**“It is the power of understanding and discovering such truths that the mastery of the intellect over the whole world of things actual and possible resides; and the ability to deal with the general as such is one of the gifts that a mathematical education should bestow.”**

**— Bertran Russell****, “The Study of Mathematics”**

Where? In business? . . . In science? . . . In technology? . . . Or in life in general? Well, I’m no mathematician at all and if just to recall the math courses I had in school, they included arithmetic, algebra, geometry, trigonometry and statistics; can’t even think of any other courses where I did some kind of mathematical computations except in physics though it isn’t officially considered a branch of math. Nevertheless school math seems to be so abstract and divorced from the practicality of real life outside the four walls of the classroom. There was even an instance in the distant past when I overheard a high school student making the comment why he had to take algebra when in the daily grind of actual life, he wouldn’t have one heck of a moment to use it.

So as not to complicate matters, it is perhaps much better if we just take up the most basic aspect of mathematics to get to an interesting discussion of the issue of mathematics’ fundamental role in whatever context we wish to handle the issue. Dealing with the much higher branches could bring us to certain complex problems only the experts can give a run for their money, so to speak. Besides, the obvious limitation set by the topic doesn’t open up a leeway to explore upper-storey considerations. As a matter of axiological concern, I’d rather look into the pragmatic and utilitarian values of the most basic aspect of mathematics–call it arithmetic, if you will–in the daily life of the common human being under normal circumstances. In this way, we veer away from the academic abstractions of the discipline and locate its usefulness in the down-to-earth nitty-gritty of human experience.

Four very important aspects of human experience that lead to knowledge are differentiation, classification, quantification and specification. In all these matters, mathematics plays an essentially crucial role. The most basic operationalization of mathematics is in being able to differentiate and classify in experience the data of perceptual knowledge. The process is so natural that on the one hand, a unit is spontaneously distinguished from another on the basis of certain obvious properties. Yet on the other hand and on the basis of the same properties, two or more similar units are deemed to be classified as belonging to the same genus or family or species technically called a “set” in the language of modern math’s set theory. In other events, one could rather find some differences in the properties of two units despite some aspects of significant similarities and thus define their intersection.

Then we closely focus our attention on a particular set of units and look at them individually. At this point, we begin to quantify and connect them. We determine the factors that make them related to each other and the conditions that make them affect each other as well. A further magnification of each of the unit with a more serious stress on its peculiarities brings us to the in-depth level of specification. We get to its detailed components and explore their systemic interconnectivity that effects functionality. Technically, we are into the epistemological realm of philosophical inquiry which fundamentally considers the importance of the basic instrumentality of mathematics. In other words, this is how we actually begin to comprehend empirical reality: through the mathematical path. The thematic aspect of mathematics is obviously a non-issue as yet but what is being established by this presupposition is the integral pre-eminence of the spontaneous, non-thematic mathematical category in human consciousness.

The normal human at her/his most basic state of being is mathematically enabled. S/he has the inherent mathematical endowment to differentiate, classify, quantify and specify empirical information because at the base of her/his epistemic platform in consciousness is the very domain of logical reasoning which is the absolute foundation of the mathematical infrastructure. Says Bertrand Russell in his ** ‘The Study of Mathematics’**:

*‘The characteristic excellence of mathematics is only to be found where the reasoning is rigidly logical: the rules of logic are to mathematics what those of structure are to architecture. In the most beautiful work, a chain of argument is presented in which every link is important on its own account, in which there is an air of ease and lucidity throughout, and the premises achieve more than would have been thought possible, by means which appear natural and inevitable. Literature embodies what is general in particular circumstances whose universal significance shines through their individual dress; but mathematics endeavours to present whatever is most general in its purity, without any irrelevant trappings.’*

Being thus grounded in logic, mathematics in its thematized form provides the structural patterns that lead us to a better understanding of an otherwise complex reality with all the series of interconnected events impossible to track down in a space-time maze. Mathematics, in this sense, facilitates us to better understand significant aspects of reality by isolating the ‘fiber’ of their quantitative dynamics from the ‘flesh’ of their empirical mechanics. The whole process is actually a simplification rather than a complexification as the non-enthusiasts of the mathematical discipline stubbornly contend.

Mathematics is the sophisticated extension and expression of human rationality thematically ‘institutionalized’ in formal logic. This thought brings us to the realization that the most fundamental role of mathematics in human life is the ‘fortification’ of certain matters of specified information and knowledge of various levels of importance by way of a thoroughly quantitative examination of their categorized and differentiated components. Common sense has its own degree of importance but not enough in attending to the complexities of higher-level problematizations. The facilitative edge of logical reasoning at that stage is never doubted as a time-tested ally. Nevetheless, in a lot of instances, the trajectory of complexification doesn’t rest within the coverage of what logic may handle but even goes farther upward at a certain height where the sophisticated process of mathematical operations are of the essence.

Mathematics, though utilized epistemically through the facility of human consciousness, is a transcendent discipline for its essentially independent character is not contained within consciousness. Had it been so, its subjective streak would have shown. But mathematics is devoid of subjectivity. From a dualistic perspective, we automatically conclude that if it is not subjective, it must be objective and hence located in the outside world. But neither is mathematics a property of what classical philosophy calls the ‘extended substance’. Mathematics is therefore not in the mind nor in the world. Like the question on the reality of the ‘soul’ raised by the Buddha in the ** Surangama Sutra**, mathematics is located neither within nor without. Perhaps its most appropriate location is Plato’s

*Realm of Universals*for in that sphere, nothing may be destroyed nor altered in eternity and perfection. In fact, the transcendent reality of mathematics could even be properly construed as higher than the ‘secured’ status of the christian ‘God’ for even the latter cannot violate the rules of logic, much less that of mathematics. This reminds me of an encounter I had some two years back with a stupid clergy of a charismatic episcopal church who argued with the intensity of a preacher delivering a passionate homily behind the pulpit that his ‘God’ is so omnipotent (all-powerful) he can even will to make two plus two become five.

(c) Ruel F. Pepa 13 May 2015

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