This post is out of date. An improved reply to the KCA can be found
here.
The
Kalam Cosmological Argument Provides no Support for Theism
0)
Introduction
1)
A contradiction follows from William Lane Craig's position
2)
Craig's reply
3)
Still a contradiction
4)
The open interval variant
5)
A contradiction in the Big Bang Theory?
6)
Continuous time and continuous changes
7)
Timeless change?
7.1)
Discrete time
7.2)
No ontological difference – God vs. God and God vs. the
universe
7.3)
No ontological difference – God vs. the universe, in even
greater detail
7.3.1)
Quiescence and changelessness
7.3.2)
Causation
7.3.2.1)
God's change, causation, and the change in the universe
7.3.2.2)
Free will, determinism and indeterminism
7.3.2.3)
Agents acting 'in and of themselves'?
8)
The meaning of 'begins to exist'
9)
The first premise of the KCA
10)
The 'Hilbert Hotel' argument
11)
Philosophical arguments against an infinite past
11.1)
The contradictory case of Tristram Shandy
11.2)
Orbits and parity
12)
The "Standard Hot Big Bang Model", a tensed theory of time,
and the KCA
13)
The KCA and a tenseless theory of time
14)
The (purported) cause of the universe: further analysis
14.1)
A single first cause?
14.2)
Changelessness and immateriality
14.3)
Timelessness and the open interval variant
14.4)
Spacelessness
14.5)
Power
14.6)
Personhood
14.6.1)
Personal explanations and scientific explanations
14.6.2)
Other properties of the alleged first cause
14.6.3)
'Free agency'
14.7)
The meaning of 'God'
15)
Conclusion
Notes
and references
0)
Introduction:
a)
In this article, I will show that the Kalam Cosmological Argument
(KCA) does not provide any
support for theism.
The
premises of the KCA are: [1]
P1:
Everything that begins to exist has a cause.
P2:
The universe began to exist.
William
Lane Craig and other theists offer a number of arguments in support
of the premises of the KCA, concluding that the universe has a cause.
Then, they provide further arguments in support of the claim that the
cause is God.
In
the first
section,
I will show that a contradiction follows from William Lane Craig's
position.
In
the
second
section, I
will address Craig's reply to the objection to the KCA that I raised
in the first section of a
previous argument against the KCA, which is the same I will raise
in the first section of this
argument.
In
other sections, I will raise other objections to the KCA, as well as
to the added conclusion – even assuming that the universe had a
cause of its existence – that the cause is God.
b)
I will focus on William Lane Craig's version of the KCA, given that
that is the most common one.
c)
Unless
otherwise specified, I assume that a tensed theory of time is true.
Craig and all other defenders of the KCA, to the best of my
knowledge, defend the KCA in the context of a tensed theory.
I
will, however, address a potential attempt to run the KCA on a
tenseless theory, just for the sake of thoroughness. Section
thirteen
deals
with that alternative.
d) On a
terminological note, I will use the word “argument”
loosely, to refer to both the formal argument, and the informal
arguments used to support the premises of the formal argument. I
think this is a common way of speaking, and context should prevent
any ambiguity despite some notational abuse.
e) Before I go on,
let me point out that I make no claim of novelty:
The Kalam
Cosmological Argument has been around for considerable time, and I
got some of the ideas I'm using in my arguments from many sources on
the internet.
In other cases, I
came up with the ideas for my arguments on my own; however, given for
how long the KCA has been debated, I have no good reason to think
that I'm the first one to come up those ideas, so I don't claim any
novelty in that, either – I merely claim that the KCA provides
no support for theism, and that this article shows that.
1)
A contradiction follows from William Lane Craig's position
William
Lane Craig and J. P. Sinclair[3]:
By
an “event,” one means any change. Since any change takes
time, there are no instantaneous events so defined. Neither could
there be an infinitely slow event, since such an “event”
would, in reality, be a changeless state. Therefore, any event will
have a finite, nonzero duration.
William
Lane Craig[4]
The
reason I hold God to be timeless without the universe is that I think
that an infinite regress of events is impossible, and, according to a
relational theory of time, in the absence of any events time would
not exist. The reason I hold God to be temporal since the beginning
of the universe is that the creation of the universe brings God into
a new relation, namely, co-existing with the universe, and such an
extrinsic change alone (not to mention God’s exercise of causal
power) is sufficient for a temporal relation.
William
Lane Craig[5]
So
if God is timeless, he is also unchanging, but it does not follow
that He cannot change. I’d say that He can change and if He
were to do so, He would cease to be timeless. And that’s
exactly what I think He did.
God
changes from
timeless to temporal.
Any
change is an event,
so
let E(0)
be the event “God changes from being timeless to being
temporal”.[6].
Now,
if t=0 is the beginning of time, then E(0) is a change that ends
precisely at
t=0, since t=0 is the first time at which God is temporal.
Since every event
has a finite, non-zero duration, E(0) has some duration e>0, and
ends at t=0.
Then, there is a
time interval of duration e prior to t=0.
That
contradicts
the
hypothesis that t=0 is the beginning of time.
2)
Craig's reply
After
someone raised the issue on his website, Craig replied[7]
to the objection I
raised in section
one of an earlier version of my argument –
which is the same
I've raised in section one of this
article, though I provided a shorter explanation of my objection
in the earlier version.
Craig
replied that God's gaining knowledge of tensed facts (for instance)
does not qualify as an event, since it's "instantaneous".
[7]
First,
his claim is false.
He
defined 'event' as 'any change', and those are obviously changes.
He
did not define 'change' excluding 'instantaneous' changes, as one can
easily see from the quotation from his book I posted earlier.
Second,
as I also showed earlier,
instantaneous changes entail a contradiction –
regardless of
whether Craig chooses not to call them 'changes' anymore.
That
aside, let's continue analyzing Craig's reply to my objection:
William
Lane Craig[7]
The
reason I give for so restricting the range of “event” is
that I’m talking about changes, and changes take time to occur.
First,
Craig does not restrict the range of 'event' at all in his
definition, and so he gave no reason for restricting the range at
all. Instead, he defined
'event' as 'any change', and then argued
from
there, that any event will have a finite, non-zero duration. So, the
'restriction' is a consequence
of his reasoning, not
a stipulative
definition.
That
is obvious in the quotation from his
book I gave for context (due
to copyright reasons, I may not post long parts of his book, but that
part suffices to make that clear; of course, I invite readers to take
a look at his book more closely in case of any doubt).
Second, that changes
take time to occur is precisely one of my points, which I use to
derive a contradiction on Craig's position.
Again,
Craig actually claimed
that changes take
time to occur.
In
fact, he claimed that there are no instantaneous events precisely
because any change takes time, and he defined "event"
as "any change".
So,
I pointed out that the change
– for
instance – from
a state S at which God does not know any tensed truths (because there
aren't any tensed facts), to a state at which God knows some tensed
truths (at t=0) is, well, a change,
and changes take time to occur – as Craig stated -, from which
a contradiction follows.
William
Lane Craig[7]
Similarly,
God’s coming to believe all tensed truths would not qualify as
an event, since it, too, happens instantaneously.
But
that is false. Since God's coming to believe at least one tensed
truth is a change, then it follows – by
his own definition – that
it's an event.
In
fact, by claiming that it's instantaneous, Craig is only
contradicting
his own claim that all changes take time.
Once
again, this follows from the
previous quotation of his book.
Yet,
in his reply to the objection I raised, Craig claims
[7]
that
God's gaining knowledge of tensed facts is instantaneous, and
therefore it's not a change in God in "this technical sense".
But
there
is no such "this technical sense" of "change" in
Craig's KCA, since – as
we can see in his book
– Craig
did
not
define
"change" at all.
The
only sense of 'change' is the usual sense of 'change' in English; in
other words, he left 'change' undefined, used the usual concept in
order to define "event" - as is apparent in the quote above
-,
and then argued
from there
– keeping
in mind the usual meaning of 'change' -, that any change takes time.
Of
course, God's change from not knowing any tensed truths to knowing at
least some tensed truths is, well, a change
in
the usual sense of the word 'change' in English, and by
Craig's own reasoning,
we
can conclude that it takes time, and thus derive a contradiction, as
I did above.
So,
in short, Craig did not define
"events"
as having zero duration. Neither did he define "change" as
having a non-zero duration, or at all. Instead, he defined "event"
as "any change", and assessed
that
events/changes have non-zero duration, as the
previous quotation
from
his book
shows
(once again, I invite readers interested in more details can take a
look at his book and see more context for themselves).
Yet,
the changes I'm talking about are obviously changes in the usual
sense of the word "change" in English – which is the
one he was using in the context of the KCA -, and assuming that they
have a non-zero duration, a contradiction follows as
explained
(I
will later
show
that, in any case, a contradiction follows regardless of whether we
assume that the changes take time or are instantaneous).
In
addition to the above, Craig claims that there is no beginning or
ending to those changes/events – which he describes as "events"
in quotes – as – he claims, beginning to move or coming
to exist do not have a beginning or ending [7]
However, there
clearly would be a beginning point of the event, say, 'God changes
from not knowing any tensed truths, to knowing at least one tensed
truth', if such event/change made sense.
A beginning point
would be a state without any changes occurring within that
state, and the same for an endpoint. And so, in this particular case,
the beginning point would be the only state at which God does not now
any tensed truths. And the endpoint would be the first state at which
God knows at least one tensed truth.
So, the claim that
such changes have no beginning or ending are false. If such changes
were possible, there clearly would have a beginning point and an
endpoint. That follows from the description of the changes, as I just
explained.
In
addition to the previous claims, in his reply
to my objection, Craig contends that in the second
and third quotations,
he was using "change" in a different sense from the sense
in which he used the word in the context of the KCA, and that in
those second
and third quotations,
he "merely" meant that God does not have the same
properties in his timeless state as he does in his first temporal
state[7].
But an analysis of
his words show that he clearly did not merely
meant that – that is only part of what he meant.
In fact, Craig said
that God changed from timeless to temporal, and ceased
to be timeless.
He did not say hat
God changed from temporal to timeless, or that he
ceased to be timeless – clearly, that would not have meant
the same, and Craig himself does not accept the possibility of
change from temporal to timeless.
So,
when Craig said that God had changed – in the second
and third quotations
– he
did not merely meant that God in his timeless state has different
properties from God in his first temporal state.
The claim of a
change is not only a claim that the properties differ, but there is
also a direction: God has some properties in his timeless
state, and changes and has some other properties in his first
temporal state: it goes in one direction, not the other.
In other words, the
change is from the timeless to the temporal state, not vice versa, so
what he meant is not merely that God's properties in his
timeless state are different from his properties in his first
temporal state: change is not directionless.
So,
that still
is
the usual sense of "change" in English, as he used in his
book, in the Kalam Cosmological Argument, as far as one can tell from
his statements.
So, in brief:
a) Craig's claim
that he used 'change' in a technical sense in his book, is a false
claim. He used it in the ordinary sense of the words.
b)
Craig's claim that he used 'changed' to merely say that God has
different properties in his timeless and first temporal states, is
also false.
Once
again, he used 'changed' in the ordinary sense of the words in
English.
c)
The fact remains that a
contradiction follows from Craig's position.
That
aside, Craig also maintains[7]
that
in any case, one can change the definition of "event" in
the second premise of the Kalam Cosmological Argument and clarify
that the events in question are events of non-zero, finite, equal
duration. Actually, if he did that, he would be withdrawing his claim
that any change takes time, rather than merely clarifying his claims.
However, that is a
side point.
The
crucial point is that if we do that, or if we we make, for the sake
of the argument, the false assumption that Craig said what he later
claimed he had said, a
contradiction still follows.
In fact, a
contradiction can be derived without any assumptions about what Craig
said, as the next section shows.
3)
Still a contradiction
In this subsection:
a) By 'event' I mean
the same as 'change'.
b) By 'P(2)' I mean
the property of knowing at least one tensed truth.
c) By 'E(2)' I mean
the event/change 'God changes from not having P(2) to having P(2) for
the first time'.
d) By 'S' I mean the
allegedly timeless state of God, at which God does not have P(2).
e) By 't=0' I mean
the first temporal state of the world – and of God.
Note that, given
Craig's account, E(2) exists. Craig may choose not to call it an
'event', or a 'change', but that is not my concern in this section.
It's clearly an event/change in the usual sense of the word 'change'
in English, so that's good enough.
While
Craig seems to claim otherwise,
the event/change E(2) has a beginning point, and it has an endpoint,
both of which one can easily show:
The beginning point
is the only state of the world at which God does not now any tensed
truths. The endpoint is the first state of the world at which God
knows at least one tensed truth.
So, we have a
change/event from a beginning point, to an endpoint.
If E(2) has a
duration e>0, then since E(2) finished at the initial temporal
state T(0), there is a temporal interval of duration e>0, prior to
T(0). But that is a contradiction, no matter how small e is.
If E(2) has a
duration zero, then since the final point of E(2) - namely, the first
state at which God has property P(2) - obtains at T(0), and the
duration of E(2) is actually zero, then it seems that the initial
point of E(2) - a state at which it is not the case that God has
property P(2) - also obtains at T(0).
Note that the change
is not said to take some small time, not even some kind of
infinitesimal, but exactly zero. It can't be that it's some
infinitesimal, either, because it ends at t=0, which is the
absolute beginning of time.
Hence, at t=0, God
has property P(2), and it is not the case that God has property P(2).
But that is a contradiction.
Someone
might suggest that E(2) does not have a zero duration, or a non-zero
duration, but somehow 'duration' does not apply to it, because it's
'partly timeless'. I will address that in section
7.
Also, someone might
object that the initial state of E(2) is not present at T(0), but at
timeless state S, and the final state is present at T(0). However, if
there is a change from some beginning point to some other endpoint,
and the duration of such an event is actually zero, then both ends
exist at the same time, and a contradiction follows. Duration is
a measure of time, not of 'timelessness' - whatever that is.
So, the person who
claims that the contradiction is somehow averted because one point is
'timeless', or something like that, would have the burden to explain
what they mean by 'timeless' and how that would allow them to avert
the contradiction...but that would clearly fail, since deriving the
contradiction is unproblematic.
