thesis

ful to think of a logically possible world as a world that it would have been in God’s power
(hypothetically!) to create, had he so chosen… In determining whether it is logically possible
that some statement is true, the constraints are largely conceptual.
So we see that, if B-properties logically supervene on A-properties, the A-properties in
question entail the B-properties, since it is not possible for those particular A-properties to
hold without the B-properties holding too.
Our prior example of lumpiness qualifies for such supervenience. One could rigorously
define lumpiness in terms of some statistical property of the entity concerned, perhaps in
terms of the variance of density over its volume. It is not possible for a substance to be uni-
formly even and yet be ‘lumpy’, just as a substance with significantly varying density cannot
be denied the term. That lumpiness is not all-or-nothing is beside to point – to the extent that
a substance can be attributed or denied lumpiness, this can be done solely on the basis of its
density distribution.
An important subtlety must be addressed, however. For any property such as lumpi-
ness, attributed by sentient beings on the basis of some phenomenal assessment, it may be
retorted that it could not supervene on the physical, since two agents may differ over how
‘lumpy’ they consider a substance to be – perhaps one always had lumpy porridge for
breakfast and so became more tolerant of lumpiness in general. However, this would be to
confuse ontology with epistemology. If lumpiness is a genuine property of substances, the
inter-subjective differences do not reflect on the property itself. In the same way, we might
say that, notwithstanding possible differences in the way that individuals may perceive col-
ours, the actual colour of an object depends only on the wavelengths of electromagnetic ra-
diation that it reflects.
Natural Supervenience
The second type of supervenience, natural supervenience is described thus (37):
Natural supervenience holds when, among all naturally possible situations, those with the
same distribution of A-properties have the same distribution of B-properties… This happens
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