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Complexity and Philosophy Workshop - DRAFT paper
The Construction of Emergent Order or
How to Resist the Temptation of Hylozoism
by Jeffrey Goldstein
Adelphi University, Garden City, NY 11530
THE APPEAL OF HYLOZOISM
Although it’s become quite popular to decry the
legacy of Newton’s scientific achievements for
bequeathing a mechanical and thereby lifeless
view of nature, Newton himself was actually
committed to an opposite sentiment, “We cannot
say that all nature is not alive” (Rae,
). For
Newton, nature was infused with qualities of
dynamism usually associated with living
creatures. The belief that nature is infused with
life all the down, even in the apparently inert, is
known as hylozoism, an antediluvian doctrine
originating in early animism but finding
sophisticated expression in ancient Greek
Philosophy and the later traditions following it.
Hylozoism is typically found along side the closely
related notion of panpsychism, the doctrine that
mental qualities also pervade nature all the way
down. Both doctrines have been held, in one form
or another, by no less a set of philosophical
luminaries than Aristotle, Descartes, Spinoza,
Kant, William James, and Alfred North
Whitehead, to name just a few.
Hylozoism has shown itself not only in
outright declarations on a fundamental organicity
pervading nature, but also in other, related
doctrines resting on the belief in the pre-existence
of certain temporally and ontologically primordial
organic properties. For example, the early
modern biological ideas of preformation or preexistence of the germ cell reveal a kind of
hylozoist orientation, although here, rather than
simply mere organicity, what pre-exists are
miniature homunculi which grow into the mature
adult during embryonic development (Richards,
1992; Rousseau, 1992). Similarly, the idea of
penspermia holds that germ cells or other kernels
of life force, pre-exist, even came from other
planets, an idea embraced by no less a scientific
exemplar than Francis Crick. Indeed, in an
important sense the current notion of genetic predeterminism can be understood as a vestige of
earlier hylozoism. A hylozoist core also can be
detected in the dictum of Rudolf Virchow, a
pioneer in cell biology, who argued that a cell
could not emerge from a non-cell, his motto
“omnis cellula e cellula“ being a kind of cellular
hylozocism (Farley, 1977).
Among those factors rendering hylozoism
philosophically attractive has been its seeming
capacity for “resolving” that age old philosophical
quandary which, in Kant’s phraseology, derived
from the fact that it would be “contradictory to
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Complexity and Philosophy Workshop - DRAFT paper
reason” to believe “that life should have sprung
from the nature of what is lifeless, that matter
should have been able to dispose itself into the
form of a self-maintaining purposiveness” (Kant
quoted in Lenoir,1982, p. 29)) Hylozoism is able
to side-step this enigmatic discrepancy for, if
nature in its heart is endowed with properties of
organicity, then the emergence of life from the
non-living need not be any more mysterious than
the unfolding of what’s already innate in it. That
is, if there is no non-animated matter to begin
with, life doesn’t need to emerge from what it’s
not. So, puff B no discontinuity, no paradox, no
conundrum, no problem! As the renowned 18th
Century French biologist Georeges Cuvier put
it, “...life has always arisen from life. We see it
being transmitted and none being produced.”
(Quoted in Farley, 1977, p. 39). Thus, no matter
whatever other philosophical merits it may
possess, hylozoism does offer the promise of
demystifying the origin of life by way of denying
there could be anything utterly destitute of life.
Although later on we will be examining in
greater detail the problematic nature of
hylozoism, we need to note here the two critical,
interrelated drawbacks which are the conceptual
prices paid for the ability of hylozoism to “resolve”
the issue of the origin of life. The first has to with
the fact that hylozoism, by its very nature, must
deny the existence of radical difference. That is,
if even the most non-life like aspect of nature
nevertheless is imbued with life, then
consequently the radical discrepancy between
life and non-life disappears. The second price
paid, indeed, stemming from the first, has to do
with how hylozoism succeeds in “resolving” the
enigma of the origin of life only by replacing this
enigma with another equally troubling one,
namely, the conundrum of why the non-living,
although supposedly endowed with life, do not
exhibit what they are endowed with. For example,
why does a rock appear inert and not life-like?
