On Intellectual Rigor

 

 Enrique I. Moreno

 

 

          Intellectual rigor is the art of convincingly defining the axioms and proving the most relevant properties of some properly bounded logically possible domain. The question arises, therefore, whether intellectual rigor is a reflexive phenomenon, that is, whether it can be applied to itself.
          At first, the answer seems to be negative, since by being an art, intellectual rigor does not exhibit the necessary characteristics of a properly bounded logical domain. This line of thought would allow one to conclude that intellectual rigor –unlike the usual matters on which it is exercised—is a creative and intuitive modus operandi. Whether this is so or not –and probably it is—the immediately interesting fact about intellectual rigor is not that of its own nature (reflexivity) or even of technique, but rather that of subject matter choice. Notice that in saying that the subject matter must be a properly bounded, logically possible domain, one allows an infinitude of subjects meeting these criteria, because the set of properly bounded, logically possible domains is an infinite –though itself bounded—domain.
          From this property of the domain set, intellectual rigor may appear as a top-down, theoretical activity, and therefore prone to mostly impractical applications. That this is usually so, it is just a consequence of the plentifulness of subject matter immediately available to the inquisitive mind, and to the fact that the set of possible instance domains does not usually intersect the set of instance domains which practical types call “the real world”. But intellectual rigor is obviously at work in bottom-up, practical application of so-called “real world” instance domains –although in a somewhat sly manner, whose process we will subsequently examine in five steps:

 

Step 1. A set of practical circumstances in the so-called real world prompts for another set of desired circumstances; this is necessity. Logical action is needed to pass from the first set to the second. But this transition cannot be outlined with intellectual rigor unless both sets of circumstances have been properly bounded, for in the real world of practical action they seldom appear so. In addition, the usually present time factor makes the prompt for action non deferrable.

 

Step 2. Action begins to operate therefore on the original circumstances not really logically, but analogically and probabilistically, that is, based on what may seem to be at the time similar past occurrences or experiences, and by trial and error until some sort of desired result has been attained.

 

Step 3. An obtained result is really the recognition of some boundaries to the set of original circumstances. This recognition makes possible attempting to establish apparent axioms and properties of the total problem set. However, since the boundaries are only apparent, many axioms may have been improperly defined, and consequently, many deduced properties of the problem set may be false –which compromises the expectation of further results. Thus, the process continues by testing hypotheses on the nature of the boundaries of the circumstance sets. This will ideally continue until the boundaries have been completely established, proper axioms defined, and useful properties proved. The more this process continues, the more intellectually rigorous solutions are found to the original problem of passing from the first set of circumstances to the second.

 

Step 4. But since “real-world” practical problems are usually determined by time, and time implies change more often than not, by the time a rigorous understanding and proven general solutions are devised, both, original and desired circumstances have changed, thus making intellectual rigor nothing more than an interesting exercise whose only utility resides in the possibility of using it as an analogy to some apparently similar problem in the future.

 

Step 5. To the extent that original and desired circumstances have changed, the process must begin again  –if the desired circumstances still prompt for action, this time using whatever amount of intellectual rigor that was gained with past circumstances as the new analogy.

 

          A corollary of this process of deriving what practical types would call “truth from action” is the synthesis of general principles, rules of thumb, etc. from the many more or less intellectually rigorous analogies accumulated over time. That these collections of general principles are not truly intellectually rigorous can be seen from the usual fact that many of these analogies are never rigorously worked out to completion, because, at a certain point, nobody cares to work out a problem that has ceased to be one. Thus though it is theoretically possible to have intellectually rigorous, valid “general principle” for the practical problem of the world of action and practical activity, we would expect, usually, that these collections be plagued with nonsense. The conclusion is that such “general principles are only inspirational aids to motivate intuition and creativity.
          With this, we arrive to the point where we see that intellectual rigor starts with intuition and creativity, and arrives to certainties, whereas practical action in the real world starts with certainties and arrives to intuition and creativity. Though more inclusive, intellectual rigor is also more practically useless. There is also an important by-product of these two modes. Intellectual rigor –if successfully applied— results in knowledge. Practical action, if successful, modifies the “real world” and produces power. But as you have been shown, most of the time, intellectually rigorous knowledge is useless because it results in logical truth –a proven set of relationships in a properly defined domain. On the other hand, power produces more power, which is usefulness itself.
          Both logical truth and power share a tendency to consolidate with similar or related logical truths or power structures, respectively. For example, logical truth discovered in a particular field of study eventually integrates into a superset of related logical truths by means of commonly intersecting sets of truths or by a newly postulated set of common axioms, or by other means. This results into larger subjects of general study, which are usually understood as “disciplines”. Likewise, a power structure tends to enlargement by imposing its superior usefulness onto weaker power structures in one way or another; we all know how power feeds on power and tends to grow out of its own momentum. What is of interest to consider at this point is the confusion associated with what can be called the “legitimacy of consolidation” (or in street terms “of size”) which is simply the perception that a large structure of logical truths, or a large power superstructure must be in some way “legitimate” due to its integration of many truths or to the aggregate usefulness of  its resulting power superstructure.
          In the case of logical truth, such perception of legitimacy leads people (i.e., the popular mind) to the perception that a given superstructure of logical truths can be expanded indefinitely to the point where an absolute, unified omnistructure may logically explain everything with sufficient intellectual rigor. In the case of a power superstructure, the perception will be that its superior usefulness can be eventually extended to control and resolve everything with the aid of its action-oriented loosely-defined principles or rules of thumb. But this is naturally a legitimacy-of-size case, and an easily discernable contradiction, since by definition, “everything that can be known” cannot be a properly defined, bounded domain, and “everything that can be controlled” is also not a properly defined and bounded domain (since we do not know what can be eventually known or controlled).
          This consideration is most relevant in observing how at every historical juncture, individuals and societies seem to propagate the myth of their excelling knowledge and /or power by letting the assumption of the legitimacy of size work quietly at all levels of individual and societal life. Thus, “legitimacy of size”  is the set of assumption that lead individuals or societies to believe (or to behave as if they believed) that a certain collection of logical truths is sufficiently intellectually rigorous as to be eventually capable of soundly explaining everything that can be explained (for example “science”) simply by virtue of its overwhelming quantity of proven statements over an overwhelming quantity of subject matter. It is also easy to understand how the public’s perception of a power structure will tend towards acknowledgement in as much as the structure’s size exceeds the capacity of any one of its individual members to understand all the details of its enormous quantity of substructures and aspects.