Antinomies are the guardians of a threshold.
It seems rather reasonable to
suppose that the universe had to begin sometime. Our traditional myths confirm it, they even
ascribe authorship to the action, and even modern mythology tells us of an
instant cero, (or is it a one?) anyway, a Big Bang explosion started everything. If we ignore the idea of an
instant cero, which presupposes an observer beyond what we are saying that
happens, i.e. the universe is the universe plus something else unrelated to it (remnants
of older mythologies) it all seems commonplace and obvious. Then philosophy
steps in (didn’t it step already?)and asks: is that a metaphor or do you really
mean it? Is it not necessary for an explosion to happen that the exploding
thing expands in something which is already there, say, space? Then space and
time were already there, are they objects? Certainly, if they were there, they
cannot be relations among objects for there were not any yet. However, if you
say that space and time were created in the Bang, then your explosion is a
metaphor, but a metaphor of what? What is the literal referent? A beginning,
but how could there be a beginning when there was not time yet? It does not make
any sense to say “the beginning of time”, for beginnings and ends are in
relation to events, and how could time be an event if events are results,
occurrences which presuppose the notion of time? Etc., etc.
Life in this planet had a beginning,
and it will certainly end when the sun becomes a red supergiant, but we cannot
project those intuitions of beginnings and ends to the universe as a whole
(unless for artistic purposes). If we do, we step into antinomies related to transcendental
concepts, concepts that are not in the league of our mathematical logic.
Kant’s first antinomy proved both
that the universe could not have a beginning and that it could not be without a beginning. This was the argument:
A. It had a beginning.
1. Then, there is a pre-time which
is empty time, where nothing precedes anything.
2. Since we cannot make distinctions
of any kind between its elements, we cannot know whether or not anything
exists, nor we can determine the starting point in relation to anything else,
so we would not know if it actually was the beginning.
∴ Therefore, the universe could not
have a beginning.
B. It had not a beginning.
1. Then, between any two moments an
eternity would have elapsed, and also an infinite series of eternities.
2. But we cannot complete an
infinite series through a successive synthesis of thought.
∴ Therefore, the universe could not
be without a beginning.
Thus, we obtain an antinomy.
The argument is based on reductio
ad absurdum as a consequence of our incapacity to think the universe in both
cases. The antinomy is interesting for it points out not to any theories of the constitution of
matter but to the limitations of our rational thinking to the construction of
causal sequences.
Let us give another argument for
the antinomy:
A. It had one and only one beginning.
1. Then, it had to be a single
space-time point starting the sequence.
2. But we cannot think about a
single point, for points are not individual objects and cannot be characterized by their
properties. In fact, none could observe it or even think about it.
∴ Therefore, the universe had not a single beginning.
B. It had no beginning.
1. But we can pick a random set of
points from such sequence and build a reference frame in relation to an
arbitrary set of properties of matter, and boldly declare the set as the
beginning. This seems to be a rather non-philosophical decision, but it is
precisely the one adopted by modern science.
∴ Therefore, the universe had a single beginning.
It does not make any sense to say
that the universe had a beginning, neither that it did not have it, as it does
not make any sense to say that Ra’s Eye (the sun, for us) sees everything, neither
that it does not see anything at all.
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