The Existence and Laws of Our Universe

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A natural explanation of the
existence and laws of our
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Quentin Smith
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Marion, Indiana
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To cite this article: Quentin Smith (1990) A natural explanation of the existence
and laws of our universe, Australasian Journal of Philosophy, 68:1, 22-43, DOI:
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AustralasianJournalof Philosophy
Vol. 68, No 1:March 1990
A NATURAL EXPLANATION OF THE EXISTENCE AND
LAWS OF OUR UNIVERSE
Quentin Smith
I. The Possibility of a Natural Explanation of Our Universe
The standard view of philosophers is that the existence of particular events
within our universe is capable of being explained in terms of initial conditions
and natural laws, but that the existence of our universe itself is a 'brute
given' that is incapable of naturalistic explanation. A supernatural explanation
of the existence of our universe may be alleged to be possible ('God created
our universe so that humans may exist and the existence of humans is an
intrinsic good'), but an explanation that appeals only to factors, situations
or regularities in nature is deemed to be in principle impossible. It is also
a standard view of philosophers that the less fundamental natural laws of
Our universe are capable of being explained in terms of more fundamental
laws of our universe, but that the most basic natural laws of our universe
are incapable of being explained naturalistically. Perhaps they can be
explained supernaturally,by asserting that God ordained them so that humans
may eventually evolve, but no other explanation is supposed possible.
I believe these standard views are undulyconservativeand that a naturalistic
explanation of the existence and basic laws of our universe is possible. By
this I mean that there is at least one model or type of explanation such
that it is logically possible for there to be instances of this type that provide
naturalistic explanations of the existence and basic laws of our universe.
The type of explanation I have in mind is employed frequently in Quantum
Mechanical accounts of microscopic events in our universe. Numerous events
are explained by Quantum Mechanics in the sense that they are subsumed
under laws that show these events are to be expected with a precise degree
of expectation. These explanations are not causal explanations in the sense
that their premises involve references to sufficient conditions of the events
to be explained, but are statistical explanations in the sense that they state
the frequencies (which may be low) with which the events occur in situations
of a certain sort. Explanations of spontaneous radioactive decays are
paradigmatic examples of explanations of this sort. For example, when an
alpha particle in the nucleus of a U238atom approaches the potential barrier
that is the wall of the nucleus, the particle has a probability of 10-38 of
tunnellingthrough the barrier. 'Tunnelling' has a special meaning in Quantum
Mechanics; something tunnels through a barrier if it spontaneously acquires
for a certain period of time the extra energy it needs to pass through the
barrier. There is no sufficient condition of the tunnelling of the alpha particle
22

QuentinSmith 23
through the wall of the nucleus, but this tunnelling is explained in the sense
that it is subsumable under the following statistical law:
(1) P(T/A)= 10-38
where 'P' stands for probability and
T = the spontaneous tunnelling of an alpha particle through the wall of
the nucleus of a U238atom, and
A = the approach of an alpha particle to the wall of the nucleus.
(1) says, in effect, that the probability of an event of the T sort (tunnelling
through the wall) being associated with an event of the A sort (approaching
the wall) is 10 -38. Accordingly, if a certain alpha particle x tunnels through
a barrier, then its tunnelling can be accounted for by the following inductive
inference:
(1) P(T/A) = 10-38
(2) Ax
[10 -38]
(3) Tx
(2) says that the alpha particle x has the property A, the property of
approaching the wall of the nucleus of a U238 atom. (3) asserts that the
particle x has the property T of tunnelling through the wall. The double
line indicates that (1) and (2) make probable (3) and '[10-38]' indicates
the degree to which they make (3) probable.
(1)-(3) illustrates the type of explanation I shall use in my constructions
of logically possible explanations of the existence and basic laws of our
universe. One premise will state a statistical law, another that a certain
particular has a certain property, and the conclusion will state (or at least
imply) that our universe exists or that the basic laws of our universe obtain.
The type of explanation I shall use bears some affinities to Hempel's
I-S (inductive-statistical)model of scientificexplanation. The main difference
between Hempel's I-S model and the model I shall use is that Hempel supposed
that I-S explanations require the explanandum-statement to be made highly
probable by the explanans-statements, whereas the model I use does not
require this.1 I agree with W. Salmon, R. Jeffries, P. Railton and others2
that high probability is not a necessary condition of statistical explanations.
But it should not go unremarked that Hempel subsequently came to
acknowledge this and in 1976 proposed a new version of I-S explanations
ESee Carl Hempel, Aspects of ScientificExplanation (New York: Free Press, 1965), pp. 381-
393.
2 See Wesley Salmon, with contributions by Richard Jeffrey and James Greeno, Statistical
ExplanationandStatisticalRelevance(Pittsburgh: UniversityofPittsburghPress, 1971);Wesley
Salmon, ScientificExplanation and the Causal Structureof the Worm (Princeton: Princeton
University Press, 1984), Chapters 2-4; Peter Railton, 'A Deductive-Nomological Model of
Probabilistic Explanation', Philosophyof Science45:206-226 (1978). The example of the
tunnelling of the alpha particle is used in Salmon's first-mentioned book on page 58 and
in his second-mentionedbook on pages 85-86.

24 Explanation of the Existence of Laws of Our Universe
which allows low probabilities. 3 I shall call this new version the neo-l-S
model of explanation and shall use this model in the construction of my
cosmological explanations. It will not be necessary for the limited purposes
of this paper to take a stand v/s ~ v/s the other modifications to Hempel's
original I-S model that have been proposed in the literature, 4 but it is crucial
to my project to affirm that the neo-I-S model retain an essential feature
of the original I-S model, that the explanations must establish a nomic
expectability of the item mentioned in the explanandum-statement but need
not casually explain it.5 The explanans-statements need not cite factors that
cause the explanandum-item but merely need to establish that this item
is to be expected (which in the new model may be a low expectability).
As is well-known, this view of statistical explanation has recently been
opposed at some length by Salmon. In his new book Salmon develops a
broad-based theory of probabilistic causality and argues that the explanans-
statements must cite a cause (which need not be a sufficient condition)
of the explanandum-item. According to this theory, the approach of an alpha
particle to the wall of the nucleus of a U238 atom is a causal process that
has the propensity of 10-38 to bring about or undergo a tunnelling through
the wall and by virtue of this fact its tunnelling through the wall (if it occurs)
has a causal explanation. It is not necessary for my purposes to counter
Salmon's arguments that explanations of particular events within the universe
must be causal, but it is necessary to show that his arguments do not apply
to explanations of the existence and basic laws of our universe. I will argue
in Section 4 that causal references are neither possible nor requisite for
natural explanations of the existence and basic laws of our universe. Causal
references are not possible since any alleged natural cause of the universe,
even if construed in accordance with Salmon's liberal criteria of causes,
would really be a part of the universe and thereby would be among the
3 Carl Hempel, 'Nachwort 1976:Neuere Ideen zu den problemen der statistischen Erklarung',
in Hempel's Aspekte wissenschaftlicherErklarung(Berlin:Walter de Gruyter, 1977), pp. 98-
123. For a pertinent discussion of this essay, see Salmon, Scientific Explanation and the
Causal Structureof the WorM,op. cit.,pp. 89-90.
4 For example,it has been argued that Hempel's requirement ofmaximal specificityguarantees
that all known relevant factors are to be taken into account but not that only relevant
factors are to be taken into account, and thereby needs to be supplemented by what Fetzer
calls a requirement of strict maximal specificity, which rules out laws that state nomically
irrelevant properties. See James Fetzer, Scientific Knowledge (Dordrecht: D. Reidel, 1981),
pp. 125-26. Also see Wesley Salmon, Hans Reichenbach:Logical Empiricist (Dordrecht: D.
Reidel, 1979), pp. 691-694.
It is also argued that Hempel's analysis of the partial entailment of the explanandum-
statement by the explanans-statements in terms of Carnap's notion of logical probability
provides no nonarbitrary way of assigning the numerical values that would warrant the
equality of the value of the partial entailment with the value of the nomological probability.
See Wesley Salmon, 'Partial Entailment as a Basisfor Inductive Logic', in N. Rescher (ed.),
Essays in Honour of Carl Hempel (Dordrecht: D. Reidel, 1969), pp. 47-82. Fetzer argues
this problem is solved by interpreting partial entailments as logical probabilities in
Reichenbach's sense, which allows their numerical equality with nomological probabilities
to be given a deductive justification (as measures of nomic expectability) in lieu of an
inductivejustification (as measures of evidential support). See Fetzer, op. cit., pp. 127-131
and 'A SingleCase Propensity Theory of Explanation', Synthese 28:171-198 (1974).
5 On page 250, note 6 and pages 352-53 of Aspects of Scientific Explanation Hempel says
that some D-N explanations are acausal and I assume he holds the same for I-S explanations.

