**A
Response to Almeida and Judisch**

** **

**Alexander
R. Pruss **

Department of Philosophy

Georgetown University

Washington, DC 20057

** **

**and
**

** **

**Richard
M. Gale**

Department of Philosophy

University of Pittsburgh

Pittsburgh, PA 15260

Abstract:

Our
new cosmological argument for the existence of God weakens the usual Principle
of Sufficient Reason premise that every contingent true proposition has an
explanation to a weaker principle (WPSR) that every such proposition *could*
have an explanation. Almeida and Judisch have criticized the premises of our
argument for leading to a contradiction. We show that their argument fails,
but along the way we are led to clarify the nature of the conclusion of our
argument. Moreover, we discuss an argument against us based on a principle of
alternate explanation incompatible with our WPSR, and show that this argument
fails.

** **

Our new
cosmological argument has generated some lively and fruitful critical
discussion.[1]
Jerome Gellman, in a friendly addition to it, developed an ingenious argument
to narrow the gap between the God of traditional theism and the creator whose
existence is proven by our argument. Whereas our argument proves the existence
of only a very powerful, intelligent and good necessarily existent creator,
leaving it open whether it is omnipotent, omniscient and omnibenevolent, no
less essentially all these things, Gellman proves the essential omnipotence of
this being.[2]
Graham Oppy criticized our argument for being question-begging[3], and Kevin Davey and
Robert Clifton developed a set theoretical objection and also tried to show
that for some of our premises there are incompatible propositions that are
intuitively just as plausible, thus resulting in a conceptual stalemate.[4] We have responded to
all of these criticisms.[5]
Michael Almeida and Neal Judisch have presented in this Journal a new challenge
to our argument which attempts a __reductio ad absurdum__ of it.[6] Their objection will
prove to be a very fruitful one, because it can be neutralized only by giving a
much more in depth account of our explanatory creator than our original
argument offered. Before we attempt to respond to this __reductio__, a brief
sketch of our argument is needed.

Our new
cosmological argument has a significant advantage over traditional cosmological
arguments in that the latter employ the Strong Principle of Sufficient Reason
which requires that every true contingent proposition actually have an
explanation, our argument needs only the Weak Principle of Sufficient Reason
which requires that every true proposition __possibly__ have an explanation:

(WPSR) For any contingently true proposition, it is logically or conceptually possible that it has an explanation.[7]

A __possible__ __world__ is
a maximal conjunction of compossible abstract propositions (a BCF in our
abbreviational terminology), with repetitions and other logical redundancies
eliminated so as to avoid to set-theoretic paradoxes. Each world is
individuated by its Big Conjunctive Contingent Fact (BCCF), which is the
conjunction of all of the __contingent__ conjuncts in its BCCF. The
argument makes use of the following two principles: The S5 system of modal
logic, whose key axiom is that if a proposition is possibly necessary, it is
necessary; and The principle of the Existential Commitment of Explanation –-
if __q__ explains __p__, then __q__ and __p__. Let “__@__” be
a name rigidly designating the actual world so that it is true that __@__ is
actual but it is possible that __@__ is not the actual world.

(1)
__@__ is the actual world and __p__ is the BCCF of* *__@__.
By stipulation

By appeal to WPSR and using the semantics of possible worlds, it follows that

(2)
There is a possible world __w___{1} that has the proposition
that ($__q)__(__q__ explains __p__)
as one of its conjuncts.

By existential instantiation it follows from (2) that

(3) The proposition that __q
__explains __p__ is a conjunct of __w___{1}.

By appeal to the Principle of the Existential Commitment of Explanation it follows that

(4) Propositions __q__
and __p__ are conjuncts in __w___{1}.

Given both S5 and that worlds share their necessary conjuncts in common, it follows that words are individuated by their BCCF.

(5)
For any worlds, __w__ and __w___{1}, __w__=__w___{1}
if and only if __w__’s BCCF is a conjunct in __w___{1}’s BCCF.

The proof of this can be found in our original paper, and Almeida and Judisch do not question it. From (1), (4) and (5) it follows that

(7)
__q __explains __p__, __q__ and __p __are all conjuncts of __@__.
From (3), (4) and (6)

Thus there actually is a true
explanation of __@__’s BCCF.

It is then
argued that this explanation must be a personal explanation in terms of some
person’s free intentional action. This person cannot be contingent, since then
a proposition reporting its existence will be a conjunct in __p__ but no
person can bring it about that it exists. Thus, this person must necessarily
exist. Appeal to various teleological considerations must be made to show that
this being probably is very intelligent, powerful and good.

