Pragmatic Information

Abstract

The goal of this paper is to define pragmatic information with a view toward measuring it. Here, pragmatic information means the content of valid signs -the key that unlocks language acquisition by babies and to human communication through language -also the content that enables biological "codes" in genetics, embryology, and immunology to work. In such systems, the inter-related layers appear to be ranked as in a hierarchy. Sounds are outranked by syllables, in turn outranked by words, and so on. In DNA, nucleotide pairs are outranked by codons, which are outranked by genes, and so on. As signs of lower rank combine to form signs of any higher rank, combinatorial "explosions" occur. With each increase in rank, the number of possible combinations grows exponentially, but the constraints on valid strings and, thus, their pragmatic value, sharpens their focus. As a result with each explosive increase in the number of possible combinations the relative proportion of meaningful ones diminishes. Consequently, random processes of forming strings or changing them must tend increasingly toward meaninglessness (invalid and nonviable) strings. The consequent outcome of random mutations is mortality of individuals and in deep time an increasing number of disorders, diseases, and the eventual extinction of populations.

Biosemiotic Entropy: Concluding the Series

“…Later, the positive term pragmatic information [18], the gold-standard of linguistic content (i.e., meaning in its most concrete and ordinary sense) which is the kind found in true narrative representations (TNRs) [18][19][20][21][22][23][24], was proposed. A TNR is simply a faithful report of a sequence of actual events experienced by one or more competent observers.…”

“…We can extract the S i from any of the relations in inequality (3), keeping all else equal by construction except for the scrambling or other physical degeneration of the S i (by adding noise, for example), the S i can be converted into unintelligible nonsense. This construction can be done by degrees where the starting S i is always the same but the resulting derivations become less and less intelligible as they approximate that vague limit where the string can no longer be recognized as a string of symbols in any language-like system at all [18]. Let all such nonsensical strings, ones that are not intelligible with respect to any particular fact(s) or fiction(s), but that remain recognizable as a string of symbols resembling those of some language, be represented as S / i .…”

“…In his foundational paper on the mathematical theory of information, it is true that Claude Shannon [56] began by setting aside what has been termed pragmatic information [18]-the kind of content that is determined by TNRs connected to the material world of experience. Shannon [56] wrote:…”

“…In the end-owing to the principles spelled out most clearly in the second law of thermodynamics as generalized to Shannon's information theory and to quantum physics by Jaynes [51], the cumulation of must invariably end in a catastrophic breakdown of the critical biosemiotic systems required to sustain life. Putting the argument, in the form made familiar by Shannon, given a community of competent sign-users who know and share the conventional signs of TNRs expressed in that language, and who have access to the same common world through shared experience, supposing only that any instantiated TNR i can be assigned a probability p i ≈ 1 of being comprehended as intended, Shannon-type information [56], constrained by its pragmatic content [18], is at a relative maximum for any TNR i while Shannon-type entropy for any TNR i , relative to the less well-formed classes, must be at a theoretical minimum. Therefore, based on the definitions from Shannon, Jaynes, and Adami, and from the proofs given earlier, we may write the following series of inequalities between the approximate equations at both ends of (6):…”

“…As Hemmo and Shenker have illustrated, valid representations require experience in the mesoscopic realm of material entities in some accessible region of space and time where competent and intelligent observers are invariably situated at definable coordinates. The upshot of this idea, one that I propose to call the pragmatic theorem, is that any content expressed in conventional (linguistic, mathematical, or any kind of abstract and even partially arbitrary) signs is dependent on the instantiation of those signs by applying them truthfully to facts already known to (or discoverable by) one or more competent observers [18,23]. Upon examination of their formal properties, as elaborated earlier in this paper, it comes out that TNRs must involve the faithful mapping of a symbol (or sequence of symbols) through the actions of one or more observer/users of the conventional signs of a shared language onto one or more known entities, relations, and events in space and time.…”