Non-Transferability in Communication Channels and Tarski`s Truth Theorem

TL;DR

This paper introduces a theorem demonstrating the fundamental limits of communication channels in transmitting propositions and their truth values, drawing parallels with Tarski's Truth Undefinability Theorem and related logical concepts.

Contribution

It establishes a formal link between non-transferability in communication channels and Tarski's Truth Undefinability Theorem, providing new insights into the nature of information transmission and logical undefinability.

Findings

No encoding-decoding can fully transmit all propositions and their truth values.

Transmitting a channel's error state leads to non-transferability.

Non-transferable codes are mathematically equivalent to Tarski's undefinability of truth.

Abstract

This article explores the concept of transferability within communication channels, with a particular focus on the inability to transmit certain situations through these channels. The Channel Non-Transferability Theorem establishes that no encoding-decoding mechanism can fully transmit all propositions, along with their truth values, from a transmitter to a receiver. The theorem underscores that when a communication channel attempts to transmit its own error state, it inevitably enters a non-transferable condition. I argue that Tarski`s Truth Undefinability Theorem parallels the concept of non-transferability in communication channels. As demonstrated in this article, the existence of non-transferable codes in communication theory is mathematically equivalent to the undefinability of truth as articulated in Tarski`s theorem. This equivalence is analogous to the relationship between the existence of non-computable functions in computer science and G\"odel`s First Incompleteness Theorem in mathematical logic. This new perspective sheds light on additional aspects of Tarski`s theorem, enabling a clearer expression and understanding of its implications. Keywords: Non-Transferability, Channel Theory, Tarski`s Truth Theorem, Semantic.