Equivalence, (Crypto) Morphism and Other Theoretical Tools for the Study of Information - Marcin J. Schroeder (Proceedings)
The meaning of information can be understood as a relationship between information systems. This study presents a brief outline of theoretical tools for the analysis of this relationship. Considering the informational character of reality, it is natural to extend the relationships between signs to include the concept of meaning as another instance of a relation between the informational entities of a sign and its denotation. However, this approach to the semantics of information does not require any specific ontological commitment, as the intention is always directed towards the object presented to us as a structural manifestation of information. Whether there is something that differs from this informational structure and is beyond our capacity to comprehend directly, or whether there are objects that are the result of our own active engagement in their formation, is a matter of ontological position, with respect to which our approach is neutral. The experience of logic tells us about the dangers of self-reference and the problem of the non-definability of the truth, demonstrated by Tarski. To avoid similar problems, we need precise theoretical tools to analyze relationships between information systems and between instances of information involved in semantics. These tools are also necessary for the definition and analysis of levels of informational abstraction that extend beyond the traditional linguistic and logical context.