Still,
and while the burden would be on the theist defender of the KCA, I
will later
take
the initiative and show that the so-called 'timeless' state fails
to be anything different from a first temporal state,
but briefly, here I will point out that the actual situation would be
one of an uncaused creator with a beginning at the first temporal
state.
In
other words, Craig description entails that there is a first state of
the world – which would be a first temporal
state
-, an uncaused God, and then a second state of the world, and so on.
However,
accepting that would contradict the first
premise of
the KCA.
So, Craig claims that the first state is 'timeless' -
whatever that might mean.
Yet, it's still a
change, and it still has a beginning point and an endpoint, as
explained above.
Denying that the
first temporal state is actually temporal, but without actually
denoting any difference, is what allows the derivation of a
contradiction as before, since what actually would be happening is an
ordinary event/change from the first to the second temporal state of
the world, but with the defender of the KCA committed to a claim that
that is not so.
Of
course, showing that the so-called 'timeless' state is
nothing but a first temporal state of the world
blocks
Craig's KCA on its own, without further arguing to a contradiction,
but the argument given so far is simpler and sufficient.
4)
The open interval variant
In
order to derive a contradiction
above,
I assumed a first temporal state, and someone might suggest that
Craig does not claim that.
In this section,
will prove that Craig's arguments and claims in the context of the
KCA (henceforth, Craig's arguments), entail that there is a first
actual temporal state of the world.
I
will prove this by contradiction, considering both the possibility
that temporal units are instants, and the possibility that they are
intervals which are not dividable into smaller ones. Considering such
possibilities is enough, since infinitely dividable intervals aren't
compatible with some of Craig's arguments, as I will show later.
I will not address
the matter of whether there is any ontological difference between
instants and non-dividable intervals as the units of time, or it's
just a matter of notation. It's not necessary to settle that matter
here, since the arguments I will give work regardless of that: if
there is no ontological difference, then the argument that only
considers instants suffices. Else, both arguments suffice.
a) Instants
If
the units of time are instants, let's assume that there is a sequence
of instants such that t(n+1) < t(n), for every n. We may take them
such that there is no instant between t(n+1) and t(n), since Craig's
position entails that time is discrete, which I will show later.
So let's define, for
every natural n, the following actual events/changes:
E(n): = 'God
comes to know that t(n+1) is past' (i.e.,
God changes from not knowing that t(n+1) is past to knowing that
t(n+1) is past).
Clearly, those are
infinitely many past actual events/changes; E(n+1) occurs
before E(n).
That's
incompatible with Craig's arguments.
Alternatively,
we might – for instance -, take the events 'God comes to know
that t(n) is present', for all n, reaching the same conclusion.
In
any case, the conclusion is that if units of time are instants,
Craig's arguments entail no infinitely many past actual events –
not even of unequal length.
So,
there is a t(0)=0, and a corresponding state of the world T(0).
Clearly,
and reasoning in a similar manner, there is t(1), and T(1), the next
instant and its corresponding state of the world, etc.
b)
Intervals
If
the temporal units are non-dividable intervals, then let's suppose
there is no first non-dividable interval I(0). Constructing a
sequence of non-dividable intervals I(n+1) < I(n) and the
corresponding changes experienced by God, we immediately get an
infinite past series of actual ordered events, which is incompatible
with Craig's arguments.
Hence,
if the units are non-dividable intervals, it follows from Craig's
arguments that there is a first interval I(0), and a corresponding
first temporal state of the world T(0). Similarly, there is I(1),
T(1), etc.
5)
A contradiction in the Big Bang Theory?
No,
of course there is no contradiction in the Big Bang Theory.
However,
I've encountered the objection that, allegedly, my reasoning to a
contradiction
proves
too much, since it would make any change from a timeless state
contradictory, and that would make the Big Bang Theory contradictory,
since the initial singularity has been seen as timeless.
Now,
the Big Bang is a hot, dense state of the universe that existed about
13.7 billion years ago. There is no point of infinite density (what
would that even mean?), or actual singularity, or a 'timeless' state.
We should not confuse a singularity in a mathematical model with
reality.
Also,
even if a model – like the one Craig
mistakenly beliefs supports the KCA
– adds
an initial point – say, a time t=0 -, that
should not be seen as existing in reality. Indeed, the model does not
allow a way out of the singularity.
That
said, let's consider the issue of the contradiction:
Even
if
we assume that there is an initial singularity of infinite density –
whatever that might mean, but that's not even defined -, and that
such singularity is timeless – whatever that might mean; also,
not even defined -, the reasoning by which I derived a contradiction
before
doesn't work in this case.
In
my reasoning, I define the following
event/change:
By
'P(2)' I mean the property of knowing at least one tensed truth.
By
'E(2)' I mean the event/change 'God changes from not having P(2) to
having P(2) for the first time'.
That
assumes that there is a first temporal state at which God has
property P(2), namely T(0)
As
I showed earlier,
in the previous
section,
I'm justified in assuming that there is such a T(0) in order to
derive a contradiction from Craig's position because that follows
from Craig's own position.
Someone
might try to define an event 'the universe changes from timeless to
temporal', and argue that the change has duration zero, because it
begins at the timeless state, and has already ended at any time 1/n,
for any natural n.
However,
in that case, the change/event does not have an endpoint. It's fuzzy.
Being 'temporal' is not a state of the universe, but a beginningless
sets of states, for all t>0. Without an endpoint, the reasoning
by which I derived a contradiction is
blocked.
6)
Continuous time and continuous changes
Another
objection that might be raised would also hold that my argument to a
contradiction,
if correct, would prove too much. The objection would go as follows:
Let's
assume that time is continuous, and so are changes in the universe.
That
might or might not be true, but it is not contradictory.
So,
let's pick any specific point in time, say t(3), and lets define the
following event:
E(t(3)):
The universe changes from its state S(t(3)) at t(3), to no longer
being at state S(t(3)).
Now,
what's the duration of E(t(3))?
Since
the changes of the universe are continuous and happen all the time,
then E(t(3)) has already happened at (t(3) + 1/n seconds), for all
natural numbers n. Hence, the duration of E(t(3)) is literally zero.
Since E(t(3)) begins at t(3), and its duration is literally zero, its
endpoint is also present at t(3). So, at t(3), it is not the case
that the universe is at state E(t(3)). That is a contradiction. So,
this reasoning must be flawed, since it would derive a contradiction
from continuous time plus continuous changes, but continuous time
plus continuous changes is not contradictory.
However,
there is no endpoint in this case. In fact, 'no longer being at state
S(t(3))' is not actually a state of the universe, but a beginningless
set of ordered states.
So,
E(t(3)) is a sort of a fuzzy event. If we can say that the duration
is zero because there are states S(t), with t>t(3), and
arbitrarily close in time to S(t(3)), then fact is that there would
be no initial point and end point at the same time, since there is no
endpoint of the fuzzy event, and so that does not result in a
contradiction.
7)
Timeless change?
Perhaps,
Craig or someone else might then claim
that
the change I use to derive a contradiction
– and
it is a change, in the usual sense of the word 'change' in English –
does not have either a zero duration, or a non-zero duration, but
somehow it's a timeless or partially timeless change, and somehow for
that so-called 'reason' one shouldn't speak of duration of them.
But
if they did that,
I would first point out that Craig claimed that the first cause is –
at least in his timeless state, 'sans the universe' -, changeless.[9]
How could then that
change be 'timeless' or 'partially timeless'? What would that even
mean?
Also,
Craig
claims now that the changes I'm talking about are 'instantaneous'.
What does Craig even
mean, then, by 'instantaneous', if not 'having a zero duration'?
But let's leave the
matter of what he meant by that aside.
Essentially, the
crucial point is that Craig applies the label 'timeless' to name a
scenario that actually should be characterized as God's existing at
t=0, with a temporal beginning but without a cause, and then creating
the universe at the next temporal instant.
By calling the state
in question 'timeless' - instead of 't=0' -, Craig is denying that
the state is temporal, from the description of the state and Craig's
arguments in the context of the KCA, one can see that it has all of
the features of an initial temporal state; in other words, it would
be an initial temporal state, which would change into a second
temporal state, and that change of course takes time.
So, in particular,
Craig's creator, if he existed, would in fact be an entity that has a
beginning in the first temporal state of the world, but no cause,
contradicting the first premise of the KCA.
I will show this in
the next two subsections:
7.1)
Discrete time
In this subsection,
I will prove that Craig's arguments entail that time is discrete, in
the following sense:
a) If the units of
time are instants, then for every two times t and u such that t <
u, there are only finitely many instants in time between the two.
Models may contain infinitely many ones, but there are only finitely
many actual instants.
b) If the units of
time are intervals, then for every temporal interval [a,b], there is
some non-negative integer N(a,b), such that [a,b] cannot be divided
into more than N(a,b) smaller consecutive temporal subintervals.
I will give proofs
by contradiction in both cases.
a) Instants:
Let's assume, that
God exists, a tensed theory of time is true, and that there are
infinitely many actual instants between times t and u, where t <
u.
Then either there is
an increasing sequence, or a decreasing one.
Let's say there is
an increasing sequence, for all natural n:
t < t(n) <
t(n+1) < u
Let's
consider the following sequences of actual
events/changes.
G(n): God changes
from not knowing that t(n) is present, to knowing that t(n) is
present.
Note
that those are actual
changes
in God's
mind.
While
it's true that those are not changes of equal duration (if they even
have a duration), that is orthogonal to the matter at hand, which is
the fact is that those are all actual
changes
experienced by God's mind.
Since
at time u or later, every
single one of
those changes G(n) has occurred (i.e, for all n, G(n) has occurred),
then the number of ordered actual changes in God's mind that are in
the sequence is
ℵ0.
Now,
the events {G(n)} would be a case of an actual infinity, according to
Craig's position, since the events are actual [1],
and
Craig's arguments are incompatible with an actual infinity, and in
particular with infinitely many actual events, one after then next.
For
instance:
William
Lane Craig:
[8]
The
second premise states that an infinite temporal regress of events
is an actual infinite.
The
point seems obvious enough, for if there has been a sequence composed
of an infinite number of events stretching back into the past, then
the set of all events in the series would be an actually infinite
set.
Clearly,
that does not depend on the length of the events, as long as they're
actual changes in the world.
William
Lane Craig:[8]
So
when we say that the number
of past events is infinite, we mean that prior to today, ℵ0
events have elapsed.
Once
again, that does not depend on the length of the events. And Craig
goes on to claim that ℵ0
events are impossible.
William
Lane Craig:[8]
Because
the series of past events is an actual infinite, all the absurdities
attending the
existence
of an actual infinite apply to it. For example, if the series of past
events is actually
infinite,
then the number of events that have occurred up to the present is no
greater than
the
number that have occurred
at
any point in the past.
While
Craig was talking about events of equal length, that is not relevant
to whether or not they're actually infinite; indeed, if the previous
paragraph actually showed any absurdity, that would be so regardless
of whether the events are of equal length.
The
case of a decreasing sequence is essentially the same.
So,
if the temporal units are instants, Craig's arguments entail that
time is discrete.
b)
Intervals
Let's
consider, then, the case of intervals, not instants.
Let
us assume that for an interval [a,b], there is a strictly increasing
sequence m(n), for all n, such that for every n, [a,b] can be divided
into m(n) different actual, smaller intervals, one before the next.
So,
for each n, let's divide [a,b] on m(n) intervals I(1,n)<I(2,n)<
...<I(m(n),n), where '<' denotes the 'earlier than' relation.
Then,
let us consider, for every n, and for every k in {1, 2, ...m(n)}, the
following distinct, actual
events/changes:
J(k,n):
God changes from not knowing that I(k,n) is present to knowing that
I(k,n) is present.
The
crucial question is:
How
many distinct actual events/changes happened in the world
during the temporal interval [a,b]?
In
yet other words, assuming that there weren't more distinct actual
events/changes than any cardinality – else, we're through -,
what is the cardinality of the set of distinct actual
changes
that happened in the world during the temporal interval [a,b]?
If
the answer is that the number is finite, then let p(0)
be that number.
Then,
we may consider the distinct actual
changes J(k,m(p(0)+3)) (for
instance), for all k in
{1, 2, ..., m(p(0)+3)},
reaching a contradiction.
So,
the number of actual changes in [a,b] is at least ℵ0.
However,
that's incompatible with Craig's arguments.
Hence,
if the temporal units are intervals, Craig's arguments entail that
time is discrete.
An
immediate corollary is that every interval that is dividable into
smaller subintervals, is dividable into finitely many smaller
subintervals such that each of them is not, in turn, dividable into
any smaller subintervals.
To
see this, let [a,b] be an interval that is dividable into smaller
subinterval. Then, there is a natural number N(a,b), such that [a,b]
cannot be divided into more than N(a,b) smaller subintervals. Let's
divide [a,b] into the maximum number of subintervals into which [a,b]
can be divided. Then, each of those subintervals is non-dividable
into smaller ones.
7.2)
No ontological difference – God vs. God and God vs. the
universe
Let's consider the
following two scenarios, ordering the states in terms of causal
priority.
Scenario 1:
First
state of the world:
Timeless
state S.
The
only object is God, which exists timelessly at S and without a cause.
Second
state of the world:
First
temporal state T(0).
God
exists temporally, and the universe exists. The change from the first
to the second state of the world, including the creation of the
universe and God's own change from timeless to temporal, takes place
because God intends to bring it about.
Third
state of the world:
Second
temporal state T(1). The objects are God, the universe, and perhaps
some other objects.
Scenario 2:
First
state of the world:
First
temporal state T(0).
The
only object is God, who exists temporally at T(0) and without a
cause.
Second
state of the world:
Second
temporal state T(1).
God
exists temporally, and the universe exists. The change from the first
to the second state of the world, including the creation of the
universe and God's own change from timeless to temporal, takes place
because God intends to bring it about.
Third
state of the world:
Third
temporal state T(2). The objects are God, the universe, and the same
other objects as in the previous scenario
(if any), with the
same causes.
The
key point here is that the so-called 'timeless' state in scenario
1 is
exactly
like
the first temporal state T(0) in scenario 2.
In other words, there is no ontological
difference
whatsoever, even if different words
are
used:
In both cases, what
we have is a first state of the world changing into the next, and so
on.
In both cases, God
exists without a cause of his existence at the first state of the
world.
