Axiomatic Basis
Provided with the unique set of tools we just assembled, we can lay out the foundations for the entire edifice of our work based on one simple, elegant, and powerful principle, that we shall call Unicity Principle. It reads:
All beings of equivalent semonic value are essentially the same.
It sounds almost utterly dumb and obvious when stated, specially after we’ve given ourselves the trouble of defining what molarity is. But if one looks closely enough, he’ll find that it encases simply ALL of the things we thus far concocted, plus myriad more not only within our framework.
I know, bold claims… but let’s start with the basics:
First off, we arrive at the obvious conclusion that the Semes, being the prima synod, is indeed the one and only absolute, for otherwise it would imply that it is not the prima synod, which would be a contradiction (for only the true prima synod could have its semonic value of ‘1’ in respect to all other beings).
Also, it helps us explain why every equally-ordered semon is equivalent, since their semonic value must be equal — a lower-order semon cannot partition into two unequally-valued sema (for instance: 3/4 and a quarter), for that would imply that they have some intrinsic feature differentiating their worth, such as their own sema, and a semon cannot itself be partitioned before even coming into being. Hence, beings of such kind (‘broken valued’) can only be made through the combination of different sema, even of those who do not share the same order as they do.
Further, the principle entails the very definition of what sema are — a featureless unit of something -, and implies that whichever properties they may possess is exogenous to themselves, because otherwise they would be a single entity (for, in their essence, they are indistinguishable). The fact that a multitude of sema exists, coupled with the Unicity Principle, implies that they necessarily must be in a partitioned state, which in turn is the mechanism that gives rise to the very Worldtree and its intricate structure. This is analogous to Leibniz’s famed “Identity of Indiscernibles”, an ontological principle which states that there cannot be two or more separate objects or entities that share all their properties — though Leibniz’s own account doesn’t quite get there, formally speaking, at least in this reader’s opinion. Making the basal entities essentially featureless , I’ve come to believe, is enough to cover that last mile of formal correctness.
One vital point must be made though, and it has to do with that very controversial little word near the end of the axiom — ‘essentially’. One must be particularly careful with his choice of words in this sort of philosophical musings, and I feel it’s important to clarify in what sense it’s being employed. “Essence” is usually understood in philosophy as that which constitutes an entity’s necessary properties (more on that later on), that is, what it couldn’t exist without. This spells trouble for our conception of sema, because the kernel of the very notion is the fact that they’re intrinsically featureless — which means: no internal properties distinguishing this semon from that semon and so on (remember that the semonic value is a structural, hence external, property). What is the essence of a semon then? We’ve already covered that: none other than pure reality. Reality is, in our book, something able to produce an affection on a given subject; but that doesn’t tell us anything about its properties, precisely because it’s agnostic regarding them — they’ll only arise as an effect of the partitioning process, after all. Rather, we can only define a semon’s properties negatively, as the ‘missing molarity’ that prevents it from reaching some other stage in the Worldtree. On the other hand, the axiom tells us explicitly that all beings of equivalent semonic value are essentially the same, which seems to imply a contradiction. After all, how can they be different and alike at the same time — something explicitly forbidden by the identity of indiscernibles? The answer lies in the fact that, though essentially the same, structurally a semon can have many — infinitely even! — different setups, and that does make a difference. In fact, it makes all the difference! Synesism is at its heart a structuralist worldview.
What that means is that an action performed over a single semon will result in a very different outcome from one performed over its second or third-order equivalents, as well as to any of their possible subsets. The reason for this difference in outcomes is the monotonicity of partition/recombination — ie, the fact that a semon can only subdivide into two or more equally-valued bits (which we already proved a necessity), and whose converse is also true (that is: only two or more equally-valued sema can be fused together into a lower-order semon). That’s what defines the kernel of action in the theory, with each individual partition/recombination constituting an event (which we shall call action) in its own right, with no jumps allowed in-between them; time itself is merely a particular ensemble of events unfolding in a particular sequence.
