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John and Peter are both men
will be an
absurdity
for a two-dimensional being. In its own representation it will take
approximately the following form:
John and Peter are both John and Peter.
In other words, every
logical
proposition of ours will seem an absurdity to it. It is
clear why this should be so. It has no concepts;
proper names
which make up its speech, have no plural. It is clear that the plural of our
speech will seem to it an absurdity.
But where are our 'idols'? What must we get rid of in order to pass on to the
understanding of relations in the many-dimensional world?
First of all we must get rid of the conviction that we see and sense that which
actually exists and that the real world is similar to the world we see. In other words, we
must get rid of the illusion of the material world. We must understand with
mind
all the
illusory nature of the world we perceive in time and space and understand that the
real
world can have nothing in common with it. We must understand that we cannot
represent to ourselves the real world in forms; and then we must understand the
conditional nature
of the axioms of our mathematics and logic relating to the unreal,
phenomenal world.
In mathematics the
idea of infinity
will help us to do this. The unreality of finite
magnitudes as compared with the infinite is self-evident. In logic we may base our
thought on the
idea of monism,
i.e. the fundamental unity of everything existing, and
consequently adopt as our starting point the impossibility of constructing any axioms
consisting of contrapositions, theses and antitheses, on which our logic is based.
The logic of Aristotle and Bacon is fundamentally
dualistic.
If we are deeply imbued
with the idea of monism, we shall conquer the 'idol' of this logic.
The fundamental axioms of our logic may be reduced to identity and contradiction,
in the same way as mathematical axioms. At the basis of them all lies the acceptance of
one general axiom, namely, that every given
something
has
something
opposite to it.
Consequently, every proposition has its contra-position, every
thesis
has its
antithesis.
To the
being of
every thing is opposed the
non-being of
that thing. To the being of the
world is opposed the non-being of the world.
Object
is opposed to
subject.
Objective
world - to the sub-
jective world. Not 'I' is opposed to 'I'. Immobility - to motion. Variability - to
constancy. Multiformity - to unity. Falsehood - to truth. Evil - to good. And, in
conclusion, to every A in general is opposed
not A.
The recognition of the reality of these divisions is necessary for the acceptance of the
fundamental axioms of the logic of Aristotle and Bacon. In other words, this logic
requires an absolute and incontestable acceptance of the idea of the
duality of the world
-
dualism. The recognition of the
unreality
of these divisions and of the unity of all
opposites is necessary for the beginning of understanding of
higher logic.
In the very beginning of this book the existence of the
WORLD
and of
INNER LIFE
was
'admitted', in other words, the reality of a dual division of everything existing, because
all other contrapositions are derived from this contraposition.
Duality
is the condition
of
our
perception of the phenomenal (three-dimensional) world; it is the
instrument
of
our perception of phenomena. But when we come to the perception of the noumenal
world (or the world of many dimensions), this duality begins to stand in our way, to
become an obstacle to knowledge.
Dualism
is the chief 'idol' we have to get rid of.
In order to understand the relations of things in three dimensions and in our logic, a
two-dimensional being must renounce the 'idol' of the
absolute uniqueness
of objects
which requires it to call things only by their proper names.
We,
in order to understand the world of many dimensions, must renounce the
idol of
duality.
But an application of monism to practical thinking comes up against the
insurmountable obstacle of our language. Our language is incapable of expressing the
unity of opposites,
just as it is incapable of expressing
spatially
the relation of cause
and effect. Consequently, we should be prepared to find that all attempts to express
super-logical
relations in our language will appear absurd, and actually will only
hint
at
what we wish to convey.
Thus the formula:
A
is both A and not A
or
Everything is both A and not A
representing the fundamental axiom of higher logic, as expressed in our language of
concepts, sounds an absurdity from the point of view of our ordinary logic, and is
essentially untrue.
We must be prepared for the fact that
it is impossible
to express superlogical
relations in our language.
The formula 'A is both A and not A' is untrue because in the world of causes the
very contraposition of 'A' and 'not A' does not exist But we cannot express their real
relation. It would be more correct to say,
A
is all
But this also would be untrue, because A is not only
all,
but also
any
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