Theories that are all encompassing within a field of knowledge have had an irresistible appeal to scientists through the ages. The extreme ambition in this direction must have been the reductionistic view of a complete hierarchy of sciences, as proposed by Auguste Comte around 1830:

According to him Physics was basic to all the sciences, and Chemistry should ultimately be based on physical principles. Likewise, living organisms no doubt manifest life through chemical processes, so Biology should in its turn be based on Chemistry. Mankind belongs to the sphere of living organisms, and so Psychology should therefore be based on Biology. Finally, Comte's own invention, social science, called Sociology, should be based on Psychology.

Quite formidable a programme to make some kind of Euclidean Geometry out of the entire body of science, and quite credulous a belief in the power of deductive reasoning! As we will see below insurmountable difficulties met even the ambitious attempts to develop a complete mathematical logic as a tool for such reasoning.

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