Almeida and
Judisch present two different __reductio ad absurdum__ rebuttals of our
argument. Using the premises of our argument, the first deduces that __@__
has __q__ and ~__q__ as conjuncts, the second that __@__ contains __q__
and some other proposition, __r__, that also explain __p__ and is
logically incompatible with __q__. The former begins with the fact that __q__
is contingent. Almeida and Judisch then reason as follows:

Since __q__ is contingent we know, too, that M~__q__ [it
is logically possible that ~__q__]. It is possible that __q__ is not the
explanation of the actual world’s Big Conjunctive Contingent Fact. But if M~__q__
then there is some world __w___{2} such that __w___{2}
contains __p__ and ~__q __and the fact that __q __does __not__
explain __p__. (59)

From the latter conclusion,
absurdity ensues. For if __w___{2} contains __p__, then, by our
argument, __w___{2}=__@__, and thus the actual world, __@__,
has both __q __and ~__q__ as conjuncts!

It is far from
obvious that the conjunction of the premises of our argument with M~__q__
entails this absurdity. Almeida and Judisch are aware of this and present an
indirect proof of this entailment. It begins with the assumption for the sake
of an indirect proof that it is false that M(*~*__q__ and __p__ and
~(__q__ explains __p__)). Then, “__every__ world __w__* which
contained __p__ would also contain __q__ and the proposition that __q__
explains __p__. But that is just to say that L__q__ (that it is
logically necessary that __q__) contrary to our assumption…”(63n15). Hence,
M(*~*__q__ and __p__ and ~(__q__ explains __p__)). This __reductio__
of our argument fails, because the claim that every world containing __p__
contains __q__ and __q__ explains __p__ means only that

(8) L(__p__ É (__q __and (__q__ explains __p__)))

whereas the authors seek the
stronger conclusion L__q__. This stronger conclusion would follow only if
in addition to (8) we had L__p__. But if we had L__p__, then __p__
would not be a Big Conjunctive __Contingent__ Fact.

Fortunately, we need
not confine the defense of our argument against the reductio based on the
attempt to deduce M(*~*__q__ and __p__ and ~(__q__ explains __p__))
from M~__q__ to a rearguard action in which we wait for someone to produce a
deduction and then show where it fails. For we are in a position to prove that
the premises of our argument entail the impossibility of this deduction.
Recall premise (1)’s stipulation that __p__ is the BCCF of __@__. Now,
our argument proves that __q__ explains __p__ in __@__, and moreover (__q__
explains __p__) is a contingent proposition since it is actually true and
entails the contingent proposition __p__ by the Existential Commitment of
Explanation. Thus, (__q__ explains __p__) is a conjunct of __p__.
Since a conjunction (like a set) is identified by its conjuncts (or members),
it follows that it is necessary that a conjunction (or set) has the conjuncts
(or members) that it has. And since (__q__ explains __p__) is a conjunct
in __p__, there is no possible world that has __p__ and ~(__q__
explains __p__) as conjuncts, and thus ~M(~__q__ and __p__ and ~(__q__
explains __p__)).

At this point one might note that since theism entails that every contingent proposition has an explanation in terms of the free actions of God and of any free creatures, an argument proving that the WPSR fails to hold in some world would also show that theism is false in that world. It would, thus, indeed be a remarkable achievement to show that the WPSR is incoherent or false, but this achievement Almeida and Judisch have not achieved in the above argument.

It is the aim of the
second __reductio__ of Almeida and Judisch to prove that the premises of our
argument entail that __@__ has __r __and __q__ as conjuncts, where __r__
is a possible explanation for the actual BCCF incompatible with the explanation
__q__:

Since __q__ is
a contingent explanation of the BCCF of [the actual world, __@__], we know
that the actual BCCF __might__ have had some other explanation __r__,
such that ~M(__r__ & __q__). (63)

They then make use of the
premises of our argument to show that if it is M(__r__ explains __p__),
then __@__ contains __r__ as a conjunct. But since it has been
established by our argument that __@__ also contains the incompatible
proposition __q__, the desired logical absurdity has been derived.

Almeida and Judisch
appear to claim that just from the fact that __q__ is a contingent
explanation, it follows that there might have been some other explanation. But
this is a *non sequitur*. To see this, observe that the claim that __q__
is a contingent explanation of __p__ is ambiguous between two claims,
neither of which is strong enough to show that there might have been some other
explanation. These two claims are:

(9)
(__q__ explains __p__) and it is
contingent that __q__

(10) it is contingent that (__q__
explains __p__).

