Logical Forms in the Quran (Pr2)

What’s fascinating about this method (of interpreting words by their constitutive relations) is that it’s not a method at all. We already do this, we understand the world, or we make sense of its problems (or hack them) by applying to a given problem a system of rules so as to establish an attack vector in relation to it. We do this so that the problem may first gain ‘functional’ identity.

Here the system of language takes care of the most basal of our cognitive operation, it allows for said problem to be articulated, albeit as a problem, but where too simple and insufficient, as it often is, to give a clear or adequate expression of the problem, being that said problem in those cases is too complex, we apply on top of the basal system of language, a more complex system this may be mathematics, physics, geometry, which offer deeper and more nuanced--albeit linguistic--articulations of the same problem. Nonetheless, the approach proves universal and uniform in its proceeding.

It simply wants to define problem x (any word or idea of your choosing) within a system z. System z in turn not only tells us what problem x is, but its role in it, and shows all the combinations in which the problem figures. Thus in the Quran, all concepts are actually built on this, quite intuitive and innate principle. It treats a concept like the Sun as a logarithm, which says that the sun is the sum of certain conditions, and then ascribes to this sum the same unified being as the sun, i.e it creates a negative sun that illuminates the positive sun. It then calls the negative sun, by a different name, i.e the moon. Thus the moon is a negative sun, or its coefficient, a concept which stands in relation to the sun as the sum of its conditions, or what in mathematical topology is called a many-to-one relation. I.e to be able to represent any complex idea in a simple, one-word formula, we need a mechanism that condenses all the elements that make up this complex notion into a simple, comprehensive yet comprehensible, form. 

In the work of thought “completed in arranging particular data, immediately taken from sense perception, like pearls on a thread--or does it face them with its own original measures as independent criteria of judgement”

  E.Cassirer ‘Substance & Function & Einstein’s Theory Of Relativity p367

Thus when we think the sun, we’re essentially constructing it out of the conditions of night, dawn, daybreak, day, sunrise etc, i.e its natural order. But we take the further, very crucial step, of treating, semiotically, the construction of the sun as an object equivalent to the sun, but whose function is to symbolize the constructive sequence rather than point naively to the object itself.

In other words, we isolate from every given idea or mental image (apple, car, sun, earth) the process of constructing them, i.e rethinking how they came to be self-evident objects in the first place, then we extract from those attempts at construction their unique modes, condition and ingredients; this reduces our otherwise self-evident and naïve ideas (or in Plato’s words ‘opinions’) into programs or models, and these programs, insofar as they are keys or instructions for accessing the things in question, are the negative form of the ideas that we’re constructing, and which have their own being. This is the role which darkness serves with respect to light, or the invisible with the visible, or falsehood with truth, or, in our chosen example, the moon with respect to the sun. Now every random idea has, as in Hegel’s system, an antithesis, and it's this antithesis that we require to access and fully comprehend this random idea. 

This is a common method in symbolic logic and mathematics that’s hardly used in language, but which seems especially tailored to be used in language. 

Plato long ago wrote that some sense perceptions are awakeners of thought, defining these as “everything, which comes into sense at the same time as its opposite”, he makes this the principle condition for thought, disclaiming that

“what does not pass into an opposite perception does not stimulate and therefore does not arouse thought” (Republic 523-524) (Cassirer’s rephrasing) 

“Just as for Plato thought becomes what it is in assertion and contradiction, in dialect, so only a perception to which this feature corresponds can become awakener and paraclete of thought” 

 E.Cassirer ‘Substance & Function & Einstein’s Theory Of Relativity p368

That being said, now apply this dynamic to every concept. Any idea that we may encounter, we say, has a coefficient, this coefficient, we elaborate, is the sum of all necessary conditions, and all the essential operations whose product is the original, given idea. A dictum can be laid that says that any concept has an opposite, and its opposite is the sum of all its conditions. Thus every thought that involves seemingly one idea, for example, car, is actually a dialectic involving a negative term along with ‘car’, this negative term embodies all the essential ideas necessary for understanding not only what a car is, but all the forms which this idea can assume, i.e it makes of ‘Car’ a transfinite concept, that involves other things which may not immediately be thought of as directly related to the idea, but which shares, in a graded sequence, some of its essential features, like any other mode of transport, which may be arranged in terms of which are more kindred to ‘Car’ and which are slightly more different. Thus in a phrase, the sum of all ideas and conditions which make up any term is a term that has as much validity and individuality as the actual term.