Indeed, it seems that no matter how hard
hylozoism has tried to rid the origin of life from
the troubling nature of the origin of a radical
discontinuity, it winds up with simply another
discontinuity, that between appearance and
reality. A further consequence is that hylozoism
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can also avoid having to come up with a cogent
understanding of the processes involved with the
coming into being of the radically novel. This also
means that hylozoism therefore is a completely
opposite doctrine than that of emergence for the
latter is challenged by precisely what hylozoism
denies, that is, the coming into being of the
radically novel.
VESTIGES OF HYLOZOISM IN
COMPLEXITY THEORY
From the above remarks it might seem hylozoism
has become merely a quaint relic of our
philosophical and scientific past, yet vestiges of
its allure can be detected in certain complexity
related theses, most notably in three related
currently influential complexity notions: first, in
Maturana’s and Varela’s notion of autopoeisis,
particularly as this idea has been formulated by
Varela with his self-referential abstract algebra;
second, in how certain modern ideas of
emergence in complex systems rely on a holistic
perspective; third. , the application of
autocatalytic structures observed in Artificial Life
to the issue of the origin of life. Indeed, a
hylozoistic cast can even be seen, paradoxically
enough, in the very appellation “Artificial Life” for
these simulations, that is, life-life dynamics have
been attributed all the way down in the artificial
world of Artificial Life in a manner not dissimilar
to what hylozoists have done with the natural
world of nature. Here we will only focus on the
first two of these vestiges of hylozoism in
complexity theory.
PAN-REFERENTIAL CLOSURISM
In previous publications, I have separated the
history of the idea of emergence into three
periods (Goldstein, 1999; 2000): the proto-period
of Emergent Evolutionism, from about 1905 to
1935, when the idea got off the ground; the midphase stage when the early conceptualization
was applied mainly to theoretical biology and
neuro-science; and the neo-emergentist period
corresponding to the advent of complexity theory
in its various guises. It was during mid-phase
emergentism that organic wholeness of
Complexity and Philosophy Workshop - DRAFT paper
emergent phenomena was conceived in terms
of a self-referential structure. Actually this was a
modern restatement of the circular kind of
causality that Kant had originally called for to
distinguish life from non-life: “its parts should
combine to form the unity of a whole by being
reciprocally causes and effects of each others
form” (quoted in McFarland, 1970). During the
mid-phase period, a similar self-referential
understanding of organic integrity reached
perhaps its apotheosis in the concept of
autopoeisis developed by the Chilean biologists
Humberto Maturana and Francisco Varela
(Maturana and Varela, 1980). Autopoeisis holds
that organic wholes are those entities which seek
to maintain the organization of which they are
the embodiment. Living wholes are selfreferential in their very essence, a network of
production processes of components which
through their interactions regenerate and realize
the network which produces them. This selfreferential circular causality operates to create
an invariant self-contained identity, a boundary
circumscribing a state of closure, the term
favored by Varela in his later work, to distinguish
his approach consisting of a logic of abstract
relations from the standard information theoretic
input/output model for self-organizing systems
(Varela, 1979; Varela, 1984 ). In an important
respect, autopoeitic “referential closure” can be
seen as a counter to the “open systems”,
information theoretic approach which, according
to Varela and Maturana, could not get to the
kernel of what maintained the integrity of on
organism over time.
Varela, concluding that his emphasis on
the self-referentiality defining organicity was
lacking a foundation in contemporary went on to
erect a mathematical formalism of self-reference,
which amounts to a sort of “pan-selfreferentialism” since it posited self-reference as
a basic logical element along with the two
conventional elements of true and false (Varela,
1979). The very possibility that autopoietic wholes
could be mathematically formalized at all was a
consequence of the fact, as pointed out later by
two Spanish Artificial Life researchers, Julio
Fernández Ostolaza and Álvaro Moreno
Bergareche, that there is a crucial difference
between organization and structure in the theory
of autopoiesis ( ): the organization is that whose
objective is the very preservation of itself;
whereas the structure is the material substrate
contingent upon the organization which the
organization utilizes for its purpose of survival.
Organization then refers to the wholeness of the
whole, the identity of this wholeness, its integrity
besides which the living organism is not intact.