In both cases, the
universe exists at the second state of the world, and exists because
God intends to bring it about, and so on.
Also,
saying that the difference between the two scenarios is that one
state – namely, S in scenario 1
– is
timeless and the other – namely, T(0) in scenario
2
– is
temporal, or that in one of them there at least one tensed fact,
whereas in the other one there are no tensed facts, would fail to
address the point, since that would simply amount to denying
that
there is no ontological difference, without explaining how
or
why
that
is so, which is a burden on the theist defender of the KCA, since we
can conclude that the states are ontologically identical, just by
looking at the description
of
those states, and regardless of the use of the word 'timeless' in the
first one.
Someone
might say that God in scenario 1
is
changeless, but not in scenario 2. However,
that is not the case: just as God changes from his first to his
second state in scenario 2, he does so in
scenario 1.
So, it remains the
case that there is an entity – i.e., God – that exists at
a first state of the world and without a cause of his existence,
changes to a second state, then to a third one, etc., regardless of
whether the first state of that entity is called 'timeless'.
Alternatively,
someone might raise the following objection:
An
ontological difference is that temporal states of God must
change
as time goes by, whereas the timeless state S in scenario
1
could
have remained unchanged. In other words, if God exists at temporal
state T(0) – as in scenario
2
–,
then necessarily,
there will be a second temporal state T(1), and necessarily,
God will change from T(0) to T(1), since his knowledge of tensed
truths will change. On the other hand, if God exists in a timeless
state S (as in scenario
1),
then it is possible,
given that first timeless state of God, that God never changes.
The
problem with that objection is that it follows from any creation
hypotheses posited by theist defenders of the KCA –
i.e.,
given what God's first state actually would be, based on the
implications of their claims –,
that it is impossible
that
God never changes given that first state, which means both scenario
1
and
scenario
2
are
indistinguishable in that regard as well, as the following reasoning
shows:
Scenario
3:
First
state of the world:
Timeless
state S. The only object is God, which exists timelessly at S and
without a cause.
Second
state of the world:
Temporal
state T(0). God exists temporally, and the universe exists. The
change from the first to the second state of the world, including the
creation of the universe and God's own change from timeless to
temporal, takes place because of God intends to bring it about.
Scenario
4:
First
state of the world:
Timeless
state S. The only object is God, which exists timelessly at S and
without a cause.
There
are no temporal states of the world.
In
scenario
3,
if God does not intend at
S
to
change from timeless to temporal, then at T(0) God just
found himself altered.
In other words, if God's intent to change does not exist at at
S,
then the change is not something brought because God intends to bring
it about, but something that happened to
God,
beyond his intent. That is so because the change under consideration
is a change in
God's state, and from his first state at S. In
other words, it's a change from
S to T(0). So,
said change cannot have been caused by God's intent only at T(0),
given that S is causally prior to T(0).
So,
if God does not intend at
S
to
change from timeless to temporal, then God found
himself changed at
T(0); the change is something that happened to
God,
not something that God brought about. But that contradicts the
hypothesis that the change in scenario
3
happens
because God intends to bring it about. Thus, at
S,
God
intends to bring about his change from timeless to temporal.
Hence,
given God's state at
S
in
scenario
3,
it is impossible that God does not change, since God can't fail to
bring about what he intends to bring about. Moreover, just as in
scenario
3
it
is impossible that God does not change, the same is true and for the
same reasons in scenario
1.
Also, the states denoted by 'S' in scenario
3
and
scenario
4
respectively,
are not the same.
Someone
might suggest that, in scenario
3,
God exercised his libertarian free will at T(0) to bring about the
change, but at
S,
he does not intend to change. However, leaving aside issues about the
coherence of libertarian free will, that is impossible for the
reasons I explained above: since the change under consideration is
God's change from
S to T(0),
it cannot have been decided only at T(0). At T(0), the change already
obtains. Also, the state S is causally
prior
to
T(0), so a change in
God's condition at S
cannot
have been decided only at T(0). Thus, as concluded above, at
S
God
intends to change from timeless to temporal.
So,
the reasoning above shows that, once again, the theist fails to make
an ontological difference between scenario
1 and
scenario
2.
Since
God's first state in scenario
2
is
a temporal state, it follows that the same is true of God's first
state in scenario
1 –
and,
for that matter, in scenario
3
-,
and that both scenario
1
and
scenario
3
should
be corrected, and the first state should not be called 'timeless'.
Someone
might concede
that there is no ontological difference between scenario
1 and
scenario
2,
but raise an objection and claim that in that scenario God exists
timelessly at his first state. So, according to this objection, the
right conclusion is not that both
scenario
1
and
scenario
3
should
be corrected, and the first state should not be called 'timeless',
but rather, that scenario
2
should
be corrected, and the first state of God should be called 'timeless'.
The
objection fails, though, since the first state of God in scenario
1
and
scenario 2
changes
to the second one, just as the second state changes to the third one,
and so on, so there is no quiescent or changeless state of God.
The
fact that the first state is not preceded by other states is not
relevant when it comes to the fact that it changes to the second,
just
as the
second changes to the third, without
any period of quiescence or lack of change.
So, there is no changelessness or quiescence. But no changelessness
or no quiescence entails no timelessness, by the way in which Craig
uses the word 'timeless' - assuming, as usual, that he means
something by it – and so the first state of God in scenario
1,
scenario
2
and
scenario
3
should
not be called 'timeless' at all.
In
any event, we do not even need the previous result, in order to show
that positing a creator that is in some mysterious sense – or
it seems an incoherent 'sense', but that aside -, 'timeless' sans the
universe, but temporal with the universe, will not help theism. So,
if a theist insists, against very good reasons, that the first state
in scenario
1
is
timeless, then we may simply posit, as an alternative, that the
universe
might
as well exist without a cause if its existence at a first state of
the world, then change to its second state, and so on. If the first
state of God is somehow is properly called 'timeless' in scenario
1,
then due to a lack of a relevant difference, the same is true of the
first state of the universe in the following scenario:
Scenario 5:
First
state of the world:
The
universe exists without a cause of its existence. Nothing else exists
– there may or may not be some things in the
universe, but nothing beyond the universe.
Second
state of the world:
The universe has
changed and exists in its second state. Nothing else exists.
Just
as God exists without a cause in scenario1,
scenario
2,
and scenario
3,
the universe exists without a cause in scenario
5.
Just
as God changes from the first to the second state of the world in
scenario1,
scenario
2,
and scenario
3,
the universe so changes in scenario
5.
Then, God in those scenarios continues to change from one state of
the world to the next, and the same is true of the universe in
scenario
5.
Thus,
there is no ontological difference between scenario1
and
scenario 2, and no ontological difference
that would justify denying that the first state of God is temporal in
either scenario, but wouldn't justify denying that the first state of
the universe is temporal in scenario 5.
Someone
might bring up 'quiescence', as an attempt to show that there is a
difference between scenario1
and
scenario 2, and/or that there is a
difference that would justify denying that God is temporal at his
first state in scenario 1, but would not
justify denying that the universe is temporal at its first state in
scenario 5. On that note, and in an attempt
to distinguish between the universe and God, Craig makes the
following claim:
William
Lane Craig:
[4]
If
not, then since the universe cannot ever
have existed in an absolutely quiescent state, the universe must have
had a beginning.
However, a
'quiescent' objection fails as well, for the following reasons:
First,
as I explained earlier, there is no sense in which the first
so-called 'timeless' state S in scenario 1
is
quiescent, but the first temporal state T(0) in scenario
2 is
not. Indeed, in both cases, what we have is one first state of
affairs that changes
into
another, second state of affairs. In both cases, God exists at the
first state of the world, and without a cause of his existence. In
both cases, also, God changes from his first state at the first state
of the world, to the second, and so on. God never remains unchanged
for
a while in
the first scenario but
not the second-
that would require time -, or differs in any way between the
scenarios, by the description of them.
Second
– and now addressing Craig's contention about the universe -,
the same can be said about the universe in scenario
5: in that scenario, the universe exists at the first state of
the world, and without a cause of its existence. Also, the universe
changes from its first state at the first state of the world to its
second state at the second state of the world, there is no previous
change, and no period during which the universe remains unchanged.
But that is exactly
what
happens in the case of God in scenario 1.
Moreover,
if, say, a particle exists in the universe at the first state in
scenario 5, then any change in such particle
from the first to the second state of the world is still a change
from the first to the second state of the universe. There is no
previous change, or period during which the particle or the universe
remains unchanged, but that is exactly
what
happens in the case of God in scenario 1.
Thus,
there is no sense in which God could properly be described as
'quiescent' at his first state in scenario 1,
but the universe couldn't properly be described as 'quiescent' at its
first state in scenario 5.
As
another objection, someone might say that in scenario1
and
scenario 2, the change from the first to the
second state of the world, including the creation of the universe and
God's own change from timeless to temporal, takes place because God
intends to bring it about, whereas in scenario
5, the cause of the change is not specified. That is completely
unrelated to the issue of whether God or the universe are 'timeless',
changeless, quiescent, etc., but in any case, we may as well further
specify the scenario and add that, in scenario
5, the change from the first to the second state of the universe
is brought about by the universe's conditions at its first state
(including, of course, any particle interactions if there are any,
etc.), regardless of whether we put that in terms of substances and
causal powers, or in terms of substances and laws, etc. Thus, the
universe, which has certain conditions in its first state, brings
about the change to its second state, just as God and his intent at
the first state brings about the change in scenario1
and
scenario 2
(and,
for that matter, scenario 3).
This further
specification of scenario 5 is not required, though: we might as well
leave it unspecified, or alternatively even make the change
indeterministic in scenario 5, so that given the first state of the
universe, there is more than one possible second state, and only one
actually obtains, introducing a certain degree of randomness. That
would not make any difference whatsoever in terms of changelessness,
quiescence, or anything that might be called 'timelessness'.
All
that aside, a theist defender of the KCA might suggest that, perhaps,
the universe did not exist at the second state of the world, but only
at some later state. However, that clearly wouldn't make a
difference, either. We may simply posit scenarios like, say, scenario
1, 2, and 3,
but without introducing the universe at the second state of the
world, and keep scenario 4
and
scenario 5
unchanged.
The same reasoning as above yields the same results, defeating the
attempt to make a distinction.
So,
to summarize, if God does not begin to exist in scenario
1
because
somehow he's 'timeless', 'changeless' and/or 'quiescent', then the
universe does not begin to exist in scenario 5
for
the same reasons, and the KCA fails, since the proponent of the KCA
does not have any argument to rule out something like scenario
5.
If,
on the other hand, God begins to exist in scenario
1,
then the KCA fails for that reason.
The
previous considerations are sufficient to show that no current
version of the KCA provides any support for theism. For the sake of
thoroughness, though, in the next
sections,
I will raise other objections, which on their own suffice to show
that no version of the KCA provides any support for theism,
independently of the previous arguments.
However,
and before moving on to those other objections, I will add another
subsection
to
this section, dedicated to an even more
detailed analysis of the comparison between God and the universe,
when it comes to beginning of existence.
While
the previous considerations in this
subsection
are
enough to establish the failure of the KCA – as explained above
-, I've found a very misguided but very persistent theistic objection
involving causation, freedom and indeterminism, which shows a serious
misunderstanding of the arguments given earlier in this
subsection, in addition to a mistaken conception
of freedom.
There
is no need for a refutation of the conception of libertarian freedom,
so I will leave such a refutation for later, and
dedicate the next subsection
to
a detailed comparison of God and the universe, in terms of
beginnings, trying to clarify any points that remained unclear in
this section, and addressing the issue of freedom only in the context
of the scenarios under consideration, but in considerable detail as
well.
7.3)
No ontological difference – God vs. the universe, in even
greater detail
Let's consider the
following scenarios, ordering the states of the world in terms of
causal priority:
Scenario 5:
First
state of the world:
The
universe exists without a cause of its existence. Nothing else exists
– there may or may not be some things in the
universe, but nothing beyond the universe.
Second
state of the world:
Temporal state of
the world. The universe has changed and exists in its second state.
Nothing else exists.
Scenario 6:
First
state of the world:
Timeless
state of the world. God exists without a cause of his existence.
Second
state of the world:
Temporal state of
the world. God exists and the universe exists. God is the creator of
the universe.
In
this subsection, I will show that Craig's arguments, or similar
theistic arguments, fail to support the contention that even though
the first state of God in scenario 6
is
a timeless state – assuming here that 'timeless' is meaningful
-, the first state of the universe in scenario
5 would be a temporal state, and the universe would be something
that has a beginning – i.e., something that begins to exist –
but not a cause of its existence.
More
precisely, Craig and other theist defenders of the KCA claim that the
universe began to exist, and that everything that begins to exist has
a cause of its existence, concluding that the universe has a cause of
its existence. Also, they posit God as the cause of the existence of
the universe, but deny that God began to exist, claiming that he is
timeless sans the universe. I will show that Craig and others do not
have any good reasons at all to make that distinction and claim or
imply that God is timeless sans the universe, but the first state of
the universe would be temporal in scenario 5.
Given that they do
not explain what they mean by 'timeless', I will assess their claims
based on their assertions about the properties of timeless objects,
more precisely changelessness and quiescence.
7.3.1)
Quiescence and changelessness
In
scenario 6, God changes from his first state
– at the first state of the world -, to his second state –
at the second state of the world. God does not remain unchanged for
a while – which
would require time.
He
changes from the first state to the next. That is precisely
what
happens in the case of the universe in scenario
5.
There
is no need to posit that there are particles in the first state of
the universe in scenario 5. However, that
would make no relevant difference, either: If
we
assume for the sake of the argument that there are particles at the
first state of the universe in scenario 5,
then any change in any particle is still a change in the universe
from its first to its second state. That's precisely what happens in
the case of God, who changes from his first to his second state.
It
is true that, in scenario 6, there is no
change in God prior to the change from his first to his second state
– obviously -, but the same is true of the universe in
scenario 5
– also,
clearly.
So,
it is not the case that God can properly be called 'changeless' at
his first state in scenario 6, but the
universe can't properly be called 'changeless' at its first state in
scenario 5, and it is not the case that God can properly be
called 'quiescent' at his first state in scenario
6, but the universe can't properly be called 'quiescent' at its
first state in scenario 5.
