The formal analysis of the logical foundations and methods of a mathematical discipline may be regarded as interesting in itself, and Abstract Algebra offers ample opportunities for such investigations. However, the present work goes beyond mere analysis and sets out to make a positive contribution to Algebra using the methods and results of Symbolic Logic.
At the present stage of the development of Mathematics, the second aim may appear to be unduly ambitious. Indeed, a book on heuristic methods published recently by a distinguished analyst (G. Polya, ‘How to Solve it’) makes no mention of Symbolic Logic. And going back one generation we may quote H. PoincarB’s comments on Couturat’s claim that Symbolic Logic could fertilise the spirit of mathematical invention.