Since autopoeisis is a matter primarily of the
organization and since this organization refers
to itself, it is amenable to a purely formal account
as the structure can be disregarded. This point
is similar to the idea, of which many computer
scientists are quite fond, concerning the radical
disjunction between software and hardware, in
which the purely formal construction of the
software can be implemented in an infinity of
different hardwares as long as the latter are
capably of performing digital operations.1
However the idea of autopoeisis might be
assessed, Varela, by believing he had to shoreit up through his algebra of self-reference,
effectively rendered it according to the hylozoist
model of positing an organic property, in this case
autopoeitic self-reference, all the way down.
Accordingly, like the above mentioned benefit of
hylozoism, Varela was also able to pretty much
duck the entire issue of how autopoeitic selfreferential invariance arose to begin. As in
hylozoism, there simply isn’t any baffling disparity
left between some stipulated pre-self-referential,
non-referential condition and later self-referential
wholeness. That’s why Varela was basically been
silent about morphogenetic transformation,
indeed, about the whole issue of “structure” as
such in contrast to “organization.” What Varela
left out however, and which remains a deep
perplexity in emergentist thought is how exactly
such referential closure could be brought about.
Of course, if self-referentiality exists all the way
down, then how it comes to be present in
referential closure is not longer so mysterious.
This is probably why Varela does not seemed to
have had much use for the term or concept of
emergence per se. In fact, a similar reticence
concerning transformation and how it can come
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Complexity and Philosophy Workshop - DRAFT paper
about is also apparent among those who have
appropriated autopoeisis in various contexts (see
Ulrich and Probst, 1984). The point being made
here is not to say that autopoeisis doesn’t have
some important insights to add, but that as an
explanation it suffers from the same serious lack
as hylozoism. And those who do get some
important mileage out of the concept, for example
Lemke (2000) do so by, in my estimation, so
changing the notion of Varela’s closure that it no
longer even carries anymore the sense of being
closed!
As a matter of fact, the referential closure
stance on emergent wholes pushes the focus
of inquiry away from how the parts can function
in making up wholes and instead overemphasizes the autonomy of emergent wholes
in relation to the parts. One result is that we are
left with the impression that such wholes are
disconnected from that from which they emerge,
a sense that having a life of their own is separate
from and lifted out of causal processes — we
are back then with even greater mystery.
HOLISM IN EMERGENTIST THOUGHT
There is another way that hylozoist tendencies
are showing themselves in the study of complex
systems, namely, the turn to a certain conception
of holism. A salient example of such holism is
the oft repeated refrain among complexity
enthusiasts of the whole being greater than the
sum of the parts. To be sure, in an important
respect this holistic move is to be commended.
Herbert Simon, winner of the Nobel Prize in
Economics, and noted trailblazer in the study of
complex systems, once put forward a
methodological principle that has since become
something of a working guideline among
complexity theorists, “... in the face of complexity,
an in-principle reductionist may be at the same
time a pragmatic holist. (Bechtel and Richardson,
1993). Notice Simon’s careful phrasing: he can
simultaneously affirm the reductionist
underpinning of scientific research and
acknowledge a heuristic value accrued from
paying attention to the whole as such. Although
Simon could thereby be seen as opening a door
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for taking emergence scientifically seriously,
ardent advocates of emergence have tended to
adhere to an in principle holism and strident antireductionism.
Holism, in coming down on the side of
the inviolability of the whole, tends to subordinate
the importance of parts even to the point of
gainsaying their explanatory significance at all.
Such an attitude to parts through considering the
whole as ontologically pre-eminent falls-out from
the holist conceptualization of wholes as pregiven, foundational structures of reality, a
conceptualization found at least as far back as
Aristotle, but emerging in a pronounced form in
the scientific work of Goethe and other
Naturphilosophes, which form the backdrop of
much of contemporary holism (Harrington, 1996).
Indeed, there is a connection between the
Naturphilosophisch conception of wholes as pregiven and their self-referential structure, the most
telling example perhaps being found in the work
of Kant (see Lenoir, 1982; and McFarland, 1970).