Moreover,
while the previous reasoning in this subsection
is sufficient to show that theist defenders of the KCA fail to
make a relevant distinction between scenario 5
and
scenario 6, an even stronger case can be
made: namely, we can see from the previous reasoning that the proper
characterization of the first state of the universe in scenario
5
and
the first state of God in scenario 6
is
that such states are not
changeless or quiescent.
This
is clear from the fact that, say, the first state of God in scenario
6
changes
to the second one, just
as the second state will change to the third one, and so on.
The
fact that the first state is not preceded by other states is not
relevant when it comes to the fact that it changes to the second,
just as the second changes to the third, without any period of
quiescence or lack of change. So, there is no changelessness or
quiescence. But no changelessness or no quiescence entails no
timelessness, by the way in which Craig uses the word 'timeless' -
assuming, as usual, that he means something by it, which by now
appears extremely doubtful – and so the first state of God in
scenario
6
should
not be called 'timeless' at all.
Still,
leaving the stronger results aside for now, given that the first
state of the world in scenario
6
is
by assumption timeless, let us posit that the first state of the
world in scenario
5
is
timeless as well.
Then,
objections based on an alleged lack of quiescence or changelessness
of the universe fail, since there is no
difference
between
scenario
5
and
scenario
6
in
terms of quiescence or changelessness. Since there appear to be no
other objections to the timelessness of the universe at its first
state, the theistic case fails.
7.3.2)
Causation
Given
the results of subsection
7.3.1),
we may as well stop at that.
Also,
it seems clear that what caused the change from the
first state to the second state in God has nothing to do with
whether the first state of God is a beginning of existence of
God, and the same goes for the universe. That seems clear by the
meaning of the expression 'begins to exist'.
Still,
and just for the sake of the argument, I will address the matter of
causation in the rest of this
subsection.
7.3.2.1)
God's change, causation, and the change in the universe
In
scenario
6,
God changes from timeless to temporal
If
God's intent to change from timeless to temporal does not exist at
the first state of the world, then at the second state of the world,
God found himself changed.
Since
nothing else was there to cause the change, then God's change was
random.
Someone
might say that God only exercised his freedom and chose to change
only at his second state, so the change wasn't random even if God's
intent to change did not exist at the first state of the world.
However,
the first state of the world is causally prior to the second
one, so a change in that first state of the world cannot have been
caused merely by something that only existed at the second state of
the world.
Since
the first, timeless state of God obtains at the first state of the
world, the cause of the change in God from timeless to temporal must
have existed at that first state of the world, unless the change was
random and God found himself changed and temporal.
So,
the possibilities are that either God changed randomly and found
himself changed and temporal, or that God's intent to change existed
at the first state of the world in scenario
6.
But
clearly, the non-theist can match that:
For
instance, if God's intent to change from timeless to temporal existed
at the first state of the world in scenario
6,
we may posit as an alternative scenario that sufficient conditions to
bring about a change in the universe from a first state to a second
state also existed at the first state of the world in scenario
5.
To
be clear, we don't need to take a stance on whether, in scenario
5,
the change would be deterministic.
We
may suggest, as a possibility, that the conditions at the first state
of the world in scenario
5
were
sufficient to bring about a specific second state of the universe
(i.e., deterministic change).
We
may also suggest, as an alternative possibility, that the conditions
at the first state of the world in scenario
5
were
only sufficient conditions to guarantee that one of, say, n
different
potential second states of the universe would come to obtain, but
which one of those states actually obtains is not determined by the
conditions at the first state of the world.
That
is all compatible with scenario
5,
so we have options.
So,
if a theist claims that non-determinism in the change from the first
to the second state is required for the first state to be timeless,
he would have the burden to explain why that is so.
However,
even if we assume that indeterminism in the change from the first to
the second state is required for the first state to be timeless, we
may still posit a timeless first state of the universe, which would
be indeterministic. In fact, there already are indeterministic
interpretations of Quantum Mechanics (QM), so why not an
indeterministic first state of the universe?
So,
even showing that indeterminism is required for timelessness would be
a dead end for the theist.
That
said, and before I move on to the next
subsection,
I would like to reiterate that I'm merely assuming for the sake of
the argument that defenders of the KCA mean something by 'timeless',
and applying the conditions for timelessness they suggest or might
suggest. However, there seems to be no good reason to think that
they're using the word 'timeless' meaningfully.
Furthermore,
and regardless of whether they're using 'timeless' meaningfully, it
seems apparent – just by the meaning of the words – that
whether the universe in scenario
5
or
God in scenario
6
begins
to exist at
the first state of the world has nothing to do with whether any
change from the first to the second state of the world is determined
by the conditions at the first state. In other words, the issues of
beginning of existence and non-determinism are orthogonal. Still,
even if they weren't, that would not help the theist's case, as I
explained above in this
subsection,
and as I will further address in the next
subsection.
7.3.2.2)
Free will, determinism and indeterminism
As
we saw in the previous
subsection,
an indeterministic first state is not a difficulty for non-theists,
though there is no good reason to assume that if there were such a
first state, it would be non-deterministic.
After
all, it is clear by the meaning of the words that whether the
universe in scenario
5
or
God in scenario
6
begins
to exist at
the first state of the world has nothing to do with whether any
change from the first to the second state of the world is determined
by the conditions at the first state. Any ambiguity in the concept
'begins to exist' is clearly not connected to whether the change from
the first to the second state is deterministic.
That
aside, let's assume – at this point, clearly against good
reasons – that somehow in order for the universe not to begin
to exist
in
scenario
5,
it is required that the second state of the universe not be
determined by the conditions of the first state.
As
I mentioned, there are non-deterministic interpretations of Quantum
Mechanics, so a non-theist may simply suggest, as a possibility that
defenders of the KCA have failed to refute, a non-deterministic first
state of the universe in scenario
5.
So,
according to this, given the conditions at the first state, there are
a number of potential second states, even though in the end, only one
of them came to obtain.
An
objection that a theist might raise here would be something like the
following:
Why,
then, the universe changed to the state that it did, rather than one
of the other states? Is that random? Theists do not have that
problem, since God has free will, and can choose indeterministically
without randomness.
Actually,
free will does not entail non-determinism, and libertarianism is not
the correct understanding of free will, as I will show later.
So, this objection is based on a misunderstanding of what freedom is.
But
that aside, this objection would be an objection to any
non-deterministic interpretations of QM, not just to a
non-deterministic first state of the world.
The
matter of determinism vs. non-determinism does not appear to be
settled, and it would be up to the theist to show that
non-deterministic interpretations of QM are not true. To be clear,
suggesting that they might not be true is not enough. The theist
would need to provide enough reasons to conclude at least that
non-deterministic interpretations of QM are probably false, if he
wants to make a case against an initial non-deterministic state of
the universe.
Another
potential theistic objection might go as follows:
Why
is it that the first state only allows for a certain number of second
states? Why not anything? Theists have an answer: God can
freely choose to bring about a certain universe, but he will choose
something good, because of who he is.
Even
leaving aside problems such as the Evidential Problem of Evil,
Problem of Suffering, Problem of Divine Hiddenness, etc., as direct
objections to God as a creator of our universe, a problem with the
theistic objection above is that the theist is assuming that there is
a creator with a certain psychological makeup. Surely, the
non-theist may as well suggest as a possibility – without even
having to commit herself to that – a first state of the
universe with certain properties that constrain the possible second
states.
7.3.2.3)
Agents acting 'in and of themselves'?
Another
objection I've encountered holds that scenario
5
should
be rejected because only free agents, as far as we know, can act 'in
and of themselves', start new causal chains, act 'without being
caused to do so', etc., and the universe is not a free agent, but God
is.
This
is not an objection to a claim that, in scenario
5,
the universe is timeless at its first state, but rather, it's an
objection to the possibility, or at least the plausibility of
something like scenario
5.
This
objection confuses causation with lack of freedom, and holds that an
agent whose decisions are caused by previous states of herself would
somehow not be free because it would be 'caused to act'.
A
way to refute this objection is to show that libertarian
freedom is a mistaken conception of freedom, which I will do later.
In
this
subsection,
however,
I will deal with this objection on different grounds:
First,
as explained in subsection
7.3.1),
the proper conclusion is not that both the first state in scenario
6
and
in scenario
5
are
timeless, but rather, that neither
of them is,
and that the assumption that the first state in scenario
6
is
timeless is false – assuming that 'timeless' is meaningful at
all.
Indeed,
all the attempts of showing changelessness or quiescence failed. That
is enough to block all present-day versions of the KCA, regardless of
any other matters.
Second,
leaving that aside, theist defenders of the KCA have not refuted
non-deterministic interpretations of QM, which would include states
of affairs not determined by previous ones, without involvement of
any agent.
It
is true that, in all the cases we've encountered, those states of
affairs require at least some non-deterministic previous conditions,
but surely the same can be said about any decisions made by any
agents we're familiar with, even if we assume that such agents are
non-deterministic.
Third,
even if we had evidence that humans are non-deterministic, we
certainly do not have any evidence of humans or any other agents
existing without any causes of their existence.
It's
true that we don't have evidence of any beings or states existing
without any previous states, either, but the point is that even in
scenario
6,
the theist is positing something that has nothing to do with our
experiences of causation, or beginnings of existence.
Moreover,
if we can nevertheless use the evidence that we do have
as a means of trying to ascertain whether a first cause would
plausibly be a personal being, we can point out the following:
The
non-theist observes that, as far as she can tell, all of the causes
of us which existed two billion years ago are non-agents, and that as
far as she can tell, everything that exists can be traced back,
deterministically or not, to only non-intelligent causes. There is no
good reason for her to come to believe that if there is a first cause
at all, it's more plausible that a first cause would be intelligent.
All
that aside, as I mentioned, I will refute the
'in and of themselves' objection
on
different grounds later,
when I refute the libertarian account of freedom.
Now,
let's move on to other, very different objections to the KCA.
8)
The meaning of 'begins to exist'
First,
let's
compare Craig's
hypothesis about the meanings of 'begins to exist' and 'comes into
being'[11],
with an alternative hypothesis AH1,
and
test the two hypothesis to see which one is closer to matching the
meaning of the words:
AH1
A.
x begins to exist at [t1,t2] iff there is a finite closed interval
[t1,t2] such that x does not exist at any time prior to t1, and x
exists at t2.
B.
x comes into being iff there is an event
– that
is, change – from a state of affairs at which x does not exist,
to a state of affairs at which it does.
Here,
"x"is just as in Craig's hypothesis – i.e., it can be
any being -, and 0 ≤ t1 ≤ t2.
As
for the interval [t1,t2], an interval seems to be required because
otherwise, there might be a problem in cases of vagueness: e.g.,
there may not be a specific instant t such that the Moon existed at
t, but at no u < t: the word "Moon" may be too vague for
that.
That
also seems to be in line with common speech: when we say that
something began on a day, or a year, etc., we're considering
intervals, not instants. Even when we speak in terms of seconds, or
millisecond, we're speaking in terms of intervals, even if very short
ones.
Under
a tensed theory of time, everyday examples will not help us test one
vs. the other, since both hypotheses yield the same results. However,
under a tenseless theory of time, the difference is striking:
Let's
assume a tenseless theory of time, and let's consider, for instance,
Napoleon.
It
seems clear that, even if the past, present and future exist
tenselessly, there is a time at which Napoleon did not exist, and a
later time at which he did.
So,
it seems that he came
into being,
and began
to exist. That's
in line with hypothesis AH1.
On
the other hand, under Craig's hypothesis, assuming a tenseless theory
of time, nothing begins
to exist, and nothing comes into being. In particular, Napoleon
neither came into being, nor began to exist. But that seems clearly
conceptually wrong. In fact, the questions of whether a tensed theory
is true and whether Napoleon came into being, or began to exist,
appear to be orthogonal.
It
seems rather odd that Craig would include tense in the definition of
"begins to exist", but he argues that, under a tenseless
theory of time, a universe with a first event did not begin to exist
just as a meter stick does not begin to exist just because it has a
first centimeter.[12]
That
argument is odd as well, though:
While
a meter stick does not begin to exist
in virtue of having a first centimeter,
that's not relevant, since having a first centimeter is a spatial,
not a temporal
claim, while "begins to exist" - at least, in this context
– is clearly about time, not space.
In
fact, the stick in question does
have a beginning
in space because
it has a
first centimeter, and similarly, even if a tenseless theory of time
is true, the stick does have a beginning
in time
as
long as there is, say, a first
year at which it exists.
It
is true that, in order for us to say a year is first,
we need to pick an order in time – from past to future, not the
other way around, but that direction is actually implicitly built-in
hypothesis 2, and in our language about time.
Also,
to say that the stick has a spatial beginning require that one picks
a direction in space to say which centimeter is first – in this
case, explicitly or by context.
A
difference is that, in the case of space, one needs to pick the
direction explicitly or by context, whereas in the case of time, it's
built in the meaning of the words, but that does not appear to be
relevant to the point that there is a beginning.
Since
to say that the stick begins to exist – in the sense that's
relevant in the context of the KCA, at least – is the same as
to say that the stick has a temporal beginning, or a beginning in
time, then it follows that the stick does begin to exist, even on a
tenseless theory of time.
Then,
it seems to me that hypothesis AH1
gives
the right result, whereas Craig's hypothesis does not.
Let's
consider a different scenario; scenario S1:
Let
us suppose that there is a t=0, and an entity B that exists at t=0.
Let us suppose that there is no time earlier than t=0. Let's further
suppose that there is no state of the world at which B does not
exist, and the actual world does not contain any timeless states of
affairs whatsoever, or any kind of two-coordinates time, or
undifferentiated time, or any such temporally counterintuitive state
of affairs[13].
Does
B begin to exist?
Does B come into being?
According
to Craig's hypothesis[11],
if a tensed theory is time is true, then B begins to exist and comes
into being, whereas if a tenseless theory of time is true, then B
neither begins to exist nor comes into being.
On
the other hand, according to hypothesis AH1,
regardless of the tensed vs. tenseless issue, B does begin to exist,
but does not come into being.
