The Combined Gas Law and a Rasch Reading Law
Many physical laws are expressed as universal conditionals among variable triplets. Newton’s second law, for example, formalizes the relationship between mass and acceleration when holding force constant (i.e., conditioning on) as F = MA. Similarly, the combined gas law specifies the relationship between volume and temperature conditioning on pressure. After transformation (e.g., log pressure + log volume - log temperature = constant, given a frame of reference specified by the number of molecules), each of these laws can be abstracted to a common form (a + b - c = constant). Note that these laws permit causal claims expressible as counterfactual conditionals. If we have 20 Liters of a gas at 2000°K under 20 atmospheres of pressure and we cool the gas to 1000°K, we will observe a decrease in the pressure to 10 atmospheres.
The human sciences, for the most part, lack laws such as those stated above and consequently lack causal stories that are universal in application: "Lacking a ‘complete (causal) theory’ of what influences what, and how much, we simply cannot compute expected numerical changes in stochastic dependencies when moving from one population or setting to another" (Meehl, 1978, p. 814, emphasis in original). In this note we build on the abstracted formalism derived above and imagine the form of a Rasch Reading Law.