As soon as wholes, however, are
considered ontological pre-given, they partake
of the same fate as hylozoism’s animation of
nature, i.e., they are pushed all the way down
into the primordial substance of nature. As a
result, the coming into being of wholes loses any
bewildering character just as the origin of life does
for hylozoism. If wholes pre-exist, then their
coming into existence is no longer an issue.
Although, as in hylozoism, there is then the
equally obscure issues of both why these preexisting wholes are not always apparent and
when they are apparent what is it that has enable
this to come to pass.
CONCEPTUAL PROBLEMS WITH
HYLOZOIST PERSPECTIVES
As briefly mentioned above, two the conceptual
problems plaguing hylozoism are its denial of
radical difference and its replacement of the
enigma of the origin of the radically different
quality of life with the equally enigmatic quandary
of why what’s supposed to be imbued with life
does not show this innate organicity. In the
Complexity and Philosophy Workshop - DRAFT paper
modern garb of complexity theory, hylozoist
tendencies likewise prematurely take the sting
out of a particularly thorny question: how is the
emergence of radically novel entities with
radically novel properties possible. In particular,
the hylozoism of today presents several deep
conceptual problems which in my opinion obviate
the usefulness of such an orientation in the study
of complex systems. In effect, hylozoist
sentiments in the study of complex systems
possess, to paraphrase Bertrand Russell, all the
benefits of parthogenesis over genuine sexual
reproduction.. That is, they want to have us
believe that radical otherness somehow
spontaneously emerges out of nature because
it is pre-given in nature. The outcome though is
as fruitful as a stillbirth.
Not the least problem with holism,
whether of ancient or modern expression, is the
same one that Aristotle had with Platonic Forms:
How is a non-material whole supposed to affect
the material world? Holists find themselves in the
unenviable position of claiming their non-material
wholes have material efficacy without quite
showing how. This is not to deny that there may
be such a thing as the so-called “downward
causation” of wholes onto parts. But if this
downward influence is thought of in terms of
something mysteriously nonmaterial then we are
in a cognitive swamp of great conceptual
unwalkability. Holists then
The other two interrelated muddles have
already been mentioned, that is, how the
ontologically pre-given wholes remain hidden;
and what process enables them to appear when
they come out of hiding. The hylozoist
perspective can be seen if the answer to the
these two questions includes something like the
conceptual strategy of an actualization of a
potential. Indeed, this sort of perspective can be
detected in several places in complexity theory,
e.g., Gregoire Nicolis’ explanation of selforganization in physical systems as the activation
of a hidden nonlinearity (Nicolis, 1989) and even
in Mitchell Feigenbaum’s explication of his
constant in the logistic map in terms of the
potential of so-called one-humped maps
(Feigenbaum, 1983). Now there may be ways in
in specific cases where the actualizing of
potentials is an appropriate conceptual strategy.
But when it is used to dodge the really difficult
issue of how the radical novel can emerge then
it becomes just some fancy footwork, maybe
pretty to look at but lacking in real scientific or
philosophical perspicuity.
A version of the actualization of potentials
but even more drastic in its refusal to deal with
the hard issue of the arising of the radically
different is that of self-generation, an idea
promulgated by the mathematician and computer
scientist Ben Goertzel (
). Relying on the
mathematician Paul Aczel’s theory of hypersets
which are sets with the property of being allowed
to contain themselves, a property going against
conventional standards of logic and set theory, a
self-generating system would consist of a
collection of components which act on each other
with a certain probability, thereby yielding new
components with different probabilities. The result
is a new collection of components which can then
be fed back into the previous system like
functional iteration or computational emergent
updating, thereby used as “fodder” for further
ongoing modifications.
Now there is nothing inherently
problematic about self-generating systems
themselves just as their isn’t for self-referential
structures or constructions as such. Indeed, as
Goertzel has shown, self-generating can provide
clever insights for computational data mining and
analysis. However, they operate in a manner that
parallels hylozoism, a fact derived from the basis
of self-generation in hyperset theory. If a set can
contain itself as a member, then this amounts to
the positing of a primordial self-referentiality. If
there is a primordial self-referentiality, however,
then we are back with the hylozoist stance of
Varela’s algebra of self-reference. It is like the
problematic nature of Escher’s famous drawing
of two hands drawing each: once the two hands
have emerged then this drawing graphically
illustrates how they maintain each other by their
cross referential relation. But the drawing
suggests, at the same time, that unless the
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Complexity and Philosophy Workshop - DRAFT paper
macroscopic image is just the macromanifestation of an infinitely small micro-seed
of their self-cross referential structure, that is, a
version of some kind of hylozoist selfreferentialism all the way down, there’s no way
the hands could have emerged in the first place!
