When considering any system for the purpose of inquiry, be it from deductive or inductive processes, a central component of the actual mechanism of consideration tends to be abstraction. By this, I mean that when one ‘considers’ a system in such a way that new information can be produced via inquiry, they are actually considering an abstraction, with the relevant characteristics of said abstraction being analogous in some way to the original system.
While this is often recognized as a crucial part of the thought process involved in making positive intellectual contributions to any discipline, the actual process and mechanism of abstraction at the conception level is often whisked away as something that can only be accounted for by referring to such nebulous notions such as intuition and induction. While I do sincerely believe that much progress has been made, philosophically at least, in the grounding of these terms on much more stable and explicit intellectual grounds, I think it is completely misguided to explain the process of abstraction as something wholly dependent on these subprocesses.
While the process of abstraction can often be modeled as an infinite series of comparing and contrasting of every individual of a given classification, comparing the presence of relevant data, there is a lot of meaning baked into the the notion of what exactly constitutes ‘relevant data’ or in more conventional words, relevant similarities between individuals. In its most simple form, the relevant similarities can be found through comparing a group of individuals and discarding all properties that distinguish one from the other. Thus the abstract property of whatever was common between the individuals is born. Of course, this presupposes that there is some commonality that all individuals share, and if one squints their eye of reason hard enough then there will always be some commonality to be found, although it may be too generic to be fertile ground for the generation of novel information. Consider a set of red figures, one can discard all distinguishing features: their shape, size, exact hue, etc. etc. Yet, one will still find that there commonality comes from the way in which they had been labeled in the first place (i.e. they are all red, thus they all have color, they all are figures, they all exist), given the assumptions packed into the way in which the individuals under examination are described. However, the abstract idea of redness emerges not from a movement from the specific to the generic, but from the generic to the specific. The abstract conception of redness doesn’t emerge because the figure has a color, but rather the figure has color because of its redness.The fact that this deduction can only logically operate in one direction to discover novel relevant similarities between individuals hints at a certain unidirectionality of the abstractive process.
In fact, some parallels can be drawn between abstraction and the pure (compared to the applied) sciences. Some could even say that we are abstracting the idea of abstraction (haha) to distinguish the differences between scientific inquiry in its applied and pure forms. The distinction can be made that, in the pure sciences, the abstractive process as applied to models, where the neutral analogies are collapsed into either positive or negative form, are the main mode of progression. Through developing models, the actual understanding of the model itself and the physical analogue is represents is advanced. In the applied sciences, on the other hand, the model itself is used for computational, engineering or design purposes. While these usages can certainly reveal novel aspects of the model and the way in which it is applied to various contexts, this second-order development of the understanding of the nature of the model is only a happy byproduct of the process. The product, the thing for which the model was being used as a tool, is the main purpose of the intellectual endeavor. In simpler words, in the pure sciences, the investigation of the model itself is the main objective, where in the applied sciences, the model is only being used as a means for some other end.
This may perhaps be why in the pure sciences, most reasoning happens at the theoretical level, with the few physical analogues that are used only being tangentially applicable (in one or two relevant respects) to the theoretical system itself. Whereas in the applied sciences, the model is used second to direct, empirical information of the system itself.