68 Informational environments
function, are mapped onto its target set (Millikan 2007). When transferring this
notion to the realm of natural information, a domain is described by the mapping rule by which a series of signals {r
i
,. . ., r
n
} relates to a source or a set of
sources {s 1 ,. . ., s n }, where that mapping rule is determined by causal, genealogical
or other regularities I e . These regularities become part of the explanation of the
recurrence or reproduction of r-signals on occasions of s being F, and they also
play the role of a necessary condition in explaining the presence and persistence
of the mechanisms in R for detecting r-signals.
A certain ambiguity is introduced into this mathematical analogy when Millikan says that the domains of natural information comprise not all possible values
that could be generated by some function (which, in some cases, may be indefinite to begin with) but those which have, in fact, been realised at the time t n of R
recording the signal. Under this interpretation, what is called the domain would
actually be the image of the function, that is a region in space and time in which
the mapping relation in question has been instantiated for a finite set of input values, and where it did so in accordance with that mapping rule which defines the
domain of the function in the former, properly mathematical sense. A mere series
of concrete instantiations of a seeming regularity by itself would be insufficient to
warrant that regularity, because some of those instantiations might have different
aetiologies. In the light of this observation, the most consistent practice would be
to refer to domains in the proper mathematical sense, where it denotes the set of
‘permitted’ input values for a function defined for some mapping rule. But then,
if we are talking about individuals and historical entities, such as populations and
species, the history of concrete instantiations will be a constituent of the empirical regularities that make up some population or species. After all, the domains
of natural information related to higher mammals would be differently shaped, in
terms of available variation, environmental conditions and selective pressures for
their ancestors, if the dinosaurs had not become extinct. Higher mammals might
not even have evolved in the first place.
There is a recursiveness to the definition of domains of natural information in
all cases that rely on regularities that are, partly or wholly, historically founded.
Conditions that have obtained at some time and place will enable or constrain regularities at some later time and place. If we treated domains as the set of concrete
instantiations of some informational relation and thus as the image of the mapping functions involved, that recursiveness might easily turn into circularity: the
domain of a natural sign would then be whatever happened to have co-occurred
to date, and the mapping rules could be identified only by recourse to that history.
Strictly speaking, they would not even be rules but, with some likeliness, amount
to mere enumerations of instantiations of co-occurrences that may be or may be
not properly supported by, and would be entirely uninformative about, underlying
regularities at the source.
On the view defended here, and certainly on the view that Millikan defends, too,
informational domains are more than arrays of spatio-temporally proximate and/
or phenomenologically similar but otherwise discontinuous, “gerrymandered” or
randomly compiled sets of world affairs in which some seeming correlation can
function, are mapped onto its target set (Millikan 2007). When transferring this
notion to the realm of natural information, a domain is described by the mapping rule by which a series of signals {r
i
,. . ., r
n
} relates to a source or a set of
sources {s 1 ,. . ., s n }, where that mapping rule is determined by causal, genealogical
or other regularities I e . These regularities become part of the explanation of the
recurrence or reproduction of r-signals on occasions of s being F, and they also
play the role of a necessary condition in explaining the presence and persistence
of the mechanisms in R for detecting r-signals.
A certain ambiguity is introduced into this mathematical analogy when Millikan says that the domains of natural information comprise not all possible values
that could be generated by some function (which, in some cases, may be indefinite to begin with) but those which have, in fact, been realised at the time t n of R
recording the signal. Under this interpretation, what is called the domain would
actually be the image of the function, that is a region in space and time in which
the mapping relation in question has been instantiated for a finite set of input values, and where it did so in accordance with that mapping rule which defines the
domain of the function in the former, properly mathematical sense. A mere series
of concrete instantiations of a seeming regularity by itself would be insufficient to
warrant that regularity, because some of those instantiations might have different
aetiologies. In the light of this observation, the most consistent practice would be
to refer to domains in the proper mathematical sense, where it denotes the set of
‘permitted’ input values for a function defined for some mapping rule. But then,
if we are talking about individuals and historical entities, such as populations and
species, the history of concrete instantiations will be a constituent of the empirical regularities that make up some population or species. After all, the domains
of natural information related to higher mammals would be differently shaped, in
terms of available variation, environmental conditions and selective pressures for
their ancestors, if the dinosaurs had not become extinct. Higher mammals might
not even have evolved in the first place.
There is a recursiveness to the definition of domains of natural information in
all cases that rely on regularities that are, partly or wholly, historically founded.
Conditions that have obtained at some time and place will enable or constrain regularities at some later time and place. If we treated domains as the set of concrete
instantiations of some informational relation and thus as the image of the mapping functions involved, that recursiveness might easily turn into circularity: the
domain of a natural sign would then be whatever happened to have co-occurred
to date, and the mapping rules could be identified only by recourse to that history.
Strictly speaking, they would not even be rules but, with some likeliness, amount
to mere enumerations of instantiations of co-occurrences that may be or may be
not properly supported by, and would be entirely uninformative about, underlying
regularities at the source.
On the view defended here, and certainly on the view that Millikan defends, too,
informational domains are more than arrays of spatio-temporally proximate and/
or phenomenologically similar but otherwise discontinuous, “gerrymandered” or
randomly compiled sets of world affairs in which some seeming correlation can