Dear Colleagues:
I have posted my view on the general issue of defining
information before, but I did not write about my own
understanding of information. I have made a reference to a
paper accessible on-line in which I write about it:
("Philosophical Foundations for the Concept of Information:
Selective and Structural Information" Proceedings of
FIS2005 (http://www.mdpi.org/fis2005/F.58.paper.pdf).
In current discussion some definitions that I quoted in my
earlier posting have become associated with me, while they
are very far from my own views. Thus, I feel compelled to
summarize my own views on the subject.
Before that, let me review the main points of my earlier
posting.
1. Definition of the concept (the classical
genus/differentia definition) is locating this concept
within the reference frame of the structure of some other
concepts. The structure of concepts is based on the
inclusion of their extensions (generality).
The most general concepts (of the highest generality) have
to be accepted as primitive concepts
(e.g. "set" and "belonging to set" in a set theory) and
their characterization is given through axioms. Other
concepts are, or can be derived from the primitive concepts
through the process of defining.
2. It is possible to disqualify a definition as incorrect,
e.g. circular, when refering in the definiens (that what
defines) to the definiendum (that what is defined). However,
without clearly distinguished extension of the definition
(the class of objects to which the definition refers) the
normative statements, such as "good" or "bad" do not have
any meaning. Only after we establish the intent of the
definition (what objects the definition refers to) we can
say: "This definition is not good, because I can give you an
example of the object which should be described by the
definition, but it isn't." (the case of too narrow, or not
enough general definition) or "This definition is not good,
because I can give you an example of an object which should
not be described by the definition, but it is." (the case of
too wide, or too general definition)
3. I am very concerned by some statements in the present
discussion that suggest that there is only one possible
definition of information. It is perfectly legitimate to
say: "In my opinion the concept of information should not
include xyz." But to say "Xyz is not information" and to
consider it a definite, absolute truth is in my opinion
dangerous. After all, we discuss a definition of information
in order to present our own ways to understand this concept.
There is nothing wrong with some variety of definitions.
With time some "orthodox" definition may be established, but
even then someone may continue to use a different approach.
To use this type of uniformizing approach before the
discussion has brought all or majority of views to attention
is something that bothers me. At this stage I would suggest
to eliminate (possibly for further improvement) only
definitions which are logically incorrect or which are very
clearly too narrow.
4. Writing a definition is much more than writing one or a
few sentences. It is true that when the conceptual framework
has been established, the task is limited to short
formulation of the definition with a reference to a couple
of concepts. I do not believe that we are at the stage with
clearly established conceptual frame. There are several
categories of definitions of information (in this discussion
and in the literature of the subject) based on different
conceptual frameworks. For instance:
a) Definitions based on common sense terminology
(e.g. "Reduction of uncertainty", "A difference which makes
a difference", etc.)
b) Definitions based on the concept of datum (or data)
assuming the existence of some structure of concepts
characterizing or defining the concept of datum.
c) Definitions based on the concept of representation (e.g.
MacKay), in which the concept of representation is build
upon some other concepts.
d) Definitions based on the concept of communication in
which communication is put in the framework of concepts such
as message, source, chanel, etc.
e) Definitions based on the concept of form based on one of
possible philosophical systems involving a distinction of
form and other components of the entities.
In each case the definition, even when it involves only few
words, actually takes into consideration all complex of
concepts.
In my opinion, it would be quite naive to expect that any
definition of a concept of a high level of generality, as I
understand information, can be formulated in terms of one or
two common sense concepts. I believe that any selection of
the definition must involve a selection of all philosophical
system in which the concept is placed. This philosophical
system will answer the questions about information defined
within it. What kind of answers about information we can
expect in the future study, if we do not provide by our
definition any philosophical tools to understand the
relationship of information to the matter, living organizms,
knowledge, consciousness, social and cultural issues, etc.?