Hence, self-generation may be plausible to talk
about the initiative of the components of a system
in reinforcing each other, but it is not a viable
way for talking about the initiative of emergence
in the first place since it amounts to emergents
emerging by their own bootstraps. Hylozoism, in
whatever version, has the unfortunate feature of
replacing one mystery by another, of supposedly
explaining one obscuring by something equally
or even more obscure.
THE EMERGENT CONSTRUCTION OF
EMERGENT WHOLES
Since hylozoist perspectives in effect dodge the
really tough questions about how emergent
wholes can come about, what’s needed instead
is an approach which squarely looks at this
difficult and instead of shirking it, grapples with
it. Previously, I’ve offered an approach to
emergence which characterizes the processes
of emergence in terms of construction, more
specifically, self-transcending constructions
(Goldstein, 2001). The basic idea there was to
offer a fresh approach to the study of emergence
given the fact that even in spite of the great
amount of research devoted to emergence in
such areas of complexity theory as far-fromequilibrium thermodynamics, dynamical
systems, and Artificial Life, it cannot be denied
that emergence has remained an elusive concept
primarily due to the lack of suitable constructs
for investigating structure and patterns (see, e.g.,
Cructhfield, 1993; Hartman, 200; Holland, 1998).
I sketched-out a constructional approach that
took quite seriously the claims made for
emergent phenomena, and then backing-in, so
to speak, from the characteristics of such
phenomena to how they might come about, that
is, what kinds of constructional processes might
be capable of bringing them about. It must be
noted that “construction” is not being in its
customary sense where it carries the connotation
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of an “external constructor”. Rather, those
processes at the heart of evolution, namely
variations and natural selection, as well as the
genetic operators of Artificial Life can be included
under the rubric of “construction” in this sense. A
self-transcending construction is one precisely
leading to an outcome that is radically
transcendent with respect to that from which it
emerges. To the degree that emergents are not
pregiven as a hylozoist perspective would have
it, but, instead, are dynamical, that is, arise over
time, then they must be in one way or another
constructed in this specific sense.
It would be too much of a distraction to
go into any more detail here as to the justification
for taking such an approach except to reiterate
that it was offered as a fresh look at emergence
with the hope it would prompt some fresh insights
into emergence. However, what I can offer here
are some hints as to what might involved in
processes of the self-transcending constructions
of new emergent wholes. Specifically, I am
offering several hints culled from areas of study
devoted to the issue of the organization of wholes
as such: Gestalt Psychology’s principles of the
organization of perceptual wholes; principles from
the design of aesthetic wholes; how selfreferentiality in grammatical structures are
constructed. Obviously, these are not meant to
be an exhaustive survey of what’s involved but
rather, as stated above, merely as hints in that
direction.
If emergent wholes are somehow
constructed out of the interaction of their parts,
and in such a manner that it makes these wholes
more than a mere amalgam of parts, then a good
starting place would not be to jump to the
transcendental source of such wholes as
hylozoist oriented holism does, but instead, stay
with the whole as it shows itself and carefully
explore first what it is about it that summons the
label of wholeness. What specifically is it about
an emergent whole that makes it a whole? In
other words, what is the wholeness of a whole?
