Formalization arises in relation to what has not yet been grasped by form. The question of the nonformalizable concerns the very experience of ungraspability and its place in reality, not merely a list of objects for which no notation has yet been found.
From Instrument to Ontology
The thesis “only what can be formalized exists” is a meta-position, not a formal theorem. The claim that formalization is universal cannot be derived from the formal system itself, nor can it be justified exclusively by its means.
Formalization serves as an instrument of description. The transition from an instrument’s usefulness to the assertion that only what it describes exists is a logical leap, an instance of instrumental reductionism.
The Givenness of the Nonformalizable
The nonformalizable influences choice and action. If something causally influences behavior, and behavior belongs to reality, then that something belongs to the structure of reality, even if it is not exhausted by formal description.
What matters here is an experienced fact: a person encounters something that eludes fixation. This ungraspability can itself become the source of epistemic movement and an attempt at formalization.
The drive toward formalization can be a reaction to uncertainty and rupture. Denial of the nonformalizable is often motivated by something that cannot itself be reduced to a formula.
The Act of Distinction and Form
Three moments can be distinguished in the formation of form:
- Encountering the unformed or the ungraspable.
- The act of distinction.
- Formal fixation.
The act of distinction and form are not identical. Form fixes a distinction; the act itself is a preformal source that is not exhausted by the result of its fixation.
The dynamics of thinking continue:
The unformed → the act of distinction → fixation in form → new unformedness.
The Formalist’s Paradox
A subject can deny the nonformalizable at the doctrinal level while simultaneously acting out of the experience of nonformalizability as the source of their own epistemic movement.
If something influences behavior, it belongs to the structure of reality. If, at the same time, it cannot be completely formalized, then reality is not exhausted by what can be formalized.
What Requires Further Distinction
Three statuses of the nonformalizable remain to be distinguished:
- a limit of formalization;
- a source from which form arises;
- a persistent background of distinction.
These statuses cannot be regarded as identical merely because each points to something that is not exhausted by formal fixation.
