The “Formalist Fallacy”

By Bruce Edmonds


This is the tendency to believe theories more if they are formalised (e.g. as sets of mathematical equations or computer simulations).

This can be simply an effect of Kuhn’s “Theoretical Spectacles” (1962) — due to the fact we can clearly see how a complex mechanism might result in some particular outcomes (due to the formal model) then we project this onto the world. That is, we fit our perception of some part of the world into the conception illustrated by the model. This is the opposite way to how science is supposed to work, where the model should be adjusted (or rejected) in light of the evidence.

Another reason for more readily accepting theories expressed in terms of mathematics is that maths has status. It used to be the case that mathematical models were the only practical formal technique, which is why science became associated with maths. Thus you are much more likely to be published in many journals if your paper is expressed mathematically, regardless of whether the formalism is used to prove or calculate anything.

If an idea is expressed in informal ways then we are freer to express doubt, as we have an instinctual idea of how slippery natural language statements can be. We know that humans are lazy and thus have a tendency to believe their own ideas, unless pretty well forced to change (e.g. by evidence). It should be the case that making ideas precise makes them easier to disprove (as in Popper 1963) but this is only the case if the mapping between the model and what it refers to is also precise. Otherwise one is free to imagine how a model could apply, giving the illusion of generality.

For example, Eckhart Arnold (2005) shows, in detail, how game theoretical models based on around the ‘Prisoner’s Dilemma’ (e.g. Axelrod 1984) fail to have empirical relevance. Other abstract models that have had many citations but do not seem to connect well to evidence include: (Schelling 1971), Hegselmann & Krause (2002) and Deffaunt et al (2002). Each of these is simple, formal but has interesting outcomes. As a result they seem apparently irresistible to other researchers with many citations and influence but no direct modelling relation with the observed world. This contrasts with modelling papers which compare simulated and real-world data (Chattoe-Brown 2018).

Do not mistake me – I think formalising ideas is very useful. It makes sharing the ideas without error or reinterpretation possible, allowing a community of researchers to critique, improve, check, and apply them (Edmonds 2000). It should also be easier to check if they actually work – for example if they do predict some unknown and measurable aspects of an observed system. It is just that formalism, of itself, does not make them more likely to be true (or the resulting models useful for anything that reliably relates to the observed world) but we are more likely to think they are, due to our tendency to project what we clearly understand.


Arnold, E. (2008). Explaining altruism: A simulation-based approach and its limits (Vol. 11). PhD Thesis. Walter de Gruyter.

Axelrod, Robert. 1984. The Evolution of Cooperation. Basic Books.

Chattoe-Brown, E. (2018) What is the earliest example of a social science simulation (that is nonetheless arguably an ABM) and shows real and simulated data in the same figure or table? Review of Artificial Societies and Social Simulation, 11th June 2018.

Deffuant, G., Amblard, F., Weisbuch, G. and Faure, T. (2002) How can extremism prevail? A study based on the relative agreement interaction model. Journal of Artificial Societies and Social Simulation 5(4), 1.

Edmonds, B. (2000) The Purpose and Place of Formal Systems in the Development of Science, CPM Report 00-75, MMU, UK.

Hegselmann, R. and Krause, U. (2002). Opinion Dynamics and Bounded Confidence Models, Analysis and Simulation. Journal of Artificial Societies and Social Simulation, 5(3), 2.


Popper, K. (1963). Conjectures and refutations: the growth of scientific knowledge. London: Routledge.

Schelling, T. C. (1971). Dynamic models of segregation. Journal of mathematical sociology, 1(2), 143-186.

Edmonds, B. (2018) The "formalist fallacy". Review of Artificial Societies and Social Simulation, 11th June 2018.

One thought on “The “Formalist Fallacy””

  1. I think it is very important, as with the KISS debate, to distinguish formal models with different relationships to data. A non empirical formal model can hardly been seen as better or worse than any other non empirical model because what _scientific_ grounds would you use to decide? If a formal model fits data to some extent then this may be a prima facie case for having some value (as it would be for a tentative ABM). However, ABM gives us a “place to stand” regarding why models may fit data but still not be very credible (for example because they are so lacking in calibration that they are infinitely “tuneable”.) One thing that improvements in methodology and more attention to data buys us is the ability to move away from the “two legs bad four legs good” style of argument. It may seem plausible to ABM that all social systems are complex (and therefore only ABM will do) but perhaps we are wrong about that and formal models _can_ capture some social phenomena. But let them _show_ us …

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