In my “God of the Naturally Insurmountable Abyss”
argument, which is an expanded Kalam Cosmological Argument, I claimed that “An
infinite regress of causes is impossible”, but never explained why this
is. Here’s my attempt as a finite being
to explain why an infinite number of things, time, causes, etc cannot exist in
reality.
The first step is to define infinity, which is
not easy to do. Webster’s online
dictionary says infinity is the quality of having no limits or end. As this Numberphile video points out, “Infinity
is not a number. It’s an idea. It’s a concept.” According to the Internet Encyclopedia of Philosophy, there are three types of infinity:
potential infinity, actual infinity, and transcendental infinity. Yikes!
This infinity stuff is difficult!!!
Most people are familiar with the potential infinity, which is
“a non-terminating process (such as "add
1 to the previous number") produces an unending "infinite"
sequence of results, but each individual result is finite and is achieved in a
finite number of steps”.
An example of potential infinity is time. Time
began at the Big Bang. Since then, we’ve
added seconds, hours, years, millennia, etc until we reached the present. When looking toward the future, we will
continue to add units of time into the infinite future. However, at any moment in time you can stop
and you have a finite amount of time between t=0 and t=0+x. The potential
future time is infinite, but it never becomes an actual infinite or a completed
infinity.
An actual infinity is also called a completed
infinity. An example of this is the set
of all numbers. One can continuously
count numbers into infinity, which is a potential infinity. The set of all numbers is an actual
infinity. Another example is length. A yard has a finite length; however, if you
were to start at the beginning of the yard and move only ½ the distance from
the start to the end, and then repeat this at ½ the distance between the ½ way
point and the end, and then repeat this at the ½ the distance between the ¾ way
point and the end, and repeat this again…..you could do this an infinite number
of times (it would never end). The act
of repeatedly measuring ½ the distance is a potential infinity. The yard is a completed infinity because it
contains a potential infinity, but a yard is not infinite. It’s important to note that an actual
infinity does not truly exist, but represents an infinite subset.
So, back to the infinite regress….an infinite
regression is a series of repeating subtractions into negative infinity. One can count backwards from t=0 to t=0-1=-1
to t=0-1-1=-2 to t=0-1-1-1-…. > -∞, but they will never actually reach
negative infinity. It is a potential
infinity because one more unit can always be subtracted from the series. It can never be completed to be an actual
infinity. The infinity symbol, ∞,
represents the concept of not having a limit, but it is not a number anyone can
count to.
If the universe has an infinite past, then as
we rewind the clock past the Big Bang, time becomes an infinite regression to
negative infinity; however, time moves forward.
Negative infinity is not a number and has no limit, so how does one move
forward from negative infinity? There is
no point to start from. Without a
starting point, there is always more time to add before the present so one
never arrives at the present. Actually,
one never arrives at a -1010,000 years either. To say otherwise is treating infinity as a
finite number and not a limitless concept.
A proposed solution is to
say that one can count from negative infinity if they never started
counting but have always been counting from an infinite past. This is
circular reasoning. The conclusion is
presupposed in the premise. This is
essentially saying that an infinite regression is possible if an infinite
regression is possible. This alone makes
the solution logically invalid, but let’s explore the possibility anyway.
Let’s say the past is represented by negative
numbers, zero is the present, and positive numbers are the future. Let’s say you never started counting but have
been counting from an infinite past. An
infinite amount of time later, you are still counting negative numbers. An infinite amount of time after that, you
are still counting negative numbers. An
infinite amount of time after that?
Still negative numbers. To say
otherwise means you haven’t really been counting from negative infinity, which
is an unlimited amount of negative numbers, but have changed infinity into a
number. But there’s a problem with
this…..adding infinity to negative infinity is the same as subtracting infinity
from itself, which has an undefined solution…but it gets worse for infinity!!
Hilbert’s Hotel is a thought experiment
created by David Hilbert, a mathematician, to show how infinity doesn’t work in
the real world. This hotel is infinitely
large and all of the rooms are full. If
an infinite number of people come, it still has room to hold them, since those
in room one can move to room two, and those in room two can move to room three,
etc. If an infinite number of aircraft carriers
come with an infinite number of buses on them each containing an infinite
number of people in them, there would still be enough room even though the
hotel is full. If an infinite number of
people leave, an undefined number of rooms remain full. If everyone in an even-numbered room leaves,
of which there would be an infinite number, there would still be an infinite
number of odd rooms occupied. If all but
five people leave, which would also be an infinite number, there will only be
five rooms filled. An infinite number of
rooms were vacated in three different ways, yet in one scenario there are an
undefined number of full rooms, in another there are an infinite number of full
rooms, and in another there are only 5 full rooms. I think it is safe to agree with Hilbert when
he said this:
“The infinite is nowhere to be found in
reality. It neither exists in nature,
nor provides a legitimate basis for rational thought. The role that remains for the infinite to play
is solely that of an idea.”
The inevitable question then becomes, “What
about God? Isn’t he also infinite?” That’s where the third type of infinity comes
in, the transcendental infinity. According
to the Internet Encyclopedia of Philosophy,
I like to think of it as qualitative infinity
instead of quantitative infinity. God is
omnipotent (all-powerful), so he can do anything that can be done. God is omniscient (all-knowing), so he knows
everything that can be known. God is
omnipresent (all-present), so he is everywhere.
“If you picture time as a straight line along
which we have to travel, then you must think of God as the whole page on which
the line is drawn.” – C.S. Lewis, Mere Christianity