QuentinSmith 25
phenomena that need to be explained. I will show, secondly, that the absence
of causal references is not sufficient to deprive my cosmological arguments
of explanatory value; specifically, I will demonstrate that my cosmological
subsumptions do not possess all the defining features Salmon associates with
acausal subsumptions that have little or no explanatory value and therefore
that my cosmological subsumptions fall outside of his category of acausal
subsumptions that are not (genuine) explanations.
The primary aim of the following sections is to contravene the traditional
assumption, recently articulated by Richard Swinburne, that 'there can be
no scientific [naturalistic] explanation of the existence of a universe; for
all that science can do is to explain how a present state of the universe
was brought about by a past state, It cannot explain why there is a universe
at all. For a similar reason.., science cannot explain why there are the
most basic laws of nature that there are'.6 The implied conclusion is that
we must resort to a supernatural agency to explain the existence and basic
laws of a universe. In addition to contradicting this assumption, I also wish
to accomplish a second aim, namely, to construct naturalistic explanations
of our universe that are not only logically possible but also approximately
empirically possible. This will increase the interest and contemporary
scientific relevance of the explanations and will enable us to take seriously
the suggestion that our universe might, in fact, have explanations of this
sort.
II. Definitions of a Universe, Spatiotemporal Positions and Relations, and
Basic Laws
My neo I-S explanations require preliminary definitionsof a universe, spatial-
temporal positions and relations, and basic laws of a universe; the construction
of these definitions will occupy us in this section and their employment
in the neo-I-S explanations in the next section. Many different definitions
are possible and I shall select the definitions that allow for the sort of
cosmological explanations in which I am interested. I shall impose a further
restriction on my definitions in order to increase the interest of my
explanations, that the definitions violate none of the concepts or principles
of contemporary cosmological theories. This restriction will enable the neo-
I-S explanations offered in section 3 to approximate with a reasonable degree
of closeness empirically possible explanations.
I begin with the definition of a universe.
(D 1) U is a universe = Df. U is a spacetime such that (i) every spatiotemporal
position in U is spatiotemporally related to every other position in
U and (ii) there is no spatiotemporal position that is spatiotemporally
related to any position in U that is not itself a part of U.
On the face of it D 1 allows there to be many universes, since it is possible
for there to be two universes U0 and U1 such that no spatiotemporal position
in U0 is spatiotemporally related to any position in UL This possibility will
6 Richard Swinburne, The Existenceof God (Oxford: Clarendon Press, 1979), p. 286.

26 Explanation of theExistenceof Laws of Our Universe
be essential to my cosmological explanations, which will make reference
to many universes.
But D1 remains fundamentally ambiguous until its key expressions,
'spatiotemporal position' and 'spatiotemporally related' are defined. The
former is defined as follows.
D2 P is a spatiotemporal position = Df. P is a point in three dimensional
space at an instant of time such that (i) the point has zero spatial
volume and the instant zero duration, (ii) between any two spatial
points there is a nondenumerable infinity of other spatial points and
between any two instants there is a nondenumerable infinity of other
instants, (iii) P is irreducible to actual or possible events (an event
= an instantaneous temporal part in the history of a point mass or
pointlike light ray) and may exist even if no event occupies it.
Condition (iii) commits me to a 'substantivalist' rather than 'relational' theory
of spacetime and thus sides me with Earman, Nerlich, Friedman and others.7
The substantivalism I assume allows that there may be empty spacetimes,
such as an empty Minkowski spacetime or an empty de Sitter spacetime,
but nothing important in my explanations hinges on this contention and
I mention it only to decrease the vagueness of the spacetime notions I shall
be employing.
If two spatiotemporal positions are to belong to the same universe, then
they must be spatiotemporally related. The definition of spatiotemporal
relatedness will be crucial to my explanations and some care must be taken
in choosing the appropriate definitions. It might seem at first blush that
the timelike, spacelike and lightlike relations defined in standard treatments
of the Special Theory of Relativity (STR) would suffice for my purposes.
For example, it might be said that two spatiotemporal positions belong to
the same universe if they are spacelike related ('topologically simultaneous')
and that two positions are spacelike related if and only if it is impossible
for them to be occupied by events that are connected by light or slower
signals. But this definition is unsuitable for my purposes, since two events
E0 and Ex that occupy two spatially disconnected universes are unconnectible
by light or slower signals and yet I do not want to say the positions they
occupy are spatiotemporally related.
If I add to the definition of spacelike relatedness the condition that the
two events are simultaneous or successive relative to some reference flame,
I will solve the above problem but a new one will take its place. Two events
are simultaneous or successive relative to some reference frame R if and
only if it is possible for light signals sent from them to arrive simultaneously
or successively at the midpoint between the places occupied by the two
events as measured from the perspective of R. A place M is the midpoint
between the places occupied by the two events relative to R if and only
7 See John Earman, 'Who's Afraid of Absolute Space?', Australasian Journalof Philosophy
48:287-319 (1970); Graham Nerlieh, TheShapeofSpace(Cambridge: Cambridge University
Press, 1976); Michael Friedman, Foundationsof Space-Time Theories(Princeton: Princeton
UniversityPress, 1983).

