Gödel’s Incompleteness Theorem
states:
“Any effectively generated theory
capable of expressing elementary arithmetic cannot be both consistent
and complete. In particular, for any consistent, effectively
generated formal theory that proves certain basic arithmetic truths,
there is an arithmetical statement that is true, but not provable in
the theory.”
To briefly state the implications of
this:
All predictions about the
future are inductive. Outside the circle. In Gödel’s language they
are “undecidable propositions.” It’s probable you’ll still
have your job next week… but maybe you don’t.
All scientific laws are based
on inductive reasoning. All of science rests on an assumption that
the universe is orderly, logical and mathematical based on fixed
discoverable laws.
You cannot PROVE this. (You
can’t prove that the sun will come up tomorrow morning either.) You
literally have to take it on faith. In fact most people don’t know
that outside the science circle is a philosophy circle. Science is
based on philosophical assumptions that you cannot scientifically
prove. Actually, the scientific method cannot prove, it can only
infer.
(Science originally came from
the idea that God made an orderly universe which obeys fixed,
discoverable laws – and because of those laws, He would not have to
constantly tinker with it in order for it to operate.)
All closed systems depend on
something outside the system.
You can always draw a bigger
circle but there will still be something outside the circle.
Whatever is outside the
biggest circle is boundless. So by definition it is not possible to
draw a circle around it.
If we draw a circle around
all matter, energy, space and time and apply Gödel’s theorem, then
we know what is outside that circle is not matter, is not energy, is
not space and is not time. Because all the matter and energy are
inside the circle. It’s immaterial.
Whatever is outside the
biggest circle is not a system – i.e. is not an assemblage of
parts. Otherwise we could draw a circle around them. The thing
outside the biggest circle is indivisible.
Whatever is outside the
biggest circle is an uncaused cause, because you can always draw a
circle around an effect.
If you visit the atheist
website Infidels, you will find the following statement:
As defined by philosopher
Paul Draper, naturalism is "the hypothesis that the natural
world is a closed system" in the sense that "nothing that
is not a part of the natural world affects it."
But according to Gödel’s
theorem, every system is dependent on something greater being outside
the system. Draper's hypothesis cannot be correct. Because the
universe is a system, it has to have an outside cause. A cause that
is not bound by time, matter, or energy, because it is outside of all
those, and they are subject to its control. A cause that cannot
itself have any cause, because it is outside the widest circle. A
cause that is infinite in every way, because it's not a system that
can be encircled. You can call that what you want; I call it God.
Atheism's denial of God flies
in the face of a basic law of mathematics.