> Shannon information theory provides various measures of so-called "syntactic information", which reflect the amount of statistical correlation between systems. In contrast, the concept of "semantic information" refers to those correlations which carry significance or "meaning" for a given system. Semantic information plays an important role in many fields, including biology, cognitive science, and philosophy, and there has been a long-standing interest in formulating a broadly applicable and formal theory of semantic information. In this paper we introduce such a theory. We define semantic information as the syntactic information that a physical system has about its environment which is causally necessary for the system to maintain its own existence. "Causal necessity" is defined in terms of counter-factual interventions which scramble correlations between the system and its environment, while "maintaining existence" is defined in terms of the system's ability to keep itself in a low entropy state.
https://arxiv.org/abs/1806.08053
Roughly speaking: The amount of computation or energy needed to perfectly reproduce a random source, such as a coin flip, is high, while the significance or meaning, for the average receiver, is low. Natural language text requires less computation to reproduce [1], but, for the average receiver, the significance is higher.