Dear FIS Friends,
I am delighted to observe the development of the discussion
of the topic belonging to the very center of my research
interests "What is information?". Sayd, thank you very much
for revisiting this important topic.
Due to sudden illness I have missed an opportunity to
present my views on exactly the same topic during FIS 2005
in Paris. I had to cancel my presentation, and you can
imagine how I regret now that I did not have chance to
present my own definition of information and its
philosophical background. I have to be content that the
paper which I was going to present ("Philosophical
Foundations for the Concept of Information: Selective and
Structural Information") is available in the Proceedings of
FIS2005 (http://www.mdpi.org/fis2005/F.58.paper.pdf).
However, in this message I do not want to talk about my
definition (although, I would be very happy if you decide to
take a look at it in my paper for the conference). I would
like to make suggestions regarding the discussion and to add
my two pennies.
I have already benefited from reading the thread of messages
and I am grateful for some interesting ideas. However, I
believe that I could benefit more, if I could be sure that I
understand well these ideas, but frequently I feel lost.
I am afraid, there is a lot of confusion in what exactly we
want to achieve. Let me elaborate on the problems which I
have encountered.
1. The initial question already calls for some
clarification:"What is THE definition of information?"
It looks like it automatically assumes that there is
one "good", "proper", or "best" definition - "the definition
of information". However, there is no reason to expect that
there is such a unique definition. Since I myself proposed a
definition which differs essentially from other definitions,
apparently I have had some reason to believe that my
definition is better than those published before.
I agree that there are some criteria which can be used to
compare definitions of information, but I do not believe
that there is possible unique answer to the question "What
is information?" without any reference to pragmatics, for
instance to the context in which this concept is going to be
used. After all, we define concepts to explain what we mean
by them. When somebody gives me logically correct definition
of some concept, I cannot say "It is wrong", but only
that "I am not interested in this concept", or that "I do
not believe this definition can be applied to what we agreed
is denotation of the concept."
There are some cases when the definition can be criticized
for incompatibility with commonly agreed hierarchy of
generality of concepts. This may sound incomprehensible, so
I owe you some explanation.
2. I assume that we are looking for the definition of the
CONCEPT of information. Thus, we are not talking about the
related but different issue of operational definition of
some magnitude, about the question how to measure something.
Simple example: It would be an error to say that temperature
IS the position of the pillaret of mercury in a thermometer.
Yes, we measure temperature by measuring the position of the
top of the pillaret, but without a theory of the thermal
expansion of liquids, this measurement is irrelevant for the
question what is temperature. Only after we have definition
of the concept of temperature, we can say that the
thermometer measures temperature. Thus, I have some
objections to Stan's definition "any constraint on entropy
production". Yes, I know he qualified his definition
as "functional" (probably similar to what I call
"operational"), but later he writes "My (2) above can be
associated with meanings". I do not understand it.
If we want to define the concept (to present its meaning),
we have to put this concept in the framework of other
concepts which are already defined (agreed), or which are
considered primitive concepts and which are characterized
axiomatically (as for instance the concept of "set"). The
latter case is when for given concept there is no more
general concept.
I do not believe that the concept of information is so
general, so at the moment I will not discuss the possibility
of considering it a primitive concept.
3. I would like to address also a delicate issue of the
logical correctness. Many of you can react that it is
wasting of time for trivialities, but I believe it is not.
In my extensive collection of various published attempts to
define information, the majority of entries are simply
incorrect.
Sometimes they have been formulated in an incorrect manner
(possibly) intentionally to express desperation on the
difficulty of the attempt to define such a general concept.
A good example is Searl's definition which could be used in
an introductory logic textbook as an instance of an error
of "circular definition" (hereafter no reference means that
references can be found in my paper mentioned
above): "Information is anything that we can count or use as
information."
This brings us to the first rule of logically correct
definition:
In the definiens (that which defines) no reference can be
made to the definiendum (that which is defined).
4. The rule should be expanded to the cases where the
reference is indirect, it means when the concept in the
definiens is defined somwhere else using definiendum. This
can happen when we put together statements coming from
different publications. Floridi gives the following example
(Entropy 2003, 5, 125-145) of excerpts from different
publications which can easily lead to a "viscious circle":
"Information is data that has been processed into a form
that is meaningful to the recipent. [Davis & Olson 1985]
Data is the raw material that is processed and refined to
generate information. [Silver & Silver 1989)
Information equals data plus meaning. Checkland & Scholes,
1990]
Information is data that have been interpreted and
understood by the recipient of the message.
