On the Proper Definition of Information

AUTHOR
Andras Kornai

ABSTRACT

Whether viewed as a Rawlsian primary good or as the building material of an entire Infosphere, the notion of _information_ plays a fundamental role in the development of CE. In the proposed paper we take a critical look at this notion from the monosemic perspective of lexical semantics (Ruhl 1989) and offer a formal definition that gives a suitable basis for CE work.

Everyday use of the term _information_ seems to rely on a metaphor of the “precious fluid”, related both to ordinary liquids like water and to less tangible but nevertheless appealing notions like energy, electricity, or chi (life force). Information can _flow_ from a source to a recipient over a _channel_, _pipe_, or other conduit, can be diluted, compressed, or stored in vessels of specific capacity, and so on: much of classical information theory can be viewed as a rational reconstruction of the fluid metaphor, with the bit as the fundamental volumetric unit from which other units such as channel capacity (bitrate) are derived by standard dimensional analysis (in this case, as bits/sec). This reconstruction turns the metaphor into a reliable tool for engineering communications devices, storage area networks, and the like, yet it leaves the “precious” aspect of the notion unexplored: from the engineering perspective any data stream is information, and it is quite unclear how one could ascribe any value, let alone an ethically central value, to bits. Yet animistic statements like `our higher being is pure information’ or `information wants to be free’ abound in the CE discourse, indeed, for many people these statements provide the main reason for engaging in the discourse in the first place. To capture these ideas one must ascribe to information some kind of identity, sentience, and volition.

1. Identity. It is one of the most striking aspects of fluids that they lack identity: pouring two glasses of wine in a pitcher results in a mixture from which the original varieties can no longer be recovered, and subparts (drops) of one fluid are indistinguishable from one another. From the perspective of everyday ontology, fluids are best viewed as mereological entities, infinitely divisible, the polar opposites of individuals (which are, by definition, indivisible). Water is H20 no matter where we find it — information, on the other hand, can generally be traced to specific _sources_ or _leaks_ based on its composition. In fact, there is a whole field of human endeavor, philology, that is largely devoted to developing methods that enable tracing various pieces of information to their sources. Since the pieces are individuated by cutting the bitstream at carefully selected points, we conclude that _linear organization_ is a defining characteristic of information. The strings AB and BA are not identical, even if their components are the same.

2. Sentience. To say that Einstein would turn in his grave, or that the principles of special relativity are violated, by faster than light travel, is to say that a specific theory (some kind of structured set of information entities or axioms) is capable of sensing something that goes against it. We do not have to take a naive animistic view of theories (just as we do not have to believe in Poseidon to believe that the sea is a dangerous place) whereby theories can sense actual events — it is enough for theories to be sensitive to statements of events. In other words, a theory imposes, by means of deductive rules, a classification on statements, which can (i) follow from the axioms (ii) their negation can follow from the axioms or (iii) be undecidable relative to the axioms. Thus we conclude that information entities come, implicitly or explicitly, with rules of composition (deduction).

3. Volition. Fermat’s Last Theorem has acquired a proof — the Riemann Hypothesis is still in need of one. The Axiom of Choice needs to be approached with care. One must respect the words of the sages. This assumption will bite you in the ass. Everyday expressions like the preceding make sense only if we take it for granted that information entities have desires and powers on their own, the way genies in bottles do. The whole meme/gene trope is meaningless without ascribing not only sentience (deductive capabilities) but also powers to change their environment, to (structured sets of) information. The absolute minimum that we need to posit is the capability of some piece of information to _override_ some other piece, and a rational reconstruction of this notion will of necessity invoke some version of default or defeasible logic.

In sum, to define information in a manner consistent with the everyday use of this term (where `everyday’ aspires at the inclusion of not just day to day discussion but the whole philosophical debate concerning CE) we must replace the classical (Shannon) notion of information by a more nuanced definition which presumes not just elementary messages that can follow each other in arbitrary order, as in the classical model, but rather structured sets of such information pieces endowed with their own deductive apparatus. Further, this apparatus must be capable of carrying not just classical but also non-monotonic inference. These considerations do not narrow down the range of possibilities to a single logical theory of identity, sentience, and volition: the full paper will use Ginsberg’s (1986) “system D” as a suitably rich metatheory to formalize the pre-theoretical notion of information in a manner suitable for capturing CE arguments.

REFERENCES

Ginsberg, M.L. Multi-valued logics. In Ginsberg (ed): Readings in Non-monotonic Reasoning. Morgan Kauffman, San Mateo CA pp 251–255

Ruhl, C. 1989: On Monosemy: A Study in Linguistic Semantics. SUNY Press, Albany

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