I’ve been out of town for a few days for a family funeral, so I haven’t followed up on my “Learned Professors” post.
As a result of my studies in logic, I have become convinced that the whole field of formal logic has stagnated since the 1920s. Although classical two-valued Aristotelian logic is widespread and has all kinds of applications from applications from electronics to computer science, there has been comparatively little progress in non-classical logic. This is largely because non-classical logics as they have developed have been either excessively cumbersome or seriously incomplete.
In the 19th century, George Boole pioneered the use of mathematics to represent the truth of mathematical statements. The methods he used were cumbersome and applied largely to classes of things. His logic was enormously simplified by the introduction of a fairly simple concept: The use of the inclusive “or”. Statements and arguments could be translated into mathematical symbolism, manipulated by mathematical methods, and reinterpreted as statements that were equally valid and equally correct, (or incorrect). Reasoning that was difficult or complex when expressed verbally could be simplified. This works well when applied to classical Aristotelian two valued logic. There is excellent agreement between the methods of symbolic logic and those of traditional logic.
However, it has long been recognized that classical Aristotelian logic has some severe limitations. In particular, the insistence that statements must be true or false, with no middle ground, fails to deal with the complexity of the real world, where ambiguity, uncertainty, lack of information, and conflicting definitions abound. It has worked best in mathematics, where objects can be defined without regard to whether they exist in nature. The perfect certainty of mathematics is entirely artificial.
There have been various attempts to extend logic and mathematical reasoning to the realm of the ambiguous and uncertain. These have not worked so well. In future posts, I will review a few of these.
More generally, in dealing with the knowledge base, I’ve been pushing the development of world history. This depends heavily the area I have called sociology. I’ve completed a pass through a historical review. Although I would like to work backward through weeks of 2016, I a setting this aside in favor of reviewing the roots of sociology in institutions and culture. History depends in particular on peoples of the world, and for these I am going through a summary review of history. This is mostly showing me what gaps still remain: Central Asia, Balkan and Scandinavian peoples, and Southern African peoples haven’t yet been fully treated. I am linking nations to particular weeks of 2017, to ease things when I get back to them. For Western Civilization, I have finished connecting cities as far as they have developed, reviewed the connections with other peoples, and I am now going through a review of how the area I call social mechanics applies. I am working on extending the connections of Balkan peoples to other peoples of the world, and getting notes on the history of Greece back through antiquity and prehistory. These are rather slow going.