Data will need to be interpreted or manipulated [to] become
information. [Warner, 1996]"
In our discussion Soren mentioned in response to Shu-Kun's
definition "Information is the amount of data compressed"
that the definition requires a definition of data. I agree
that it is a very important point as frequently data are (I
am writing "are" as I am attached to the old good style of
the singular form of this noun "datum") defined as a special
type of information. If we define data as something (WHAT?)
that can be recorded in a newspaper, book, magnetic memory,
etc., the definition becomes very, very narrow.
However, I have additional objection to Shu-Kun's
definition. I do not understand in what sense information is
an AMOUNT of something. So, is the ontological status of
information secondary to the status of data? Information
does not exist, but is only a number which describes how
much data have been compressed, or as I suspect was Shu-
kun's intention, to what amount the data have been
compressed? It seems to me very difficult to understand,
even harder to accept.
5. There are many examples of confusion caused by the
problem with the distinction of quantitative characteristics
of the concept of information (measures of magnitudes) and
the concept itself. Similar confusion can be found when
someone identifies information with entropy. There are many
possible ways to characterize quantitatively information.
Tsallis (Entropic Nonextensivity: A possible Measure of
Complexity) writes about twenty different generalizations of
entropy. I could add a half of dozen multi-parameter
generalizations of entropy developed in the seventies and
eighties. This means more than two dozens of families of
entropies, each with infinite, uncountable number of
members. And each author of a new generalization has a good
reasons to claim the importance of its creation.
On the other hand, I believe that entropy does not measure
information, but the capacity of the system to
receive/increase information, and that for information in a
system we should use an alternative measure; the value of
this measure can be associated with familiar magnitude of
relative entropy or Kullbach-Leibler distance from the
uniform distribution, but it can be introduced independently
from any other concepts (see Entropy 2004, 6, 388-412 at
http://www.mdpi.org/entropy/papers/e6050388.pdf/).
For our
present discussion it is important that there are many
different categories of measures of information, each with
infinite number of members.
Thus, even if we ignore all logical and ontological reasons,
defining information in terms of entropy or any other
measure leads to the question what is the difference between
information defined in terms of different measures?
6. Lets look now at the most popular "definition" of
information, which although not introduced directly in the
famous book of Shannon and Weaver, definitely has been
derived from the correspondence of entropy and uncertainty
described there:
"Information is reduction/resolution of uncertainty."
There are two generic meanings of the word "uncertainty"
known to me. One is the "lack of information", the other is
a psychological state of distress caused by lack of
information. In either case the definition clearly violates
the first rule that the definiens MUST NOT refer to the
definiendum.
Yes, the definition can be saved by considering uncertainty
as a psychological state described in behavioral terms, but
then its denotation becomes very narrow.
As a diggression, it is interesting that this
famous "definition" is most frequently used by those who
following Shannon declare absolute disinterest in the
meaning of information, as it is not a subject of concerns
for engineers. But it is quite clear that the psychological
interpretation cannot be applied in this case.
Imagine a young man who proposes to young lady by e-mail:
"Would you marry me?" His level of uncertainty is very high.
He gets response "Gwulp brdean hrwut." The message is
definitely carrying some information (we can count its
entropy, so we can measure the amount of information
received.) Do you think young man's uncertainty reduces?
Coming back to the "definition" using the concept of
uncertainty in the definiens. Someone can object that this
word has different, non-generic meaning. Then it has to be
provided, and in its defition no reference to information
can be made. I wish good luck those who want to pursue this
way of defining information, but I have confes my scepticism
about the success.
But with this we arrive to another logical issue.
7. Although for stylistic reasons the second rule (below) is
not always applied in the strict form, I would expect that
logically correct definition should have the classical genus-
differentia form, or at least should be equivalent to the
definition in such a form:
"A is B, such that C"
where A is definiendum (what is defined), B is a genus of A,
i.e. the concept which is more general than A defined
earlier, or already known, and C stands not for the concept
but for all statement how A differes from all other species
of B (i.e. all other concepts less general than B).
For instance in "Man is a two-leg animal without feather"
A= "man"
B= "two-leg animal"
C= "without feather"
This is this famous example of the definition given to
students by Aristotle teaching in his Lyceum how to define
concepts. It has been made so famous by the student who next
day brought to Lyceum a chicken shaved of its feather.
Isn't it all that too obvious to be brought to your
attention? Believe me not. We are just arriving to the
nucleus of the problem in defining information.
8. The classical genus-differentia definition places the
concept defined in the framework of other concepts in a very
specific way. The necessary (and usually difficult) step is
to find a genus for the concept, and the more general
concept has to be defined, the more difficult is the task to
find a genus for it.
This is the reason why so many definitions of information,
logically correct, are not very convincing.
Consider the definition (not entirely logically correct)
from the influential book written by Fred Dretske "Knowledge
and the Flow of Information":
"Roughly speaking, information is that commodity capable of
yielding knowledge, and what information or signal carries
is what we learn from it."