Quentin Smith 27
if R is at rest relatively to M and it is possible to send light signals
simultaneously from M to the two places and for these signals to rearrive
at M simultaneously. This entails that two events are spacelike related only
if they belong to the same spatially continuous universe, since two events
in two spatially disconnected universes cannot emit light signals that intersect
at a midpoint between the places the two events occupy. Unfortunately,
however, this definition is too restrictive for my purposes since it divides
into a number of different universes spacetimes that I wish to treat as one
universe. Suppose that a spacetime has negative curvature (the spacetime
is hyperbolic and ever expanding) and contains two galaxies receding from
one another at a combined velocity greater than that of light.8 An event
E2 on one galaxy cannot be timelike or lightlike related to an event E3
on the other galaxy since no signal at or below the velocity of light can
connect them. But they cannot be spacelike related either, at least not if
the above modified definition is adopted. To be spacelike related, there must
be a midpoint between the places occupied by two events relative to a
reference frame R. But something is a midpoint M between the two places
relative to R only if it is possible to send light signals simultaneously from
M to the two places and for these signals to rearrive simultaneously at M.
If the two galaxies at which the two events E2 and E3 are located are receding
from each other at a combined velocity greater than the speed of light,
then there is no place M from which signals could be sent simultaneously
to both galaxies such that the signals would rearrive at M. It would follow
that E2 and E3 are not spacelike related and therefore belong to different
universes, which is not the result I wish.
There is, however, a definition of spatiotemporal relatedness, based on
the General Theory of Relativity (GTR), that is suitable to my purposes.
The relations in question are constitutive of cosmic time and I shall call
them relations of cosmic simultaneity and cosmic succession. Definitions
of these relations require antecedent definitions of a 'surface of simultaneity'
and a 'spacelike hypersurface'.
(D3) S is a surface of simultaneity of a local Lorentz frame F at t~ =df.
S is the best of all and only those spatiotemporal positions related
to F at t~ by the relation SIM. Any position P stands in SIM to
F at tl if and only if F is a world line of a possible observer and
to, tl and t2 are successive times on F such that (i) it is possible
for a light signal to be sent from F at to to P and rearrive at F
at t2, and (ii) the time At elapsed between the emission of the signal
from F at to and the rearfival of the signal at F at t2 obeys the
equality At/2 = the temporal distance from to to t~, = the temporal
distance from tl to t2.
(D4) H is a spacelike hypersurface = df. (i) H has three spatial dimensions
and is temporally instantaneous; (ii) H is the set of interlocking
s For a discussionof such situations,see W. Rindler,'Visual Horizonsin World Models',
MonthlyNotesof theRoyalAstronomicalSociety116:662-77(1956),andRichardSwinburne,
Spaceand Time,2nd ed. (NewYork;St.Martin'sPress,1981),Chapter13.

surfaces of simultaneity of the spatiotemporal positions P0, PI.... P.,
where each P is different local Lorentz frame at a certain instant;
(iii) Each of the positions P0, P~.... P, is assigned the same value
f(P) by the function f from the spacetime U of which H is a
hypersurface to the reals, the function f being such that it increases
along every future-directed timelike or lightlike curve of U.9
We now can define cosmic simultaneity and cosmic succession:
(D5) The spatiotemporal positions P~ and P2 are cosmically simultaneous
= df. (i) P1 and P2 cannot be occupied by events that are connected
by light or slower signals; (ii) P~'s surface of simultaneity coincides
locally with the same spacelike hypersurface with which P2's surface
of simultaneity coincides locally; (iii) the function f assigns the same
valuef(P) to Pl and P2.
(D6) The spatiotemporal position P3 is cosmically later than the
spatiotemporal position P2 = df. (i) P3 can be occupied by an event
that is an effect of an event occupying either P2 or a position
cosmically simultaneously with P2; (ii) P3's past-directed light cone
is intersected by a segment of some spacelike hypersurface with
which P2's surface of simultaneity coincides locally; (iii) P2's future-
directed light cone is intersected by a segment of the spacelike
hypersurface with which P3's surface of simultaneity coincides
locally; (iv) the function f assigns a higher value f(P) to P3 than
to P2.
The definition of being cosmically earlier is the inverse of D6 and need not
be given. A diagram should render the definitions D3-D6 more intuitively
comprehensible:
///
///÷o
A, B and C are world lines of possible observers. E~ is an event that occurs
at the spacetime position A at tl and E2 is an event that occurs at the
position B at t~. El and E2 are cosmically simultaneous; they occur on the
9 For a discussionofthe cosmictimefunctionf, seeS.W.Hawking,'TheExistenceof Cosmic
TimeFunctions',Proceedingsof the RoyalSocietyA 308:433-35 (1968),and Peter Kroes,
Time."Its Structureand Rolein PhysicalTheories(Dordrecht:D. Riedel, 1985),pp. 14-18.

QuentinSmith 29
same spacelike hypersurface t~ and the position they occupy is assigned
the same value by the function f (which is reflected in the numeral 1 in
the designation 't~' for the hypersurface to which they belong). The segment
of the hypersurface t~ depicted in the diagram consists of the interlocking
surfaces of simultaneity of the positions at which E~, Ez are located and
of the position C at t~. The interlocking of the surfaces of simultaneity
of the positions at which E~ and E2 are located may be taken to imply
that a light signal sent from A at to will reflect off Ez and rearrive at A
at t2, (with the equality described in D3 being satisfied) and that the same
holds for a light signal sent from B at to to E~.
Definitions D3-D6 require spacetime to satisfy certain technical
conditions,1° which may be intuitively summarized by saying that spacetime
has a past and future direction and that time travel into the past is impossible.
It must be emphasized that the cosmic time here defined is relative to
a way of dividing the spacetime into spacelike hypersurfaces (technically,
'foliating' the spacetime into 'leaves'). There are an infinite number of different
ways of foliating the spacetime, each resulting in a different temporal ordering
of the spacetime positions, and there is no intrinsic or 'right' way to foliate
the spacetime. But in some cases there is a simplest way. If a universe
is isotropic (looks the same in all directions from any given point) and
homogeneous (matter is evenly distributed), then the simplest foliation results
from identifying each hypersurface with a plane of homogeneity. At each
event on the plane the density and pressure of matter and the curvature
of spacetime is the sameJ ~ Our universe is (approximately) isotropic and
homogeneous and so there is a privileged cosmic temporal ordering in the
sense of a simplest ordering, but I shall allow many of the universes I discuss
in Section III to be inhomogeneous and anisotropic.
Cosmic time as defined in D5 and D6 resolves the two problems we
found with the two STR-based definitions and spatiotemporal relations. The
first definition involved the association of spacelike relatedness (topological
simultaneity) with the impossibility of connectedness via light or slower
signals; that is, it identified spacelike relatedness with D5, i. This definition
was problematic since it entailed that two events in disconnected universes
are spatiotemporally related. D5 solves this problem by adding conditions
(ii) and (iii) to the condition (i) of spacelike relatedness; these added conditions
entail that causally unconnectible events in disconnected universes are not
spatiotemporally related via simultaneity since there is no spacelike
hypersurface with which the surfaces of simultaneity of the positions of
both events coincide. D5 and D6 also solve the problem with the second
STR-based definition of spacelike relatedness, which added to D5, i the
condition that there is some midpoint between the places of the two events
at which light signals from the two events could arrive. This posed a problem
mThe technicalconditionsare that spacetimeis connected,time-orientable,time-anisotropic,
time-linear,achronal,Hausdorff,paracompact,stronglycausal,and has a positive-definite
metricg+abandan Alexandrovtopology.
" For a discussionof these planes of homogeneity,see Charles Misner,Kip Thorne,and
JohnWheeler,Gravitation(NewYork:W.H.Freeman,1973),pp. 713-725.

