Redefining Reality - The Intellectual Implications of Modern Science

had turned their attention to logic in hopes that an analysis of the
needed to keep mathematics as the basis of all that was certain.
The heart of traditional logic is the law of the excluded
middle: the claim that either a sentence or its negation, but not
both, must be true. Either you have a brother or you do not. If
you know that one claim is true, then you know the other is
false. And if you know that one is false, then you know that
the other is true.
A paradox is a sentence, or set of sentences, that contradicts itself.
That is, it must be true, but its truth implies its falsity. Because
the law of the excluded middle holds that a sentence cannot be
true and false, paradoxes present an affront to the basis of logic
itself. Logicians were examining purported paradoxes generated
by the logical system, which if authentic, would undermine the
underpinning of our most rigorous form of thought.
This is also what Dodgson was playing with in his famous
work for children. When Alice follows the White Rabbit down
the hole, Carroll wrote, “Either the well was very deep, or she
fell very slowly, for she had plenty of time as she went down to
look about her, and to wonder what was going to happen next.”
of Galileo that all objects close to the surface of the Earth fall
at exactly the same rate. If we take seriously the possibility that
Alice is falling slowly, then we take seriously the possibility
that the immutable laws of the universe no longer apply.
We have entered a realm where the Enlightenment
presupposition of a well-behaved universe whose rules are
accessible to our rational faculties can reasonably be denied.
Reason implies nonsense. Reason is not ultimately justifying
but ultimately self-defeating. Wonderland represents the death
of the rationalist project.
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