Poor Dretske must have spent lots of time thinking what to
write before he put on paper the word "commodity." The first
reason why this definition is not acceptable to me is this
bizarre choice of the genus for information. I do not say
that Dretske could not use the concept of commodity, but it
just makes his definition not interesting.
But there is another reason why many perfectly correct
definitions lose my interest, and why I am not interested in
pursuing Dretske's line of reasoning about the meaning of
the concept of information. Dretske is using in his
definiens the concept of knowledge, as if knowledge was a
primary concept with respect to information. This makes his
definition as narrow, as the psychological version
of "uncertainty definition". I do not believe that knowledge
can be defined in without any reference to information. Thus
Dretske's definition is doomed to become circular, or
trivial.
9. For me the concept of information is so intersting
because it describes an entity which can be found in many
domains of our inquiry. Thus all definitions which restrict
the domain of denotation to only few instances of
information, no matter how logically correct, are just not
intertesting.
I need a tool of big power, a definition which refers to all
phenomena identified as involving information in
communication, thermodynamics, computer science, genetics,
cognitive science, etc.
If the definition directly refers to very narrow domain, as
for instance when information is restricted to psychology,
it is just not very interesting. For me it is not much
better than using what Webster Dictionary can tell us about
information.
This applies to some cases where the concept considered is
of independent interest. For instance Fisher's information
is for me interesting as a potential special instance of
more general concept. Actually, Fisher never defined clearly
the concept of information. He only considered a measure of
information in a sample, quite likely understood by him as a
source for knowledge, about the value of the parameter in
the population provided the first moment exists. Thus, it is
difficult to place Fisher's information among the
definitions of the concept of information, even if the work
of Fisher is interesting for itself.
10. In this discussion Bateson's definition of information
as "a difference that makes difference" has been recalled.
It achieved a status of a celebrity, right next
to "uncertainty definition". It is charmful, seducing. I can
imagine that it can have special appeal to those who like
esoteric style of conversation. Little jewel, like zen koan
or haiku. I can imagine exalted pseudo-intellectuals
saying "I tells me so much about information..."
But actually it tells us nothing. Its popularity is based on
open-endedness. You can put into it whatever you want, and
it looks like it works. Actually it doesn't.
There is a definite difference between beer and water. It
makes big difference to me whether waiter brings me one or
the other to the table. But it is not information.
More seriously. Bateson "definition"'s appeal comes from:
- logically incorrect use of a relative noun without its
referents. Difference between what? Whatever? I remember how
much I enjoyed elementary school jokes such as "The bird has
one leg from the other". I could laugh many times from the
same sentence tasting its absurdity. But now, I am an adult,
and after grading thousands of homework assignments of my
students with similar curiosial sentences written without
any intention to entrtain me, it is not funny anymore.
- Bateson is using an idiom in English "to make a
difference". Try to translate his definition into another
language and you will see how much it loses in its appeal.
In my mother tongue (Polish) it becomes dull and shallow.
To give full justice to Bateson's "definition" it has one
good aspect. It refers to the concept of "difference" which
points to the concept of variety. And this way leads to
philosophical foundations which are in my opinion
appropriate for the concept of information.
The issue of such philosophical foundations is of great
importance for interesting definition of information.
11. Why so many attempts to define information seem
questionable?
Let me explain my opinion. In many attempts the concept of
information was being placed through the definition in the
framework of other concepts which were supposed to be
simple, easy, intuitive. Especially last qualification is
dangerous. It is illusion that the definition referring to
intuitively obvious terms is the best, easiest to
understand. Only someone very naive can believe that the
concept of such great generality as information can be put
into a framework of simple, intuitive, daily-life concepts.
To have interesting general concept of information we should
look for a framework of extensive, rich philosophical
tradition. There were some attempts to do it. All direction
of defining the concept of information in terms of
the "form" was based on this assumption, although in some
cases the motivation was simply ethymology of the
word "information". It has source in an old idea in
Aristotelean tradition of the concept of substance. Form
informs matter, matter materializes form to become
substance.
I do not want to go too far in talking about this direction
(see for instance P. Young The Nature of Information, 1987),
but for the reasons which I explained in my FIS 2005 paper,
I believe another approach is better.
For this discussion, I would like to express my deep
conviction that the general concept of information requires
for its foundations an appropriate rich philosophical
tradition with its developed conceptual framework.
I myself have selected probably the oldest philosophical
tradition of Europe and Asia of the study of one-many
relation. Someone not satisfied with my definition can look
for different foundations and their different use. But I
believe that as long as information is defined in terms
of "uncertainty" or similar concepts which are just simple,
easy, obvious, the outcomes are not likely to be
interesting.
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 Fri Sep 2 14:26:45 2005