in that events in two galaxies receding from each other at a combined velocity
greater than that of light would be spatiotemporally unrelated and thus belong
to different universes. D5 and D6 solve this problem since if there is no
midpoint between the places of the two events (in the sense relevant to
the argument) the two events will still be spatiotemporally related since
either there is some hypersurface H with which their surfaces of simultaneity
both coincide or with which one of their surfaces coincide and which intersects
the past/future light cone of the other place. Note that D6, i does not imply
that P3 is later than P2 only if P3 can be occupied by an event that is an
effect of an event occupying P2. This would reintroduce our original problem,
for if P3 and P2 are located at two galaxies receding at a combined velocity
greater than that of light and they are not on the same hypersurface then
they would be spatiotemporally unrelated, since a light signal could not
be sent from one to the other. D6, i instead implies that P3 is later than
Pz only if P3 can be occupied by an event that is an effect of an event
occupying either P2 or a spatiotemporal position cosmically simultaneous with
Pz Manifestly, there is a position cosmically simultaneous with Pz that is
located within P3's past light cone, even if P2 is not.
The last definition we need for our cosmological explanations involves
the phrase 'a basic law of a universe':
(D7) L is a basic law of a universe U = Df. (i) L explains other laws
of U but is not itself explained by other laws of U, and (ii) L does
not obtain in all universes if there is more than one universe.
An example of a basic law of a universe is
(L1) For any x, if x is a light signal, then x travels in a vacuum at 186,000
miles per second.
If L1 is a basic law of a universe U0 there is no contradiction in supposing
that there is another universe U~ in which LI does not hold and in which
L2 holds instead:
(L2) For any x, if x is a light signal, then x travels in a vacuum at 185,000
miles per second.
However, if a law L explains and is not explained by other laws of a
certain universe U, and obtains in every universe (assuming there is more
than one universe) then L is not a basic law of a universe. I shall call it
instead a 'metalaw'. The expression 'other laws of U' in D7, i refers to
laws applying to U other than metalaws.
III. A Neo-I-S Explanation of the Existence and Basic Laws
of Our Universe
Suppose there is a universe U1 very much like our own and that due to
an intense gravitational field associated with a collapsing star in one of
its regions the world lines of particles and light rays in that region converge
and terminate in a singularity. I shall call this singularity a 'black hole
singularity'. The singularity is not a part of the universe UI since it neither
is a part of nor occupies any of the spacelike hypersurfaces the sequence
of which comprises U1. The singularity is a zero-volume point but it does

Quentin Smith 31
not have three spatial coordinates and therefore is not a point in the 3D
space of U1. It also does not have a temporal coordinate and for this reason
also it is not a position or an occupant of a position in the 4D spacetime
of U1. Rather, it is a boundary or edge of the 4D spacetime of U1, a point
where some of the timelike and null curves in Ul come to an end.12
Let us call this singularity S and suppose that S is not only a boundary
of UI but a boundary between U~ and another universe U0. S is an endpoint
of some timelike and null curves in U1 but a beginningpoint of the timelike
and null curves in U0. In respect of its property as an endpoint of some
curves in Ul, S is a 'black hole singularity' but in respect of its property
as a beginning point of the curves in U0 S is a 'big bang singularity'. A
diagram will enable this scenario to be described more exactly:
/
/// ....i/ l
7
~2 The idea that singularities are not parts of4D spacetime is familiar in contemporary thinking.
For example, Robert Geroch and Gary Horowitz write in 'Global Structure of Spacetimes',
GeneralRelativity,ed. S.W. Hawking and W. Isreal (Cambridge: Cambridge University Press,
1979), pp. 256-57: 'The key idea of what is now widely accepted as the most fruitful
definition of a singular spacetime is the following. General relativity, as it is usually formulated,
requires a manifold with a smooth Lorentz metric. This formulation leaves no room for
points of the manifold at which the metric is singular. Indeed, it is even hard to see how
one could modify the theory to admit such "singular points," for it is only through the
metric that one acquires the ability to identify the individual points of the manifold as
events. One cannot isolate, as additional physical events, points at which the metric is badly
behaved. In short, it seems to be a necessary part of general relativity that all "singular
points" have been excised from the spacetime manifold'.

32 Explanationof theExistenceof Lawsof Our Universe
The bottom two rectangles represent a small contracting region R of two
successive spacelike hypersurfaces of U~, with t2 being later than tL The
spatially three dimensional region R (the region of the collapsing star)
contracts until it is 'crushed out of existence' at the singularity S, which
is not a spatially three dimensional region but a spatially zero dimensional
singular point. X~ and x2 are world lines of particles involved in the collapse
of the star and these lines end at S, where the particles cease to exist. The
top two rectangles represent the universe U0 in the early phase of its existence.
The region of space constituting the spacelike hypersurface t'~ of U0 is
involved in a big bang explosion and expands, becoming the larger region
constituting the later hypersurface t'2. X'I and x'2 are world lines of particles
involved in the big bang explosion.
If U0 is to count as a distinct universe from UI, which is a necessary
condition of the development of my cosmological explanations, then none
of the spatiotemporal positions in U0 can be related to any of the
spatiotemporal positions in Ul. This will be the case only if it is not true
both that S is cosmically later than x~ at tz (or any other position in UI)
and cosmically earlier than x'~ at t'l (or any other position in U0). That
this is not true can be proven on the basis of definitions D2-D6. S is cosmically
later than Xl at t2 only if S has a surface of simultaneity which coincides
locally with a spacelike hypersurface H, such that a segment of H intersects
the future light cone of xl at t2. But S has no surface of simultaneity that
coincides locally with a spacelike hypersurface H since S does not have
three spatial coordinates and three coordinates is a necessary condition of
possessing such a surface (see D2-D4). For similar reasons, S is not cosmically
earlier than x'~ at t'~. Moreover, since the future light cone of Xl at t2 ends
at S (is inextendible beyond S), any light signal capable of being sent from
x~ at t2 terminates at S; this entails that x~ at t2 is not cosmically earlier
than x'~ at th, since this relationship between them would require that the
future light cone of x~ at t2 extend to and intersect the hypersurface to
which X'l at t'l belongs. And these two spatiotemporal positions are not
cosmically simultaneous, since they do not belong to any common spacelike
hypersurface; they cannot belong to a common one since no hypersurface
is extendible through the singularity S, regardless of which way U0 and
U~ are foliated into different spacelike hypersurfaces.
Since S is neither cosmically later, earlier nor simultaneous with any position
in U0 or U~, it follows, according to my definition of spatiotemporal
relatedness, that S is spatiotemporally unrelated to the positions in both
Uo and U~. S instead bears to these positions the relation of 0 being a
spatiotemporal boundary of O. More exactly, S bears to the relevant positions
in U1, such as Xl at t2, the relation of 0 being the future boundary of O.
S is a future boundary of xl at t2 if and only if no future directed timelike
or null curve extended from x~ at t2 is extendible beyond S. S is a past
boundary of x'~ at t'l if and only if no past-directed timelike or null curve
extended from x'~ at t'~ is extendible beyond S.
The result that the positions in U0 are spatiotemporally unrelated to the

