Resurrecting Dretskean information 19
Hence, at least as much additional or “redundant” information must be produced
at the source as will have been cancelled out by the intervening noise and equivocation. If for example 50% of the information produced at the source is lost in
transmission or if 50% of what is received at R is, in fact, not produced at the
source, and if the losses are randomly distributed over the set of signals under
consideration, the number of bits will at least have to double.
To begin with, IN-1 says that there must be some reduction of possibilities
at the source s in order for information to obtain (a condition that will receive
some qualification in the first section of Chapter 4). For example if there are eight
equiprobable antecedent states at the source, it takes three binary decisions and
thus three bits of information to attain a state of certainty. For sixteen equiprobable states, the required amount of information will be four bits. If the set of possible states determined at t 0 composes only the actual state that will be observed
at t 1 , and thus if the probability of s 1 to obtain is 1, no information is generated.
Entirely static conditions at the source, with no intervening factors that could
produce an altered state of affairs, would be a case in point. If, in contrast, a set of
(roughly) equally possible states at the source at t 0 approaches infinity, and hence
if the actual state s 1 at t 1 is extremely improbable to obtain, the realisation of s 1 is
equally rich in information.
On this analysis, it appears that, to quote Weaver (1949, 14) again, “the words
information and uncertainty find themselves partners”. Prima facie, uncertainty
seems to be related to unwelcome phenomena like noise that interferes with communication, and it raises a semantically relevant problem that was first identified
by Bar-Hillel and Carnap (1952) and hence christened the “Bar-Hillel Carnap
Paradox” (see Floridi 2004): the authors observed that, on a formal analysis, a
self-contradictory sentence carries the highest amount of information, so that “it
is too informative to be true” (Bar-Hillel and Carnap 1952, 8). In the face of such
unwelcome implications, Weaver highlights the distinction between what he calls
“undesirable” and “desirable” uncertainty (1949, 12f ). The latter is to be found
in the freedom of choice at the information source in selecting a message from
a set of possible messages. Hence, a higher degree of freedom is correlated with
a higher degree of uncertainty. If no alternative possibilities to some message
exist at the source, there will be no information. As the alternative possibilities
multiply, so does the amount of (desirable) uncertainty – and hence the amount of
information that is available.
In thus distinguishing between uncertainty – and hence information – that is
desirable vs. undesirable to sender or receiver, and in referring to the degrees of
freedom at the source in selecting a message, it is implied that the information in
question has to be sent by, or to originate in relation to, an intentional agent, that
is a sender with a purpose. Only a sender with a purpose will be capable of goaldirected action that allows for some degree of deliberation as to what goals shall
be attended by what means and on what grounds. Only such a sender will be in a
position to select a message from a variety of alternative possibilities.
There seems to be an ironic twist in the positions adopted by the mathematical and the naturalistically inclined semantic theories of information: on the one
Hence, at least as much additional or “redundant” information must be produced
at the source as will have been cancelled out by the intervening noise and equivocation. If for example 50% of the information produced at the source is lost in
transmission or if 50% of what is received at R is, in fact, not produced at the
source, and if the losses are randomly distributed over the set of signals under
consideration, the number of bits will at least have to double.
To begin with, IN-1 says that there must be some reduction of possibilities
at the source s in order for information to obtain (a condition that will receive
some qualification in the first section of Chapter 4). For example if there are eight
equiprobable antecedent states at the source, it takes three binary decisions and
thus three bits of information to attain a state of certainty. For sixteen equiprobable states, the required amount of information will be four bits. If the set of possible states determined at t 0 composes only the actual state that will be observed
at t 1 , and thus if the probability of s 1 to obtain is 1, no information is generated.
Entirely static conditions at the source, with no intervening factors that could
produce an altered state of affairs, would be a case in point. If, in contrast, a set of
(roughly) equally possible states at the source at t 0 approaches infinity, and hence
if the actual state s 1 at t 1 is extremely improbable to obtain, the realisation of s 1 is
equally rich in information.
On this analysis, it appears that, to quote Weaver (1949, 14) again, “the words
information and uncertainty find themselves partners”. Prima facie, uncertainty
seems to be related to unwelcome phenomena like noise that interferes with communication, and it raises a semantically relevant problem that was first identified
by Bar-Hillel and Carnap (1952) and hence christened the “Bar-Hillel Carnap
Paradox” (see Floridi 2004): the authors observed that, on a formal analysis, a
self-contradictory sentence carries the highest amount of information, so that “it
is too informative to be true” (Bar-Hillel and Carnap 1952, 8). In the face of such
unwelcome implications, Weaver highlights the distinction between what he calls
“undesirable” and “desirable” uncertainty (1949, 12f ). The latter is to be found
in the freedom of choice at the information source in selecting a message from
a set of possible messages. Hence, a higher degree of freedom is correlated with
a higher degree of uncertainty. If no alternative possibilities to some message
exist at the source, there will be no information. As the alternative possibilities
multiply, so does the amount of (desirable) uncertainty – and hence the amount of
information that is available.
In thus distinguishing between uncertainty – and hence information – that is
desirable vs. undesirable to sender or receiver, and in referring to the degrees of
freedom at the source in selecting a message, it is implied that the information in
question has to be sent by, or to originate in relation to, an intentional agent, that
is a sender with a purpose. Only a sender with a purpose will be capable of goaldirected action that allows for some degree of deliberation as to what goals shall
be attended by what means and on what grounds. Only such a sender will be in a
position to select a message from a variety of alternative possibilities.
There seems to be an ironic twist in the positions adopted by the mathematical and the naturalistically inclined semantic theories of information: on the one