Biology Reference
In-Depth Information
Fig. 21.5
Rosen's modeling
relation. N = the natural
system, or the part of the
Universe exhibiting
regularities; F = the formal
system; 1 = causal entailment;
2 = encoding; 3 = inferential
entailment; 4 = decoding/
actualization
Natural Law
(embodied in the human observer)
4
N
System
F
System
1
3
2
n = the registration or recording of the history of the Universe in the structures of
the environment and genomes of organisms
i
1
= the inverse of morphism i in Fig.
21.3
; cell language (Sect. 6.1.2) (?), and
k
1
= the inverse of morphism k in Fig.
21.3
; cognition (?)
If Eq. 21.6 turns out to be correct, and if the commutative diagram in Fig.
21.4
can be divided into two halves, each denoted as the natural (N) system and the
formal system (F) system, following Rosen (1991) (see Fig.
21.5
above), the Class
III category shown in Fig.
21.4
may be represented as shown in Eq. 21.7, where
natural transformation
p may be identified with
ontology
and
natural transforma-
tion
q with
epistemology
.Ifp=q
1
, or equivalently, q = p
1
, then N and F would
be isomorphic (Lawvere and Schnauel 2009, p. 40) and our Universe would be a
self-knowing universe, a conclusion reached in Ji (1991, p. 236) via a totally
independent route without depending on any category-theoretical argument.
p
N
F
(21.7)
q
If the conjectures formulated above prove to be true in the future, the Class III
category presented in Fig.
21.4
for the first time may be justifiably called the
category theory of everything (cTOE).
Two applications of cTOE suggest themselves:
(1) Popper (1978) divides our universe into “three interacting sub-universes”which he
calls world 1 (the physical world, both living, and nonliving), world 2 (the mental
and psychological world), and world 3 (the world of the products of human mind,
including “languages; tales and stories and religious myths; scientific conjectures
or theories, and mathematical constructions; songs and symphonies; paintings and
sculptures. But also aeroplanes and airports and other feats of engineering”. cTOE
suggests the following internal structures of Popper's worlds:
World 1 = Gnergy-Mattergy
World 2 = Mattergy-Liformation
World 3 = Liformation-Infoknowledge.