QuentinSmith 33
positions in Ul, and hence that Uo and U~ are distinct universes in the sense
of D 1, enables us to develop a cosmological scenario that allows for a neo-
I-S explanation of the existence of Uo. Suppose that there are 10 billion
black hole singularities that bound different regions of U~ but that only
one billion of these singularities also have the property of being big bang
singularities that are past boundaries of other universes. In the other nine
billion cases, the black hole singularities are not associated with the 'birth'
of another universe. Given this, the existence of the universe Uo can be
provided with the following neo-I-S explanation, where 'U' expresses the
property of 0 being a big bang singularity that is the past boundary of a
universe and 'B' expresses the property of 0 being a black hole singularity
that is thefuture boundary of a region of a universe.
(1) P (U/B) = .10
(2) Bx
[.10]
(3) Ux
If 'x' stands for the big bang singularity that is the past boundary of our
universe, then (1)-(3) gives an answer to the question 'Why does our universe
exist?' by providing a neo-inductive-statistical explanation of our universe's
existence. Our universe U0 .exists because there is a black hole singularity
Bx bounding another universe U1 and ten percent of Ul's black hole
singularities are also big bang singularities that are past boundaries of other
universes. A further analysis of explanations of this sort will be given in
the following sections, but first let us develop our cosmological scenario
so as to provide a neo-I-S explanation of the basic laws of our universe
U0.
It is arguable that the following laws L1-L4 are basic laws of our universe;
these laws describe the strength of the four forces relative to the strong
force (set at one):
LI: For any x, ifx is a strong force, then x has the value 1.
L2: For any x, if x is an electromagnetic force, then x has the value 1/137.
L3: For any x, ifx is a weak force, then x has the value 10-5.
L4: For any x, if x is a gravitational force, then x has the value 6 x 10-39
These laws are basic in that they (a) explain other laws of our universe
but are not explained by any other laws of our universe, (b) do not obtain
in all universes if there are more than one universe.
Let us accept the speculation of many physicists that the first interval
of Planck length (10-43 second) of the big bang explosion of our universe
is occupied only by superparticles interacting by means of the superforce.
Following this interval and before the end of the first interval of 10-4 second
the superparticles become differentiated into the various types of hadrons
(e.g. quarks) and leptons (e.g. electrons) and the superforce becomes
differentiatedinto the gravitational, strong, weak and electromagnetic forces.
This differentiation occurs through symmetry breaking, which occurs in

34 Explanationof the Existenceof Laws of Our Universe
chance or random ways. The chance ways in which the symmetry is broken
determine the values of the basic physical constants. In our universe, the
symmetry breaks in such a way that the forces acquire such values as the
value 0.511 MeV for the mass of the electron.
Since the symmetry breaks in chance ways, it is to be expected that if
the same initial conditions at the Planck era obtain in different universes
then the values of the basic constants will be settled in different ways in
different universes. Suppose there is another universe U'0 that is past-bounded
by a singularity that future-bounds a part of U~ and that in U'0 the first
Planck-lengthinterval consists of superparticles interactingvia the superforce.
Subsequent to this interval, the symmetries break in random ways and the
four forces and the elementry particles emerge with different values than
they possess in our universe. In U'0, we may say, the strong force is greater
by 2% than its value in our universe U0 and consequently quarks do not
combine into protons and no atoms (and thus no stars and galaxies) are
formed. Other values obtain in other universes that are past-bounded by
singularities that future-bound parts of U~. Let us suppose that of the ten
billion black holes in U~,two hundred of them are past boundaries of universes
that have the same basic laws (including LI-L4) as our universe U0. In
these two hundred universes, the symmetry present in the interaction of
the superparticles via the superforce breaks in a way that results in values
of the four forces and elementary particles that are identical with their values
in our universe. This allows for a neo-I-S explanation of the basic laws
of our universe U0. As before, let B express the property 0 being a black
hole singularity that is the future boundary of a region of a universe. Let
L express the property 0 being a big bang singularity that is the past boundary
of a universe with the set So of basic laws, where So is the set of all and
only those basic laws that obtain in U0. Thus we have
(4) P (L/B) = .00000002
(5) Bx
[.00000002]
(6) Lx
If x stands for the singularity that is the past boundary of our universe
U0, then (4)-(6) explains why our universe has the set So of basic laws
rather than some other set. The reason is that x is a black hole singularity
in the universe U~ and .00000002 of Ul's black hole singularities are past
boundaries of universes that obey the set of basic laws So.
I should observe that there are laws governing symmetry breaking and
that statistically explain the obtaining of the basic laws L1-L4 but that (in
my scenario) these laws obtain in all universes and therefore are metalaws
rather than basic laws of our universe. Thus, my earlier statement that L1-
L4 are not explained by other laws of our universe (i.e. by any law applying
to our universe but a metalaw) is not vitiated by the explanation of L I-
L4 by the laws of symmetry breaking.

QuentinSmith 35
A neo-I-S explanation of the initial conditions of our universe, such as
the amount of mass-energy initially present in it, can also be given but
its construction should be obvious given the above considerations and I will
not pause to give it here. Instead, I shall pass to the more interesting task
of showing how the cosmological scenario envisaged can be developed so
as to provide explanations of the existence of every universe and set of basic
laws that is postulated or implied in the explanations. This is desirable, since
the explanations (1)-(3) and (4)-(6) explain our universe U0 only at the
price of introducing another universe U1 as an unexplained given. The
existence and basic laws of Ut can be explained along the lines of (1)-
(3) and (4)-(6) if we suppose that Ut also began in a big bang explosion
and that the singularity that is the past boundary of U1 is the future boundary
of a black hole region of another universe U2. If we suppose that ten percent
of Uz's black holes are associated with singularities that are past boundaries
of other universes, then the explanation (1)-(3) will also explain the existence
of U~, assuming that 'Bx' is taken to refer to the black hole singularity
in U2 that is associated with Ux. Further, if we suppose that U1 obeys the
set S~ of basic laws and that .00000002 of U2's black holes are associated
with universes obeying Sz, then (4)-(6) will explain the basic laws of UI,
with a suitable reinterpretation of 'L'. The existence and basic laws of U2
can be explained along similar lines, in terms of another universe U3. U3
can be explained similarly in terms of U4 and so on without end. The only
constraint is that each of these universes have basic laws (and initial
conditions) that permit the formation of black holes; universes that have
laws or initial conditions that do not permit their formation can be formed
from universes in the series U~, Uz, U3.... Un ... but they are 'dead ends'
in the line of universes and are not partly bounded by black hole singularities
associated with other universes.
In the scenario we are envisagingthere is no universe that exists unexplained
and no set of basic laws whose obtaining is unexplained. Our ultimate 'brute
facts' are not the existence of a universe or the obtaining of a set of basic
laws of a universe but the existence of an infinite series of universes and
the obtaining of the metalaws common to every universe in the series. There
is a reason (explanation) why each universe in the series exists but no reason
why this infinite series of universes exists rather than some other series
or no series at all. And there is a reason why each universe obeys the set
of basic laws it in fact obeys, but we do not know why all the universes
obey the set of metalaws they all in fact obey rather than some other set
or why there are metalaws and laws that are obeyed at all. As before, there
still are limits or stopping points of naturalistic explanation but these stopping
points are pushed back further than hitherto thought possible, from the
existence and basic laws of our universe to the existence and metalaws
of an infinite series of universes.
It remains to show that the model of naturalistic explanations involved
in these explanations is acausal (section 4) and that the cosmological scenario
envisaged is approximately empirically possible and the best candidate

