individual language elements could and should be combined. The syntax of natural languages is much more complex (see appendix A2) than that of formal artificial languages. The syntactic rules of an artificial language must be complete and unambiguous because, for example, a compiler program which translates written programs into computer code cannot call the programmer to clarify semantic issues.
Knowledge of the conventions applying to the actual encoding as well as to the allocation of meanings is equally essential for both the sender and the recipient. This knowledge is either transferred directly (e.g., by being introduced into a computer system or by being inherited in the case of natural systems), or it must be learned from scratch (e.g., mother tongue or any other natural language).
No person enters this world with the inherited knowledge of some language or some conceptual system. Knowledge of a language is acquired by learning the applicable vocabulary and grammar as they have been established in the conventions of the language concerned.
4.3 The Third Level of Information: Semantics
When we read the previously mentioned book B, we are not interested in statistics about the letters, neither are we concerned with the actual grammar, but we are interested in the meaning of the contents. Symbol sequences and syntactic rules are essential for the representation of information, but the essential characteristic of the conveyed information is not the selected code, neither is it the size, number, or form of the letters, or the method of transmission (in writing, or as optical, acoustic, electrical, tactile or olfactory signals), but it is the message being conveyed, the conclusions, and the meanings (semantics). This central aspect of information plays no role in storage and transmission, since the cost of a telegram, for example, does not depend on the importance of the message, but only on the number of letters or words. Both the sender and the recipient are mainly interested in the meaning; it is the meaning that changes a sequence of symbols into information. So now we have arrived at the third level of information, the semantic level (Greek
semantikós
= characteristic, significance, aspect of meaning).
Typical semantic questions are:
a) Concerning the sender:
– What are the thoughts in the sender’s mind?
– What meaning is contained in the information being formulated?
– What information is implied in addition to the explicit information?
– What means are employed for conveying the information (metaphors, idioms, or parables)?
b) Concerning the recipient:
– Does the recipient understand the information?
– What background information is required for understanding the transmitted information?
– Is the message true or false?
– Is the message meaningful?
Theorem 13: Any piece of information has been transmitted by somebody and is meant for somebody. A sender and a recipient are always involved whenever and wherever information is concerned.
Comment: Many kinds of information are directed to one single recipient (like a letter) and others are aimed at very many recipients (e.g., a book, or newspaper). In exceptional cases, the information never reaches the recipient (e.g., a letter lost in the mail).
It is only at the semantic level that we really have meaningful information, thus we may establish the following theorem:
Theorem 14: Any entity, to be accepted as information, must entail semantics; it must be meaningful.
Semantics is an essential aspect of information, because the meaning is the only invariant property. The statistical and syntactical properties can be altered appreciably when information is represented in another language (e.g., translated into Chinese), but the meaning does not change.
Meanings always represent mental concepts, therefore we have:
Theorem 15: When its progress along the chain of transmission events is traced backward, every piece of information leads
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