The 'faculties' in the Quran (Part 2)

Quality over Quantity

This system, call it a concinnity, is one the development of which would allow us to know which system to apply to which, a system that would solve Gödel’s incompleteness theorem and prove that such a system exists that is consistent in itself and could prove the truth of every one of its statements. And since the value of any given system of reference is found in the way it’s applied and the way it helps us construct objects of experience, we can easily add to this that those objects of experience are simply other systems of reference viewed from this or that system of reference, meaning a perspective is a solution of some sort to another’s parochial perspective. Here we have a complete system compactified by the formal interdependence of its constituent elements. The Quran gives us a clear case of this, in the chapter titled ‘Yusuf’, chapter 12:

“O father I saw eleven constellations and the sun and the moon prostrating to me.”— Quran 12:4

The significance of this verse lies in the meaning of eleven, which, drawing from the Quranic conception of number, stands for an ‘exponent’; meaningful both in the mathematical as well as the linguistic sense. Its meaning is constructed out of the terms, Ahad, which denotes a representative, exponent, and Ashr, which means ten, and ten in the Quran signifies a state of ‘completion’, but completion in the sense of being ‘modular’ or modularity, of something ‘consisting of separate parts that, when combined, produce a whole. Now if we combine the two, Ahad and Ashr, we get a ‘mereological’ unit, i.e., a part of a whole. The term ‘Ahad’ emphasizes parthood, but when used in the context of experience comes to mean ‘exponent’ or representative of a whole.

"Imagine˺ how many peoples We have destroyed before them! Do you ˹still˺ see any of them?"— Quran 19:98

So what does it mean that Yusuf saw eleven constellations? It means that he saw a microcosm. The great in the small, the many in the one, that is, a state of perfect modularity but specifically as pertains to the faculties as his career path would later reveal. This may be explained by analogy to the concept of ‘methodology’ or ‘doctrine’, something that one possesses that allows him to know how to react or treat certain situations or problems (which is the Quranic meaning of Elm علم or phronesis). This can be ascribed to mathematics, a system general enough to allow us to count objects, solve complex statistical problems, even interpret the motion of objects that we can’t even see like light and magnetism.

A stronger, more explicit case of Ahad Ashr is found in the Leibniz chain rule, a method for finding the derivative of a composite function → if y is a part of u and u is a part of x, then by extension, y is a part of x. This rule explains verse 4 of chapter 12 and gives us the gist of what Joseph saw and is an abstract way of defining mereology. If we could reduce mathematics to a finite set of principles, even if the number of those principles is one hundred, the expression ‘ahad ashar’ would still apply, because number in the Quran is qualitative, not quantitative. It refers to states of being, order, relations, compositions, and processes irrespective of quantity. As Bertrand Russell put it,

“Quantity has lost all mathematical importance which it used to possess, owing to the fact that most theorems concerning it can be generalized so as to become theorems concerning order.”— B. Russell, Principles of Mathematics (p. 158)

The defining characteristic of any formal system is compositionality. Thus, given any mathematical rule or concept that’s universal enough, the fundamental principles comprising it can be reconstructed by rules of inference, that is, logical rules that explain how conclusions are obtained from certain premises in any formal system of logic. A formal system can be thought of as a house, i.e., by a house we think of a structure of some sort that fulfills a defined set of conditions, a place that has rooms, one of these rooms a living room, the other a kitchen, another a bedroom, a bathroom, maybe a garage or an attic. These are the concepts in terms of which a ‘house’ is generally thought, and depending on which part we add or remove, the concept of house can be altered.

