their physical state and their physical laws agree
on all else, while denying that the laws are determined by
the state. Lewis's Humean Supervenience importantly
maintains the stronger claim.
3. Physicalism and Physical determination
In order to clearly distinguish Thesis 2 from Physicalism,
we must remark that the following condition on acceptable
analyses is accepted by the Physical determinationist, but
not by the Physicalist:
Non-circularity condition: The intrinsic physical state
of a non-alien world can be specified without men-
1 Cf. Carroll 1994
163