1.2.5.6 Godels Theorem




A brilliant young Austrian mathematician then dealt a blow to Hilbert's plan.

If we take as an example the statement

'This mathematical assertion cannot be proved'

If it is not true
then one has a contradiction and mathematics is not consistent.

If it is true
then mathematics is not complete.

Thus mathematics cannot be both consistent and complete at the same time

One must deduce that
in any closed system

undecideable propositions exist