Redefining Reality - The Intellectual Implications of Modern Science

Which number rules are true? The easy answer would be that there
not establish a complete set of rules for arithmetic.
sentences similar to the sentence “This sentence is false.” If it is
true, then it is false, but if it is false, then it is true.
Any attempt to create rules would allow such sentences as
“This sentence is unprovable” to be proven; thus, we would
have sentences that can be proved but are false. Alternatively,
we could strengthen the rules to exclude these sentences,
but then, because we can no longer prove the sentence “This
sentence is unprovable,” we would have true sentences that
cannot be proved, making the system incomplete.
Any set of rules would either be unsound (include false
sentences) or incomplete (not allow all true sentences to
be proved).
Interestingly, the collapse of certainty
came from Britain in the late 1800s:
Lewis Carroll’s
in Wonderland and Edwin Abbott
Abbott’s
Many Dimensions.
Alice in Wonderland was written
by Lewis Carroll, the pen name
of Charles Lutwidge Dodgson, a
mathematical logician at Oxford.
Because of the ascent of non-
Euclidean geometry and the attempts
In Alice in Wonderland
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