Readers
will use their own intuitive grasp of the words, of course, but mine
tells me that hypothesis AH1
gives
all the right results again: to come
into being
seems to entail that there is a state at which the entity in question
does not exist, followed by one in which it does, whereas to begin
to
exist seems to indicate an initial time or moment of existence.
I
don't know whether hypothesis
AH1
is entirely
accurate, but it does seem to be much closer to capturing the meaning
of the words than Craig's
hypothesis[11].
Another
alternative (say, hypothesis AH2) would be just like hypothesis
AH1
but allowing open
and semi-open finite intervals.
Hypotheses
AH1
and AH2 given the
same verdict in daily cases, under either a tensed or a tenseless
theory of time, but there would be a difference in, say, open models
of the universe with a metric-finite past, assuming an intrinsic
metric.
In
any case, both alternatives seem to fare much better than Craig's
hypothesis, at least in all the cases tested above – in which
both hypotheses AH1
and
AH2 seem
to give the right results, but Craig's does not.
In
addition to that, it seems clear that, when people ordinarily says
'begin to exist', they're not making obscure claims about
timelessness – which, if coherent at all, does not seem to be a
concept that most people even grasp.
So,
it seems clear that Craig's
hypothesis about the meaning of 'begins to exist'[11]
is
false.
It's
true that Craig might simply stipulate what he means by 'begins to
exist', rather than making a claim of meaning, and someone might
suggest that Craig is doing merely that.
That
doesn't look like that to me – though I would grant that Craig
is rather obscure -, but there is no need to get into that: Even if
Craig merely stipulated what he means by 'begins to exist', or even
if he presented a hypothesis and we assume – against good
reasons, as explained earlier in this section – that such
hypothesis [11]
is
true, his arguments fail to provide support for either the
first or the second premise
of
the KCA, as the following sections will show.
9)
The first premise of the KCA
Let's
turn now to the question of whether there are good grounds for
believing that everything that begins to exist has a cause.
William
Lane Craig maintains that the first premise, namely the claim that
everything that begins to exist has a cause, is intuitively clear.
Moreover, he claims that there is empirical confirmation of that.
He
tries to back up that claim by appealing to our intuitions about
causation – what he calls "metaphysical" intuitions
-, and by bringing up scenarios that purportedly show the absurdity
of denying it, such as, say, horses popping into existence uncaused.
[14]
However,
all of those scenarios would also be a case of denying other
candidates to being intuitive principles, such as the principle that
every event/change of the form "B comes into existence"
- or, more generally, every event/change – has a cause.
So,
let's consider the following alternative principle:
AP1:
Every event (i.e., every change) has a cause of why it happens.
In
other words, someone may not accept that everything that begins to
exist has a cause, while accepting that, for instance, every
event/change has a cause. They don't need to actually deny
that everything that begins has a cause, but simply not affirm it.
Actually, AP1 is also debatable, and I'm not suggesting that we
ought to accept it, but the point here is that it's an alternative
that avoids any of the issues raised by Craig, and – at least
to me – it seems more intuitive, so if we are to accept a
principle, AP1 seems good enough.
That
would not commit us to assuming that only events/changes have causes,
of course – just as Craig does not assume that only that which
begins to exist has causes -, but that's beside the point.
The
point is that this is an intuitive alternative (though still
debatable), and that none
of the scenarios that Craig brings up – like a horse coming
into existence uncaused – would present any problem for that
position, since that position holds that events/changes
would
not happen without a cause.
On
the other hand, using
Craig's definition of 'begins to exist'[11],
the issue of 'timelessness' alone is a serious problem: without
a good understanding of what that even means, plus
good reasons to adopt it, there appears to be no justification for
believing that kind of principle that Craig proposes, even if we
assume that the claim is coherent – which
we
don't have sufficient reasons to believe.
Still,
there is no need to settle the matter of what 'begins to exist' mean.
Let's consider the following definition of 'temporal beginning'.
TB:
X has a temporal beginning if and only if:
a)
X exists at some time t, and has existed for a finite amount of time
before t (zero counts as finite).
b)
If 'timeless' is coherent, then there is no state of the world at
which X exists timelessly.
Let's
consider the following questions:
Q1)
Do we have sufficient reasons for believing not only that every event
has a cause, but that everything that has a temporal beginning even
when no change is involved, has
a cause?
In other words, do
we have sufficient reasons for believing that every X that has a
temporal beginning has a cause, even when there is no change from a
state of affairs at which the X in question does not exist, to a
state at which it does?
Q2)
Do we have an epistemic obligation to believe that everything that
has a temporal beginning even when no change is involved,
has
a cause?
Q3) Should we
believe that everything that has a temporal beginning comes from a
change/event 'X comes into existence'?
In
order to assess our intuitions on the matters [15]
of Q1 and Q2, we would need to consider unusual scenarios, such
as S1.
I have to say that I
don't have any general intuition that, in such scenario, B would have
a cause.
In fact, in some
scenarios, my intuitions tell me otherwise:
For
instance, in S1, let us stipulate that B is the
universe, or a multiverse, and there is nothing else that exists. Or
let's stipulate that B is an omnipotent being, and let's stipulate
that, at t=0, there are no other beings – no timelessness
involved.
In those cases,
intuitively, I'd say that B begins to exist but may well not have a
cause. At least, I have no intuition that B would have a cause.
Someone
might protest that I'm constructing scenarios that would be
exceptions to the principle, but the scenarios in question are
counterintuitive and we shouldn't use them as a guide.
However,
in order to construct scenarios in which one could test whether one
has an intuition that every X that begins to exist has a cause,
independently of whether there is a change/event 'X comes into
existence', it seems to me one needs precisely to separate
temporal beginnings of existence from changes/events, and
that does not happen in ordinary cases.
Otherwise,
it might be that what's intuitive to one is just the principle that
every event – that is, any change – has a cause,
and the correlation with a temporal beginning arises because it just
happens to be the case than, in daily life, things that have a
temporal beginning are just those things X for which there is a
change/event 'X comes into existence' - i.e., a change from a state
of affairs at which X does not exist, to one at which it does.
So,
in
order to accept something like 'everything that begins to exist, has
a cause' as intuitive, one would not only have to lack an intuition
that, in some scenarios, some beings that begin to exist would
probably not have
causes: one would have to have an intuition that those beings would
plausibly
have causes.
As
for Q3, there appears to be no intuitive reason to think that that's
always the
case.
In
fact, if time had a beginning point (which can't be ruled out on
intuitions alone), it seems more than intuitively clear that there is
no event 'time comes into existence': a change from a state of
affairs at which there is no time, to one at which there is time,
seems to be impossible, for reasons similar
to those used to derived a
contradiction earlier.
So,
it seems intuitions do not support an affirmative answer to Q1,
Q2 or Q3. [16]
As
for empirical reasons, someone might try to use objects in daily life
as examples, and claim that everything that begins to exist, also
comes into existence, and that would allegedly support Q3.
However,
that's really empirical evidence, but simply the consequence of the
definitions, for any object not as old as the universe. [17]
So,
it seems that we're at the very least justified in not affirming that
every X that has a temporal beginning,
comes
from an event 'X begins to exist', or that everything that has a
temporal beginning, has a cause.
Finally, someone
might raise the issue that cosmologists who worked on the Big Bang
model did not come to the conclusion that they had resolved all the
mysteries and moved on, instead of looking for causes.
However, it's clear
that the model does not provide an understanding of the
universe beyond a certain point, where effects from forces other than
gravity should be taken into consideration.
In other words, it
makes perfect sense that scientists would try to figure out the
causes of a very hot, dense, and small universe that existed about
13.7 billion years: indeed, we don't know the causes; a theory that
only considers gravity but no other forces is inadequate to provide a
good understanding of it.
But those scientists
seem to be asking the question: 'Where did that hot, dense, really
small universe come from?' (or similar ones), on the understanding
that before the first state of the universe that can be
analyzed with present-day models, there were other states of
the universe that are beyond the descriptive capabilities of current
scientific understanding – states that later changed into
a state that is within said capabilities.
In
other words, they apparently were/are looking for the causes of an
event/change, as well as for a model of how the universe works
under conditions not covered by present-day models.
So,
it seems that Craig's arguments fail to provide support for the
premise; at the very least, there is no epistemic obligation to
accept it – and that's not even counting
issues related to indeterministic interpretations of Quantum
Mechanics.
Still,
even if we grant the first
premise
for
the sake of the argument, Craig's arguments do not support the second
one.
Someone
else might come up with new arguments, but it's a heavy burden,
especially given that all arguments in support of either premise have
failed so far, and the KCA is a very old argument, which as been
debated at length. In any case, the burden would be on them, of
course.
10)
The 'Hilbert Hotel' argument
One
of the arguments that Craig gives in support of the second premise of
the Kalam Cosmological Argument intends to establish that an actual
infinity is metaphysically impossible – though there is no
claim of logical impossibility.
Let's
assess Craig's argument:
William
Lane Craig and J.P Sinclair[18]:
But
now let us imagine a hotel with an infinite number of rooms and
suppose once more that all the rooms are occupied. There is not a
single vacant room throughout the entire infinite hotel. Now suppose
a new guest shows up, asking for a room. “But of course!”
says the proprietor, and he immediately shifts the person in room #1
into room #2, the person in room #2 into room #3, the person in room
#3 into room #4, and so on out to infinity. As a result of these room
changes, room #1 now becomes vacant, and the new guest gratefully
checks in. But remember, before he arrived, all the rooms were
occupied! Equally curious, there are now no more persons in the hotel
than there were before: the number is just infinite. But how can this
be? The proprietor just added the new guest’s name to the
register and gave him his keys – how can there not be one more
person in the hotel than before?
Such questions are
the result of an ambiguity about what it means for there to be “more
persons” in the hotel.
For
instance, if by “more persons” one means “all the
persons who were there remain, and there is at least one who wasn't
there, but now is there”, or if one means that the set of
guests after the new arrival (let's call it “GF1”)
minus the set of guests before the new arrival (let's call it “GI”),
has a greater cardinality than GI
minus
GF1
[19],
then
are are more persons (more precisely, one more) after the new guest
checks in.
On
the other hand, the set of guests in the beginning GI
has
the same cardinality as the set of guests after a new guest arrives,
GF1,
so if by "GF1
has
more persons than GI"
one means that the cardinality of GF1
is
greater than that of G1,
then there are no more persons after the arrival.
That
the sets have the same cardinality only means that there is a
bijection between the two sets, which is not only not
counterintuitive, but is actually obvious:
it's
the same as comparing the set of natural numbers N
(i.e.,
{1, 2, 3, …}), with the set of non-negative integers N0
(i.e., {0, 1, 2, 3,...}).
So,
in the usual mathematical sense of cardinality, N and N0
have the same number of elements, but that only means there is a
bijection between the two (which is, again, obvious, since we can
define F: N0
→ N,
F(k) = (k+1)).
On
the other hand, there is one number in N0
that is not in N
(namely,
0), so in that sense, there is one more element – also, the
cardinality of N0
minus
N
is
1, which is greater than the cardinality of N
minus
N0,
which is zero. So, understanding “more elements” in
either of those senses, it is the case that N0
has more elements than N (one more, to
be precise).
The case of the
hotel is no different in that regard; making the example concrete
does not change the fact that any puzzlement arises from the
ambiguity about what's meant by “same number”:
In
the same sense of “same number” in which N0
has the same number of elements as N –
namely, in the sense that there
is a bijection between the two-, the sets of guests after and before
the arrival have the same number of guests.
And
in the two senses I mentioned above in which N0
has one more element than N,
there
is one more guest after the new guest arrived.
If
the example shows something counterintuitive, that's not the actual
infinity, but the infinite hotel
– which
of course we could never build – the practical impossibility of
communicating with infinitely many people at once, etc.
But that does not
appear to be a problem for, say, infinitely many galaxies, or
infinitely many universes (in some sense of “universe”
used in modern cosmology), infinitely many particles, etc.
So, if one explains
what one means by "more", then there is no problem
whatsoever, regardless of whether there is a unique usual meaning of
"more", according to which there are (or there aren't) more
persons after the arrival.
I actually doubt
that only one common meaning of "more" exists, but that is
beside the point.
The point is that
there simply appears to be nothing remotely puzzling here, but merely
a confusion that arises from some ambiguity in what is meant by
"more".
The rest of the
arguments against an actual infinity are based on that ambiguity as
well.
For
instance, Craig expresses some sort of amazement at the alleged
strangeness that even if (denumerably) infinitely
many
more guests arrive, the number of guests is the same as before.[18]
As
in the previous case, there is no puzzlement at all if what's meant
be "same number" is explained:
The
set of guests after the infinitely many (more precisely, ℵ0)
new guests arrive (let's call it GFℵ0)
has all the members of the initial set of guests GI, and it
also has infinitely many guests that GI does not have.
Also,
GFℵ0
minus GI has infinitely many guests or
members, whereas GI minus GFℵ0
has zero.
On
the other hand, there is a bijection between GI and GFℵ0.
All
that is clear, and there is no puzzlement.
The
question "Are there any more guests?" is not be problematic
once one explains what's meant by "more guests".
It
would be somewhat ambiguous to say that there would never be a single
person more in the hotel than before, as Craig does[18],
but as before, once one clarifies what one is saying, the puzzlement
should disappear: in the usual mathematical sense of cardinality,
there are no more persons, which is to say nothing but that there is
a bijection between the set of guests before the new infinite ones
arrive, and the set of guests after they do arrive.
In the two other
senses I mentioned above, there are more people after the arrival.
All
of this is straightforward, so there should be no need to delve any
further into it: Craig's "Hilbert Hotel"
argument provides no good reason to reach any conclusion about
whether actual infinities exist, or whether or not they're
"metaphysically possible", since it is just the result of
terminological ambiguity and the resulting confusion.
11)
Philosophical arguments against an infinite past
In
addition to the Hilbert
Hotel argument against
an actual infinity, Craig presents other philosophical arguments
against an infinite past on a tensed theory of time – not
against all actual infinities.
Before
I go on, I have to admit that an infinite past on a tensed theory of
time appears counterintuitive to me. However, on the other hand, so
does a beginning of time!
That
aside, the question is whether there are enough reasons that would
settle the matter in the sense that, on a tensed theory of time, an
infinite past is indeed impossible.
