An Example of Epistemic Reduction in Cognitive Science
A description of theoretic and explanatory reductions and their features is followed by an example of epistemic reduction of a model in cognitive psychology to models in computational neuroscience. The paper also aims to visit the notions of implementation, realization and explanation with respect to reduction as they might be relevant. Only epistemic reduction and its features are discussed in order to restrict the scope of this paper though other forms of reduction exist. Opinions on reductions in general are presented in the final section.
Historically, there have been two models of epistemic reductions: theoretic reductions and explanatory reductions.
1. Theoretic reduction and its features
A theory in one domain of science is termed as reducing theory, say T1, and a theory in another domain is said to be the reduced theory, say T2. Nagel (1961) provided the following features of theoretic reduction that relate T1 and T2 :
Deductibility: T2 is reduced by T1 if T2 is logically deducible from T1
Connectability: T2 is reduced by T1 if T2 is logically deducible from T1 while being aided by “certain statements” that contain expressions from both T2 and T1. These additional statements were termed as bridge principles or reduction functions.
Nagel was essentially saying that the information presented by T2 is invariably contained in T1. Inter domain theories and interlevel theories are reduced in this manner. Nagel took for granted that the theories were prescribed in a formal language amenable to first order logic. Work regarding the nature of bridge principles has been discussed in detail by Sklar (1967) .
2. Explanatory reduction and its features
Reduction in the sense of “explaining a whole by explaining its parts” is applied to scientific accounts that do not yield a law or theory. These accounts may be in the form of observed facts, generalizations of varying scope and/or mechanisms. It makes use of two features: the account provided by reducing statements is termed as the explanans and the account provided by the reduced statements is termed as the explanandum. These terminologies were proposed as per deductive-nomological (DN) models concerning scientific explanations . In the posed argument, the explanandum is to deductively follow as a sound conclusion from the premises of the explanans where the explanans is true. This is the deductive component or feature of the argument. In the explanans at least one of the premises should be a natural law without which the deduced conclusion should not be plausible. This is the nomological component or feature of the argument. What constitutes the lawhood of a statement is a philosophical debate that is beyond the scope of this paper. In more lay parlance, the explanandum provides descriptive statements about a phenomenon and the explanans provides statements about the cause of the phenomenon.
There are other forms of explanations that avoid DN model’s reliance on deterministic laws. These forms of explanations rely on statistical observations and though the generalizations have limited scope they inform the user of at least that limited circumstance.
3. Example of epistemic reduction in cognitive science
In cognitive psychology the concept of memory is elucidated in terms of models and mechanisms. The Atkinson-Shiffrin model is a popular one. An explanatory reduction where this model is reduced by ones in computational neuroscience is illustrated in this section.
The Atkinson-Shiffrin model  postulates that human memory is composed of multiple reserves which support the mechanisms of encoding, storing and retrieval of information. These reserves are labeled as sensory, short-term and long-term memories depending on the time elapsed between the point when information was first encountered by the organism through sensory organs and the point when it was retrieved. Figure 1 illustrates the other assumptions of the model pertaining to the directionality in flow of information.
Figure 1: Atkinson-Shiffrin model (taken from Wikimedia Commons)
It is hypothesised that these mechanisms are within the brain. Without further explanation about how they occur in the brain one can still make use of such information in order to provide an account of things like: how do people in general recant a series of numbers presented to them? However one wouldn’t be able to account for how cranial injuries affect such mechanisms. As is typical of any model, there is something that is outside the scope of what the model explains. By applying explanatory reduction and reducing the Atkinson-Shiffrin model by ones in computational neuroscience we can account for all the information presented in Atkinson-Shiffrin model and answer various other relevant questions pertaining to memory.
Computational neuroscience models of memory such as Hopfield networks utilise statistical information about stereochemical processes affecting neuronal synapses in various parts of the brain. Such models have been able to replicate the persistence of information within the computational network. Depending on how long the information persists in the models, one can explain distinctions such as working, sensory, short term and long term memory as well as the flow of information from one area of the brain to another [5, 6]. The models can predict how lesioning or injuring a part of the brain can influence memory and even the way in which associative thinking can come to exist which, the cognitive psychology models couldn’t account for. In computational neuroscientific models, the statistical information about physico-chemical mechanisms at the synapses capture the information present in mathematical conceptualizations of natural principles concerning chemical potentials and thermodynamics. So in that sense even these neuroscience based explanations can be further reduced to statistical mechanics. In the final section a much more “greedy reduction” is proposed.