PRINCIPLES OF PERCEPTUAL WHOLES
Complexity and Philosophy Workshop - DRAFT paper
Although Gestalt Psychology grew out of a long
tradition of holism in Germany which, as
described above, posited wholes as pre-given,
ontological facts, nonetheless, Gestalt
Psychology’s study of perception has been
concerned with how parts are organized in such
a way as to “construct” a perceptual
whole.(Köhler, 1947). Since their focus, then, has
been not just on any old organization of parts,
but how the parts fit together to form a whole,
gestaltism can be turned to as a source of insight
into precisely what constitutes the wholeness of
emergent wholes. Kurt Koffka, one of pioneers
in Gestalt Psychologist stated, “It has been said:
the whole is greater than the sum of its parts. It
is more correct to say that the whole is something
else than the sum of its parts., because summing
up is a meaningless procedure, whereas the
whole part relationship is meaningful.” (Koffka,
1935, p. 176). Gestalt Psychology has typically
conceived the perception of organized wholes
through an adumbration of several principles of
“organization” or “grouping” what Koffka talked
about in terms of parts which “fit” each other, or
a “good continuation” or “joining”:
< Figure/Ground;
< Closure: One of the features of a pattern which
make it appear as a whole is it having some
sense of closure so it can be distinguished from
the background;
< Proximity;
< Similarity;
< Symmetry;
< Continuity: tend to prefer continuous figures,
like a cross, we see two intersecting lines not
four lines meeting at center;
< Uniformity: a strongly unified part of a field will
look as uniform as possible;
< Internal vs External Forces of Organization or
Forces Within vs Without:
Here is not the place to assess the merits of any
of the principles of this list, but merely to point
out that principles such as these are what serves
to make wholes wholes. Therefore, to the extent
that emergent wholes are constructed this
constructional process would need to take heed
of such a list. This point will be reinforced by the
similar way of thinking about wholes described
in the next section.
THE CONSTRUCTION OF AESTHETIC
WHOLESTHE CONSTRUCTION OF
AESTHETIC WHOLES
The wholeness of artistic products has been a
primary concern of artists. For example consider
these three quotes from famous artists:
Delacroix: “before knowing what the picture
represents you are seized by its magical accord”
(quoted in Dewey, 1934, p. 145).
Paul Klee: “the aim of our theoretical work is
always in one form or another, the organization
of differences into unity, the combination of
organs into an organism. ...” (quoted in Barratt,
1980, p. 282.
Mattisse: “the relationships between tones
[colors] must be instituted in such a way that they
are built up instead of knocked down. A new
combination of colors will succeed to the first one
and will the give the wholeness of my conception”
(quoted in Dewey, 1934, p. 136).
This concern for aesthetic wholeness has
perhaps had its most intense commitment and
expression in Islamic design since the Quranic
injunction against pictorial representations of the
deity and the prophet led to a turn to abstract
geometrical representations of divine unity
(Burckhardt, 1976). These abstract geometrical
forms to portray unity and wholeness can be a
door into abstract principles of design about
wholeness which parallels in certain ways the
Gestaltist’s views on the organization of
perceptions into unities.
The principles of Islamic representations
of wholeness can be summarized as follows
(derived from Burckhardt, 1976; and, Critchlow,
1976):
< the center, periphery, and in-between regions
are all important with the design balanced in its
focus on all three;
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< a heterogeneity of sizes and shapes linked by
common “threads” as well as a mix of repetition
and the unexpected;
< regions concentrically layered from the center
out are connected;
< the use of symbols of the unity of oppositions,
e.g., circles, squares, crosses, six pointed stars,
octagons, and so on;
< interlocking and interweaving, both locally, and
across the whole picture which serve to hold the
whole together;
< parts are demarcated as well as connected to
the whole;
< the use of modularity and scaling, including
the golden proportion and its fractal scaling;
< various symmetries;
< a harmony of simplicity and complexity.
Moreover, the overt design can, on analysis be
found to rely on covert patterns acting as a sort
of blueprint for wholeness (see Critchlow, 1976).
It is crucial to emphasize that the organization of
the design exhibited as wholeness is not
something apart from the parts but is how the
parts are made to fit with each other and the
whole. This wholeness is a “unity in multiplicity”
where each part has an indispensable function
and in that sense at least is not downplayed in
relation to the whole. Rather the whole is
precisely that which is constituted by the parts in
their interrelationships.
CONSTRUCTING SELF-REFERENCE:
DIAGONALIZATION
As discussed above, organic wholeness has
been thought of in terms of referential closure
from Kant through Maturana and Varela into the
neo-emergentist focus on autocatalytic networks.
