“A scientific model seeks to represent empirical objects, phenomena, and physical processes in a logical and objective way. All models are simulacra, that is, simplified reflections of reality, but, despite their inherent falsity, they are nevertheless extremely useful.”
– learner.com, Scientific Modeling
The problem here, outside the various and contradictory ways in which ‘objective’ is defined, is that beyond very simple phenomena, phenomena so simple that they can only exist within a laboratory setting, scientific models are not especially useful. Any reduction from the original system being modelled has to be a demonstrably valid reduction, i.e. partial differentials cannot be assumed to vanish, they must be demonstrated to do so (which is where Dawkins’ claiming that Aristotle supported reduction as an investigative tool does not qualify as a defence of reductionism, since Aristotle is clear that the reduction has to be demonstrably valid, whereas reductionists make no attempt to validate the reductions they use). Not only is it next to impossible to demonstrate that partial differentials vanish between actually existing systems and their scientific models, the majority of them don’t.
Scientific models are, not ontologically valid (or are inherently false, as stated above), and are always also metaphorical, since the perspective that science views as objective is what things are for themselves and for other things, not what they are for us, which is an impossible actual perspective. Scientific models are generally evaluated using the following criteria:
1. Ability to predict future observations
2. Cost of use, especially in combination with other models
3. Refutability, enabling estimation of the degree of confidence in the model
(the above list included “Ability to explain the past”, but the misuse of this criteria in pseudo-sciences such as evolutionary psychology and sociobiology led me to leave it out. While it is valid for historiology, historiology isn’t all that relevant in discussing modern natural science. It also included “aesthetic appeal”, using Ockham’s Razor as an example, but since Ockham’s Razor is arguably the most disproved theory in the history of science, I left it out as well).
However, if partials do not vanish (or become irrelevant overall to the results of using the model to predict observations) Keynes criticism of Pigou’s economics applies to all science:
“The pitfalls of a pseudo-mathematical method, which can make no progress except by making everything a function of a single variable and assuming that all the partial differentials vanish, could not be better illustrated. For it is no good to admit later on that there are in fact other variables, and yet to proceed without re-writing everything that has been written up to that point.”
Keynes, John Maynard (2010-12-30). The General Theory of Employment, Interest and Money (p. 232). Signalman Publishing. Kindle Edition.
The obviousness of the failure of mathematical reductions in the social sciences arises from the relative complexity of the matter being studied, not any intrinsic difference in the topics, although the reflexive nature of some social sciences does add even more complexity, since what is being studied is not merely intelligible, but intelligent, the results of the study have a reflexive impact on those studied. In any case, once the so-called ‘hard’ sciences begin to study anything with any systemic complexity, mathematical method fails, and the result is precisely the type of pseudo-mathematical method Keynes is criticizing. We have been operating on the invalid assumption that reality is mathematical, not that mathematics, as a language designed for ontology, approximates nature. This is the same error made by those who see reality as approximating Euclidean geometry, when of course it is the other way around.
The reduced models of mind, or psyche, are held onto optimistically by neuroscientists and cognitive scientists when evidentially they do not work. This is nothing but a favouring of ideology over evidence that science specifically claims to be immune from. The positive is that the reduction can be demonstrated to be invalid, the negative is that a majority of researchers in the field prefer to hold onto the invalid reduction than consider other possibilities, which in itself is evidence of the common behaviour of the human mind. The double failure, then, is both in the reduction, and in a prior and subsequent failure to look at evidence regarding cognition from one’s own cognitive experience. The argument that such evidence is ‘merely subjective’ is a ridiculous one, since the thought has neither been demonstrated to involve the subject, merely the self, nor can ‘objective’ study properly appropriate its object, since the object of cognitive science is precisely thinking, something that can only be directly experienced as one’s own thinking.
While reduction is a valid method in specific cases, any reduction has to be validated in that it accounts for all aspects of the phenomena under consideration. Any failure to account for specific aspects indicates an invalid reduction. As an example, in recent studies of “split-brain” patients to attempt to determine the number of operative “minds”, demonstrated that the reduction of mind to physical brain processes is an invalid reduction, since the reduction failed to account for both the separability (in laboratory controlled tests) AND the unity in usual behaviour. If the reduced model can only account for one OR the other, yet both are observed, then the reduced model has to be abandoned. It’s not enough to simply say that under the reduced model a difficult question is indeterminate, because the indeterminacy is not, as is quantum indeterminacy, a basic inability to observe two possible results, but instead both are observed, and the failure is to account for both given the theoretical framework used. Since other possible frameworks do provide a means for accounting for both sets of observations, evidentially the reduction is invalid.
The question, though, in terms of analysing systems that are too complex for a simple model to provide any predictive value whatsoever, is that the model has thereby lost any validity. If it is not actually a description of reality, nor has any predictive validity, is extremely expensive to use (use of scientific method costs up to 40x attaining the same results with other methodologies used in knowledge work), and is 100% refutable since it has neither observable nor predictive verifiability, by the tenets of modern science itself, modern science itself is a failure as a worthwhile model of reality.