Thus, regardless of their semonic equivalence, no two sema are ever fully alike (which, again, is a corollary of the identity of indiscernibles principle). That translates into the fact that an action will never result in the exact same outcome if applied to different signatures, and enables our understanding of how they can all be essentially the same and yet different, while also providing a philosophical justification for the scientific method as the most efficient manner for probing reality: through trial and comparison with a established benchmark (eg, null-hypothesis and statistical significance).
Let’s now list and schematize the mais results, which we’ll regard as the theory’s postulates:
0. Unicity Principle (or Identity of Indiscernibles)
As we’ve already seen, it formalizes the notion that no two or more absolutely-equivalent entities may exist (if they are absolutely-equivalent, they must be one and the same), for that would be in contradiction with pretty much the entire edifice we’ve so far erected.
1. Principle of Plentitude
Basically it means that everything that can exist does exist. This is a natural extension of the fact that the semonic value of a system always remains invariant. When we consider this together with a semon’s partitioning, the natural conclusion is that the “missing” quanta — from the perspective of someone inside that system — must go somewhere in the process, which in a physical sense would translate to the existence of multiple universes sprouting every time a partitioning takes place (note: this is only valid in the case of basal sema, which we’ll talk about on the next section). Our own universe, with its particular set of features and unique evolution, is thus but one of many others in which the conditions are only so slightly different, and yet they were all made possible only by each other’s very existence. Or, to be blunt: completeness.
2. Instantiation Principle
It states the impossibility of a property to exist that is not possessed by some object or ensemble of objects. In other words: not only everything that can exist does exist, but the all-existing whole also must encompass every other property within it as well, such that there can’t be any meaningful property, feature of quality that can’t be embodied by some instance of itself. Also referred to as soundness.
3. Coherence Principle (or Principle of Sufficient Reason)
This principle asserts that there can be no entity that isn’t accounted for, or, in other words, no effect that follows without a cause. Note that this does not refer to the classic notion of causality, which is temporal in its constitution; rather, cause and effect here are of a semonic nature — such that, for example, a semon can partition into two, three or a thousand other sema, but the product of this process can never result in a semonic value for the sum that is greater or lesser than the original whole, however distant or otherwise disconnect they become, and vice-versa. If a change in the semonic value of the system is accounted for, what it means is that there must be another, extraneous system involved in the process. Or, in the latinized form: ex nihilo nihil est.
4. Multiplicity Principle
This principle says that a semon cannot partition without, in the process, producing an increased quantity of entities. Put differently: the emergence of number in the universe is a direct result of its continued branching. So the more specific an entity, the more constituents it requires, and the further it is from any given synod; you can’t be large and stay at the top at the same time.
5. Anti-reflexivity (or Principle of Stratification)
This one, with the messiest name, is perhaps the most important, and part of the reason is because of how deeply it challenges our intuitions of how the world is or should operate. It states that the supremum (or ultimate instance) of a given property can’t be placed alongside the elements that property describes. In plain language, what that means that the “ideal” or consummate of some quality X is not any of the objects that X applies to. Consider the example of natural numbers: what is the highest natural number? Obnoxious undergrads will tell you such thing does not exist, since whatever number you come up with, I can always add one more to it and make it larger, but as a matter of fact it does — it’s just not a number. Not a regular one at least: the largest natural number is an ordinal, and it’s called omega, or ω, the order type of the natural numbers. Similarly, one could argue that the “perfect friend” (where perfection is akin to being the most of something) is not a friend at all, but perhaps a partner or a lover; and the perfect lover is not a lover, but a fling or one-night-stand, and so on. Deep down we all feel something like this must be true, but we just assume “perfection” isn’t a real or attainable thing. Rather, it is the case that when categories reach their maximum they overflow and tap into the next level of description (or, in our case, a lower-ordered stage). This relates to Synesism by the fact that sema are featureless things that only gain their properties when partitioned, so to even have a quality to speak of one must first be in a lesser form of existence (ie, it must be manifest). The more thought we put into this principle the more instances we can find of it in our familiar landscape — from ideas to people themselves, there’s always that little asterisk at the side of everything we encounter preventing it from being ‘flawless’ to our own eyes; but deep down we know that, had that smirch not been there, the entire edifice of our affection might disappear as well. Tragic perhaps, but just the way things are.
