Actuality and Potentiality
Both the formative actuality and the materiable potentiality are positivities and not mere “nothings”. They are distinguished both formally and in the actualization of an entity. Those two positivities – two positions, two thetic aspects – are put one in face of the other, i.e., a position ob another; therefore, between them, an ob-position. Both are positives, but correlatives, since the capacity of being determinate is the capacity of being determinate by a determinative act; and the determinative act is the act of being of the capacity of determination. In a way that, in this conception, form and matter – as called in Aristotelian philosophy – are correlative and cannot properly occur if separated, in this sense: form is a form that determines.
Much better, then, is to use the expression “actuality and potentiality”. Actuality is the actuality of a potentiality; potentiality is the potentiality of an actuality. Actuality is what determines; is the determinative capacity of the determinable capacity of a potentiality. The determinative actuality to which is not “ob-posit” the possibility of being determined, would lose its power. In a way that the Dyad, qua itself, is a sort of universal substance, is what “sub-exist” in all things, since all things emerge from it. In Aristotelian language, matter is a primary substance, is ousia prote, and form is a secondary matter, ousia deutera. The finite being is the composition of those two positivities. That is also the Pythagorean thesis, with a distinction that substance is only one, a same reality with a twofold capacity to determine – its active aspect – and of being determinate, which is the passive aspect.
Thus, all that is finite is a product of such opposition, and that is the reason why, within the arrangement of the Pythagorean laws, the opposition law comes in second, following the law of unity; it derives from the law of unity, since opposition implies two unities: determinative unity and determinate unity; thence emerges the idea of category. The first Pythagorean category is substance, but substance in a sense of being simultaneously its oppositions, i.e., of being two positivities, which are the formative fact and the materiable potentiality that emerge in any finite being.
Now, this conception is perfectly adequate to the fundamental thought of Aristotelianism, as well as Scholasticism and all well-oriented philosophy. Difficulties that may – philosophically – arise and that should be solved at the concrete part of Mathesis, concern to the distinction between actuality and potentiality, if it is either a real, physical distinction, or not. We adopt the Pythagorean position that there is no abyss between actuality and potentiality, since the finite actuality – that belongs to the beta context – and the potentiality – that only belongs to the beta context in its passive sense – are inseparable and constituted under two different formal aspects, with different functionalities, reason why the Scotists, for instance, affirm this correlative aspect and admit that the actuality corresponding to the beta context (not the actuality of alpha context) is nothing more than the actuality of the potentiality, and potentiality is no more than a potentiality of the actuality.
This discussion should be clarified further on. Beforehand, we know that, for our mathetic conception, it is perfectly clarified, since, in the beta context, which is the context of things ab alio, of finite things, actuality cannot be totally separated from potentiality. Such actuality must be an actuality somehow potential, in an also passive sense, for the contrary it would be a pure actuality and pure actuality can only happen within alpha context, the context of the being a se. The Scotist position, inevitably, must emphasize as fairer and safer than the Thomist one (as a school of thought, of the epigones), not of St. Thomas in particular, since opportunely we shall demonstrate that the legitimate thought of St. Thomas would accept the Scotist solution.
We have now, perfectly established, the two first laws: the law of one (the law of unity) and the law of opposition, that rule all things, including the things of alpha context, since, as we have established, between the Hen Prote and the Hen Deuteron, the two ones, the first and the second ones, exist an opposition, but a transcendental one, not such as the opposition of beta context, in which the limits can be physically determined, whilst in the former (alpha context) is a determination of roles (or functions), since the Father (as generator, the Will, Omnipotence) and the Son (as generate, the Knowledge, the Intellect) are distinguished but, nevertheless, an infinite Omnipotence necessarily implies an infinite Understanding, the Omniscience, which also implies the former, thus forming both the same nature, although with different roles.
Law of Opposition
Now, all that is finite is a product of such opposition between determinative actuality and determinable potentiality. The number 2 symbolizes such law, such logos of opposition. All things of beta context, all finite things, comprise at least two orders of being. There is always an alternation, an opposition, an ordination of its composing elements, of its tectonic. All entities of beta context have a tectonic duplicity, a duplicitous structure. There are always opposite dyads, expressed through pairs of contraries, which constitute polarities, not only of all philosophize but of all of the most primary classifications and human divisions. It is not possible to study any being without considering, at first, its aspect of unity, and, secondly, its dualistic aspect, i.e., the aspect of oppositions within its tectonic or that rules its way of being. Therefore, there is opposition between the active-passive principle of the determinative and the passive-active of the determinate, from where emerges all heterogeneity of finite beings. Determination establishes the limited and the illimitable, since all things are formally unlimited, but materially limited. All things can be visualized under the angle of its unity, as under the angle of its duality; all things can be seen as a bundle of contrary oppositions, as stated by the Pythagoreans. No human knowledge about something is perfect if not studied under the aspects of its unity and its oppositions, dyadcally classified and constitutive of its own being. The two fundamental laws are, therefore: law of unity and law of opposition. Opposites are indispensable, necessary, and – within beta context – absolute. Dyadic rules all things and, at the same time, transcend all finite things.
The fundamental opposition – that manifests in all beings – is the principle of all finite entities. Hence, the opposition is presented as fundamental in Pythagoreanism. The opposites are face to face, one is referred by the other, both correlatives, since the formative actuality is the formative actuality of a materiable potentiality, as the materiable potentiality is the materiable potentiality of a formative actuality. Therefore, both constitute the hipokeimenon in the Greek sense, the ultimate subsistence of the universal substance.
Thus, we have come to the two first laws. Now, from a forming reference between those two, from this relatum, from this “being ab aliud”, this necessary referring of an ab aliquid (to other), a relation is necessarily formed (from the opposition), since those opposite entities are analogized by a common term. Those entities of beta context are opposites that constitute the same reality, thence emerging the third law, the law of relation, also called law of series, which we shall discuss in the next chapter.
 “The context of the absolutely simple, in Mathesis, is called alpha context, while the context of the relatively simple and of composts of any specie is called beta context.” (The Wisdom of the Principles, p. 158)