18 Informational environments
some way from the mathematical theory of communication, as originally proposed by
Claude Shannon and Warren Weaver (1949). That theory was not concerned with
natural information and its role in animal cognition but with technical requirements for reliable signalling in telecommunications. Although one might argue
that it is thus wholly irrelevant to the explanatory purpose at hand, it has continued
to influence the debate for many decades and remains a common reference point
for all sorts of theories of information, including the semantic concept of information introduced by Yehoshua Bar-Hillel and Rudolf Carnap (1952) and refurbished
by Luciano Floridi (2004). Even in theories that are far removed from Shannon
and Weaver’s original purposes in grounding theories of meaning in a notion of
natural information, the mathematical theory of communication remains a reference point. This influence is most prominent in Dretske (1981) but has proven
somewhat difficult to parse and has been countered with accounts that partly or
wholly distance themselves from the mathematical paradigm (e.g. Millikan 2001;
Skyrms 2010; more on this debate in the following section).
2
The mathematical theory of information, at the time of its introduction, was duly
concerned with genuine engineering problems in telecommunications, namely
with the requirements for reliable and effective transmission of messages between
sender and receiver – signal rates, channel capacities, measures of levels of the
noise that interferes with signal transmission and the degrees of redundancy that
could compensate for noise-induced loss (Weaver 1949). However, there is a core
set of tenets of the mathematical theory that can be formulated without reference
to senders and receivers of signals as intentional communicators of messages – and
arguably also without implicitly presupposing their presence. The minimal formal
characteristics of information can be summarised in the following two definitions:
(IN-1) Any sequence of events in which a set of possible states of affairs at the
source {s 1 ,. . ., s n }, as determined at t 0 , is reduced by that state s 1 within the set
which turns out to be the actual state at t 1 , is an instance of information. The
amount of information x involved is measured as the logarithmic function
x = log 2
1
_
p
from the probabilities p of antecedent states to the actual state.
3
In a second step, the conditions for the transmission of information will be
accounted for, so that the relation between the transformations of probabilities at
the source and those at the receiving end is determined:
(IN-2) The reduction of possibilities at the source must be sufficient to reduce the
uncertainty on the receiving side R under conditions of “lossy” transmission.
Transmission is lossy
(a) if information produced at s is lost in equivocation, or
(b) if noise added to r compromises the information received at R.
Information is successfully transmitted only if an amount of bits is
received that reduces the possibilities to an extent that is sufficient
for specifying R’s response.
some way from the mathematical theory of communication, as originally proposed by
Claude Shannon and Warren Weaver (1949). That theory was not concerned with
natural information and its role in animal cognition but with technical requirements for reliable signalling in telecommunications. Although one might argue
that it is thus wholly irrelevant to the explanatory purpose at hand, it has continued
to influence the debate for many decades and remains a common reference point
for all sorts of theories of information, including the semantic concept of information introduced by Yehoshua Bar-Hillel and Rudolf Carnap (1952) and refurbished
by Luciano Floridi (2004). Even in theories that are far removed from Shannon
and Weaver’s original purposes in grounding theories of meaning in a notion of
natural information, the mathematical theory of communication remains a reference point. This influence is most prominent in Dretske (1981) but has proven
somewhat difficult to parse and has been countered with accounts that partly or
wholly distance themselves from the mathematical paradigm (e.g. Millikan 2001;
Skyrms 2010; more on this debate in the following section).
2
The mathematical theory of information, at the time of its introduction, was duly
concerned with genuine engineering problems in telecommunications, namely
with the requirements for reliable and effective transmission of messages between
sender and receiver – signal rates, channel capacities, measures of levels of the
noise that interferes with signal transmission and the degrees of redundancy that
could compensate for noise-induced loss (Weaver 1949). However, there is a core
set of tenets of the mathematical theory that can be formulated without reference
to senders and receivers of signals as intentional communicators of messages – and
arguably also without implicitly presupposing their presence. The minimal formal
characteristics of information can be summarised in the following two definitions:
(IN-1) Any sequence of events in which a set of possible states of affairs at the
source {s 1 ,. . ., s n }, as determined at t 0 , is reduced by that state s 1 within the set
which turns out to be the actual state at t 1 , is an instance of information. The
amount of information x involved is measured as the logarithmic function
x = log 2
1
_
p
from the probabilities p of antecedent states to the actual state.
3
In a second step, the conditions for the transmission of information will be
accounted for, so that the relation between the transformations of probabilities at
the source and those at the receiving end is determined:
(IN-2) The reduction of possibilities at the source must be sufficient to reduce the
uncertainty on the receiving side R under conditions of “lossy” transmission.
Transmission is lossy
(a) if information produced at s is lost in equivocation, or
(b) if noise added to r compromises the information received at R.
Information is successfully transmitted only if an amount of bits is
received that reduces the possibilities to an extent that is sufficient
for specifying R’s response.