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Induction is the process by which we obtain predictive laws or theories ormodels of the world. We consider the structural aspect of induction. We answerthe question as to whether we can find a finite and minmalistic set ofoperations on structural elements in terms of which any theory can beexpressed. We identify abstraction (grouping similar entities) andsuper-structuring (combining topologically e.g., spatio-temporally closeentities) as the essential structural operations in the induction process. Weshow that only two more structural operations, namely, reverse abstraction andreverse super-structuring (the duals of abstraction and super-structuringrespectively) suffice in order to exploit the full power of Turing-equivalentgenerative grammars in induction. We explore the implications of this theoremwith respect to the nature of hidden variables, radical positivism and the2-century old claim of David Hume about the principles of connexion amongideas.

Abstraction Super-structuring Normal Forms: Towards a Theory of Structural Induction