The Expressional Limits of Formal Languages in the Notion of Observation

TL;DR

This paper explores the fundamental limits of formal languages in representing observation across epistemic, quantum, and phenomenological contexts, highlighting inherent irreducibility and transcendental aspects.

Contribution

It introduces a novel analysis of observation's expressional boundaries in formal languages, integrating epistemic, quantum, and phenomenological perspectives.

Findings

Observables are irreducible atoms without further syntactical content.

A transcendental continuous substratum underpins the observational frame.

Formal languages have inherent limits in fully capturing observation phenomena.

Abstract

In this article I deal with the notion of observation in the most fundamental sense and its representation by means of formal languages serving as expressional tools of formal-axiomatical theories. In doing so, I have taken this notion in two diverse contexts. In the first as an epistemic notion that refers to its interpretation in a formal mathematical environment and then to its interpretation in a quantum mechanical environment. The second context in which I tried to approach the notion of observation is that of a phenomenological constitution basically as it is described in E. Husserl's original works. Assuming that in phenomenological constitution mathematical objects are special cases of perceptual objects including consequently objects of a quantum mechanical measurement, the question is to inquire on the limits of their description in the language of a formal-axiomatical theory. On one hand, I derive an irreducibility on the level of observables as indecomposable atoms without any further syntactical content in formal representation and on the other a transcendence of a continuous substratum self-constituted as a kind of impredicative synthetic unity on which to define an observational frame and generate a predicative universe of discourse.