It is clear that (9) is insufficient to show that there might have been some other possible explanation incompatible with __q__. After all, all that (9) claims is that (__q__ explains __p__) is a conjunct of the actual world and that there are some possible worlds of which __q__ is not a conjunct. It in no way follows from this that there are some possible
worlds of which (__r__ explains __p__) is a conjunct for some __r__
incompatible with __q__. But if (9) is insufficient to show the possibility of an incompatible explanation, neither is (10) sufficient to show it, because in fact (9) entails (10). To see this, observe that if (9) holds then (__q__ explains __p__) is a possible proposition. By the Existential Commitment of Explanation, (__q__ explains __p__) entails the proposition __q__ which is contingent by (9), and hence (__q__ explains __p__) is not a necessary proposition. Thus, (__q__ explains __p__) is possible but not necessary, and hence it is contingent, if (9) holds.

It is thus obvious
that Almeida and Judisch’s __reductio__ must be employing a stronger version
of the principle of sufficient than our

(WPSR) For any contingently true proposition, it is logically or conceptually possible that it has an explanation.

Their __reductio__ requires
instead:

(WPSR2) For any contingently true proposition, it is logically or
conceptually possible that it has an explanation, __a__, and it is logically
or conceptually possible that it have another explanation, __b__, such that __a__
and __b__ are logically incompatible.[8]

We grant that the
conjunction of (WPSR2) with the premises of our argument does entail the
logical absurdity that __@__ has the incompatible conjuncts __q__ and __r__.
This is check-mate for our new cosmological argument only if (WPSR2) is
plausible and moreover more plausible than our (WPSR). It will be argued that
it is neither.

That it is less
plausible follows from the principle of modal conservatism—that the weaker of
two propositions is more likely to be possible than is the stronger one, in
which a proposition __a__ is weaker than a proposition __b__ just in case
__b__ entails __a__ but __a__ does not entail __b__. By this
principle (WPSR) is more likely to be possible, and thus is more plausible than
(WPSR2), since (WPSR) is entailed by but does not entail (WPSR2). Thus, if we
had to choose between accepting (WPSR) or accepting (WPSR2), the epistemically
reasonable thing to do is to accept (WPSR). And, as a result, the epistemically
reasonable thing to do when confronted with a choice between accepting our
(WPSR)-based cosmological argument and accepting the (WPSR2)-based reductio of
it is to accept the former.

Almeida and Judisch might try to make (WPSR2) look plausible by appealing to ordinary cases of true contingent propositions, such as that Smith’s briefcase is on his desk is explained by the proposition that he left it there but also possibly explained by the incompatible proposition that his wife left it there. But it would be a hasty generalization indeed to generalize, as does (WPSR2), from these ordinary cases of true contingent propositions; for a world’s BCCF is a very strange bird, as is seen in the fact that unlike the former propositions, if it possibly has an explanation, then it actually has one.

Alternatively,
they might argue for a more modest conclusion: not that (WPSR2), when taken in
full generality, is plausible, but that it is plausible that the specific case
of there being a possible explanation of __p__, the BCCF of the actual
world, satisfies (WPSR2). In correspondence, Almeida has suggested that it is
possible that __p__ be explained in terms the free intentional free action
of Odin or of some other god or great genius. However, as the second part of
our argument shows, __p__ can be explained only by the action of a __necessarily
existing__ person. Pagan gods and geniuses are not conceptually suitable
candidates for having necessary existence. Furthermore, it is implausible that
there would be more than one necessarily existing intelligent being. It must
be borne in mind that the proposition, __q__, that explains __p__ is
existentially quantified, saying only that there necessarily exists a very
powerful, intelligent and good being who freely brings it about that __p__.
Being general, __q __leaves it open for us to fill in the details of the
exact nature of this being in many different ways and what its reason for
creation might be. But we must be careful not to confuse the __epistemic__
possibility that there are different necessary explainers of __p__ with the __logical__
possibility that there are. There are exactly ten __epistemic__
possibilities for the 10^{100}th digit of p, namely 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9, but there is only one
__logical__ possibility.

But we need not confine ourselves to the negative task of showing why attempts to make (WPSR2) look plausible fail, since we are in a position to present a positive argument for its implausibility. This argument is based on the fact that when (WPSR2) is conjoined with a compossible conjunction of propositions, namely the premises of our argument, a contradiction is entailed whereas no contradiction is entailed by the compossible conjunction alone. The second reductio has painted itself into a corner. For it must employ (WPSR2). But (WPSR2) entails (WPSR). And, thereby, if the reductio argument succeeds, it applies to itself, becoming impaled on its own sword.

There is an alternative principle of explanation to (WPSR2) that will enable the Almeida-Judisch reductio to avoid self-immolation, since this principle does not entail (WPSR). This Principle of Alternate Explanation holds that,

(PAE) necessarily, for any contingent proposition __p__ that has
an explanation __q__ it is possible for there to be an alternate explanation
__r__ of __p__ which is incompatible with __p__.

