Reduction and Elimination in Philosophy and the Sciences

notion of time and requires that something exists in order
for time to exist.
The generative conception can accommodate
backwardly finite but closed universes that begin at a
singularity. But it is hard to conceive of our universe as
such, since so little information about it could be stored at
such a single spatial point. The initial conditions would
have to consist in finite values of various fundamental
parameters at that point. Theories of the universe based
on general relativity that ignore quantum effects yield a
singularity with infinite values of the fundamental
parameters at that point. But such a singularity is not a
candidate for an initial slice as the values of the
parameters are not well defined.
Recent efforts to construct a theory of quantum
gravity for our universe that integrates general relativity
and quantum theory offer hope of avoiding this problem of
a Big Bang singularity at which parameters cannot be
defined. They mostly have the consequence that the linear
temporal ordering among events breaks down, i.e. that
time doesn’t make sense, close to the Big Bang when the
universe is smaller than the Plank scale. If universes in
accordance with such theories are coherent, they too
would lack an initial condition and so it would seem could
not be generated.
A second problem for the view that our universe is
generated concerns the direction of generation. For any
generated universe there is an extrinsic direction of time
given by the direction of generation (and by the temporal
asymmetry in the notion of a fundamental dispositional
property). And in our universe there are temporal
asymmetries found in intrinsic features that mark a
subjective direction of time. They are generally regarded
as based on the thermodynamic condition of increasing
entropy. Such asymmetries include the way actions affect
the future not the past, organisms age, and scattered
rubble doesn’t suddenly cohere to constitute a building. A
problem arises for the generative conception if there is no
good reason to believe that these intrinsic and extrinsic
directions coincide. For part of the appeal of the view that
our universe is generated comes from its incorporating the
compelling intuition that what is present was generated by
the laws and what seems subjectively to be the past.
Why might the direction of generation and our
subjective direction of time diverge? The direction in which
time seems to be flowing in the universe might be the
opposite to that in which the universe is generated. From
our perspective on the direction of time we say that our
universe is 13 billion years old, but if the universe has a
finite duration and its fundamental laws are time-reversal
invariant, then it could be generated from the other end,
and we should say instead that we have another 13 billion
years or so before the Big Crunch, if we take the direction
of generation to be the direction of time. Given these
assumptions then, it is logically possible that our universe
is generated in the counterintuitive direction. However, this
should worry us no more than the logical possibility that we
are brains-in-vats, so long as we have good reason to
believe that our universe is generated in the intuitive
direction.
Tim Maudlin (2007, pp. 130-5) addresses this
problem for the generative conception, adding to our
assumptions of a temporally finite universe and timereversal
invariant fundamental laws the empirically well
supported assumption that there is low entropy at one
temporal end of the universe and high entropy at the other.
Maudlin’s idea, as I understand it, is that we could explain
Two Problems for NonHumean Views of Laws of Nature — Noa Latham
why entropy increases given the assumption of the
fundamental generative laws and the condition that
entropy starts off low. But we could not explain a decrease
in entropy given the assumption of the laws and the
condition that entropy starts off high. As we observe an
entropy gradient over time in our universe, this asymmetry
in explanation makes it much more reasonable to suppose
that the universe is being generated from the lower
entropy end than from the higher entropy end, and hence
that the intuitive direction of time coincides with the
direction of generation.
Where I think Maudlin goes wrong is in setting up a
biased contrast that misleadingly gives the impression that
for possible universes with our generative laws there are in
a natural sense more of them with low to high entropy
gradients than there are with high to low entropy gradients.
The semblance of asymmetry comes from taking as one
option that the universe has a low entropy beginning,
ignoring knowledge that it has a high entropy state at its
other end, and pointing out that it would be highly likely to
evolve into a high entropy state. This is then compared
with the option that the universe has a high entropy
beginning, ignoring knowledge that it has a low entropy
state at its other end, and pointing out that it would be very
unlikely to evolve into a low entropy state. Each of these
options embraces something and ignores something we
know about our universe. But what the first option
embraces—that the universe has a low entropy state—is
something that would be considered highly improbable if
we knew nothing about which universe was actual, while
what the second option embraces—that the universe has a
high entropy state—is something that would be considered
highly probable if we didn’t know which universe was
actual.
I suggest that to determine what it is reasonable to
believe about our universe we should not skew our
understanding by suppressing knowledge in this
asymmetrical way, but should begin with what we do know,
namely that the actual universe contains an entropy
gradient with extremely low entropy at one end. The
salient fact is then surely that from the nature of timereversal
invariant laws, there is a natural 1-1 mapping of
universes with a low to high entropy gradient onto
qualitatively identical universes with a high to low entropy
gradient. This leaves us without a reason for believing our
universe is generated from the low entropy end rather than
the high entropy end.
Nevertheless, there might be empirical reasons to
reject the two assumptions we were making—of a
temporally finite universe and of time-reversal invariant
fundamental laws. Rejecting either of these assumptions
would support belief in a coincidence of the direction of
generation and the subjective direction of time. For if the
universe is closed at one end and infinite at the other, it
could be generated from the unique slice at one end but
could not be generated in the other direction. Current
estimates of the rate of expansion of the universe suggest
that it is forwardly infinite, though this could be revised if
evidence of a lot more “dark matter” arises. And although
both general relativity and the Schroedinger equation are
time-reversal invariant, a quantum theory involving a
Collapse Postulate is not. Whether such a postulate is
among the fundamental laws of our universe is currently a
debated feature of the interpretation of quantum theory.
But should it be so, and (as is widely supposed) there
cannot be a time-reverse of such a postulate, then the
universe couldn’t be generated in the counterintuitive
direction.
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