Prime Hypostasis

In the closing section of the Prolegomena, Kant discusses the endeavor of placing metaphysics onto a sound foundation (which is the project of the Critique of Pure Reason) and then setting it up as a proper scientific discipline, capable of generating synthetic judgements a priori.

“To discover the means how the endeavors of the learned may be united in such purpose, I must leave to others. In the meantime, it is [not] my intention to persuade any one merely to follow my propositions, or even to flatter me with the hope that he will do so; but attacks, repetitions limitations, or confirmation, completion, and extension, as the case may be, should be appended. If the matter be but investigated from its foundation, it cannot fail that a system, albeit not my own, shall be erected, that shall be a possession for future generations for which they may have reason to be grateful. It would lead us too far here to show what kind of metaphysics may be expected, when only the principles of criticism have been perfected, and how, because the old false feathers have been pulled out, she need by no means appear poor and reduced to an insignificant figure, but may be in other respects richly and respectably adorned.”¹

We view the endeavor of computational metaphysics as improving the principles of criticism, happening within the tradition of the Critique. The following text is an attempt to synthesize an insight from the twentieth century regarding the relationship between truth and provability with the terminology of the Critique.

Hypostasis is a specific type of representational misunderstanding. It occurs when reason, being confronted with fundamental stabilities in experience, erroneously sublimates them into entities assumed to be somehow stable within themselves.

That is, the stabilities in intuition (Anschauung) are turned into something that – supposedly – can be stable in absence of intuition. Those stabilized stabilities are hypostasized space, time, causation, partition and necessity. They are the data format trying to be its own content².

In order for those pseudo-objects to spawn and endure, reason needs to think them in their totality, that is, needs to think them beyond all possible experience. The problem is, of course, that the relational stabilities only exist in the application of functions to a given set of information³. This set of information – that is raw sensibility in Kant’s lingo – is always specific and itself never a totality. Turning the stabilities into a totality regardless is reason stretching beyond itself. In doing that, the necessary antinomy of pure reason arises, and those hypostasized totalities impose themselves onto the topology of reason as unresolvable knots in thought. On the one hand, those objects are among the most natural parts of our world and can be thought locally, on the other hand they strictly cannot be thought globally. They simply fall apart. They are functions that are defined for all objects of experience, but undefined outside of that domain. Space as an experiential appearance works as a model of relational properties but space as a self-stable entity can never be fully conceptualized as infinite nor as finite. Time as the representation of a stepwise change along an entropic gradient emerging from a bounded observer being confronted with computational irreducibility is a sensible necessity, but time as a self-stable entity breaks apart since it could not have had a beginning, nor could it be without beginning and yet have passed.

Causation works as a local model of information preservation over a variety of state transitions but as a self-stable totality needs a first cause itself. And in a similar way, the local notion of necessity thought as a totality needs to self-justify at some fundamental level. All of this points to the fact that all of those are ill-shaped thoughts. Their objects cannot be confirmed nor disproven by any possible experience and assuming them regardless generates a number of directly contradicting necessities which reveal what Kant calls the dialectical illusion of pure reason (Prolegomena §52). Therefore the epistemologist must step back in order to formally see that all those non-entities have been generated by the same faulty principle (hypostasis) and stop the application of that principle.

The entities mentioned so far are just a necessary set of specific cases arising from the architecture of human reason and its default settings and representational languages⁵. There can, and have to be precisely those four types of totalization: totalize the data-formats (space, time), the data-makeup (compound, partition), the data-relations (causation) and the condition for any specific datum (necessity of existence). But there is yet a more general type of hypostatization to be found in all possible kinds of human reason, one that underlies all the specifics of the protagonist-entities of the antinomies of pure reason. It is the result of applying the same faulty principle to the notion of truth⁶ itself.

The hypostatization of truth – although it constitutes what is probably the greatest metaphysical sacrilege – is of an almost perfidious subtlety, since truth seemingly manifests itself in all types of judgements and is furthermore to be encountered – and needed – anywhere one happens to look, indeed being the most stable structural principle of all, one that is common to all concepts and all critiques. And, as is the case with space/time/causation/partition/necessity, truth needs to be recognized as ideal (in the Kantian sense, not in the Platonic sense) and not part of the data. Truth, in its various definitions and demarcations, is the condition of the possibility of structure in concepts and of all theories. It even is the condition of the possibility of all languages. It is reason’s sorting-tool which allows reason to build the relations in which it operates in the first place.