4. Consider implementation, realization and explanation with respect to reduction
If a function is realized by a configuration of physicalities, that configuration is said to be the way in which the realization was implemented. It is possible that one may want to apply this style of thinking to evaluate informational content of a theory in order to figure out what type of meaning (realization) arises by virtue of the given explanation (implementation). I speculate that in this paradigm, one can figure out if a reduced theory is a different implementation and thereby provides a different realization or not. Though this paradigm is not explored further in this paper, the objective here is to prod the reader to speculate along these lines.
5. Opinions on reductionism in general
According to me cognitive systems are conglomerations of information with the added functionality to react to information. Cognitive systems can react to themselves in a recursive manner. This view is built using a systems perspective and interpreting Shannon Entropy as a congruent representation of Gibbs Entropy. The idea that Gibbs Entropy and Shannon Entropy are congruent isn’t shared by all who come across the notion of entropy. And this style of “greedy reductionism” in which theories from cognitive psychology perspective are reduced by information theory does not bode well with various scholars though it is conveniently used by systems designers and cybernetics researchers. I’m presenting this information to indicate that even this level of theory reduction is possible and in use. However, I’m also aware that the set of all birds isn’t a bird in itself. There is certainly a different informational content at different levels of inspection and the whole ends up being greater (sometimes drastically and unexpectedly different) than the sum of the observed parts. This can be due to a posteriori knowledge obtained by observing a part within the information domain which was previously unobservable without having the rest of the parts at the level of inspection.
So what must be done with a reduced theory once it is found to be reduced by a reducing theory? The reduced theory may be discarded or it may be rectified and merged into the reducing theory in order to improve the verbiage of the reducing theory. Or, the reduced theory might be retained to act as a scaffolding for better understanding the reducing theory. And, it seems like both theories might stay in vogue at least for the sake of explaining to newly initiated scholars about how the process of reduction was done in that field.
All forms of information – incoherent, inconclusive, incomplete or otherwise – do find their way into academic and collegiate discourse. It is typical of people to personify or anthropomorphize science and I feel this lends a different flavor to the discourse. The flavor more appealing to me does not include personified or anthropomorphized science. To me, science is an opensourced and crowdsourced human endeavor to collectively make sense of what is, what has been, what can be and what ought to be. It is an activity carried out by a commune. Science is not a cognitive system to be able to interact with information even though it is information. Science does not inform us of anything, compendiums of science and scientists do, including the vagrant or excommunicated ones. The natural universe is obviously the largest of such compendiums. If the crowd demands reduced theories and explanations or reducing theories and explanations, then simply provide them.
 Nagel, Ernest (1961). The Structure of Science: Problems in the Logic of Scientific Explanation, 353–354.
 Sklar, L., 1967, “Types of inter-theoretic reduction”, The British Journal for the Philosophy of Science, 18: 109–124. in Batterman, Robert, “Intertheory Relations in Physics”, The Stanford Encyclopedia of Philosophy (Fall 2012 Edition), Edward N. Zalta (ed.), Retrieved on 16th September 2012 from: http://plato.stanford.edu/archives/fall2012/entries/physics-interrelate/
 Woodward, James, “Scientific Explanation”, The Stanford Encyclopedia of Philosophy (Fall 2012 Edition), Edward N. Zalta (ed.), Retrieved on 16th September 2012 from: http://plato.stanford.edu/archives/fall2012/entries/scientific-explanation/
 Atkinson, R.C.; Shiffrin, R.M. (1968). “Chapter: Human memory: A proposed system and its control processes”. In Spence, K.W.; Spence, J.T.. The psychology of learning and motivation (Volume 2). New York: Academic Press. pp. 89–195.
 Bliss, T.V. P. & Collingridge, G. L. (1993). A synaptic model of memory: long term potentiation in hippocampus, Nature, 361(7), 31-36.
 Durstewitz D, Seamans JK, Sejnowski TJ (2000). “Neurocomputational models of working memory”. Nat Neurosci. 3 (Suppl): 1184–91.