36 ExplanationoftheExistenceofLawsof Our Universe
currently available for a naturalistic account of why our universe exists and
obeys its basic laws (section 5).
IV. Rejection of the Causal Model for Naturally Explaining Our Universe
The model used in the explanations in the last section is the neo-l-S model,
which explains the existence and basic laws of our universe by subsuming
them under statistical laws and thereby providing them with a nomic
expectability of some degree. Are the statistical laws used in these
explanations reflections of underlying causal regularities and, if not, are the
statistical subsumptions (1)-(3) and (4)-(6) thereby devoid of significant
explanatory value?
This issue can be made more precise in terms of the theory of causality
Salmon develops in Scientific Explanation and the Causal Structure of the
WorM. In this work Salmon articulates a notion of probabilistic causality
that he argues to underlie all genuine statistical explanations. (Subsequent
page number references in this sectionrefer to this book.) Salmon distinguishes
between causalpropagation and causal production (p. 139).
Causalpropagation is defined in terms of a causal process, the latter being
the world line of a material body (e.g. a car) or light pulse (e.g. from a
distant star) that transmits its own structure from some spacetime position
A to a different position B. Spacetime positions are understood here in
accordance with GTR and STR (pp. 140-141), the latter being a special
case of the former, and thus can be interpreted in light of my definitions
in section 2 (although Salmon himself does not delve into this subject). A
causal process propagates a causal influence from an event at A (the cause)
to an event at B (the effect) by transmitting its own structure (or a mark
or modification thereof) from A to B. Causal propagation involves a temporal
distance between the cause and effect and a continuous spatiotemporal path
between the cause and effect along which the causal influence is propagated.
(Salmon adopts our usual practice of talking of the cause as earlier than
the effect but maintains that strictly speaking the temporal relation is
symmetric and that we are entitled only to speak of a temporal separation
of the two events [p. 176].) The causal influence propagated is probabilistic;
that is, the process carries with it probability distributions for engaging in
causal interaction of various types. A causal interaction is an intersection
of two or more causal processes that produces a modification in the
intersecting processes (p. 171).
Causalproduction is defined in terms of this causal interaction. The causal
interaction is an event C that consists of the intersection of the two (or
more) causal processes. This event C produces a change in the two causal
processes, a modification or 'mark' of the structure of the processes that
persists 'after' the interaction. These changes are produced simultaneously
with C, such that the cause and effect in these interactions do not have
a temporal separation.
Let us try to map these causal relations onto our cosmological scenario.
Suppose a star reaches its Schwarzschild radius at t~ in the region R of

QuentinSmith 37
the universe U1 and begins to contract rapidly to a black hole singularity.
The contraction of the particles and photons of the star may be understood
as causal processes, processes that stem from the events xl at tt, x2 at tl,
etc., that consist of the star reaching its Schwarzschild radius. May we say
that these causal processes all intersect at S, the point of the black hole
singularity? And may we say that this intersection is a causal interaction
in which modifications are produced in the causal processes, such that the
processes emerge from the interaction with the structure of causal processes
involved in a big bang explosion? If we can say this, then we can say that
a causal influence is propagated from events at tt in the region R of universe
UI to the singularity S, such that the causal processes that transmit this
causal influence carry the probability of .10 for undergoing a causal
interaction at S that produces a modification of these causal processes from
star-contraction-processes to big-bang-explosion-processes. This will imply
that the causal interaction occurring at S, which is an effect of the events
in R at tl, is the cause of the big bang explosion that begins the universe
U0.
This mapping fails since four necessary conditions are not met. First, if
the intersection of the causal processes at S is to be an effect of the events
in R at t~, then the intersection must be temporally distant from the events
in R at tl. But they are not temporally distant since they are not related
by relations of being cosmically earlier or later. Second, if the intersection
of the causal processes at S is to be a causal interaction among the processes,
then the intersection must occur at a spatiotemporal position, since causal
interactions occur only at spatiotemporal positions. But S is not a
spatiotemporal position but a boundary to such positions. Third, if the
intersection at S is a cause of the big-bang-explosion-structure of the causal
processes that evolve in U0, then the intersection at S must be temporally
distant from the times at which these processes possess this structure. But
S is not, since S is spatiotemporally unrelated to the times at which these
processes possess this structure. This third reason also shows that the big
bang explosion cannot be understood as a 'conjunctive fork' (pp. 158-168)
whose common cause is the intersection at S of the causal processes
originating in R. There is a conjunctive fork only if there are two or more
separate effects of the same cause, such that the cause occurs earlier than
the effect. But the intersection at S is not a cause of any effect in U0 since
it is not earlier than any event in U0. Fourth, if the intersection at S is
to be a causal interaction whereby modifications are produced in the
intersecting causal processes, then the processes must be identifiable (must
be 'the same processes, but modified') on both sides of the intersection,t3
This implies they must be world lines of the same material bodies and photons.
But the mass-energy of the collapsing star ceases to exist at the singularity
(is 'crushed out of existence') and the mass-energy that appears on the other
~3Salmon admits (p. 181) that the processesmay also be construed as diflerent processes
after the interaction,but suggeststhat it is at least possibleto regardthem as the same
processes(depending,apparently,on the criteriaofidentityone uses).