Truth is not only encountered but also discovered⁷ everywhere we look, as if it had already been there all along, which leads us to suspect its existence beyond all things. Even though we might say „truth is a property of sentences“, we still project truth into the thing in itself.

Truth seems to be, even though it can be defined, recognized, computed, explicated and checked, independent of all those endeavors. A constructive notion of truth, which excludes the law of excluded middle, looks interesting at first, second and nth sight but nevertheless seems reductionist, merely descriptive, missing out on actuality, missing the mark of the deep, the true truth beyond.

Similar to the case of dreaming a partial awakening from the pre-critical dogmatic slumber within this very slumber by realizing that color, smell and sound are not part of the world, but still believing that space, time and entropy are, we witness the dreaming of the awakening from the pre-computational dogmatic slumber within this very slumber, whenever people claim that „truth is a property of sentences“ but at the same time assert that the principle of the construction of all true sentences – that is, provability, the possibility of a finite, stepwise, gapless synthesis/derivation⁸ of a well-formed statement, starting with the axioms of a given formal system – is less encompassing than truth itself. But if truth is a property of sentences then it cannot exceed the powers of the construction principle of all true sentences⁹; the truth-property must be assignable to statements as formal objects by some formally specifiable procedure that operates on them. (And any such procedure within a formal system is a proof protocol, and the truths it reaches are precisely those it proves.)

In that, accepting incompleteness (the existence of a true but unprovable statement within a given system) is to admit into the system itself a non-formalizable notion of truth, that is not a formally assignable property of sentences, which is to suspend the system, so that it is groundless and levitating, from a hook that is attached to nothing. Here we realize, that asserting that truth is sentential, while at the same time asserting that provability and truth are distinct, that is, that truth exceeds all sentential apparatus – instead of treating truth as the hypostatization of provability – while simultaneously failing to see the significance of the resulting antinomies spawning left and right, is a sign that we are slumbering peacefully through a thunderstorm.

As of today, finitist stances seem to draw quite some skepticism. We suspect this is because when thinking about constructivist mathematics and its implications, one still consciously or unconsciously applies the notion of finiteness to the thing in itself, where the notion does not make a whole lot of sense. The notion of infinity doesn’t either, but at least this one does not consist of a clearly defined set of decidable functions, constraining the nature of the thing in itself in a weirdly specific way. But finiteness is nothing that can be used on the things in themselves. It is to be used in the space of phenomena. Finiteness is not a claim beyond the realm of phenomena in the first place, infinity is. This is the difference. Classical mathematics and constructive mathematics, in so far as foundational debates are concerned, are not competing for a claim on the things in themselves even if many people involved in the debates might think they do. They compete for the proper structure of epistemology and, in that, reason itself; and here we see that only hypostasis can give birth to classical mathematics, it is pre-critical in a foundational sense, no matter how well it works as a practical approximation or as a powerful theoretical formalism in so many cases. Constructive mathematics in turn, is critical in a foundational sense. It is the result of reason critiquing not just the transcendental ideas, arising from the forms of intuition and the categories of understanding unified by apperception, but the complete set of languages which it can use to think anything.

Even though all of this has already been said and done in other words, nowadays, within a large number of philosophical discourse spaces, it is considered good form to claim that the „whereof one cannot speak“ i.e. the infinity/uncomputability of deep reality, unfortunately cannot be grasped within the limited framework of the human mind and formality itself. But in this very case there is, once again, the speaking of that of which one cannot speak – that is, one imagines doing so and elevates oneself above the limits of knowledge in order to invent untenable metaphysical entities, which one then places above what is possible, thereby viewing the possible as reductionist. A computational-constructivist stance is often perceived as claiming, in impermissible simplification, to penetrate everything, stubbornly excluding what does not fit into this rigid world view. However, the actual problem lies in the fact that if one believes that their mind allows them to overcome the limits of the formally possible, they are mistaking dogmatic etiquette for critical thinking – but the foundational formalism in which philosophy is done cannot contain hypostatized elements.