Re: OT: reality (wasRe: Atlantean)

Staving Gary Shannon:


>So many shakey asumptions!  How many members are there
>in the International Organization of Solopsists?
According to several members I've asked, one.

On the subject of unprovable statements, we have Gödel's incompleteness
theorem.
Consider a rule-based system of logical inference which is sufficiently
complex to describe its own axioms and rules of inference.
It is then possible to formulate in that system a statement to the effect
of "Given the axioms and rules of inference of this system, this statement
is unprovable." (Gödel described a method for doing so.)
If the statement were to be false, then it would be possible for the system
to prove a falsehood. It would therefore be inconsistent, and useless as a
method for obtaining truth.
In a self-consistent system, therefore, the statement must be true. It is
therefore unprovable. Thus the existence of true but unprovable statements
is a logical necessity.

Pete

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