side of the singularity is not the mass-energy of the star, merely modified,
but new mass-energy that appears ex nihilo with S as its past boundary.
Spatially 3D mass-energy cannot pass through a singularity that is spatially
OD and reemerge in the 3D space 'on the other side' of the singularity.
Indeed, we cannot even literally say that the causal processes of the collapsing
star 'intersect' at S since intersection (at least in Salmon's sense) is of spatially
3D processes at a spatially 3D position; all that we can literally say is that
S is the spatially OD point towards which the spatially 3D processes converge
and at which they cease to exist (the 'point at which they converge' being
'the point at which they cease to exist as spatially 3D processes').
I should emphasize that though S is not a part of a universe I regard
S as real rather than as a mere idealization (the concept of S is different
than S, the instance of the concept). Being part of a spatiotemporally 4D
universe is not a necessary condition of existence. There is no contradiction
in the idea that there exists a zero volume spatial point that (1) lacks three
spatial coordinates, that (2) is not assigned a temporal coordinate f(P) by
a function f from 4D spacetime to the reals, and that (3) is a past or future
boundary of positions that possess these coordinates. S is a very unusual
sort of existent, a physical singularity, at which the laws and coordinates
of 4D spacetime break down, but being unusual is not the same thing as
being self-contradictory and thus my theory (and contemporary cosmological
theories) are not reduced to incoherence by the assumption that there are
physical singularities.
'But is it not incoherent to say that S is real but does not exist in time?
How can a spatially OD point exist timelessly?' Let me make clear that
S does exist timelessly if 'time' is used in the sense of my definitions, for
S does not exist in cosmic time. One is free to construct some other definition
of time if one wishes and say that S exists instantaneously or enduringly
in this new sense of 'time', but the possibility of constructing such a definition
does not impugn my case that S does not exist in cosmic time and eo ipso
is a boundary between U0 and U1 that makes them two different and
spatiotemporally disconnected universes in the sense of my definitions (which,
I would add, are not arbitrary but are based on contemporary cosmology).
Let me pass now to some more general considerations pertinent to the
issue of the causation of universes. The reason why S or events in U1 cannot
be causes of U0 are instances of more general principles that rule out a
priori the possibility that the existence and basic laws of a universe have
a natural causal explanation. There can be no natural event or process C
that causes a universe U since C must occupy at least one spatiotemporal
position P that is cosmically simultaneous with or earlier than (or 'temporally
distant from', if we wish to preserve Salmon's temporally symmetric
definition) the position(s) occupied by the event(s) or process(es) it causes,
and by virtue of this spatiotemporal relatedness P would be a part of the
same universe as the position(s) of C's effects. This prevents C from causing
U to exist or obey its basic laws since it entails that C itself is a part of
U and obeys it basic laws. (Note that in conformity with D1 the parts of

QuentinSmith 39
a universe are said primarily to be spatiotemporal positions and are said
derivatively to be the events or processes that occupy these positions.) Now
no natural event or process can cause itself (recall that I am operating with
[arguably intuitively plausible] definitions of a universe that rule out closed
timelike curves; see footnote 10). This implies that at best C can cause
all the parts of U but C, which is insufficient for C to cause U since U
is caused by C only if the whole of U is caused by C.
Salmon believes that unless statistical relations are underpinned by causal
explanations the statistical subsumptions do not provide explanations. If so,
the statistical relations between black holes and big bangs do not provide
an explanation of the existence of our universe U0. But there is reason to
think, however, that Salmon's theory of nonexplanatory subsumptions does
not apply to our subsumptions (1)-(3) and (4)-(6) involving U0. Salmon's
argument is based on a division of subsumptions into two classes, the class
A of explanatory subsumptions that express causal relations and the class
B of nonexplanatory subsumptions that possess two defining characteristics,
namely, (B0 they do not express causal relations and (132) they express
relations that can be explained causally (pp. 135-136). An example of a
subsumption that belongs to class B is the subsumption of a sample of gas
under the ideal gas law PV = nRT, which relates the pressure (P), volume
(V) and temperature (T) of the gas and indicates how these quantities vary
as functions of one another. This law does not express a causal relation
but the relations it expresses can be explained causally. An increase in the
pressure of the gas might be caused by an increase in temperature (through
heating the container of the gas) or by a decrease in volume (through moving
a piston connected to the container). However, the acausal subsumptions
(1)-(3) and (4)-(6) involving our universe U0 do not possess all the defining
characteristics of class B and therefore not only fall outside of Salmon's
class of causal explanations but also outside of his class of nonexplanatory
subsumptions. (1)-(3) and (4)-(6) possess the characteristic B~ since they
do not express causal relations, but they do not possess the characteristic
B2 since the relations they express cannot be explained causally, as the
foregoing arguments have shown. Thus, Salmon's theory of nonexplanatory
subsumptions does not provide sufficient justification for the thesis that the
subsumptions (1)-(3) and (4)-(6) are nonexplanatory. In the absence of other
good arguments that such subsumptions are nonexplanatory, I suggest that
we rely on the intuition that they are explanatory and that they form a
third class in distinction from classes A and B, namely a class C of acausal
explanations. But whether only cosmological explanations such as (1)-(3)
and (4)-((6) are members of this class is a difficult issue that is neither
necessary nor possible to address here.
V. The Issue of the Approximate Empirical Possibility of the Neo-I-S
Explanations of Our Universe
I understand this issue to be of the extent to which the situations postulated
in my neo-I-S explanations conform to currently accepted scientific laws.This

is too large a subject to deal with adequately or with any great precision
in the space remaining but a few suggestive comments should deepen the
interest and relevance of my explanations. These comments are best made
in the context of a brief comparison between my explanations of our universe
and those that some other contemporary theories might be alleged to provide.
Two of the most relevant contemporary theories are Peter Landsberg's and
John Wheeler's oscillating models of the universe, ~4according to which the
universe undergoes many cycles of expansion and contraction, the present
expansion phase belonging to the most recent of these cycles. These two
models differ in some respects (e.g. Wheeler's but not Landsberg's allows
values of the fundamental constants to fluctuate from cycle to cycle) but
they are similar in respects pertinent to the present discussion. These two
theories might be thought to provide empirically possible explanations of
the existence or basic laws of our universe. On Wheeler's theory, for example,
it might be alleged to be possible to form neo-I-S explanations of the present
cycle in terms of previous cycles. For example, if the set of basic laws
So instantiated in our present cycle were instantiated in .00000002 of the
previous cycles then the obtaining of these laws in the present cycle might
be subsumed under this statistical law and thereby provided with this degree
of nomic expectability. It seems to me, however, that these oscillating models
fail to provide empirically possible explanations of the existence or basic
laws of our universe for two reasons.
The first reason is that it is logically impossible for them to do so, inasmuch
as they do not postulate different universes, in the sense of D 1, but successive
cycles of one and the same universe. Landsberg and Wheeler both talk
of 'earlier cycles'15 than the present one and imply that one cycle is
spatiotemporally related to the next. Thus, even if the existence, initial
conditions or basic laws of our cycle could be explained inductive-statistically
or deductive-nomologicallyin terms of previous cycles that would not amount
to an explanation of the existence, initial conditions or basic laws of our
universe but merely of one phase in the temporal history of our universe.
The second reason the Wheeler and Landsberg models cannot provide
empirically possible explanations of our universe is that these models violate
known laws of physics and therefore cannot provide empirically possible
explanations at all, even of the alleged 'present cycle' of our universe. The
Landsberg and Wheeler models violate the Hawking-Penrose singularity
theorems. Landsberg and Wheeler both admit that the singularity theorems
predict that our universe begins in a singularity and that this singularity
disallows any earlier cycles of our universe. But Landsberg and Wheeler
declare, on the basis of unclear and unargued for philosophical principles
(Nature does not provide us with infinities [such as singularities of infinite
densities] '16 and 'Physics is by definition that which does go on its eternal
JaseeMisner,ThorneandWheeler,op. cit., pp. 1196-217,andPeterLandsberg,'TheBeginning
and End of the Universe'in Nijmeegse Studies in De Filosofie van De Natuur En Haar
Wetenschappen4:77-108(1985).
~sMisner,ThorneandWheeler,op. cit.,p. 1217.
16Landsberg,op. cit.,p. 84.

