A measure for intrinsic information

We introduce an information measure that reflects the intrinsic perspective of a receiver or sender of a single symbol, who has no access to the communication channel and its source or target. The measure satisfies three desired properties—causality, specificity, intrinsicality—and is shown to be unique. Causality means that symbols must be transmitted with probability greater than chance. Specificity means that information must be transmitted by an individual symbol. Intrinsicality means that a symbol must be taken as such and cannot be decomposed into signal and noise. It follows that the intrinsic information carried by a specific symbol increases if the repertoire of symbols increases without noise (expansion) and decreases if it does so without signal (dilution). An optimal balance between expansion and dilution is relevant for systems whose elements must assess their inputs and outputs from the intrinsic perspective, such as neurons in a network.