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Reason
Since it requires another statement to prove a statement, it becomes obvious that, in order to demonstrate, one has to
start with something as indemonstratable, or they will demonstrate endlessly. When the indemonstratable is self evident, we
call it an axiom, and it can be used to prove things that are not self evident, but an axiom is not proved. If it is proved,
then it is a theorem, and it will require another axiom to prove it. As such, the process can go one forever, and we can conclude
that nothing is provable. Yet, the statement nothing is provable is self contradictory, because by its own premise, it cannot
be proved. Logic would dictate that its negation is true: everything is provable. But then it would have to be proved that
if not A, then non A holds, and by our original philosophy that would end in endless demonstration. Is what we have here are
two philosophies that seem to be true on the surface, but that contradict one another. This is known as duality, and all musings
end in it. It was the Danish physicist who said “The great truth is a statement whose opposite is also a great truth.”
These two opposite truths are called thesis and anti-thesis.
Science
In looking at nature, the scientist makes a guess, called an hypothesis, to explain what might be going on. An experiment
is conducted, and if the hypothesis is verified, then it is elevated to theory status. But it is only called a theory because
all other possible explanations are not ruled out. When we say that something is a fact, we are really only agreeing that
it is self-evident.
2 paradigms
With a rectangular coordinate system you need only two numbers to specify a point, but with a triangular coordinate system
--- three axes separated by 120 degrees -- you need three. However, a triangular coordinates system makes use of only 3 directions,
whereas a rectangular one make use of 4.
Both the square and the equilateral triangle are useful for measuring area because they are regular polygons that tessellate.
The regular hexagon tessellates as well, but it is too complex to measure area with. If you measure area with the unit triangle,
the three regular polygons that tessellate will have whole number areas. But if you measure area with the unit square you
have the advantage that its height is the same as any of its sides.
Semantics
Take the statement: "If you measure the area of a triangle with a unit square, you have the advantage that its height
is the same as any of its sides." The reason that we know that "its height" refers to the unit square and not
the triangle, is that triangles don't have their height the same as their sides. One meaning of the phrase is silly and the
other makes sense. Thus the reader choses the sensical meaning, and thereby gives meaning to the phrase. But perhaps the meaning
we called silly, is not so silly. Perhaps if we extended ourselves far enouph, we could model a universe where triangles have
their height the same as their sides without being a straight line. Anything is possible and all words have an infinite amount
of meanings. The reason our languages succeed, is that we understand one another. We are all the same, or are sort of a collective
conciousness if you will.
Oneness
All is one. For example, seeming opposites, like deduction and induction, can be seen as the same thing, even though deduction
goes from the general to the specific and induction from the specific to the general. With deduction we say that we give the
reasons that something is so, and with induction we say that experience tells us that something is so. Deduction always has
atleast two premises that connected infer a conclusion. But can not the experiences from which we draw a conlcusion in induction
be the premises for an uncertain deduction, and all is one? Another example that all is one is that though a blank page is
the antithesis of a drawing, it could be considered a drawing of nothing.
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