I
used to think that there were – though not for the same reasons
as Craig -, but after further consideration, reading
counterarguments, and so on, I have to admit I can't find such
reasons.
To
be clear, on a tensed theory of time, there is no infinite ordered
chain of events, one after the other, with a beginning point, since
it's impossible to reach an infinity by a finite number of instances
of finite addition. Moreover, that is true regardless of whether the
events are of equal duration – assuming an intrinsic metric of
time; else, how close they are is a conventional matter -, or even
whether the past is metric-finite. Indeed, even if the lengths of the
events added up to a finite number, the fact is that it's not
possible to reach an actual infinity by finitely many times adding
something finite.
However,
the real question is whether a beginningless series of ordered
past events, one after the other, is possible, under a tensed theory
of time.
Craig
maintains that that is impossible, pointing to the objectivity of
temporal becoming under a tensed theory of time, and presenting some
arguments that allegedly would result in contradiction.
I
will consider the arguments that purportedly show some absurdities in
a moment, but before that, I'd like to point out that if the
objectivity of temporal becoming on a tensed theory of time precluded
an infinite past, it would also preclude a metric-finite past but
with infinitely many past events/changes.
On
that note, when Craig replies to the objection that some of his
arguments resembles Zeno's paradoxes.[20],
he maintains that there are two
crucial differences: the events are of equal duration and actual in
his argument whereas the intervals are potential and unequal in
Zeno's paradoxes.
However, at least the equal or unequal duration
of the intervals is not a relevant difference, as long as each of
them involves actual events/changes, since in any case, there would
be infinitely many instances of temporal becoming in the past,
regardless of whether they're all temporally equidistant from each
other.
So,
the question remains: does the objectivity of temporal becoming
precludes the existence of infinitely many instances of temporal
becoming in the past, one after the other?
Actually,
it seems that what would be ruled out is the existence of such
instances with a beginning point. In other words, what would be ruled
out is a first temporal
state
T(0) without any changes within it, followed by the next such state
T(1), and so on, until reaching a time T(ℵ0).
However,
if there is no beginning point, between any two events there would be
only finitely many ones, so there would be no infinity to be reached
from
any point.
So, there is no contradiction, only counterintuitiveness. However, a
past with a beginning point is also counterintuitive.
Moreover,
modern physics has taught us that while our intuitions about time are
good enough in daily life, we should be wary about extrapolating them
to the whole universe (or even some parts of it, like, say, a
galaxy).
So,
it seems that on intuitions alone, the matter can't be settled.
Let
us now consider Craig's arguments that purportedly show some
absurdities in the case of an infinite past without a beginning.
11.1)
The contradictory case of Tristram Shandy
One
of Craig's arguments against an infinite past is based on the story
of Tristram Shandy. [21]
Shandy
is a man who writes his autobiography, at a rather slow pace: it
takes Shandy a year to write the events of a single day.
According
to Craig, if Shandy had been writing from infinity, that would lead
to absurdities, and so – as Craig argument goes – we
should reject an infinite past because it's obviously coherent to
write an autobiography at that pace.
However,
Craig does not provide any good reason to believe that it's obviously
coherent – or, indeed, coherent – to write an
autobiography at that rate counting
from infinity.
What
is obviously coherent is to write such an autobiography starting
at a specific day.
Moreover,
there is a good reason why Craig does not provide any good reasons to
believe that it's coherent to write an autobiography at that rate
while having kept that pace 'from infinity': namely, such a deed is
logically
impossible.
To
see why this is impossible, let's suppose otherwise, let's suppose
the number of past years has the order type of the non-positive
integers, and let's enumerate the past years in the following way:
[22]
Last
year is 0, the previous year is -1, and so on. For instance, if this
year is 2012, then 2011 is 0, 2010 is -1, 2009 is -2, and so on.
Now,
let F be a function from the set of non-positive integers into itself
such that for all non-negative integers r
and n,
F(-r) = -n if
and only if -n
is the
most recent year Shandy wrote about during the year -r.
For
instance, if, in the year -2000, Shandy wrote about a day in the year
-300001 and about a day in the year -300000, then F(-2000) = -300000.
Given
the rate at which Shandy writes, and given also that, when writing
his autobiography, Shandy never writes about his future, we have the
following conditions:
1)
F(-r) ≤ -r.
2)
F(-r-365) = F(-r) - 1.
By
induction:
3)
F(-r-2*365) = F(-r-365-365) = F(-r-365) - 1=F(-r) - 2
4)
F(-r-k*365) = F(-r) - k, for
all non-negative k.
So,
in particular, taking r=0.
F(-k*365)
= F(0) - k ≤ -k*365.
Hence,
for every natural number k,
5)
364*k ≤ -F(0)
That's
contradictory, as easily seen by taking (for instance) k
= 1 + (F(0)*F(0)).
So,
the Tristram Shandy scenario fails to show that infinitely many past
years are impossible.
Someone
might suggest that precisely the fact that we reach a contradiction
is what should lead us to the rejection of such an infinite past.
However, that would be a confusion, as it should be clear from the
previous proof: what's logically impossible is the scenario itself,
and it's not surprising that absurdities follow from a contradiction,
since everything follows from a contradiction.
Surprisingly,
Craig actually acknowledges that the scenario is contradictory, yet
claims that because it's "obviously" coherent to
write one's autobiography at a rate of one day per year, the problem
is with the infinity of the past.
I
have to confess that I find that reply puzzling. Clearly, the task of
writing one's autobiography at a rate of one day per year from
infinity is logically impossible. I honestly do not understand
what else is needed to reject the argument.
Incidentally,
there is a contradictory scenario about the future that strikes me as
similar to the 'Tristram Shandy' scenario:
Alice
Shandy writes a novel, and the story is set in her future. She always
writes about future days. Also, it takes Alice a year to account for
what happens in one day in her novel, and she always writes her novel
in sequence. In other words, she writes about what happens on some
day d1,
and after she finishes writing about d1,
she moves to the day after d1,
without jumping to any later day.
Also,
for any number n, Alice spends more than n years writing her novel.
The
'Alice Shandy' scenario is contradictory, but that does not warrant a
conclusion that an unbounded future is metaphysically impossible.
Someone
might insist that the task of writing a novel about the future,
writing about consecutive days at a rate of one day per year, is
obviously coherent, and so the fault must be with the idea of a
potentially infinite future, but it seems apparent to me that such a
reply would be very mistaken.
The
'Tristram Shandy' scenario strikes me as similar, but in any case,
that's only a curiosity. I would say that should in any case reject
the 'Tristram Shandy' scenario because it's contradictory, and so the
fact that it results in absurdities does not tell us anything about
whether an infinite past with the order type of the negative integers
is metaphysically possible.
Still,
while the proof above should be
enough to debunk the Tristram Shandy
scenario, in case someone is not persuaded by it, let me point out
that the proof in question does not depend on whether a tensed or a
tenseless theory of time is true. But an infinite past seems clearly
logically possible if we assume a tenseless theory of time, just as
an infinite future is.
Also,
somebody might suggest that there might be even more
past years, changing order types,
etc.
However,
that would be beside the point:
The
point here is that the previous proof shows that if the set of past
years is of the same order type as the set of non-negative integers,
the Tristram Shandy case is logically
impossible.
Therefore,
the Tristram Shandy scenario fails to present any challenge to the
possibility of an infinite past in which the set of past years has
the same order type as the set of non-negative integers, and so it
fails to show that infinitely many past years are impossible.
11.2)
Orbits and parity
Another
one of Craig's arguments against an infinite past on a tensed theory
of time is based on a scenario involving planets completing
infinitely many orbits.
First,
he claims that somehow it's absurd that if Jupiter completes 2.5
orbits for each one Saturn completes, they would both have completed
the same number, if they have been orbiting the Sun 'from eternity
past'. That would be somehow a "magical" result[23].
Now,
apart from the fact that any planet, star, etc., has a finite
expiration date, the fact is that there is no absurdity at all.
As
in the case of the Hilbert
Hotel argument,
this is merely a confusion with words.
That
the number of orbits is the same if they've been orbiting forever and
there is an infinite past merely means that there is a bijection
between the set of orbits completed by one of the planets, and the
same set for the other planet.
Of
course, again in reality planets
don't
last for that long, but that is not at all relevant.
Indeed,
no one is suggesting that planets
might
do that: we know enough about physics to tell otherwise.
Incidentally,
in any case, the number of orbits completed from
any given time would
be finite, and there would be nothing like Jupiter falling
"infinitely far behind Saturn", or that the "disparity"
has become increasingly greater from
infinite,
etc.: again, there is no beginning from which to count to infinity.
William
Lane Craig:[23]
For
a cardinal number n
is
even if there is a unique cardinal number m
such
that n
=
2m,
and n
is
odd if there is a unique cardinal number m
such
that n
=
2m
+
1. In the envisioned scenario, the number of completed orbits is (in
both cases!) ℵ0, and ℵ0 = 2ℵ0 = 2ℵ0 +
1.
Actually,
using usual mathematical definitions of “even” and “odd”
– and those definitions match common usage of the words -,
integers
are
even or odd, but not transfinite cardinals.
So,
using the words in their usual sense, ℵ0
is neither odd nor even.
Also,
that ℵ0
=
2ℵ0
+
1 only means that there is a bijection between ℵ0
and
(ℵ0
x
{0, 1} U
{1}),
and that ℵ0
=
2ℵ0
only
means that if there is a bijection between ℵ0
and
(ℵ0
x
{0, 1}). But that's all true [24].
Surely,
going by the definition Craig provides, ℵ0
would be both odd and
even, and so would be any other transfinite cardinal, but that is not
at all a problem,
as
long as one keeps in mind what Craig means by the words.
12)
The "Standard Hot Big Bang Model", a tensed theory of time,
and the KCA:
Back to Craig's
argument, he claims that what he calls the "Standard Hot Big
Bang Model" (SHBBM), supports the second premise of the KCA. He
also claims that a tensed theory of time is true.
W.
L. Craig and J. P. Sinclair[25]
The
standard Hot Big Bang model, as the Friedmann–Lemaître
model came to be called, thus
describes a universe which is not eternal in the past, but which came
into being a finite time ago. Moreover – and this deserves
underscoring – the origin it posits is an absolute origin ex
nihilo. For not only all matter and
energy but also space and time themselves come into being at the
initial cosmological singularity. As Barrow and Tipler emphasize, “At
this singularity, space and time came into existence; literally
nothing existed before the singularity, so, if the Universe
originated at such a singularity, we would truly have a creation ex
nihilo” (Barrow and Tipler
1986, p. 442). On such a model the universe originates ex
nihilo in the sense that it is false
that something existed prior to the singularity.
There
is no good reason to think that we can assume the model to be an
accurate description of the universe beyond a point at which there
was a hot, dense and very small universe – but not
– a singularity of infinite
density (what would that even mean?).
Moreover,
there is no need to add a singular point, even if one keeps
extrapolating backwards in time, nor a way of getting out of the
singularity, so to speak.
However,
let's let all that pass, and let's assume, for the sake of the
argument, that the model Craig offers in support of his arguments is
indeed an accurate portrayal of the early universe.
Then,
under such assumption:
1)
There is a time t(1) in the past, such that the average density d(1)
of the universe at t(1) was greater than the density at a time in the
year 2000 (any time) d(0), so there is a change from a universe with
a density d(1) to a universe with a density d(0).
Thus,
the model entails that there is at least one event/change, E(1),
which happens in semiopen interval [t(1), t(0))
2)
Let's suppose the model entails there are at least k events, E(1),
E(2), E(k), where E(j) happens in the semi-open interval [t(j+1),
t(j)), and 0 < t(j+1) < t(j), for all j between 1 and k.
The
average density of the universe from E(k+1) began to the present day,
is bounded, and so is less than some number d(M).
Since
the model predicts that the density tends to infinity as we
move back in time, there is some time t(k+2), such that 0 < t(k+2)
< t(k+1), and such that d((k+2)) > d(M).
So,
there is a change from a state of the universe with density d((k+2)
to a state of density d, such that d(M) > d > d(k+1), and
that's the event E((k+1)), which happens in the interval [t(k+2),
t(k+1))
Thus,
on this model, there is an infinite temporal regress of events,
which Craig claims is impossible.
Note
that even if the events are increasingly shorter, that would be an
actual infinity under a tenseless theory of time, or under a
growing-block tensed theory.
Craig claims that even on
presentism, an infinite regress of events/changes is an actual
infinity.
If
so, then Craig's "Hilbert Hotel" argument has a false
conclusion.
Furthermore,
according to Craig, this model entails that time has a beginning at
the singularity.
If
so, we could then conclude, on the assumption of this model, that the
universe contains an infinite regress of events with a beginning
point, and so no tensed theory of time is true: even though the
duration of the events is not equal, and even though the sum of all
of the durations is convergent, the fact remains that it's not
possible to reach an actual infinity of events by finitely many times
adding a finite number of them, starting with only a finite number
(in reality, the model offers no way out of this "singularity",
and adding it is at best superfluous; without that addition, what we
get is a beginningless series of past events/changes, but that's no
better for Craig's position).
But
what if we drop the assumption that we can extrapolate arbitrarily
back in time, and actually take into consideration the fact that
we're not justified in applying General Relativity to a very small
universe, where forces other than gravity should be taken into
consideration?
In
that case, all we could say is that the universe was in a hot, small,
dense state S1 at some time t over 13 billion years ago, which seems
to have came after a state S2 whose description is beyond
present-day understanding of physics.
So,
the state S2, and the event E(S2,S1): = "The universe
changes from its condition at S2 to its condition at S1" are
both beyond the present-day understanding of physics. And that
is it: There is no suggestion of a beginning of time,
or of the universe, or anything of the sort.
There
is a beginning of the states of the universe whose
description is within the present-day understanding of physics. Of
course, that fact provides no support whatsoever for the second
premise of the Kalam Cosmological Argument, and thus neither does the
"Standard Hot Big Bang Model".
The
same is true of modern cosmology in general: there is no claim that
there is a beginning of time; models with a metric-finite past only
call for new physics to describe things that are beyond present-day
understanding, but that is all.
So,
science does not provide support for the KCA.
