In some applications of models of complex systems in social sciences and economics two weaknesses can be observed. Specialists in social theories tend to apply mathematical complex systems models, analogies and metaphors without a proper delving into their meaning in the original domains. It can be seen when studying some works on complexity, chaos theory and the similar concepts used in economics and various disciplines of social sciences.

On the other hand, mathematicians, physicists, etc., often tend to apply their models to social phenomena without referring to more sophisticated characteristics of social/economic systems. It results in simplifications limiting relevance of such models to social reality, and in some cases it makes them useless from the point of view of social and economic theory and practice.  

All those abuses are partly caused by vague definitions of complexity applied in the studies of socio-economic phenomena. In his search for explaining the meaning of complexity Seth Lloyd identified 31 definitions of complexity.  Later  this number increased to 45. There is not any commonly accepted definition of complexity and such a definition seems neither needed nor achievable but a deeper understanding of the meaning of complexity in the study of society, which can be in some way depicted as “complexity of complexities”, is needed.

Two basic meanings of complexity can be distinguished – “hard” (objective) complexity expressed with mathematical models of objects of study independent of observer and “soft” (subjective, constructivist) complexity developed in social sciences, and reflecting the relations between an object of study and the observer. 

The aim of the paper is to present a survey of interpretations of complexity applicable in the studies of social systems. The survey includes both “hard” (objective) complexity and “soft” (subjective) complexity.  

Conclusions resulting from the paper can be used by social scientists and economists applying ideas drawn from complexity studies as well as by those who apply mathematical models of complexity in studying various phenomena in society, economy and finance.  

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