Logic and the Mechanisation of Reason

Michael Shenefelt and Heidi White, If A Then B: How the World Discovered Logic, (New York: Columbia University Press, 2014).

This is a truly unique book. It is a history of logic, but it is not a normal history. Not too many existential quantifiers here nor barbers requiring a shave. The book seeks to put the study and development of logic into a social and cultural context. It is perhaps a reflection of the centrality of logic to our notions of reason that we have not seen such detailed contextual studies of logic before, even though in other domains, including the physical sciences, such approaches abound.

The authors argue that logic emerged in Ancient Athens because it had a rich, vibrant and open public sphere. Discussion in the public sphere revolved not just around rhetoric and the finer arts of persuasion, but also argument and counter argument. The authors contend, therefore, that it was no accident that logic first emerged in Ancient Athens. Socrates, Aristotle and Plato might weep should they say what now passes for the public sphere despite centuries of intellectual advance.

This is also related to another point, made by many historians of science, namely that naturalistic inquiry also emerged in Ancient Athens because of, with Solon the law giver, the advent of formal laws governing social relations. Put the two together and you have laws of logic.
That’s the argument.

The most interesting aspect to the argument, however, can be found in the early modern period especially the connection between the mechanical philosophy, or mechanism, and formalised treatments or reason. Here’s a key passage from an excellent review of the book at the Mathematical Association of America

In keeping with their emphasis on social history, the authors assert that symbolic logic is “a consequence of an age of machinery” (205), brought on by the Industrial Revolution in Great Britain, Germany, and Italy. Witnessing the “immense power of mechanical operations” (214), logicians were themselves encouraged to adopt a mechanical approach, advocating reasoning by manipulating symbols in a formal way according to fixed rules. This big-picture approach glosses over some significant perspectival differences among logicians and it fails to adequately credit intellectual influences, but it provides a way to link what is happening in logic to what is going on in society. The authors realize that the existence of parallel features in society and logic is no proof of causality and that connecting developments in logic to trends in society is necessarily conjectural (223–224), but they do want to maintain that large-scale mechanization of industry is at least one of the causes that spurred on the new developments in logic (215, 224). They acknowledge personal and intellectual factors behind the innovations as well (the formal analytic trend in British mathematics, Frege’s desire to ground the certainty of arithmetic upon rigorous logical foundations), but they insist on giving significant weight to social movements.

It’s easy to see how one could draw a link between the mechanical world view, the development of symbolic logic and those, what Marc Davis calls, “engines of logic” namely computers. One could argue then that symbolic logic was an attempt, witting or not, to combine a comprehensive ontological world view, mechanism, with the mind through the mechanisation of reason. In this way Descartes’ mind-body duality would be swept away, and with it the mind-body problem.

That’s a stretch. I haven’t read the book, although I do have it.

Perhaps I ought to read it and provide a wee review.

I tend to think that logic is algebra. A simple and dumb statement, I know, but It’s interesting how with algebra one uses rules and set procedures to find an unknown quantity or quantities from those known. Kinda similar to logic, no? But then again, one can say, with logic one in a sense already knows the conclusion it being implicit in the premises you know analysandum and analysans and all that. Grrrh, my brain is fried.