O-truth: Truth as an Approximation of Observer Models to Real Space Objects

2023

Truth is illusive. Regardless, it is a foundational concept across domains of knowledge, from scientific inquiry to logical reasoning. Traditional definitions often lack the generalizability required to encompass the diversity of opinions encountered in different contexts. This paper introduces a comprehensive mathematical framework aimed at defining truth in a manner that is both generalizable and applicable to a wide range of statements, including empirical scientific truths and abstract logical propositions.

Nothing contained in this paper is truly novel. In a way, it is simply an explicit statement of what has been implicit in the ages-old efforts of physics as a field of inquiry.

The framework leverages Many-Worlds Logic to represent possible models within a computational space, integrates information theory to quantify discrepancies between models and reality, and accounts for observer effects and quantum limitations. By formalizing these elements, we believe that the theory provides a robust mechanism for measuring truth as the convergence of models towards an underlying reality, acknowledging that absolute truth remains unattainable due to inherent uncertainties and observer constraints.

Furthermore, we emphasize that no real-space variable can be known in its absolute sense. Our instruments and senses provide only approximations to unknown “true” values. The act of defining a variable such as “mass” or “temperature” already presupposes models and calibrations that recursively invoke still other variables, culminating in an infinite regress or at least an iterative refinement. Thus, each “measurement” is itself a model-based inference about some deeper reality.

Truth

Truth is defined as a distance measure: how accurately a computational model represents its real counterpart. It is quantified by assessing the discrepancy between the model and the actual state of the relevant piece of the universe.

Model (Computational Space)

The Computational Space: $$\mathcal{M}$$ is an abstract mathematical space consisting of all possible models. Each model $$ M \in \mathcal{M} $$ is characterized by a set of variables and their interrelations.

Reality (Real Space)

Real Space: $$\mathcal{R}$$ represents the true state of the universe or the system being modeled. It is characterized by the actual values of variables, denoted as $$ \{X_1^*, X_2^*, \ldots, X_n^*\} $$.

Importantly, we do not have direct access to these $$X_i^*$$ values in a strict sense. Every “measurement” or “observation” that attempts to ascertain $$X_i^*$$ inevitably involves further instruments or conceptual frameworks. Thus, $$\mathcal{R}$$ is the hypothesized reality “behind” our observations, not a set of directly known values.

Observer

An Observer is an entity that perceives and interacts with reality, influencing the information available for model construction. The observer's limitations and perceptual mechanisms are integral to the framework.

Variables

Variables are atomic or composite descriptors that capture properties or states within both the model and reality. For example, variables such as "horse," "tail," and "geographical location" are considered.

However, these “variables” themselves come with the caveat of being observer-dependent constructs: we carve them out of the continuous flux of reality using our conceptual categories and measuring devices.

Model and Reality Representation

Definition (Model Space)

The Model Space: $$\mathcal{M}$$ is defined as:

$$\mathcal{M} = \{ M_1, M_2, M_3, \ldots, M_k, \ldots \}$$

Each model $$ M_k \in \mathcal{M} $$ is characterized by a set of variables $$ \{X_1, X_2, \ldots, X_n\} $$ and their interrelations.

Definition (Real Space)

The Real Space: $$\mathcal{R}$$ is the true state of reality, characterized by:

$$\mathcal{R} = \{X_1^*, X_2^*, \ldots, X_n^*\}$$