Beyond Incompleteness
Sven Gelbhaar
24.03.2019
Back in 1910-1927CE, an attempt was made to enumerate all conceivable
mathematical knowledge in one cohesive system. This resulted in the /Principia
Mathematica,/ wherein premises were postulated, and their results or conclusions
were then utilized by subsequent entries to arrive at a list — a cohesive list
of all mathematical functions and their abstract derivatives. As the reader
undoubtedly already knows, a young mathematician at the time by the name of
Kurt Goedel proved that no such system can be all-inclusive by codifying extant
postulates as self-referential systems themselves. Meta-knowledge, in other
words. What the reader might not already be aware of is that a philosopher by
the name of Georg Wilhelm Friedrich Hegel did something just as cunning years
prior.
Hegel stipulated that for the human will to be free, that it needs to be
unbound. That is to say that the will needs to have an infinite scope in order
to be truly free. I’ll leave the rhetoric as to why for the reader to find out
for themselves, but be consoled, he goes into this rather early in his famous
work /Philosophy of Right/. I also cover this in paper 47 of my /Occam’s
Razor/ series, entitled /Response to Hegel’s free will argument/.
And so we come to the point of this paper. How do we extend anything into the
realm of the unbound? How do we add an infinite scope to our postulates?
Certain properties are inherently infinite: Set theory, as Goedel proved; The
very concept of infinite scope as per the Hegelian argument; and the following
of my own addition. To this list we can add dimensions in themselves, such as
space and time. Any meta-concept wherein Zeno’s paradox can be applied, which
Planck almost destroyed for us with his pesky Constants, but certainly Planck
no longer has any sway with every “discovery” of new fermions and quarks that
are touted in the physic’s community these days.
The concept of Meta- itself is another viable method of bringing Incompleteness
to bear. We see this with the multiverse theory, wherein supposedly every
conceivable alternate reality is said to “exist” in a separate universe of its
own.
The supreme will of god(s) is falling out of favor these days, which used to be
a potent method of Incompleting any veritable system of things/widgets/sets.
God having a will concerning the meta-verse that s/he/it operates in is, as
Hegel and the Meta- both suggest, could imbue any concept with infinite scope.
Last and least importantly there is the concept of randomness. Most people
believe in this concept intuitively, although the intelligentsia know that this
is a myth from a practical standpoint. As Physics in and of itself testifies,
this world is deterministic; causality is an active principle in the world we
inhabit. Determinism cannot result in anything random. Mathematicians create
stochastic mathematical functions by throwing in variables to a running timer
so that when user input is detected the timer spits out a “random” number, as
to the computer/calculator/what-have-you the input comes at a “random” point in
time and content. This, as any rational creature could tell you, is not
exactly random. It is simply tying in so many variables together that it cannot
be predicted with any reasonable amount of resources, but is ultimately
predictable.
Just for the sake of irony, I will end my list of liberating conceptual
frameworks here. Undoubtedly someone more clever than I will append his or her
own addition to this paper in due, finite, time.
Notes for this paper:
Can willing (itself) be regulated by the will? Can I will myself to
will/desire something at a specific point in time? I think this is something
that can be done through practice, thereby adding a Goedel-ian aspect to will
which leads infinite scope and thereby freedom of will. Allow me to
demonstrate:
Freedom concerning will requires the will to act of its own volition with
infinite scope.
If the will cannot self regulate, it could become the environ’s slave. A 1:1
relationship could, or rather does, occur with certain stimuli:response
relationships.
The Will, being self-regulated, can overcome such obvious dependence or
isomorphicism to reality.
super-stratum: certain conceptual frameworks (set theory) imbue substrata with
infinities; inverse of this is planck X / non-zeno’s.
floating in a sea of infinities you’ll therefore chance across islands of
non-infinities analogy: d-branes / multiverse theories
30.03.2019: the decimal place of the last digit of pi or other irrational
numbers, although I’m not entirely sure how you’d tailor these to Incomplete
something.