Quentin Smith 41
way [and thereby bypasses predictions of singularities]'17), that the universe
did not begin in a singularity and therefore that a cyclical universe is possible.
But these philosophical dismissals of the singularity theorems are
unconvincing, if only for the reason of their excessive vagueness, and do
little more than distract attention from the fact that their cosmological models
violate the singularity theorems without a physical justification for doing
so (such as might be provided by a quantum theory of gravity). Inasmuch
as their scenarios violate accepted laws and are not shown to obey instead
other, better justified, laws, their scenarios cannot be classified as empirically
possible.18
The theory I outlined approximates an empirically possible theory to a
greater degree in this respect since this theory is consistent with the singularity
theorems. As I explained in the past two sections, I regard each universe
as beginning with a big bang singularity and I disallow any spacetime path
to be continued through these singularities or through the black hole
singularities. But I do not want to suggest that there exists a currently accepted
theory that shows our big bang singularity to be a black hole singularity
of another universe. Not only is there is no such theory but there is no
known solution of the equations of GTR that shows a singularity of one
of these sorts to also be a singularity of the other sort. It is important to
note in this regard that the solution implying 'the Einstein-Rosen bridge'
is not such a solution. The Einstein-Rosen bridge presupposes two
disconnected universes, each being partly bounded by a black hole singularity,
such that the two singularities become joined and form a nonsingular bridge
between the two universes. This differs from my scenario if only for the
reason that it does not explain the existence of either universe but merely
describes how they can become connected through their black holes.
The cosmological scenario I outlined is nearer to that suggested by a
question E. Wigner once asked Wheeler in a panel discussion. 'Is it possible
to imagine the explosion of a black hole. Is that nonsense?'19 Wheeler
responded that 'Zel' dovich and Novikov proposed it some years ago--the
idea that there are in addition to black holes, white holes, and that they
should vomit forth matter the way a black hole sucks in matter.'2° But
Wheeler's response here is mistaken or at least misdirected. White holes
are not black holes that explode in big bangs but are retarded pieces of
the big bang that act like 'black holes in reverse', i.e. they spew forth matter
rather than suck it in. It is false that a white hole singularity S also has
the property of being a black hole singularity, such that S both sucks in
matter (e.g. from a collapsing star) and spews forth matter. The white hole
singularity only has the property of spewing forth matter. Therefore, it is
~7 Misner, Thorne and Wheeler, op. cir.,p. 1996.
18 The issue of the empirical possibility of the oscillating universe model is discussed at greater
length in Quentin Smith, 'The Uncaused Beginning of the Universe', Philosophy of Science
55:39-57 (1988) and 'World Ensemble Explanations', Pacific Philosophical Quarterly 67:
73-86 (1986).
~9 See Harry Woolf (ed.) Some Strangeness in the Proportion (Addison-Wesley, 1980), p. 383.
20 Ibid.

42 Explanation of the Existenceof Laws of Our Universe
not an exploding black hole. Wigner's vague suggestion is better fleshed
out in terms of the scenario I suggested, where one and the same singularity
S has the property of sucking in matter (qua black hole singularity) and
spewing forth matter (qua big bang singularity). Such singularities are not
white hole singularities but are in a class sui generis. But unlike white holes,
they are disadvantaged in not (yet?) having been derived as solutions to
the equations of GTR.
I would like to close this section by mentioning that a remaining apparent
candidate for 'empirically possible explanations of the existence and basic
laws of our universe' are the vacuum fluctuation cosmogonies of Tyron,
Gott, Zel'dovich, Atkatz and Pagels, Brout, Englert and Gunzig and others.21
These cosmogonies postulate an empty background space from which 'our
universe' fluctuates in accordance with Heisenberg's uncertainty equation.
These theories might be thought to provide a neo-I-S explanation of the
existence and basic laws of our 'universe' in that the background space
engages in numerous vacuum fluctuations and only a small percentage of
these develop into full-scale 'universes' and an even smaller percentage into
'universes' with our basic laws. Thus the existence of 'our universe' might
be explained by being provided with a nomic expectability to a degree of
ten percent and the obtaining of its basic laws might be explained by being
provided with a nomic expectability to a degree of.00000002. These vacuum
fluctuation cosmogonies do provide empirically possible explanations, or
so at least I have argued,2z but they are not explanations of the existence
or basic laws of universes in the sense of D1. What fluctuates is not our
universe in the sense of D 1 but merely a branch of our universe; the fluctuating
branch is spatiotemporally connected to the background space and therefore
is a part of the same universe as it. The whole universe, the background
space plus all of its branches, is not provided an explanation by these
cosmogonies; all that is explained is the existence or basic laws of its branches.
21 See E.P. Tyron, 'Is the Universe a Vacuum Fluctuation', Nature 246:396-97 (1973); J.R.
Gott, 'Creation of Open Universes from de Sitter Space', Nature 295:304-07 (1982); L.P.
Grishchak and Y.B. Zel'dovich, 'Complete Cosmological Theories', in M.J. Duff and C.J.
Isham (eds.) Quantum Structureof Space and Time(Cambridge: Cambridge University Press,
1982), pp. 409-22; D. Atkatz and H. Pagels, 'Origin of the Universe as a Quantum Tunnelling
Event', Physical Review D 25:2065-073 (1982); R. Brout, F. Englert and E. Gunzig, 'The
Creation of the Universe as a Quantum Phenomenon', Annals of Physics 115: 78-106 (1978).
22 See Quentin Smith, 'The Uncaused Beginning of the Universe', op. cit and 'World Ensemble
Explanations', op. cit.
In an important recent article, Chris Mortensen has argued that a theory partially modelled
on Tyron's can provide explanations of the existence of our universe. See his 'Explaining
Existence', Canadian Journal of Philosophy 16:713-22 (1986). Mortensen argues that if
we eliminate the background space the existence of our universe can be given an explanation
on the basis of 'a probabilistic theory of Tyron's kind' (p. 715). However, Tyron's theory
uses physical probabilities (relative frequencies or propensities) and it is logically impossible
for these probabilities to be used if the background space is eliminated, as I have argued
in 'Explaining the Existence of the Universe' (mimeograph, 1987). But it seems arguable
that Mortensen's theory might be workable if his probabilities are interpreted instead as
logical probabilities or subjective probabilities, although I confess that at this point I cannot
see how this suggestion might be concretely fleshed out.

QuentinSmith 43
Therefore, these explanations are not candidates for explanations of the
existence and basic laws of our universe.
These considerations suggest that if we are interested in models of logically
possible naturalistic explanations of our universe we must look elsewhere
than in the oscillating and vacuum fluctuation cosmological models of
contemporary theory. I have offered a cosmological theory in outline that
both provides a logically possible natural explanation of the existence and
basic laws of our universe (and every other universe) and approximates
to a reasonable degree an empirically possible explanation. Although its
key component is not derivable (at least as far as is presently known) from
the equations of GTR, it is consistent both with the singularity theorems
and with other areas of contemporary cosmological thought. For these
reasons, I suggest that the types of explanation illustrated in the preceding
sections are the ones we should take most seriously when we are
contemplating in a naturalistic spirit the mystery of our universe.23
Marion, Indiana Received March 1988
Revised June 1988
23 1am gratefulto a referee for thisJournalfor stimulatingcommentson an earlier version
ofthispaper.

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