Atomic Structures In The Quran - Part 3

Section 6: The Semantics of Atomicity

If you've grasped the main idea of the atomic concept, then you should understand what's meant when we say that the Quran is a compendium of atomic terms. Thus, what we need is something akin to a complex number to unlock for us that extra 'semantic' dimension.

🔍 Methodological Definition:

Let's simplify our definition to say that the words of the Quran are the kinds of words the understanding of which demands that same inductive approach we applied to the word 'mass'. The meaning of a term can only be obtained when we analyze it. It must be analyzed until we have obtained that vivid, intuitive sense-impression which under normal circumstances we know only intuitively but don't necessarily have the right words in which to put it.

This means that we must adopt a 'pragmatist' approach. It's noteworthy to mention the fact that 'pragmatism', was an idea developed by C.S Peirce, founder of semiotics. If we say that the atomic concept is a normal word, but a word whose meaning depends entirely on the way we use it', then we'd be leaning towards, or adopting a 'semiotic' approach; for under normal circumstances we don't really interpret words, but directly use or employ them.

💡 Language Insight:

And this is a point worth highlighting, because it shows that our language use is primarily 'functional'—our tendency to not reflect deeply on the meaning of words but instead, take them for what they commonly imply, though naive, is itself evidence for the general functional tendency of language.

We want to know what a word means in order to use it, and in most cases, we want to use them in the best way possible. But the problem is whether we've understood a term deeply enough as to know how it should be used: for we must take this general 'functional tendency' as an indication of an innately felicitous disposition in language itself, that the word captures some 'sense' or 'meaning' that is wanting of expression, even if the expression given to it is erroneous.

🧠 Baldwin's Definition:

Professor Baldwin defines implication as "the meaning by which belief, the attitude of acknowledgement in judgement, is rendered" (The Meaning Of Meaning 1923 - Appendix D - §5).

If 'meaning-making' is the essential function of a word, then implication is the effect of a meaningful word.

And this is typically where the analysis of a word, the 'linguisticality' of normal language use stops; for we usually want to know what the interlocutor intends to say—we see no need to go beyond 'semantics' (in the conventional sense of 'what I think they mean in the moment'). The tendency which gives us the atomic concept is opposite to this—we want to reverse the process of implication, call it 'explication', and reach the eidos of the word, that 'essential' thought for whose sake the utterance or the word was made.

🌩️ Implication vs Aporia:

That spellbinding effect of 'implication' really originally belongs to the atomic concept, because, when we know what we want to say, but can't find the word as we said earlier, we're truly experiencing what's called implication, a process which in normal circumstances is transient and would lead us to some other associated idea. That a dark cloud should evoke 'rain' as a subsequent judgement, is indeed implicational but, inasmuch as that aporia we typically reach when we suddenly lack the language tools to give something a precise definition.

This is what an aporia is. The failure of some 'meaningful' idea to find a proper host, though contradictory, and properly speaking 'aporetic', is actually a good thing, for here, more than anything, it shows the purity and standalone-ness of the idea; for what the idea should imply here is the discourse at large—the failure at 'passage' is really a 'wanting of passage', but not to this or that case, or this or that 'equivalent' and at best 'approximate' term, but to 'any possible approximation'.

The value of the idea is in how it 'can be used in a discourse'. And that silence or 'impasse' we call aporia is discursive, articulate or critical silence that anticipates a case to eventually subordinate to the criteria of the idea.

Section 7: Aporia and The Uncertainty Principle

⚗️ Physics Parallel:

The aporetic apotheosis of the Platonic dialogue is wrongly understood, if understood as meaning 'uncertainty' in an occlusive and defeatist sense, and this is actually the same problem we confront in large language models, and even quantum mechanics—the exception is that in those areas it's remedied with probability. Heisenberg's 'uncertainty' principle, in our interpretation, is the physics' variant of the platonic aporia.