5. In my attempts to find a definition of information which
includes a wide range of entities that I believe can be
viewed as instances of information, I have found that the
only common concepts involved in the description of all
instances of what I believe is information are variety and
unity. Since it seemed to me that information should be
related to actual or potential transition from variety to
unity, and the relationship of one and many is one of only
few most fundamental topics of philosophy, I have used this
relationship as foundation.
6. Thus my DEFINITION OF INFORMATION is as follows:
INFORMATION IS AN IDENTIFICATION OF A VARIETY, where
identification is understood in terms of the one-many
relation as a characteristic or complex of characteristics
of the element of a variety (the “many”) which select,
distinguish one out of many, or alternatively, as an
internal structure of the many which gives the variety its
unity.
7. This alternative produces apparent opposition of the two
forms of information, selective and structural. The
opposition is only apparent, as the two types are
inseparable. The elements of the variety can have distinct
internal or individual characteristics only if they have
their own internal structures. The structure of the variety
carrying “structural information” can always be considered
one of a variety of potential structures out of which it is
selected. Thus, the selective and structural forms of
information are rather dual manifestations of the uniform
concept of information derived from the dual relationship of
one and many. The selective aspect of information is more
salient when the identification of the one out of many is
predominant through its own individual characteristics,
while the structural aspect is salient when the
identification is rather through the participation of the
element in the structure of the variety. Both aspects can be
present at the same time, as for example in the way of
selecting “the first red ball on the left”. When we refer
to the color of the ball, we refer to the selective aspect,
when we refer to the location in the variety of balls “the
first on the left,” we use the structural aspect of
information.
8.Thus, we can consider information only when there is some
predefined variety (the “many”) and when with this many
there is associated some unity (the “one”). The association
of the one with the many is information. Sometimes there is
no such association, and the quantitative characteristic of
the information is zero. For instance if the variety
consists of the six possible outcomes of casting
an “honest” die, and the one is the actual outcome of the
cast, there is no association of the one and the many. The
measure of information in this case is zero. If the die
is “loaded” so that in every cast only the outcome six
appears, the association is strongest and the quantitative
characteristic of information is maximal. With an
appropriate choice of the measure we can for instance assign
the value to this case log 6. The die can be partially
loaded, and the value of the measure would vary between the
two extremes. This simple example is signalizing the
difference between the usual quantitative characteristic of
information in terms of entropy which corresponds to the
concept of information derived from “uncertainty”
or “surprise”, and more compatible with the one-many based
approach to information, alternative measure (see my paper
on this topic, Entropy 2004, 6, 388-412 at
http://www.mdpi.org/entropy/papers/e6050388.pdf/)
However, as long as we are searching for the conceptual
framework for information the discussion of its quantitative
aspects is not necessary.
9. The definition of information as identification of a
variety is definitely very general, but I believe it does
not include anything which could raise objection "this
definitely is not information".
When I presented this definition in December in Tokyo at
Information 2004 Conference, some of listeners had
objections that "Basicaly it says the same as
the 'uncertainty definition' but in a different way when we
think about uncertainty as multiplicity causing
uncerttainty". Others have found correspondences with other
definitions, "if we understand..." Thus, it looks like the
definition of information as identification of a variety
meets intuitive understanding of information not only mine.
10. The use of the term "identification" may cause some
objections: Can't you find better word? "Identification" has
already had generic meaning which is compatible (although is
not identical)with the meaning in the definition when we
talk about selective information, but is quite far from the
meaning of structural information. To identify has strong
association with selection, but not with structure.
I could not find better term. For instance "unification of
the variety" would shift the meaning towards structural
information, but also could cause confusion with
uniformization of variety. Thus, "identification" seems, if
not "good", then "good enough".
With kind regards,
Marcin
Marcin J. Schroeder, Ph.D.
Dean of Academic Affairs and Professor
Akita International University
mjs@aiu.ac.jp
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Received on Wed Sep 14 12:01:25 2005
