I.

A cynical take on quability is that it plays the role of a scapegoat. There are many loose ends in theory, and worse, a handful of insidious circular references give it the flavor of a just-so story. I can present the courage of convictions in defense of its eventual consistency (shortly before such scrupuli lose all importance in face of the asemic horizon). So far, however, we find great utility in phraseology regarding quables versus quability conditions and, maybe more critically, the “systemic sources of quability. Our mix of technical (tempo, physics, diegesis) and ersatz-technical content lends cement-like solidity to the gravel-like spread of heuristic analyses that connect theory to human affairs. But this is a cynical, pessimistic view.

An understanding of quability closer to its historical role in theory foregrounds its connection with adequacy as an “image of thought” in opposition to essentialism. Essentialism is a n’est rien que: the essential mother is nothing but a mother — not mortal nor feminine, abstracted from all other non-motherly considerations. But the adequate mother is a mom, it fulfills the general adequacy to generally accepted criteria of motherhood. Quability is a huge, dizzying generalization of adequacy. More precisely, a long stairwell in which each level is quable to the next abstraction of quability conditions; more precisely yet, a general graph, made readable by its physics. (Welcome to asemic horizon, there’s a lot to read in order to become fluent).

There’s a third view (as in the parable of wise blind men groping different parts of an elephant) of quability that stops at qua, the Latin particle. By now I have to resort to Google to find the primary sources at asemic-horizon itself, but there’s a good quotation to repeat here:

Music theory is the only way in which the ability to understand flamenco guitar music can be decoupled from the indefinitely specific experience of gitano jerezano life. But note how music theory refrains from demoting the qua to an in facultatem — literally any music theorist will tell you there are indefinitely many theories of the valuable ways to arrange musical sound. This is how the civilizational achievements of guitarra flamenca can be conveyed as quability conditions. Despite his payo (non-gypsy) condition, Capullo de Jerez proves himself by fire (and not by theory) quable to gitano flamenco. It’s not that Capullo can be proven adequate to flamenco, it’s that the numinous formula of the duende (the diabolus in musica that at critical moment takes over an artist’s soul in Andalucía) is verified true by him.

In this third view, quability is something between an epistemological inversion (not unlike subjective probability) and a cop-out, a method for sidestepping epistemology. Here the value of music theory is openly recognized, but music is irreducible to music theory; what’s more, Capullo de Jerez is presented as the quability final boss to flamenco music, itself much more general than music theory. Theory is a bridge between “kid with a Casio keyboard” and “Bud Powell wowing Arthur Rubinstein” — and often a useless bridge for lack of sufficiently large axiologies.

II.

There’s a fourth view. It was awkwardly aluded to in a private post (passwords given back in 2019 still work; often akwardly alluded to, but left unexplained. In this view quability theory is an extramathematical generalization of probability theory. Now, mathematics is literally concerned with knowledge, while quability is a kind of bundle or membrane of strategies to eschew preoccupations with knowledge — we insist on following Vija Kinsky, this is theory, I deal in theory.

Our previous presentation of probability theory was sidetracked by minor technical-mathematical concerns; this type of neurosis, where the quability of nonmathematical uses of math jargon and equations is continually doubted and pieces of excess rigor come through, should be more common, not rarer. (There’s the issue that so many interested in theory are not mathematically trained; but each of us gives what they can). Let us give it another go.

The core mystery of probability theory is the sample space . In a pedagogical setting where all uncertainty has to do with a pair of dice, the sample space has elements like (1,1), (1,2) &c. each representing the outcome of the first and second die. But in general the sample space can be indeterminately (but not arbitrarily) weird. The best way to proceed is simply to imagine it contains events labeled . Here we’re still doing mathematics, albeit mathematical theory (in a close sense to music theory).

In probability theory, we proceed to define “random variables”, which are actually neither random nor variables; rather, they’re functions mapping each elementary event . It’s here that we want to depart from mathematics and sail towards the asemic horizon. Random variables are said to be real-valued (or vector-, or even simplex-) because that’s what the function map to; in jargon, it’s their image. But we’d like functions of the unlabeled sample space to have images that are not conventionally mathematical. This move would swap ordinary equality ( for the loose philosophical concept of adequacy.

But why resort to equations when we had a perfectly convincing heuristic account of adequacy with Capullo and all that? Because “random variables” are not just any function. We need yet another mathematical notation for the SOS (set of subsets) of $\Omega$ (in the simple case of a coin flip — . Call this . Then the Laws of Probability demand of a random variable that

for every sensible K; this is called measurability to ; n shorthand,

If this is true, a probability measure that assigns elements of . But again, to move on from probability to quability, we need to loosen up all the implicit set theory going on here. We need the domain of $X$ (the sensible choices of $K$) to be very general and extramathematical — discourses, scenarios, diegesis, etc. At the same time we need to preserve something like the mathematical indefinition of what the sample space looks like — a bag of whatevers labeled .

What the hell does it earn us? It gives us the concept of sigma-algebras (which we may as well demathematize and call “sigmas”), and the idea that adequable observables must be measurable to some sigma. Snap back to the usual jargon and we see the passage from quable (observable) to quability condition (sigmas) plain as day.

Again, why? Because it constrains versions 1 (cynical), 2 (adequacy) and 3 (qua as in facultatem) — ultimately all heuristics that let us play fast and loose — within a framework that does still bear qualification — but serves as the quability requirements for quability systems to earn that hallowed name.

IV.

We should, every time equations show up, warn against the temptation to overmathematize, or even mathematize at all. The agitating nucleus of mathematics practiced outside metamathematics is set theory, and here we’re consciously drifting away from it precisely to practice non-formal philosophical theory. I borrow from mensurability like I borrow from Crystal Castles and hope this gets us moving forward faster and stronger?

Why a renewed urgency at the expense of “theory without end”? Because developed societies are fucking coming apart at tear points of our making. We need General Axiology; how to find it?