"Whoever comes with a good deed will be rewarded tenfold."— Quran 6:160

"مَن جَآءَ بِٱلْحَسَنَةِ فَلَهُۥ عَشْرُ أَمْثَالِهَا"

In such a verse, tenfold is usually thought of in the quantitative sense, i.e., the deed times ten, or instead of, say, one dollar, you have ten. But as regards this verse, this is only approximately true. In actuality, tenfoldness means that the thing is scalable or exponential. Thus, a good deed, say a donation or any charitable act, is not simply multiplied by itself ten times and that’s it, but rather, grows and continues to grow in proportion to its long-term effect. The true measure of such deeds lies in their scalability and their ability to foster long-term growth and prosperity, like an investment for which one continues to reap the benefits for as long as the thing lasts, only that such an investment in the context of the verse is subject to continue long after the person’s passed.

Thus, the Quran encourages us to think in terms of mathematical logic, being itself built on mathematical-logical principles. In defining number qualitatively, it directs us to think about things not as self-evident, given objects, i.e., accidents, but in terms of constructions, sequences, performed by our minds, in a manner that’s totally unbeknownst to us.

"Will you not then be mindful?"— Quran 32:9"أَفَلَا تَذَكَّرُونَ"

Deduction & Inference

“Will they not ‘be mindful’?” تَذَكَّرُونَ here, is the same word used to mean ‘male’, directly capturing the idea of thought as a constructive and sequential process. What makes the term morphologically valid as both a form of ‘thought’ as well as a gender description is the common, underlying property of reproducibility or autopoiesis, and this is clearly shown in the chain rule that we just referenced. That is, inasmuch as the male is the biological repository and seedbed for the genetic material of a species, so is a thought the seedbed for all its presuppositions, i.e., how we arrived at it, and implications, i.e., all its connotations. Thus, God indirectly asks us to think things through and not settle for what seems to be.

Thus, what we said about ‘rules of inference’, those which make up the subject of propositional and formal logic, is contained within the one expression ‘Thekr’, and the rules by which to conduct this form of thought are the same ones that are treated in the disciplines of logic.

Given an object, say a house, we’re asked to perform an abstraction of it so that its value is deepened by no longer thinking of it as ‘given’. What we’ve done here is to think of ‘house’ as a modularity of various facets, subsuming it under a system of rules. The fact that these ‘given objects’ are indefinite, i.e., require elaboration, means that in them are nested features that are the real psychological material for the assimilation of what he calls the scientific concept. Thus, the given object, those words we use to (not even denote but) designate things, are but a shorthand pointing to deeper, more inclusive conceptions.

"The indefiniteness of the memory-images of our actual sensations involves that, along with the vivid and immediately present, sensuous intuitions in the real process of consciousness, pale residua of them are always found, which retain only one or another feature of them; and it is these latter, which contain the real psychological material for the construction of the universal presentation."— Ernst Cassirer, Philosophy of Symbolic Forms (Vol. 1, p. 182)

This is the kernel of verse 4 of chapter 12. Objects are ascribed the form of permanent modularity; an immediate, first principles approach to all manner of things. Having established this, all else can be derived either granularly, by differentiating in the object progressively finer details of it, or coarsely, by defining the building blocks that make up the object. All of which can be made out from that simple, foundational rule of thinking of things as shorthands. The Quran has a myriad of terms by which to designate every critical stage in the progress of thought. For instance, in our active construction of concepts, the commonly used term is ينظرون.

"Will they not observe the Camel and how it was created?"— Quran 88:17

"أَفَلَا يَنظُرُونَ إِلَى ٱلْإِبِلِ كَيْفَ خُلِقَتْ"

Here ينظرون cannot be adequately made sense of without comparing and differentiating it from the terms يرون and يبصرون, as these terms are closely related in such a way that they make up a series or spectrum scaling the degree to which objects of experience relate to our faculty of understanding, best defined by Kant as the faculty of the mind that processes and organizes sensory input to produce coherent knowledge. In other words, a scale measuring the extent or degree to which we understand things. This, of course, presupposes a criterion, a criterion implied by the notion of Theker. It’s the scope within which our understanding of any particular object is encompassed. Or the “Constancy and all-round differentiation of the presentational content, signified by a definite word.” The broader the context in which we view something, the better we understand it. A difference must, therefore, be made between perception, i.e., immediate sense data, analysis or observation, and comprehension.

