Paper - Categorical Social Science: Theory, Methodology and Design by Sallach (2012)

This conference paper from 2012 - cited at length here - is very encouraging as I try to work on category theory within Hodges' model. This is timely too, as a new (northern) academic year begins - post to follow ...

Sallach, D.L. Categorical Social Science: Theory, Methodology and Design. In: Conference Paper - 4th World Congress on Social Simulation. Taipei, Taiwan (September 2012). https://www.researchgate.net/publication/275584554

"The prospect of representing social processes at multiple scales, at an arbitrary level of detail, is likely to produce rich, interwoven models with the potential to provide a more effective map of historical and policy-oriented dynamics. However, this potential will also raise significant challenges in validating such a model [15].

One approach to managing the complexity (both conceptual and computational) of social models is to move them toward a higher level of abstraction."

"Category theory requires specification of a type of mathematical object in terms of identity, composition, and a group of morphisms that preserves their structure. This definition of objects and morphisms, in conjunction with two standard axioms (associativity & identity), defines a framework that is simple enough to be broadly applicable."

Conclusion:

"The present analysis introduces more analytical potential than can currently be demonstrated. Nonetheless, it makes a case for the relevance of category theory for the representation of social applications, and illustrates a variety of ways in which these conclusions are, or ultimately can become, compelling.

Category theory provides a rigorous yet expressive formalism for representing and integrating challenging modeling domains. It is also a formalism that can support extensive theoretical and modeling syntheses, while still maintaining appropriate levels of exactness. These strengths make CT particularly appropriate for providing a mathematical foundation for computational social science.

Ultimately, it is important to return to the issue of the validation of social models. The practical use of historical and/or policy-oriented models is highly dependent upon their credibility. Category theory provides a formalism that can be precise when applied to theory, explicit during the design stage, and definitive at the assessment stage, while also attending to the consistency of intermediate stages. It deserves serious exploration and investigation."