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generated starting from the axioms and rules of the language.33 An axiomatic system that has “off the grid” strings is incomplete in that there are certain strings the axioms are unable to generate unless more axioms were added to make it complete. However, this could also make it internally inconsistent. A complete system, on the other hand, is one where all possible propositions are decidable or meaningful, that is, all nodes are “on the grid.” Euclid’s 5th axiom, for example, was “off the grid” and made the system incomplete.
33 Dr. Stamp. The Aiomatic Colour Game. 10.
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