"He Who created seven heavens, one above the other. You will never see any imperfection in the creation of the Most Compassionate. So look again: do you see any flaws?"— Quran 67:3

The verse cites the faculty of Basar specifically, as it’s the Basar, the understanding, not the observation nor the mere perception, that’s called in to grasp these high principles and the machinery of the universe in general.

"Then look again and again—your sight will return frustrated and weary."— Quran 67:4

"ثُمَّ ٱرْجِعِ ٱلْبَصَرَ كَرَّتَيْنِ يَنقَلِبْ إِلَيْكَ ٱلْبَصَرُ خَاسِئًۭا وَهُوَ حَسِيرٌۭ"

Analysis pairs with ينظرون, perception with يرون, and يبصرون with comprehension or understanding proper. This scheme conforms with our own, in that we start off with these transient and accidental sense impressions and transition to their observation and analysis, and finally to their comprehension or understanding. Here, in conformity with the notion of modularity, no supremacy is given to any function over the other, i.e., neither the understanding, embodied in بصر, is stronger than any of the other two faculties, nor perception, embodied in يرون or الرُّؤْيَا (which also refers to dreams), weaker than the others. Each, as God put it in chapter 36, persists in its own course. If we start with الرُّؤْيَا and ride the assumption of its marginal role in the constellation of Quranically-defined functions, we’ll find verses containing evidence to the contrary, as in chapter 96 verse 14:

"Does he not know that Allah sees ˹all˺?"— Quran 96:14"

أَلَمْ يَعْلَم بِأَنَّ ٱللَّهَ يَرَىٰ"

"And that ˹the outcome of˺ their endeavors will be seen ˹in their record˺,"— Quran 53:40

"وَأَنَّ سَعْيَهُۥ سَوْفَ يُرَىٰ"

Clearly, perception, if we can call it that, is not a marginal or weak function, but rather the inception of an idea, an opening function that makes way for the others. It’s, therefore, the most ‘immediate’ and by the same token, the least differentiated of the three perceptual functions, hence the same word is used to describe ‘dream’, which makes sense, being that dreams are nebulous and inexact, like any object when first intuited from the stream of consciousness. The import and value of الرُّؤْيَا is doubled when, in the nebulosity of the data in whose determination it specializes as a function, a considerably large space is left vacant as to the ‘scope’ of meaning that a given sense datum can hold.

This condition is permanent and applies to every object of thought, however complex our formulations of them grow, however advanced our knowledge of them become. As long as every limit reached can be made a postulate for another, more differentiated formulation of it, that الرُّؤْيَا is functional at every level. Besides this, we see that every proposition, every judgment we make with respect to an object contains all these functions simultaneously. This is another modular feature. An object made by الرُّؤْيَا, though vague, must still be conceived as vague. We know by this that it’s mediated by the faculty of the understanding بصر which forms the ‘conceptual’ proportion of the overall ‘ratio’, that is, the ‘understandable’ in it, which is the very idea of its ‘nebulosity’ or vagueness.

The function of observation or analysis, نظر, to which belongs the idea of the ‘potential’ meaning of the object, is our active synthesis of it. Thus, it’s primarily through Basar (understanding) that we can make judgments regarding our impressions of the object and to know if it’s vague or if it’s ‘to be made sense of’, and it’s through الرُّؤْيَا (perception) which is always carried intuitively, that we can form immediate sensory data and intuitions. Lastly, it’s through the function of observation نظر that we begin to make sense of those sensory data.

Thus, we see that the functions of the mind work together and in an organized manner, that to each function is assigned a specific task, and each function accrues from others and combines them in different ways. Rather, any one function is just a certain way of arranging the others, of placing them in a certain order.  The question here resurfaces, which we’ve raised at the beginning of the text.

Follow us into Part 3...