It's not so much a perplexity, if carefully thought through, but an indication that we've reached the most foundational layer of our epistemological approach, a condition we always presuppose, and never consciously start our analysis with, but which is revealed to us at the end - Like the conclusion of a syllogism. The true purpose of this newfound awareness of our limitation is to reverse (or indicate the reversal of) the original scheme. The uncertainty or aporia is now to be the vehicle by which analysis is performed. This is what we called 'explication'.

📊 Aristotelian Method:

Unusual when formulated this way, but it's a commonplace, something we do all the time. Aristotle's investigations always start with a general classification of the domain of analysis, here's built a database of forms, classes, and categories, groups, subgroups, divisions and subdivisions, a thoroughgoing mapping of the subject, you know... Aristotle's way of doing things.

If asked why we should approach our subject this way, you may reply, rhetorically: well, how else can one do it, precisely the question this query is meant to raise, a question indicative of aporia, because it evokes doubt as to the ontological validity of our epistemic approach. This 'classifying' approach breaks down at certain, particularly abstract levels, graduating into a Russellian paradox or a Bradliean regress, an Eleatic loop. And it becomes evident that a different approach must be taken.

The classifying approach, when approached merely as a certain method (when explicated), shows what classification is for; we want to map out our domain of study in order to set up the conditions for a unifying thesis (The synthesis -> if we take implication as the thesis, and explication as the antithesis).

What this thesis is, is simply the exposition of the underlying abstract individual, the individual to which all the classifications are ultimately reduced.

🔬 Metallic Example:

Consider zinc, silver, gold, and copper - different types of metal. What makes them metals is that they share the same set of properties: malleability, conductivity, crystal lattice structure, electron mobility, and so on. What makes them different is that they possess these properties at different intensities. We can imagine a control panel that allows us to derive all metals simply by adjusting electron mobility here and reducing conductivity there.

We find that every modification to one property directly affects the others - for instance, increasing malleability typically decreases hardness, while increasing strength reduces ductility. Yet every stable configuration we observe, where specifically adjusted property rates balance each other out, gives us a recognizable metal. Thus we can say that each type of metal is simply a unique profile detailing the specific intensities at which all core metallic properties stabilize together.

We clearly see that 'metal' is the property-space itself, governed by specific relational rules where properties interact in predictable ways. This implies a Pareto frontier inherent within the metallic structure - and every type of metal represents a Pareto-efficient solution within this possibility-space."

📐 Optimization Framework:

So when we classify metals, we're really mapping the solution-space of an optimization problem constrained by the laws of physics and chemistry. Each element is nature's answer to: "What's the best configuration given these particular priorities?". What we've done here is that we've taken the problem of aporia and turned it into an index for a systematic approach.

Think about how Heisenberg's uncertainty principle was spurred by the mathematical analysis he had immersed himself. We reach the same conclusion, that is, of uncertainty, when we see that metal, in itself, is only something which experience gives us, and in 'experience' we don't see metal, for metal here is an abstract individual; rather, we get something that represents metal. It's true that metal consists of general properties, but even those properties are instantiations of it - Not metal as such, the 'thing in itself', and when our attention falls upon any one of those properties it is a compression of the whole property space we called metal so that we are seeing our choice property by way of the whole system.

-"I remember discussions with Bohr which went through many hours till very late at night and ended almost in despair; and when at the end of the discussion I went alone for a walk in the neighbouring park I repeated to myself again and again the question: Can nature possibly be so absurd as it seemed to us in these atomic experiments?

"When the first terms seemed to accord with the energy principle, I became rather excited, and I began to make countless arithmetical errors. As a result, it was almost three o'clock in the morning before the final result of my computations lay before me. The energy principle had held for all terms, and I could no longer doubt the mathematical consistency and coherence of the kind of quantum mechanics to which my calculations pointed. I had the feeling that, through the surface of atomic phenomena, I was looking at a strangely beautiful interior, and I felt almost giddy at the thought that I now had to probe this wealth of mathematical structures nature had so generously spread out before me. I was far too excited to sleep, and so, as a new day dawned, I made for the southern tip of the island, where I had been longing to climb a rock jutting out into the sea. I now did so without too much trouble, and waited for the sun to rise."

