Pre-Meaning: Some thoughts  

Copyright © Constantin S. Chassapis

The degree of pre-meaning is approached here as a measure of the potentiality of a state-sequence to carry meaning.

Meaning and complexity are strongly related.

We will name state-sequence any sequence of states (for example: LASER light intensity time-series, English, Greek or formal texts, DNA-sequences, WEB SITES, etc.), 1-state the element (atom) of which the state-sequence is made of, s-state a combination of s 1-states. These 1-states may represent numbers, symbols, images, concepts, or even Internet sites! Also, any s-state can be considered an 1-state in an appropriately redesigned experiment or analysis.

We will use the term state-space or alphabet for the set of 1-states. In the general case where we do not discuss an actualized state-sequence but any one, or all potential ones within a given context, we will use the term syntactic-space.

We will use the term semantic space to denote the meaning that a syntactic space carries with clear understaning of the fuzziness this term carries.

The union of syntactic and semantic spaces builds what we may call a conceptual space.

If therefore "meaning" is that "abstract" quality of a semantic space that reveals the very existence of it, we understand the degree of pre-meaning as being that measurable "dust of meaning" related to the complexity, or to the hidden information of the elements of the related syntactic space. In some cases, the "dust" of meaning can be related to the dust of some attractor of some phase space.

How one can understand what is the meaning of meaning? The answer is linked to the fact that meaning is the result of the alteration of a representation, and this alteration, that is usually a result of "experience", is where meaning lies. Positioning this discussion in the general theme of the complementarity of structure and dynamics, we may relate the syntactic space to "structure" and meaning to "dynamics" in the sense that semantic information (meaning) is quantified by its usage and "usage" implies dynamics. This subject is particularly abstruse because meaning is build upon differentiation of meaning. The aforementioned "representation" carries meaning by itself, and, the meaning arising from the "alteration of the representation" is still meaning, albeit of a somewhat different degree.

Meaning therefore also exists outside of the semantic space. It possesses a strong meta-semantic dimension.

Let us accept, for the moment, that a "core" set is the alphabet of a syntactic space. Meaning, evidently, exists outside the "core" set and there is no reason to assume that it will exist "inside" that extended space that arises from all conceivable combinations of the core states. We can put therefore, in a first approximation, the existence of meaning in a parallel space, in a "dictionary set", where there is a correspondence of the entries with the 1-states and with all combinations of them.

In a case like this, "creation of meaning" may arise from a situation where the evolution of the probabilities of the 1-states (and of all s-states), alters the contents of the "dictionary". The process of alteration, a catastrophe-like process that is very probable that it will be understood with the help of Neural Nets theory.

One may note that the probabilistic substructure of a syntactic space is already linked with the possible meaning of it. One can argue therefore that the degree of pre-meaning is not absolute, is not unique (since it is linked by a feedback loop to meaning), and therefore the measurability of the degree of pre-meaning is under question. The answer is as follows.

Obviously, meaning is not unique but, we can "freeze" a syntactic space (in the form of a state-sequence) and measure its degree of pre-meaning. It is more than possible that the same space in another "place and time" will have different meaning. In that case it will also have different degree of pre-meaning.

The interesting aspect of such a procedure is that one can define extrema on the degree of pre-meaning, even some kind of average degree of pre-meaning related to a specific syntactic space, investigating therefore the capacity of a particular space as a carrier or as a channel of meaning. This can even be connected to cultural ways of representing "reality".

A theory of the degree of pre-meaning should take under consideration the fact that meaning is related to organized information. The more meaning we make, the more information we have used, but, the less information we are obliged to use in a future meaning-generating process. Raw information (in the layman's sense) cannot convey any meaning, except from some kind of minimal meaning to be defined. Meaning arises from the reduction of information, from the exploitation of the reducibility of information. Meaning is a result, the result of information processing. This cannot escape being true for the degree of pre-meaning too.

Work in progress

The mathematical framework needed for the definition and discussion of the degree of pre-meaning is set. The degree of pre-meaning is defined. The degree of pre-meaning is linked to disorder. Simple meaning-creating acts are explored using the degree of pre-meaning and the "laws of learning" are unveiled. A systematic study of the degree of pre-meaning for several pre-existing state-sequences with very different probabilistic substructures is in progress. Also, various subjects and questions are raised and analysed, subjects like: (a) the finiteness of state-sequences, (b) the resistance of state-sequences to destruction, (c) optimum alphabet reconstruction and (d) time-series prediction. An appropriate generalization of the degree of pre-meaning is made using a Renyi block-entropy and Minkowski distances between s-states. The essentially non-linear character of meaning is investigated.

Last updated: June 7, 2008.