Biology Reference
In-Depth Information
Rosen (1991) provided the mapping in Eqn. (1) with a natural interpretation in
terms of Aristotelean causes: the effect B has material cause A and efficient
cause f . In this particular system A and f have only final cause, namely B; the
function of A is to serve as material from which B is made, while the function
of f is to fabricate B.
What about formal cause? In the above mapping fA
B there is nothing
that can explicitly be interpreted as formal cause. Here, we would have to
assume that formal and efficient cause are inseparably part of f (think of sculptor
f carving a sculpture according to a vision which exists in her mind only).
However, there are clearly situations where formal cause is, at least partly,
associated with a separate object (think of an electronic engineer building a
circuit board according a design on paper, or a polypeptide being synthesised
according to the nucleotide sequence in a particular mRNA).
To account for objects that serve as formal causes of, for instance, macro-
molecular synthesis, the mapping in Eqn. (1) clearly needs an additional entity.
Rosen (1989) suggested the more general formulation
−→
fA
×
I
→
B
(3)
ai
→
b
=
fai
where I is a set of templates or blueprints. In this formulation f is the efficient
and I the formal cause, although the separation need not be absolute; part of the
formal cause can remain associated with f itself.
There are two problems with this formulation. The first is that it leads to a
logical paradox when an i
I is the blueprint for f itself, in the sense that f is
an element of its own range (Rosen, 1959a, 1962). No mapping can be defined
before its domain and range are stipulated; however, if the range contains the
mapping itself as an element, it cannot be stipulated before the mapping is given.
Thus, in the words of Rosen (1959a), 'neither the mapping f nor its range can
be specified until the other is given'.
The second problem is that I appears in the mapping with the same status as
A, namely as a material cause. However, the role of I is purely informational;
logically, any particular i
∈
I should be associated with f as the pair fi.We
should rather consider fi as the efficient cause in which the formal part has
been made explicit: f is an agent acting on the information contained in i.In
these terms the mapping would be
∈
→
fi A
B
a
→
b
=
fia
(4)
with fi is an element of the Cartesian product f
I.
Readers interested in how these mappings can be formally composed (com-
bined) into fabrication networks are referred to Rosen (1991). In the following
×
