The problem of modern logic is at bottom no other problem than that of
formal thought and of the origin of thought-forms. Professor Dewey in
the excellent essay which appears as the leading article of this number
says: “Any book of logic will tell us what this conception of thought
is: that thought is a faculty or an entity existing in the mind apart
from facts and that it has its own fixed forms with which facts have
nothing to do—except in so far as they pass under the yoke.” This is
the old conception of thought, rightly criticised by Professor Dewey,
for, closely considered, it turns out to be dualistic. However, as soon
as a proposition is recognised to contain or to rest upon dualism, it
becomes a problem. The problem of modern logic is, How can we arrive at a
monistic conception of logic, how can we rid ourselves of the dualism on
the one side of facts not yet rationalised by the method of thought-forms
and on the other side of mind with its empty thought-forms assimilating
facts to its own nature.
Our solution of the difficulty has been proposed, in the sense outlined
by Professor Dewey, in “Fundamental Problems.” Professor Dewey, according
to our opinion, is right when he says there is no such a thing as
transcendental thought, or pure thought, thought by itself. And there is
no such a thing either as fact, crude irrational chaotic fact. The world
of fact, indeed, is a cosmos and no chaos; there never was a chaos and
never will be a chaos, for the laws of form are an essential and the most
characteristic feature of the world.
Can there be any question how the order found in thought-forms originates
in a world in which the inorganic and unfeeling mineral crystallises in
a regular shape according to strict mathematical laws, i. e. the laws
of form? A world in which the plant grows not otherwise than according
to strict mathematical laws building up roots and stem and leaves and
petals and stamens and all other organs obedient to a certain plan which
will vary according to circumstances, but throughout consistent with
the principles of formal laws? Can there be any question that in this
world of cosmic harmony thought-forms will develop in feeling beings as
a microcosm exhibiting the same regularity and conformity to law as do
in this world all other things animate and inanimate? Our pure, i. e.
merely formal, thought is an abstraction which serves the purpose of
comprehension. And so is the concept “matter,” being that which produces
sense-impressions. There are no such ghosts as pure matter or pure
thoughts in reality.
Modern logic, so far as we conceive it to be right, is by no means an
overthrow of the old formal Logic, generally called Aristotelian. It is
simply an amendment made in order to exclude an erroneous interpretation.
And so is modern mathematics not so much a revolution as an extension
of the old Euclidian system. It is a revolution only against a certain
unclear conception of mathematics according to which this science is said
to rest upon axioms, these axioms representing absolute truth—unprovable,
incomprehensible, and mysterious.[21]
The main truth of monism is that reality forms one indivisible whole
and all our concepts are mere abstractions representing certain parts
or certain features of the whole. As soon as we try to think of any
of them as things in themselves we become involved in inextricable
contradictions. It appears as if the formal sciences contained some
truths which were absolute and independent of actual reality. But let any
one think of any number, of 2 or 3, and he will soon find that conceived
as absolute beings they are meaningless and unthinkable.
This is not to say that numbers are phantoms, but that conceived as
absolute beings they are phantoms. Numbers and all formal concepts
represent something real, they represent pure forms. And form is as much
a part and feature of reality as is matter and energy.