CHALLENGES FOR THE LOGIC OF SOCIAL RESEARCH: TO GRASP RATIONALITY, TO DEAL WITH COMPLEXITY
Witold Marciszewski · 2006
The two Herculean tasks ‐ to define rationality, as a basis of social order, and to tackle complexity of social phenomena ‐ require harnessing potent forces and resources of logic. One needs ‘basic logic’, that is, logical calculi to have rules of correct reasonings, then methodological reflexion on the use of mathematical models in social sciences, at last some additions to basic logic. The last involve theoretical computer science to judge the power of algorithms used in modelling, and a study of practical reasoning in social interactions; such a study is provided by the theory of games and decision-making. All that jointly deserves to be called the logic of social research. 1 1. Logic, mathematical modelling, and artificial societies The theory of logic, insofar as we attain to it, is the vision and the attainment of that Reasonabless for the sake of which the Heavens and the Earth have been created. This enthusiastic belief in logic as expressed by Charles Sanders Peirce, is what Evert W. Beth referred to with the motto of his seminal study Semantic Entailment and Formal Derivability (Amsterdam, 1955). In that study Beth succeeded in grasping an essential feature of ‘that reasonabless’ which one finds in first-order logic and the accompanying metalogical reflexion. This is just a part of the idea of rationality, but a part significant enough to be taken it as the starting point of discussion. Beth’s study, inspired by some Gentzen’s idea, offers a very important logical contribution to the notion of rationality. His predicate logic system called semantic tableaux is much worth attention for it represents the most algorithmic approach in solving the problem about an inference whether it is logically correct. It is not the only system of this kind but the one which historically was the first in a chain of similar systems, and is a fitting example to represent this whole chain. The problem of whether a formula of predicate logic is logically valid can be solved in different ways. Some of them involve the guessing of premisses from which the formula in question could be deduced; this gives us opportunity to show invention, but does not guarantee success. In other strategies, 1 This paper was supported with financial means of the State [Polish] Committee for Scientific