W. Heisenberg 'Physics & Philosophy' (1958)

⚡ Configurational Space:

We can infer from this that determining say 'conductivity' is a determination of the phenomenon 'metal' through that metal or metals whose structure is optimized for high conductivity. think silver, or copper, you know. Remember here that in this 'configurational space', we're dealing with general properties of metal, with metal alone, there's no silver or copper or gold, but only a kind of 'Pareto distribution' of facilities, each stable configuration of this space then becomes what we recognize as specific metals, and each of these metal is only a 'configurational property' of metal, or a Pareto-solution for some 'underlying', but fundamental 'inequality' inherent within the system of metal.

Section 8: Hermeneutics & Measurement

⚖️ Platonic Insight:

In the Platonic dialogues the conclusion of the dialogue is that the 'proof is in the pudding'—the meaning of justice is the actual process of interrogating justice (ironic as that sounds)—the meaning is the process of finding its meaning, just as a mathematical operator is 'meaningless' in itself unless some example of its use is shown.

Similarly, we can't know what justice is unless we see a legal application; certainly here one may agree or disagree with the 'correctness' or 'exactness' of application, but that really only shows that there is some 'ideal' as to how it should be used. Precisely the sensibility we find in mathematics where only measurement counts and at whose summit things like the uncertainty principle and the continuity hypothesis rear their head, and this is what in a different circumstance we'd call aporia.

📐 Mathematical Connection:

If anything, it shows that the Socratic method is inherently mathematical, if by mathematical we mean, 'to approximate', 'to approach'. In mathematics this property is known as 'analysis'.

Now think of that intuition or 'aesthetic' sense where we know what we want to say but lack the words; that is exactly the sense that we have when thinking of the exactness or inexactness of the application of some word. The critical tendency that develops in those cases is the same aporia, but an aporia in which a meaning is 'latent', i.e., acknowledgement, but whose perfect 'concretion' is 'wanting' or 'pending'.

🎯 Baldwin's Control Sphere:

In Baldwin's terms, the 'control sphere' in which predication occurs is vacant, and always is, unless some example, recognized to be only approximate, is given.

💭 Cartesian Parallel:

Think of Descartes' well-known maxim, I think, therefore I am—only think of it as the same attitude of the word whose meaning you are trying to obtain.

As you see, the more critical we grow in our approach to language, the more 'mathematical' it tends to be, hence the emphasis on 'function words'.

🔗 Semiotic Operations:

The utility of Peirce's semiotics lies here in our description of the relation between implication, the sense-yielding but wordless idea, and how 'significance' is developed from and around it—those are operations which Peirce's semiotic science attempts to formalize, and it's what George Steiner discerningly dubs as a further 'translatory' dimension through which a word must pass before it becomes 'meaningful'.

It means that there's a framework that mediates grammar and content that links them, and that it's by comprehending this framework that we can actually properly apply the language in question. In other words, I must learn and grasp the 'semiotics' of, say, the Arabic language in order to understand Arabic as an Arab might.

💡 Fluency Formula:

If 'dreaming' or 'thinking' in a particular language means that you are fluent in it, then imagine having a formula the acquaintance with which allows you to think in that language without knowing much else of the language, because in this case you can use the formula as the square root of any possible idea—that is, understand some idea, any idea, by the rules which the formula prescribes. We did this with the Quran in the last video.

📚 References:

• Charles Sanders Peirce, Collected Papers (1931-1958), on pragmatism and semiotics

• James Mark Baldwin, Dictionary of Philosophy and Psychology (1901-1905), on implication

• Werner Heisenberg, Physics and Philosophy (1958), on uncertainty principle

• Aristotle, Categories and Posterior Analytics, on classification and scientific method

• René Descartes, Discourse on the Method (1637), on cogito ergo sum

• George Steiner, After Babel (1975), Chp4 translation and meaning