(PAE) says both more and less than (WPSR) does; for, on the one hand it does not require that every true contingent proposition possibly has an explanation, but, on the other, requires that every true contingent proposition that actually has an explanation also actually has another explanation that is incompatible with the former one. Now the conjunction of (PAE) and (WPSR) entails (WPSR2). Since, as we have just seen, (WPSR2) is incoherent, it follows that (PAE) and (WPSR) are logically incompatible. We must thus choose between (PAE) and (WPSR).

One
consideration in favor of the (WPSR) is that there are controversial philosophical
doctrines about which (WPSR) can remain neutral but (PAE) cannot, thus
rendering it more likely that (PAE) is false than that (WPSR) is. For example,
the (PAE) is incompatible with the Kripkean doctrine that there exist entities
whose origin is essential to them. For suppose that it is essential to me that
I come from a union of sperm __A__ and egg __B__. Then that I exist is
explained by __A__ and __B__ having come together. Moreover, by the
Kripkean doctrine, this is an essential property of me: in every world in which
I exist, it is true that __A__ and __B__ came together. Therefore, there
is no world in which my existence is explained by a proposition incompatible
with the one based on __A__ and __B__ coming together, which is a
counter-example to (PAE) but not to (WPSR).

Yet another counter-example concerns explanations of the one and only basis of propositions that report the obtaining of a moral obligation. One such explanation of moral obligation propositions is the divine command one according to which their sole basis can be found in their being commanded by God. Another is the contractarian account of them as arising from the consent of people. There also is the natural law account that finds their basis in our having received a certain kind of nature. If any one of these three accounts of the only possible source of moral obligations is true, and well one of them might be, there is a counter-example to (PAE) but not (WPSR).

Furthermore, the
(WPSR) is __prima facie__ compatible with being generalized to
non-contingent propositions: they might, for instance, be all taken to be
self-explanatory. However, the PAE is clearly false of necessary propositions,
since presumably these are to be explained in terms of necessary propositions,
and no possible proposition is incompatible with a necessary proposition. The
falsity of the (PAE) in the case of necessary propositions cautions one not to
think that there is something about the nature of explanations that ensures
that there are always alternate explanations. Because of all of the above
considerations, the WPSR is to be preferred to the PAE.

At this point in the
discussion, Almeida and Judisch might want to avail themselves of a radical
move: hold onto (WPSR2), or even just the weaker (WPSR), but restrict it in
such a way that one could deny that it is possible for a world’s BCCF to have
an explanation. This is the sort of move a Hempel, Salmon or Grünbaum would
make when confronted with our new cosmological argument. But someone who denies
the possibility of a world’s BCCF having an explanation is in effect denying
the possibility that theism is true, for it is a necessary conceptual truth
that if theism is true, than there is an explanation for the actual world’s
BCCF. Again, we are confronted with a question about the relative degree of
plausibility of rival propositions. Is it more plausible to think that theism
is possible than to think that it is impossible for there to be an explanation
of a world’s BCCF? Most people, including atheists, have a __prima facie__
modal intuition in favor of the former. But our __prima facie__ modal
intuitions, although conversation beginners, are not conversation enders.
However, plainly, the onus is on the denier of these intuitions to show why
they cannot be trusted. And this is something that neither Almeida and Judisch
nor anyone else that we know of has succeeded in doing.[9]

[1]. “A New Cosmological Argument”, Religious Studies 35 (1999), 461–476.

[2]. “Prospects
for a Sound Stage-3 of Cosmological Arguments,” __Religious Studies__ **36**
(2000), 195–201.

[3]. “On
‘A New Cosmological Argument’,” __Religious Studies__ **36** (2000),
345–353.

[4]. “Insufficient
Reason in the ‘New Cosmological Argument’,” __Religious Studies__ **36**
(2000)

[5]. “A
Response to Oppy and to Davey and Clifton,” __Religious Studies__ 38 (2002)
89-99.

[6]. “A
New Cosmological Argument Undone,” __International Journal for the Philosophy
of Religion__ 51 (2002), 55-64. References to this article are included in
the body of the paper.

[7]. Our
original formulation did not restrict this to __contingent__ propositions,
but following Kevin Davey and Robert Clifton we now make the restriction. The
notion of explanation for necessary propositions is an obscure one, requiring
further research into mathematical explanation, and we do not need to go there.

[8]. That these alternative explanations are incompatible is required by the second reductio, for if it were just a case of explanatory or causal overdetermination, no absurdity could be deduced.

[9]. We are grateful to Michael Almeida for interesting discussions of these issues.