13)
The KCA and a tenseless theory of time
Craig's
KCA is entirely based on a tensed theory of time, but to be thorough,
I will consider in this section whether it could work on a tenseless
theory.
On a tenseless theory, and going by Craig's understanding
of "begins to exist", then the second premise of the KCA is
not true.
As
a matter of fact, on a tenseless theory of time, nothing
begins
to exist in the
sense of "begins to exist"
proposed by Craig,
since there are no tensed facts.
However,
his understanding of 'begins to exist' does
not seem to match common usage,
so someone might reject it and still try to make the KCA work.
Yet,
there are insurmountable problems for that task:
First,
as earlier
sections
show,
Craig's philosophical arguments against an infinite past fail even
under a tensed theory. That does not change on a tenseless theory.
Second, while a theist might try alternative arguments, that
might also be said of a KCA run on a tensed theory; in any case, the
burden would be on the claimant, but the KCA has been discussed for
many years, and it's hard to see what kind of new argument might
work, after every argument so far failed.
Third,
arguing against an infinite past on a tenseless theory has very
counterintuitive results, and even though our intuitions might not be
reliable, usually KCA defenders try to appeal to intuitions, so
counterintuitiveness is at least a problem.
For
instance, on a
tenseless theory of time, it appears that the past, the present and
the future are ontologically equivalent. So, it seems then that any
successful argument for the metaphysical (or logical) necessity of a
beginning of time could be adapted to be an argument for the
metaphysical (or logical) necessity of an end
of time. At least, that is very
counterintuitive,
Perhaps,
an alternative would be for a theist to argue for the claim that even
if a beginning of time may not be logically or metaphysically
necessary, it is at least factual.
However,
that kind of argument would have to be empirical, and there is no
support in present-day cosmology for such a claim: even if a
scientific model posited no infinite regress of events the universe
in a very narrow
sense of the word "universe",
they would probably make no claim about an entire series of past
events, which might comprise an older universe, multiverse, etc.
In
any event, there seems to be no good reason to assume
such impossibility.
So,
for all of the reasons given earlier in this section, it seems that a
KCA run on a tenseless theory of time would fail as well.
14)
The (purported) a cause of the universe: further analysis
Given
that there
seems to be no sufficient reason to accept the first premise of the
KCA,
then it seems the argument failed.
Still,
assuming that the universe had a beginning and a cause, earlier in
this article, I've analyzed some of the consequences of the
properties assigned by William Lane Craig to the cause of the
universe, showing that a
contradiction is entailed.
I
also assessed Craig's
reply to that contention,
showing that it's inadequate.
In
this section, though, I will assess mostly other arguments in which
Craig uses conceptual analysis in order to support of some of the
claims about the properties of the cause of the universe, whose
existence is allegedly established by Kalam Cosmological Argument.
[26]
14.1)
A single first cause?
Before
addressing the conceptual claims, I will assess a different one:
According
to Craig, the philosophical arguments in in the KCA show that there
is a first cause, not only a cause of the universe.
In
addition, he claims we ought to posit a single cause, not many,
allegedly due to Occam's razor. [9]
Even
assuming that the KCA succeeded in establishing both a cause of the
universe and a first cause, that would not be a proper use of the
razor:
First,
if we do not know what caused a hot, dense state of the universe that
existed about 13.7 billion years ago, there is no warrant for
believing that it had a single cause, or that that particular cause
was in turn uncaused.
Cosmologists
understand that, and keep trying to find better models – models
that can describe the early universe as well -, rather than assuming
that the hot, dense, early universe was just brought up by a single
uncaused cause, so science can go on.
Second,
even if we knew that something caused the universe, multiverse, etc.
- i.e., that there is a previous cause that does not match, for some
reason, any description used by physics, today or in the future -,
and even if we knew that there is some uncaused cause, there would
appear to be no reason to make any assumptions about the number of
causes of the universe/multiverse, etc., or that said cause or causes
are uncaused. Who knows?
Still,
let's leave that aside for the sake of the argument, and assess the
rest of Craig's arguments for the properties of the cause of the
universe, assuming that said cause would also be the first cause.
14.2)
Changelessness and immateriality
Craig
maintains that the first cause must be "changeless", since
an infinite regress of changes cannot exist. [9]
But
from no infinite regress of changes one can only infer from that is
that there has to be a first change, not a 'changeless' state, unless
'changeless' only means a first state with no previous changes.
However
– assuming for now that Craig's claim of changelessness is
meaningful -, Craig seems to mean a lot more than the lack of
previous changes by "changeless", since he claims that the
first cause exists in a state of "absolute changelessness",
which [9],
which is allegedly impossible for particles and the like. So, it
seems that he's not only claiming that there was a first
change/event. But if he's claiming something else, then it seems
changelessness does not follow from a lack of infinitely many past
changes.
In
any case, I've already
showed
that a first state of God wouldn't be changeless, and if we assumed
it is, the same would be true of a similar first state of the
universe.
In
addition, Craig claims that, since the first cause is changeless, the
first cause is also immaterial.
However,
that's another mistake, since the first cause proposed by Craig
changes
just as the universe does,
in a similar
scenario.
Leaving
aside potential problems with the concept of "immaterial",
clearly the conclusion is not warranted, as the claim that the cause
is changeless is not warranted, either.
14.3)
Timelessness and the open interval variant
In
earlier
sections,
I
already
made
a
detailed
case
against
the claim of timelessness of God as the first cause.
In
this subsection, I will consider an alternative: someone might accept
infinitely many past events/changes without a beginning point, and
then still claim that God is temporal with creation – on a
tensed theory of time -, and timeless without it.
That's
incompatible
with Craig's position,
but someone else might raise that issue.
However,
that would be of no help for the defender of the KCA: not only do the
arguments in support of the premises fail just
as
before,
but if the proponent of the KCA accepts infinitely many past
events/changes, then they ought to accept the possibility
of
infinitely many past years,
since the difference in duration of the events/changes, and whether
they are equally long, are
not relevant matters from the perspective of whether a tensed theory
of time allows such infinite regress.
However,
the possibility of infinitely many past years defeats the KCA, as one
might simply posit that, perhaps, there is an infinitely old universe
or multiverse, before the states of the universe describable by
present-day physics
14.4)
Spacelessness
The
property of spacelessness allegedly follows from timelessness and
immateriality.
Since
I already showed that the claim of timelessness fails, that is
sufficient to show that the claim of spacelessness fails as well,
since it's unwarranted.
But
let's leave that aside for the moment and for the sake of the
argument, and let's also assume that the timelessness claim makes
sense. Then, why can't, say, a multidimensional manifold be timeless?
Why not some sort of field?
There
is no need for particles, for instance.
Note that it wouldn't
help to say that any field would "immediately"
change,
make
particles, etc., since with the same criterion, any "timeless"
object also "immediately" changes, as
the previous arguments
show.
And
if a field or something like that can be "timeless", but
can't be immaterial, then timelessness does not entail immateriality,
anyway.
So,
the claim of spacelessness only adds more problems to the
insurmountable problems an argument for theism based on the KCA
already has.
14.5)
Power
According
to Craig, the first cause must be very powerful, since it caused all
of "physical reality" to exist, without any material cause.
[9]
Leaving
aside issues about the concepts of "material", and
"physical", and of course the decisive objections I
explained earlier, the claim that the object in question is very
powerful does not follow from that.
In
other words, given the assumption that some entity is the cause of
the universe, it might be – purely for example – that the
object in question is only capable of causing things like our
universe or similar ones, and is incapable of acting within them, or
making much of anything else, etc. There are plenty of options.
Moreover,
it might as well be incapable of changing at all, so it wouldn't be
able to learn anything at all.
14.6)
Personhood
Craig
gives three arguments in support of the claim that the first cause is
personal:
14.6.1)
Personal explanations and scientific explanations
Craig
claims that, as Swinburne "points out", there are two kinds
of explanations: personal and scientific. [9]
Of
course, Swinburne argues for that, but the matter is surely
contentious.
Craig
does not defend the distinction, and it would be beyond the scope of
this article to show all that's wrong with Swinburne's claim, but I
will point out that a personal agent acting on some volition can also
be put in terms of a law and some conditions.
For
instance: "If agent A decides X, then X happens", and
"Agent A decides X" would be a way of putting it in such
terms.
If
an agent with a "timeless" volition is posited as a cause
of the universe that is temporal with the universe, and one assumes –
against
very
strong
reasons – that
the claim is coherent, then one might as well posit some non-personal
timeless stuff, with the property that it causes –
deterministically or not – the universe.
There
would be initial conditions too, but – one could say, mirroring
the theist's claims – not initial in a temporal sense, but in
the (mysterious) "timeless" sense in which Craig's deity
would be timeless, and whose coherence I'm assuming in this
subsection
and
merely for the sake of the argument.
14.6.2)
Other properties of the alleged first cause
Craig
maintains that, is based on his previous conclusions, the first cause
is timeless, immaterial, beginningless, uncaused, and spaceless. [27]
However,
as I've shown in the previous sections of this article, those
previous 'conclusions' are at best unwarranted, when not
clearly untrue, so this claim fails as well.
14.6.3)
'Free agency'
The
third avenue Craig takes, in order to support the claim that the
first cause is personal, is based on what he calls "free
agency", and "agent causation". [27]
While
I have no objections to the claim that, say, humans sometimes act on
their own free will, that does not have anything to do with
non-determinism; further, the kind of "freedom" posited by
Craig should not be characterized as "freedom", but more
properly randomness, and randomness surely does not require
agency, or even minds.
But
let's take a look at the matter in more detail:
First,
Craig claims that because the agent is free, he can bring about
things in absence of previously conditions determining it. [27]
That
clearly is not a good characterization of human freedom, and while
Craig is talking about God, he's using an understanding of freedom
allegedly based on human freedom.
Yet,
indeterminism in humans has nothing to do with freedom in humans –
or rather, it might get in the way.
To
see that, let's consider the following
scenario:
Alice
has been a good police officer for ten years.
She's
kind, committed her job, good to her children, and so on.
Now,
one morning, Alice goes to work as usual.
The
police get a call about a domestic disturbance, and Alice and another
officer are sent to the address they're given.
When
they arrive there, they encounter Harry, a thirteen-year old kid high
on drugs, acting completely irrationally.
He
tells Alice: 'You're a police officer, so you're evil. Why don't you
shoot me?'
Alice
has no reason at all to shoot Harry.
He
poses no threat to her, and can be easily arrested if needed.
However,
it's clear that she has the power to shoot him, and
is free to choose whether to shoot him.
All
she'd have to do is pull her gun, point it at Harry, and shoot.
No
one would see that coming, so no one could stop her if she did that –
no human, anyway; the point is that she wouldn't be stopped.
But
Alice – of course – feels no inclination whatsoever to
shoot Harry, does not shoot him, and follows procedure.
The
point is that saying that Alice can
shoot Harry, that she
has the power to
shoot him, that she is free
to choose whether to shoot him, etc., means that she would shoot him
if she chose to do so,
that she's not being
coerced, etc.
It
does not at all mean
that, even given Alice's mental state at the time she chose to
follow procedure, and even given all
the conditions of the world at that time and previous times –
including Alice's goals, beliefs, character, etc. -, it was still
possible that Alice would shoot Harry.
On
the contrary, if, given all those previous states, it was possible
that Alice shot Harry, then it seems that there is a possible world W
with the exact same past as ours prior to Alice's decision to follow
procedure, at which Alice shot Harry instead.
But
that is not an
exercise of freedom, in the usual sense of the words. Rather, it's an
unfortunate event that happens to Alice.
To
see this, let's consider Alice's mental processes leading to her
'decision' to shoot Alice – say, decision D. Alice never
considered shooting her, and had no desire, intention, etc., before
decision D happened.
However,
at some time, earlier states of the world, including her earlier
mental processes did not determine her later mental processes. There
is an event "Alice decides to shoot Harry" that happens
irrespective of any previous states of Alice's mind, and no matter
how much Alice would loath being a murderer.
All
of Alice's previous reasoning, desires, behavior, intentions, etc.,
are incapable to stop 'decision' D from happening. But how's
that Alice's decision?
It
seems D is not a decision Alice made, but rather, it's something that
happened to Alice.
It's
not something Alice could have anticipated, or prevented: at some
point her mental processes changed from normal to 'shoot Harry',
without forewarning, and without any cause in previous mental
processes.
Someone
might claim that necessarily,
there is always some hidden
reason to shoot people, or to do anything one
can do, but that would have to be argued for, and even then, that
would not change the fact that, in that case, Alice could not have
prevented his mental processes from changing at some point from
normal to 'shoot Harry', no matter what she did before – and
that change could not be reasonably said to be her decision,
since she had never considered that before, and the change took her
by surprise.
Those
considerations show that that kind of thing should not be called
'freedom', but more like 'an unfortunate kind of randomness'.
That
does not mean that human non-determinism isn't true. But that is
surely not required for freedom, and in fact, it might undermine it,
as the previous scenario shows.
Perhaps,
there are situations after which, after assessing the pros and cons,
a human is undecided between A or ¬A; if so, maybe there is a
truly random outcome generator for such cases (which might involve
also several mutually exclusive options: A1, A2, A3,...)
However,
if that is the case, that is not required for free will: a random
generator that delivers 'decisions' in cases in which the mind
remains undecided clearly does not result in more freedom than a mind
that actually makes decisions.
So,
if there is such indeterminism, as long as the indeterministic events
happen when a person is undecided (based on her previous feelings,
desires, reasoning, etc., she is undecided and does not cause any
outcome), maybe that
randomness is compatible
with free will, but that's all.
On
the other hand, if there is an indeterministic feature of human
behavior that happens to be like Bob's example above – i.e., if
it happens against everything
that the person stood for, his previous considerations, etc. -, then,
and as the previous example shows, that kind of indeterminism –
at least, when it happens – would actually preclude free
will; rather, the 'decision' would be an unfortunately random will.
There
is another way to see this, taking into account that even under
the exact same
preexisting conditions – including, of course, the previous
mental states of the libertarian-free agent.
So,
let's consider the following scenario (relativizing time as
required):
Alice
is a libertarian-free human, and at t(s), the state of worlds W and
W' is exactly the same – that includes, of course, Alice's
mental processes.
