Metaphorical Extension (Part 3)

Magnitude & Identity

Being that understanding and all its corollaries, imagination, reference, inference, conjunction, disjunction show a gradual process, we can say that the gradation can only take place on a spectrum, inasmuch as the transitive relation observed between the day and night happens on the spectrum of light; now we see that both transitions are compartmentalized, that they consist in ‘phases’, the compartmental or graded aspect is distinct from the spectrum, and serves, it seems, to designate or modulate it, in other words, what compartmentalizes the spectrum is something other than the spectrum. The Quran uses the term ‘Nur’, luminescence to describe the notion of light spectrum, this is owing to

the fact that in a number of occasions, it describes the moon as a luminary, a source of ‘nur’. Also saying that God is the nur of the heavens and the earth, which left some wondering why he didn’t use something stronger, like Wahaj وهاج, (beaming), and the answer is that nur in its gradience expresses movement, guidance and revelation.

There’s no spectrum without gradation, and what’s gradation but a rapid movement amongst points adjacent or contiguous to one another, that is, the spectrum is given only its various transitive points, and this transition, in turn, gives the perception or illusion of a gradual change or alteration. This directly pertains to motion, which as Alexander defines

The meaning of motion is, as was noted before, not that the poin\t of space itself moves as if it were a material body shifting its place, but that the time of a point ceases to be present, and the present is transferred to another point continuous with it.

ٍSpace, Time & Diety (p272)

Now if the number of these phases is, as Hume thought, innumerable, as any spectrometer or color wheel displaying brightness, intensity and saturation levels, or if you prefer ‘Zeno’s race-track paradox show, why should the moon consist of only 8 (منازل). The answer is given in the verses themselves; it’s because what’s measured is not the ‘modularity’ or rate of the spectrum, but the modularity of that which grades or compartmentalizes it. Hence why God says that he’s the Nur نور of the heavens and earth, here, he modifies the concept with himself.

Now the Quran gives clear accounts of all 8 phases, and these can be seen in the following figure. The dynamics between these various phases we believe are represented in their clearest form in the principles of propositional calculus, and the basic operations of arithmetic, especially when expanded into binary or Boolean Algebraic form;

• Addition is a simultaneous negation,

• negation is a simultaneous addition;

• One side increases but only as the opposite side decreases

• The result is a compromise of both.

Now we graduate from this into simultaneous addition and simultaneous subtraction. Algorithmically, this would be (1:0)(0:1)(1:1)(0:0). 

• Simultaneous addition is multiplication,

• Simultaneous subtraction is division.

Now if we count the operations of which each side is capable, we reach eight total operations, 4 for each side. This is where basic arithmetic graduates into propositional calculus, the number of whose operations is five. In other words, we add individuality to the sum of operations and essentially repeat the same process. The conception of substance issues from determinations of this dialectical form, specifically, when the number of operations reaches a specific number, here 8, as only in 8 do we define the position of x with respect to y, i.e these operations aim at defining the operands of an operation, i.e the sides of a spectrum. Empirically, this is impossible to detect, as all we see is the object, yet on reflection, it becomes clear that, in merely standing in opposition to the object, the same arithmetical principles are being applied in real time. There’s you then the object, the object then you, you together with the object, and you and the object outside of this relation.

In Kant, the definition of substance aligns with that of number and naturally arises out of certain basic operations, or as he put as

“the successive addition of one to one (Homogeneous) other”

“The pure image of all magnitudes, for outer sense is space; that of all objects of the sense in general time, the pure schema of magnitude, however, as a concept of the understanding, is number” (B181 I 182) 

Now celestial mechanics, as we noted, are ultimately reducible to these relations, or let’s say, that these relations are the Quran’s way of expressing them. We find in propositional calculus operations such as disjunction and conjunction which emulate the relation between the night and day as the Quran describes it in chapter 91; saying that the day unveils, and the night conceals.

A parallel can easily be drawn between concealing and disjunction, unveiling and conjunction. When trying to understand things, the direction of the scheme is always from negativity to positivity, since we don’t have a full sense of the concept that we’re trying to understand. The addition side appears only in affirming that movement from negation to addition, or let’s say, in successively capturing that movement.

If asked, why should the Quran use celestial mechanics as a way of representing these relations and not representing the equations of mathematics directly, we reply that the linguistic formulas are themselves no different than the equations of mathematics; they would be equivalent to what B.J Whorf describes as pattern symbolics.

“It is an expression of pattern symbolics, an analytical method that grows out of linguistics and bears to linguistics a relation not unlike that of higher mathematics to physics. With such pattern formulas, various operations can be performed, just as mathematical expressions can be added, multiplied, and otherwise operated with; only the operations here are not addition, multiplication, and so on, but are meanings that apply to linguistic contexts”

B.L Whorf ‘Language, Thought & Reality’ p226

The point of mathematical physics is to describe physical processes, and in this respect, it’s identical with language, the difference is in the concepts used and the rules that govern their use, and when we look at those expressions we find, that they describe those mechanics with a precision no less rigorous than a mathematical equation would.

It’s for the sun to catch up with the moon, nor can the night outrun the day, for each travels in an orbit (or course) of its own.

لَا ٱلشَّمْسُ يَنۢبَغِى لَهَآ أَن تُدْرِكَ ٱلْقَمَرَ وَلَا ٱلَّيْلُ سَابِقُ ٱلنَّهَارِ ۚ وَكُلٌّۭ فِى فَلَكٍۢ يَسْبَحُونَ 36

If we examine this, we find the expression of ‘not catching up’ to be very consistent with a certain pattern in our reasoning, namely, the relation between the concept ‘triangle’ and the various occasions in which the triangle can appear in experience. Now the relation between the sun and moon is highly expressive of this; for the moon is nothing in essence but something which determines, a criterion, which, like the triangle, can never be exhausted in experience, as Kant put it.

“The concept of a dog signifies a rule in accordance with which my imagination can specify the shape of a four-footed animal in general, without being restricted to any single particular shape that experience offers me or any possible image that I can exhibit in concreto” (B180 I A141)

The idea of rule here is synonymous with the concept ‘determiner’ or ‘measurer’ in general, and as a ‘rule’, itself can never be determined except medially through an instance or example, here the validity of the approximation--frustrated by the magnitude of the concept is equally as important, this is the semantic role which the sun fulfills. The sun validates each successive determination, as well as the inexhaustible concept, i.e the moon, and it’s in this relational continuum in which the determiner can only relatively determine, and the validator can only relatively validate, that the understanding comes to life. Or let’s say the faculty of understanding arises from a contradiction. In the context of metaphorical extension, it’s virtually impossible, in using a concept like tree, to exhaust all the ways in which it could be used, or all the things to which it can be used, yet its use, is only valid in the limitation which it faces on its course.

The scheme may thus be described;

The night-day dynamic capture and symbolize the movement of understanding and reasoning independently of any subject or object, the moon-sun dynamic, the moon the mind or any concept serving as the context as it moves across the spectrum of night and day and the sun viewing and affirming the successive steps made by the former, that is, it idealizes the idea of movement and progress inasmuch as the moon the idea of assimilation or measure.