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Metafísica y Persona. Filosofía, conocimiento y vida
Año 14, Núm. 27, Enero-Junio, 2022, ISSN: 2007-9699
A Short Logical Review of the Kalām Cosmological
Argument
Una breve revisión lógica del argumento cosmológico Kalām
UPAEP Universidad, Puebla, México
josemartin.castro@upaep.mx
-
gument as presented by W. L. Craig. This discussion suggests the argument fails at being
Keywords:
order logic.
En esta breve contribución discutimos la validez lógica del argumento cosmológico
no es lógicamente correcto si admitimos una distinción entre variables de primer y segun-
do orden.
Palabras clave: -
den, lógica de segundo orden.
Introduction
In 1979 W. L. Craig published a book—The Kalām Cosmological Argu-
ment—
would require a proper and longer review, here we focus, for reasons of sim-
1
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plicity (and, overall, popularity), on the basic core of the argument, which
runs as follows:
1. Everything that begins to exist has a cause of its existence.
2. The universe began to exist.
C. Therefore, the universe has a cause of its existence.
The reason why we pay attention to this particular piece of argumen-
tation is its undisputed logical structure. Indeed, when presented in this
fashion, the argument seems to be logically correct or formally flawless.
And such a claim, in turn, seems to get confirmed every time the usu-
al critiques question all but the structural validity of the argument: the
typical assessments presume, at least tacitly, that the argument is valid
when they accept premise 1 as uncontroversial, attack premise 2 on the
grounds of some interesting distinctions (Kaiser, 1944; Kenny, 1969; Fo-
gelin, 1990; McQueen, 1994; Sobel, 2004), but bypass any examination of
the logic behind the argument.
However, even if these criticisms are interesting in themselves, they dis-
regard a logical aspect that, by our lights, should not be diminished. Hence,
given this situation, in this short contribution we discuss the logical validity
suggests the argument fails at being logically valid if we admit a distinction
1. An alternative interpretation
So, prima facie, the argument appears to be some sort of Barbara syllogism,
and hence, a valid argument that would look, more or less, as follows:
1. All Begin-to-exist is Caused-for-its-existence.
2. All Universe is Begin-to-exist.
C. Therefore, All Universe is Caused-for-its-existence.
However, on a second reading, we can observe a subtle but crucial
distinction that is missing when we assume this syllogistic parsing: while
premise 1 appears to quantify and predicate over individuals, premise 2
and the conclusion appear to predicate and quantify over domains. If this
distinction is not clear, consider the next representation of the original
argument that allows us to see the situation in a more transparent setting.
Let
Ex
stand for x begins to exist and
Cyx
for y causes the existence of x. Then
the argument would have the next structure:
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A Short Logical Review of the Kalām Cosmological Argument
1. ∀
x∃y(Ex ⇒ Cyx)
2.
EU
∴
∃yCyU
But then, notice, there is an important issue that is often overlooked,
the universe is the locus in which things exist, that is to say, it is a domain,
but not another thing. We can try to explain this distinction by exemplifying a
couple of questions. Consider the query
glass of water, the question makes perfect sense; but the question
does not seem to be equally meaningful, because the universe, unlike the
computer, does not appear to be another thing among things. The universe,
unlike the computer, is not anywhere.
To bring this point home consider the next gedankenexperiment. Imagine
Alan has been born and raised in a small apartment. Its walls are painted
titanium white and, as usual, it is divided into a kitchen, a living room, a bed-
it lacks windows or doors to the outside, and so Alan, like once happened to
Mary (Jackson, 1982), has no notice of the world outside the apartment.
books there is a personal computer, a laptop. Clearly, the laptop, as well as
the books and the desk, exist in so far as they are there, inside the apartment.
And thus Alan can say, with perfect utility, that the laptop is here and now,
right there or over there, that it was not here before and, of course, that it will
not be here eventually. Nevertheless, it also seems clear that Alan cannot do
same way he can pinpoint the computer, for that would imply the apartment
is, like the laptop and the books, another item within the apartment, which
sounds absurd.
This experiment has to pay its dues, though. First, as Strawson (1948) has
pointed out, facts are not to be found in the world; but if, as Sommers (1980)
and Englebretsen (2006, 2012) have argued, facts are not in the world, then
they have to be properties of the world. Hence, domains, like the universe,
by their constituents, but a domain is not a constituent
of itself. Using an example by Englebretsen: the soup I had this morning
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can say the universe is laptop-ish (in so far as laptops are constituents of
the universe), but it is not universe-ish (since the universe is nowhere to be
found within the universe).
-
er order variable, say
U
, for the universe (hence the expression
EU
in premise
argument does not follow from 1 and 2 since we cannot unify
x
(in premise
1) and
U
and second, respectively). Doing otherwise would result in a fallacy of com-
position or a category mistake (by unlawfully transferring properties of indi-
viduals to domains).