Later,
Alice libertarian-freely chooses A at W, and B at W', even though the
states of the worlds prior to Alice's decision were the same (A is
different from B).
In
other words, W and W' are exactly the same until Alice's mental
processes diverge.
Now,
let p be a Planck time, and n a non-negative integer, starting with
0.
Let's
consider times t(s)+n*p, and the states of W and W', W(n) and W'(n)
respectively.
Let
n(l) be the last n such that W(n) = W'(n).
Since
the 'decision' was made even given the exact same
prior conditions, it seems that the 'decision' happened between
t(s)+n(l)*p, and t(s)+(n(l)+1)*p = t(s)+n(l)*p+p, in other words, the
'decision' was made in
not more than a Planck time.
That's
way too fast for any human conscious decision, though. So, it becomes
clearer that the first indeterministic event E that distinguishes
between W and W' is same random alteration of Alice's mental
processes.
Someone
might suggest that, previous processes in her mind made E in
probable, but weren't enough to bring it about, something still
altered her mind randomly; let's assume that that would be a coherent
interpretation of probability (else, this objection fails already).
Even
then, the fact would remain that her mind was altered without a
cause, and with nothing she could do earlier to stop it; moreover, in
some cases, the improbable
'decision'
might happen. And in those cases in which the improbable
'decision'
happens – i.e., the decision that her previous mental processes
made improbable – we're
back with something like the unfortunate case of the
libertarian-free police officer.
Someone
might still object that, if such a random change in her mind
happened, she still could have changed her mind, and refrained from
carrying out the decision – in the case of the first
example,
the shooting.
The
problem is, though, that if you can have such a random event between
t(s)+n(l)*p, and t(s)+(n(l)+1)*p, it seems you can have another one
at
every single Planck time that follows, until
the "decision" that was completely against everything the
person previously stood for, actually happens.
But
let's suppose someone introduces some fuzziness in some way –
which they would have to explain, of course; else, the previous
reasoning stands. Even then, the fact would remain that the agent
would have a random component – a change in her mind she can't
bring about, because it happens no matter what she tried previously;
it's just that we wouldn't be able to see that by means of analyzing
the process step-by-step, but all of the other reasons I've given
above remain.
A
theist might say that that's 'actually the agent acting', or
something like that but – whatever that means -, the fact would
remain that that would a partially random agent acting, not one in
which mental processes are sufficient to bring about behavior; it
would be an agent with a randomly altered mind – i.e., a mind
that suffers some alterations that have no sufficient causes; it's
akin to dice-throwing, and in some cases, it might go against
everything the agent had stood for up till then.
So,
for all of the previous reasons, the claim that non-determinism is
required for freedom ought to be rejected.
That
does not mean we can't act of our own accord, of course. We can and
sometimes do have freedom; it's just that indeterminism is not
required for that.
Now,
there is an objection available to the theist, which seems to be
Craig's position: namely, that is lack of causal determination
that is required for freedom to exist, not lack of determinism.
However,
if an event is determined by previous conditions, then it seems it's
causally determined too, since some the previous conditions would be
causes. How would it be otherwise?
It
seems puzzling.
But
regardless, we can make a case against the requirement of causal
indeterminism independently. If causal indeterminism is true, then no
matter what Alice does up to some time t, all of her thought
processes, intentions, desires, memories, reasoning, are all
insufficient to bring about her decision. So, it seems that the
"decision" might just happen to her, and she might still
shoot Harry.
Again,
the theist might say that that's the agent acting. But how can she
act so quickly - indeed, instantaneously?
Humans
aside, someone might posit that the first cause is God and is not
deterministic, even though as we saw by analyzing the case of humans,
indeterminism surely isn't a requirement for freedom, and can at best
hamper it.
However,
that fails as well, as explained earlier,
since – at least – one may as well posit a
non-deterministic universe as an alternative that the theist defender
of the KCA has failed to refute.
Of
course, the non-theist need not be committed to indeterminism, or an
indeterministic universe, or a first cause, etc.; she may simply
posit that there are alternatives that the theist defender of the KCA
hasn't refuted.
14.7)
The meaning of "God"
As
previous arguments show, Craig's arguments fail to support the
conclusion that there is a first cause, or a cause of the universe,
or that – assuming that there is such a first cause -, the
cause has the properties he claims it has.
But
there is one more point I'd like to address here, and it's about the
meaning of "God":
William
Lane Craig:[28]
5.0.
Therefore, an uncaused, personal Creator of the universe exists, who
sans the universe is beginningless, changeless,
immaterial, timeless, spaceless, and enormously powerful.
This,
as Thomas Aquinas was wont to remark, is what everybody means by
“God.”
Actually,
that is not what everybody means by 'God'.
Plausibly,
it is not even be what most
people mean by 'God', or what most
philosophers mean
by 'God'.
For
instance, by 'God', Richard Swinburne[29]
means
"a person without a body (i.e., a spirit) who necessarily is
eternal, perfectly free, omnipotent, omniscient, perfectly good, and
the creator of all things".
There
is nothing in Craig's description quoted above that entails
omnipotence, omniscience, moral goodness – let alone moral
perfection -, etc.
Moreover,
Swinburne explicitly denies that timelessness is part of the meaning
of 'God'. [29]
But
let's take a look at the matter from another perspective:
If
an omnipotent, omniscient, morally perfect creator of all other
beings existed, and moreover he intervened in human history, but he
were not timeless, it would be hard to find many people saying that
God does not exist, on account of a lack of timelessness (assuming
that "timeless" is meaningful, that is).
The
same goes for changelessness.
On
the other hand, if an entity like the one Craig describes existed
(assuming again that the description is coherent),
but – for example – he were not omniscient, not
omnipotent, not morally perfect (or even morally good), and never
intervened in human history – no afterlife, either -, it seems
to me that plenty of people would be inclined to say that God does
not exist, without
committing an error.
In
fact, even if the Kalam Cosmological Argument – or, more
generally, any argument – succeeded in showing that the
universe has a cause, and even if further argumentation succeeded in
showing that said cause is an intelligent being with some of the
properties Craig ascribes to him in the previous quotation – or
all of them, assuming they all make sense -, that would still not
establish that God exists, in the sense the word 'God' is used by
many, plausibly most theists, and would be compatible with –
for instance – deism.
15)
Conclusion:
The KCA provides no
support for theism, both on William
Lane Craig's version of the Kalam Cosmological Argument, and on many
other actual or potential versions.
Furthermore,
there appears to be no good reason, based on present-day science or
philosophy, to suspect that that's going to change: there are
numerous problems, and several of them appear clearly insurmountable.
Notes
and references:
[1]
Source: William Lane
Craig and J.P. Sinclair, "The Kalam Cosmological Argument",
in "The BlackWell Companion to Natural Theology", Edited by
William Lane Craig and J. P. Moreland, © 2009 Blackwell
Publishing Ltd. ISBN: 978-1-405-17657-6
Page 102.
[3]
Source: William Lane
Craig and J.P. Sinclair, "The Kalam Cosmological Argument",
in "The BlackWell Companion to Natural Theology", Edited by
William Lane Craig and J. P. Moreland, © 2009 Blackwell
Publishing Ltd. ISBN: 978-1-405-17657-6
Page 106.
[4]
Source:
http://www.reasonablefaith.org/site/News2?page=NewsArticle&id=5673&printer_friendly=1
[5]
Source:
http://www.reasonablefaith.org/site/News2?page=NewsArticle&id=5971
[6]
The choice of the
change in God from timelessness to temporalness as the event is only
one possibility.
There are
alternatives. For instance, let say the actual world contains a state
of affairs S at which God exists timelessly.
Then, at S, time
does not exist, so it's not the case that God knows that time exists.
On the other hand, at t=0, God knows that time exists.
Let E(1)
be the event “God comes to know that time exists”
Another alternative
would be:
At S, there are no
tensed facts. So, it's not the case that God knows any tensed truths.
At t=0, there are tensed facts, so God knows tensed truths. Thus,
God's mind changed – he came to know tensed truths -, and one
can consider the event E(2) “God changes from not knowing any
tensed facts at S, to knowing some tensed facts at t=0”.
[7]
Source:
http://www.reasonablefaith.org/site/News2?page=NewsArticle&id=9269
[8]
Source:
William Lane Craig and J.P. Sinclair, "The Kalam Cosmological
Argument", in "The BlackWell Companion to Natural
Theology", Edited by William Lane Craig and J. P. Moreland, ©
2009 Blackwell Publishing Ltd. ISBN: 978-1-405-17657-6; page 116.
[9]
Source:
William Lane Craig and J.P. Sinclair, "The Kalam Cosmological
Argument", in "The BlackWell Companion to Natural
Theology", Edited by William Lane Craig and J. P. Moreland, ©
2009 Blackwell Publishing Ltd. ISBN: 978-1-405-17657-6. Page 192.
[10]
https://en.wikipedia.org/wiki/Big_bang
[11]
W.
L. Craig and J. P. Sinclair
In
affirming that things which begin to exist need a cause, the
mutakallim
assumes
the following understanding of that notion, where “x”
ranges
over any entity and “t”
ranges over times, whether instants or moments of nonzero finite
duration:
A.
x begins
to exist at t iff
x comes
into being at t.
B.
x comes
into being at t iff
(i) x exists
at t, and
the actual world includes no state of affairs in which x
exists timelessly, (ii) t
is either the first time at which x
exists or is separated from any t′
< t at
which x existed
by an interval during which x does
not exist, and (iii) x’s
existing at t is
a tensed fact.
Source: William Lane
Craig and J.P. Sinclair, "The Kalam Cosmological Argument",
in "The Blackwell Companion to Natural Theology", Edited
by William lane Craig and J. P. Moreland; pages 184, 185.
[12]
Source:
William Lane Craig and J.P. Sinclair, "The Kalam Cosmological
Argument", in "The BlackWell Companion to Natural
Theology", Edited by William Lane Craig and J. P. Moreland, ©
2009 Blackwell Publishing Ltd. ISBN: 978-1-405-17657-6; page 184.
[13]
Assuming
here, and for the sake of the argument, that "timeless" is
coherent.
[14]
Source:
William Lane Craig and J.P. Sinclair, "The Kalam Cosmological
Argument", in "The BlackWell Companion to Natural
Theology", Edited by William Lane Craig and J. P. Moreland, ©
2009 Blackwell Publishing Ltd. ISBN: 978-1-405-17657-6; page 182.
[15]
Of
course, a potentially serious problem may be the reliability of our
intuitions in such cases, but that's no help for someone claiming
that the first premise ought to be accepted, or even merely that it's
rational to do so.
[16]
Readers,
of course, will check the matter by their own intuitions, as always.
[17]
Incidentally, if we take objects in daily life as examples for
inductive arguments, we might as well conclude that no object is
timeless, or that all personal beings came into existence, and so on.
[18]
Source: The
Blackwell Companion to Natural Theology
Edited
by William lane Craig and J. P. Moreland; page 109.
[19]
By
“Set A minus set B” I mean the set C whose elements are
all the elements that are in A, but are not in B.
[20]
Source:
William Lane Craig and J.P. Sinclair, "The Kalam Cosmological
Argument", in "The BlackWell Companion to Natural
Theology", Edited by William Lane Craig and J. P. Moreland, ©
2009 Blackwell Publishing Ltd. ISBN: 978-1-405-17657-6.
Page
119.
[21]
Sources:
For
Craig's argument: William Lane Craig and J.P. Sinclair, "The
Kalam Cosmological Argument", in "The BlackWell Companion
to Natural Theology", Edited by William Lane Craig and J. P.
Moreland, © 2009 Blackwell Publishing Ltd. ISBN:
978-1-405-17657-6
Pages
120-124
The
contradiction was first proved by Josh
Dever, in "Worlds Apart", Taiwanese
Journal for Philosophy and History of Science, 10 (1998).
[22]
I'm
stipulating 1 year = 365 days and ignoring leap years, for the sake
of simplicity; a more complicated proof would include leap years, but
it's clear that the contradiction does not depend on whether we count
leap years. Also, the stipulation that the past has the order type of
the negative integers is reasonable, given that Craig considers that
we should reject that alternative due to the 'Tristram Shandy'
argument.
[23]
Source:
William Lane Craig and J.P. Sinclair, "The Kalam Cosmological
Argument", in "The BlackWell Companion to Natural
Theology", Edited by William Lane Craig and J. P. Moreland, ©
2009 Blackwell Publishing Ltd. ISBN: 978-1-405-17657-6
Page
120.
Incidentally,
the 'orbits' argument also fails to distinguish between a tensed and
a tenseless theory of time.
[24]
I'm
using the definition of the cardinal of an ordinal n
as
the least ordinal m
that
can be put in a one-to-one correspondence with n
(ordinals
are sets, and so are cardinals), but that's not important here. The
relevant point is that there is no absurdity or counterintuitive
result, once one takes into consideration what the words actually
mean, under any mathematical definition of cardinality.
[25]
Source:
William Lane Craig and J.P. Sinclair, "The Kalam Cosmological
Argument", in "The BlackWell Companion to Natural
Theology", Edited by William Lane Craig and J. P. Moreland, ©
2009 Blackwell Publishing Ltd. ISBN: 978-1-405-17657-6; page 130.
[26]
Source:
William Lane Craig and J.P. Sinclair, "The Kalam Cosmological
Argument", in "The BlackWell Companion to Natural
Theology", Edited by William Lane Craig and J. P. Moreland, ©
2009 Blackwell Publishing Ltd. ISBN: 978-1-405-17657-6
Pages
191-194.
[27]
Source:
William Lane Craig and J.P. Sinclair, "The Kalam Cosmological
Argument", in "The BlackWell Companion to Natural
Theology", Edited by William Lane Craig and J. P. Moreland, ©
2009 Blackwell Publishing Ltd. ISBN: 978-1-405-17657-6
Page 193.
[28]
Source:
William Lane Craig and J.P. Sinclair, "The Kalam Cosmological
Argument", in "The BlackWell Companion to Natural
Theology", Edited by William Lane Craig and J. P. Moreland, ©
2009 Blackwell Publishing Ltd. ISBN: 978-1-405-17657-6
Page 194.
[29]
Swinburne,
Richard "The Existence of God", Second Edition.
Clarendon
Press Oxford.
Page
7.
