Logical Basis of Common Sense

Citation

Adamatzky, A. (1998), "Logical Basis of Common Sense", Kybernetes, Vol. 27 No. 2, pp. 200-201. https://doi.org/10.1108/k.1998.27.2.200.2

What is a logical reasoning? How does formal logic relate to uncertainty of human language? Is there a logic in a common sense? Is there a common sense in a logic? Dr Kulik rises and tries to answer these questions in his book.

Since Aristotle until the beginning of the twentieth century the four categorical propositions formed the base of the “proper” reasoning: “all elements of X are in Y”, “no elements of X are in Y”, “some elements of X are in Y”, and “some elements of X are not in Y”. On the considering of X and Y as the sets or geometric planar figures we can express these categorical propositions via Gergonne relations: “X ⊂ Y”, “X ⊂ Y‐”, “X ∩ Y ¬ Δ” and “X ∩ Y‐ ¬ Δ”. Let x and y be some elements of the sets X and Y then the last two propositions can be expressed in the inclusions: “x ∈ Y” and “ x ∉ Y”. The author proves that if the reasoning system of all possible premisses and consequences has no collisions the interrelations between the terms of the system can be represented by the inclusions of different nonempty subsets of some finite sets. It is demonstrated that taking all premisses as nodes of graph and inclusion relations as the edges we can apply powerful techniques of graph theory and algorithms for the investigation of the logical reasoning.

The first, introductory chapter sets humanistic aspects of common sense. Its main theme is Homo cogito in the world of logical myths. The evolution of classical logic is discussed in the second chapter. It leads the reader from the Aristotlian syllogistic through algebra of sets to discovery of possible errors of George Cantor. “The reasoning is the graph”, the third chapter claims. It analyses connections between graph theory and reasonable propositions, abstract models of reasoning, collisions in reasoning and deductive interference of predicate calculus. Here a reader can enjoy explicit graph interpretation of the famous logical paradoxes. The appendix presents the interpretable system of the logical inference with the program realization.

The book is controversial. It balances at the edge of bright ideas and trivial propositions. It considers the problems that attracted the greatest minds during the centuries. And it will be unforgivable to expect the solution of all these problems from the author. As Professor Pospelov writes in his Foreword: “Acquaintance with the contents of the book, if a reader lives in the world of solid mathematical and logical concepts, can induce the whole spectrum of reactions: from stormy admiration to complete rejection of the author’s interpretations of the facts which were stated centuries ago”. I would not say the book is mathematical or philosophical in their modern academic understandings ‐ it rather speaks in the language of the Renaissance. I expect the multi‐modal reaction of the auditorium on this book but the pleasure of reading will be one of the modes.