To further illustrate this issue, consider the next counterexample:
1. Everything that begins to exist has a place within the universe.
2. The universe began to exist.
C. Therefore, the universe has a place within the universe.
Clearly, even if we grant the truth of the premises, the conclusion does not
seem to be quite right, for the universe does not have a place, let alone inside itself.
At this point, however, the skeptical reader may think that such a basic
analysis cannot possibly defeat or even undercut the original argument. So,
let us consider some possible objections a skeptic may entertain so far.
Objection 1. Back to basics. Before moving to the previous logical analysis,
both individuals and domains. After all, we can rightfully talk about indi-
viduals and domains as things. And so, there is no use for the distinction
-
viduals and domains. Thus, the original argument stands as is.
Answer 1.
when we recognize that a concept is analogical we do it not just to show sim-
1
)
and a domain-thing (say, a thing
2
Objection 2. Fill in the blanks. Well then, simply introduce what is missing.
Just add the lost distinction, that is to say, make explicit what is implicit, for
example, as follows:
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A Short Logical Review of the Kalām Cosmological Argument
1. ∀
x
∀
X∃y
((
Ex
v
EX
) ⇒ (
Cyx
v
CyX
))
2.
EU
∴
∃yCyU
Answer 2. The problem with this second objection, however, is that given
such a set of premises (or a similar one) the conclusion should be something
like
∃y(Cyb
v
CyU)
—where
b
stands for an arbitrary individual—, which is
fair enough, but is not felicitous because such a conclusion is far from being
the original one. The original one is categorical, whereas this second conclu-
true, not for relevant reasons, but by coincidence; nevertheless, that is not
what the original argument aims at.
Objection 3. Kill the messenger. But why should we use this kind of logical
analysis anyway? Why should we accept this logical analysis as the right
one? After all, there are several ways in which we could analyze an argument
and, perhaps, by following the principle of charity, we should concede this
argument is just a plain, valid syllogism, a Barbara syllogism as it were, and
so we are using an unnecessary complex logical analysis that does not make
justice to the original argument.
Answer 3. Granted. It may be the case that we are overanalyzing the ar-
gument, but there are, at least, two problems with this objection: i) suppose
the argument is just a plain syllogism. A plain syllogism cannot cope with
binary relations, but the argument requires the binary relation of causation,
thus the argument is not just a syllogism; nevertheless, suppose we over-
look this lightweight issue and accept the argument is a plain syllogism—
say, given an adequate parsing of the original argument, as above. Still, ii)
of logical analysis sanctions, then we are at odds if we try to avoid falla-
cies of composition or category mistakes. Thus, rejecting this sort of analy-
which would leaves us ill-prepared to counter said ill-formed arguments.
Objection 4. Be in the here and now. Fine, but the universe is a thing we can
here, here in the univer-
is pointing to the universe here (and now). In which case the logical analysis
u
,
instead of
U
. This is consistent with how we usually talk about the universe
and its beginning, as if both were things, thus, the claim that the universe is
something that requires a higher order representation only seems far fetched.
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Answer 4. This fourth objection may sound reasonable in principle, but is
not imply we are ostensibly denoting it. As Sommers (1980), van Fraassen
(1995), Simons (2003), Bunge (2006), and Englebretsen (2006, 2012) have in-
dependently argued, when we talk of universes as domains they are (more
likely) totalities of things
1
, not maximal things
1
. Thus, using
u
would not be
ontologically fair neither for individuals nor for the universe. And so, al-
though it is true that we sometimes talk about the universe and its beginning
as if they were things
1
, that does not imply they are things
1
. Englebretsen
Objection 5. A second wind. Fair enough, but maybe the proper analysis for
this argument should be mereological rather than logical in the classical sen-
se. Perhaps the universe is the mereological sum of its parts, and if so, then
the universe is not a domain or thing
2
, but indeed a single maximal thing
1
, in
which case, the argument would make sense.
Answer 5. Remarkably, this last objection does hold some water; howe-
-
gular but a plural term for a plural collection, in which case the original
argument is still in trouble, for the original argument does not seem to be
accepting a mereological parsing. Hence, maybe something in the lines of
far, the original argument is not successful because, even if we grant such
a mereological reading, the conclusion would still not follow: premise 1
would be talking about properties of non-maximal things
1
, while premise
2 would be talking about properties of the maximal thing
1
, but such pro-
perties are not necessarily coextensive.
Conclusion
And so, to wrap this up, in this short contribution we have discussed
-
gests the argument fails at being logically valid if we perform a distinction
-
tion is clearly open to discussion and we do not claim this interpretation
is knock-out, we think this short logical review is interesting in so far as it
provides an alternative treatment of a popular argument whose fragility
might stem from a logical issue, say, and not necessarily from an over the
top cosmological problem.
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A Short Logical Review of the Kalām Cosmological Argument
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