Shannon’s information theory (IT) provides a rigorous framework to quantify the amount of information that a system Y has about a system X, irrespective of what the information is about. IT metrics count the (logarithm of the) number of different states of system X that system Y can distinguish based on Y’s available information (or, conversely, the missing information on X’s state). This information can be translated into a binary file that represents the information that Y has on the state of X.
Shannon’s information measures hence concern the representation of information, while purposefully disregarding its significance to the recipient. In IT, the information system Y has regarding system X is the same whether or not Y can extract value or meaning from its ability to differentiate among some of the states of X. In cognitive sciences, instead, the focus is on semantic information, that is, on the meaning that the information carries for the receiver.
To use D. M. MacKay‘s words, semantic information is “difference that makes a difference” for the receiver. Accordingly, not all distinguishable states contribute to the amount of semantic information. Daniel Dennet in his new book gives a recursive definition of semantic information as “design worth getting“. Design refers to the use of “semantic information to improve the prospects of something by adjusting its parts in some appropriate way“. In other words, semantic information is defined by the fact that it can be leveraged to determine the form, or the design, of something for the benefit of the recipient. Semantic information hence depends on the receiver, and it need not be represented or saved to have an impact on the receiver’s design. Semantic information is valuable, and misinformation and disinformation are its perversions.