Two important preliminary comments: As with any classification of human constructs and activities, the following classification should be viewed as trying to identify some ideal forms, while recognizing that ideal form do not exist in reality. Real phenomena typically exhibit a mix of ideal forms, but still it is useful to have such ideal forms in mind. Also, the following classification should actually be attributed to the way the theories are presented and/or perceived not to the theories themselves. That is, the classification of a theory does not depend on inherent characteristics of its contents but rather on the behavior of the corresponding research community. Still, for simplicity, I will sometimes talk about theories rather than about the typical way that they are presented.
I call a (presentation of a) theory (or a field) modest if it makes no direct claims on reality. An archetypical example is pure (classical) mathematics. A modest (presentation of a) field defines abstract concepts without eluding to their possible realistic motivation. In particular, these definitions make no reference to reality, although they can be applied in reality.
I call a (presentation of a) theory (or a field) suggestive if it does claim to provide a description (and an understanding) of some aspect of reality, but its actual contents holds regardless of whether this claim is valid or not. A good example is the theory of computation. Such a field defines concepts that abstract intuitive notions about reality and it typically eludes to these intuitions. In particular, these definitions are explicitly aimed at describing some aspects of reality, yet the actual definitions are independent of reality (i.e., they are interpreted by their contents not by reference to reality). The field suggests that the study of these definitions sheds light on reality, but the validity of the study is independent of reality (and only its relevance to reality depends on the reality, typically via the adequacy of the initial definitions).
I call a (presentation of a) theory (or a field) imposing if it insists that it reflects reality, and this insisting is an inherent part of the presentation and is never decoupled from it. Examples abound in the social sciences (especially in economics), and are marked by insisting that the theory is the sole and unique description of some aspect of reality. Indeed, these theories deny any gap between them and reality, and even insist that reality must fit their assumptions and predictions (such that any apparent mismatch is either denied or attributed to an error in the view of reality). In a sense, these theories are imposed on reality.
Thus, one main difference between suggestive and imposing presentations refers to their view of the gap between the theory and reality. Suggestive presentation openly admit the gap, while suggesting that some insights into reality can nevertheless be drawn from the theory. Imposing presentations either deny the gap or admit it only when pushed to the wall. Either way, these imposing presentations blur the distinction between the theory and reality, and tend to force the theory on reality.
Another main difference between suggestive and imposing presentations refers to the scope and/or extensiveness of reference to reality. A typical suggestive presentation abstracts a few intuitive notions that refer to reality, whereas a typical imposing presentation insists on providing a full description of a full slice of the world.
Personally, I advocate suggestive theories and presentations. It is good to be explicit about the motivation of the notions defined and the studies conducted. Still, one should clarify that the definition and study are independent of reality, and admit that the applicability of the theory to reality is not something that can be argued within the theory. It is good to suggest that the theory may shed light on reality, but one should not insist that there is no gap between the theory and the reality; such a gap always exist.
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