Some notes on the incompleteness theorem and shape grammars

The paper presents a critique of the Shape Grammar paradigm viewed through the lens of the incompleteness theorem of Gödel. Shape Grammars have been extensively researched through many lenses. Their productive systemic nature was the focus of the first papers along with more recent treatises in the field while their use in analysis of known building styles has been extensive and a proven mechanism for style analysis. It is surprising though that use of Shape Grammars in actual design in practice however has been minimal. The architectural community has not actively used the paradigm in the design of real buildings, probably because of the rigid analytical approach to style and rules, following from the academic analysis that the paradigm has been subjected to. However I propose that there is another underlying reason, other than the rigid approach to construct a Shape Grammar. The nature of the concurrent application and creation of the rules lies close to the incompleteness theorem of Gödel, that uses a multitude of Turing Machines to prove that a from a set of True Axioms -A- we will never be able to determine if all sentences are true, without having to invent new axioms, outside the initial set -A-, thus unproven in terms of their true or false nature. Negation of this possibility drives us to the conclusion that true Design can never be feature -complete and thus can never be placed in a trusted framework that we all agree or believe it to be the complete truth.