An access into how self-referential structures can
be constructed is afforded by a look at how selfreference comes about through grammatical
constructions of sentences. A self-referential
sentence is by definition one that refers to itself,
e.g, the following four sentences:
(1) This sentence is written in English.
(2) This sentence has five words.
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(3) This sentence is grammatically correct.
(4) This sentence is a sentence.
In each case, it is the opening phrase “This
sentence” which is the marker that indicates that
what the sentence is referring to is itself. There’s
nothing particularly significant in using the phrase
“This sentence” to construct a self-referential
sentence since it could be replaced by some
other device to indicate self-reference, e.g.,
putting a box around the sentence:
The sentence in the box is in English.
Sentence 4 is a bit more complicated since it is
not only referring to itself, it also referring to itself
about what it is, i.e., a sentence, whereas what
the previous sentences, 1, 2, and 3 are referring
to themselves about is not the fact of being a
sentence but, instead, about the language, the
number of words, and its grammatical status.
There is nothing particularly unusual about such
grammatical constructions and accordingly, there
shouldn’t be any controversy about whether such
sentences are semantically meaningful. (By the
way, cross-reference is an indirect form of selfreference in that it includes two or more things
referring to each other in a circular fashion, so
that ultimately the circle comes back to from
where it started so it amounts to an indirect form
of self-reference (see Grim, Mar, St. Denis, 1998;
and , Hellerstein, 1997).
In mathematical logic, the construction of
self-reference is often understood in terms of
diagonalization (Smullyan, 1994). First, for an
expression (AexA for short) of the sentence,
substitute for ex the literal quotation of the whole
statement. This is actually much easier than it
sounds, for example, start with sentence 10:
(10). John is reading Moby Dick. (“Moby Dick”’’
ex)
and substitute the whole sentence (10) for ex to
yield:
Complexity and Philosophy Workshop - DRAFT paper
(11) John is reading “John is reading Moby Dick”
Strictly speaking, sentence (11) is not yet selfreferential for it merely asserts John is reading
sentence (10), not itself, sentence (11).
a fixed point attractor in the logistic map at certain
ranges of the parameter value. Indeed, fixed
points show that a recursive function have
become self-referential in regards to the
variable).
Conclusion
Now consider the sentence:
(12) John is reading the diagonalization of
sentence (11).
Since the diagonalization of (11) is {John is
reading “John is reading >John is reading Moby
Dick’”}, sentence (12) is {John is reading “John
is reading >John is reading >John is reading
Moby Dick=>”}, or:
(12A). John is reading the diagonalization of John
is reading >John is reading Moby Dick=.”
The diagonalization of expression (12A) then
would be:
(13) John is reading the diagonalization of (12)
or {“John is reading the diagonalization of >John
is reading Moby Dick.=”}.
Sentence (13) then asserts that John is reading
the diagonalization of (12), but the diagonalization
of (12) is (13) itself! Therefore, sentence (13)
asserts that John is reading the very same
sentence itself (13)! Accordingly, sentence (13)
is purely self-referential.
Whatever the construction process necessary for
emergent wholes, is it would need to mimic in
some sense diagonalization. Our brief review of
diagonalization shows that achieving pure selfreference is difficult since the action of referring
has to be completely bent back around to itself,
a complete, not partial, fulfillment of circularity.
That’s why neither self-reproduction nor recursion
are purely self-referential, the former because
what’s being reproduced is not itself but a
facsimile thereof, the latter because the feeding
back consists of a new value not just the same
old value (unless, of course, the recursive
function has become a fixed point, for example,
Hylozoist strategies are certainly a temptation for
the way they manage to avoid the really “hard
problem” of emergence. It might seem that we
are also falling into a hylozoist cast by presenting
what could be taken as a form of “pan” selftranscending constructionalism. However, selftranscending constructions are by their very
nature not pre-given, but refer, instead, to a
dynamical process of the coming into being of
the radically original. Therefore, they are not
offered as an easy way out of the dilemma as to
what’s involved with the latter but rather as
admitting that accounting for the emergence of
wholes requires difficulties that hylozoist
perspective merely shun.
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1. See Pylyshyn