Whenever the most beautiful is perceived, ugliness arises,
the least beautiful. Whenever good is perceived, evil exists,
its natural opposite.
Thus, perception involves opposites: reality and fantasy are opposing
thoughts; difficult and simple oppose in degree; long and short
oppose in distance; high and low oppose in height; shrill and
deep oppose in tone; before and after oppose in sequence.
The truly wise accept this and they work diligently without allegiance
to words. They teach by doing, not by saying; are genuinely helpful,
not discriminating; are positive, not possessive; do not proclaim
their accomplishments, and because they do not proclaim them,
credit for them can never be taken away. 1 |
OVERVIEW
For members of Western cultures—native speakers of one or more
of the Western Indo-European (WIE) languages—the above passage
from the
Tao Te Ching seems somewhat alien. We Westerners regard
"natural opposites"—pairs of
polar terms—not as closely
related and mutually-determining, but rather, as disparate, separable,
as if their oppositeness provides the ONLY relation between them. As
Alan Watts puts it,
| By and large Western culture is a celebration of the illusion
that good may exist without evil, light without darkness, and
pleasure without pain, and this is true of both its Christian
and secular, technological phases. Here, or hereafter, our ideal
is a world in which "there shall be no more death, neither sorrow,
nor crying, neither shall there be any more pain; for the former
things are passed away." (Revelations 21:4) 2 |
In the present paper, we deal extensively with the polar terms
theory
and
practice. Initially we focus on theory, disclosing and developing
inter-connections between the "parts" of an axiomatic system. Then in
the Discussion section, we consider some of the implications for practice,
the "practical" repercussions, of these developments of theory.
The moment we mention the topic of
theory, we risk losing most
of our audience. In accord with the so-called Western cultural "illusion,"
good, practical people scorn theory—"mere" theory. It has no bearing
(we say) on the pragmatic concerns of realistic, practical folks. It
just doesn't matter.
We sympathize with this attitude. We have developed more than a passing
acquaintance with what passes for theory among Westerners, and a great
deal of it seems not to make a difference in practice. Furthermore,
we suggest why not. Characteristically Western theories systematically
eliminate the observer from consideration. And by so doing, such theories
deny that any transacting occurs between an observer and her/his theories.
But if the theorist has no effect on his theories, and/or the theories
have no effect on the theorist, it should come as no surprise that such
theories "just don't matter."
(The fact that the revolutionary physicists of the beginning of the
Twentieth Century first introduced the notion of "taking the observer
into account," and found ways of building this notion into their theories,
means only that their theories remain inconsistent. What relativity
and quantum theory give with one hand, they take away with the other.)
In the present paper, we do not use Western theories (nor Eastern ones
either). Instead, we utilize an
entirely non-traditional theoretical
system, based on assumptions created, or generated (or whatever-one-does-to-produce-assumptions)
by a particular person—Alfred Korzybski (1879-1950)—in a particular
time-and-place (mostly Chicago, during the period 1921-1943) rather
than by anonymous "tradition." Our theoretical system takes the observer
into account in a systematic fashion. Hence we DO show the transacting
that occurs between observer and theory. We deal with a new class of
theories:
lived theories, which do make a difference to the people
that use them.
We invite our readers to join us in exploring territory which seems
unfamiliar to everyone, ourselves included—and find out just what
kind of a difference it makes to rely on lived theory.
INTRODUCTION
For a very long time, humans have "known" in principle that the Earth
we live on orbits the Sun, has the shape of a flattened spheroid, rotates
on its own axis, etc. But not until someone got off the surface of the
Earth and went far enough out to see it as having an uninterrupted contour
did anyone
know these things experientially. Those first photographs
of the Earth made from off-planet provided a polar-opposite, a contrast
to our earthbound experience which irreversibly altered our perception
of, and our relation with,
terra firma. Experientially, it became
a planet—
our home planet—and we became inhabitants-of-a-planet.
The human race has yet to finish assimilating this major alteration
of our perceptions, and working out its consequences.
Similarly, we humans live as social organisms embedded in a matrix called
both
culture and
language. This matrix consists ultimately
of human "doings" in the human environment, the Earth's biosphere. The
terms
culture and
language serve to name aspects of these
"doings".
Language comprises the
self-reflexive sub-category
of these "doings," within which we humans can get explicit about the
"doings" (including "language") which make up the matrix. This matrix
appears highly diverse, with many different cultures (which students
of culture classify by geographical region, by the level of technology
employed, etc.) and many different languages (which students of language
classify into linguistic families, super-families, etc.).
Here too, in principle we "know" a lot about this matrix—e.g.,
about language and about the reciprocal relations between humans and
language. But a part of what we "know" appears somehow askew. For example,
in English,
language functions as a noun, "the name of a person,
place, thing, etc." In our unguarded moments at least, we treat the
term
language as if its referent, "that which the term
language
designates," comprised a static-and-unchanging THING. When we look candidly
at what we DO, however, it seems more apt to represent the referent
as a process or processes, using a verb,
to language, created
for the purpose. Then we can say, succinctly, that we humans
language,
that we engage in
languaging.
The term
languaging includes our speaking-and-listening, writing-and-reading,
signing-and-receiving-signing, etc. It also includes the bodily movements
which accompany our speaking-and-listening.
A) BODILY MOVEMENTS AND SPEAKING: SELF-SYNCHRONY
As long as a human continues living, her/his body-parts—e.g. chest,
left thumb, head, right knee, etc.—make small movements. Any given
movement begins, continues for a while, and then stops or else changes
direction. Also, the process of speaking itself consists of making a
series of small movements. When a human speaks, any locution s/he emits
consists of a string of "syllables." When observed in sound movies made
at 24 frames per second and studied with a time-motion analyzer, the
small bodily movements which accompany speaking maintain a precise relationship
to the syllables which make up the locution which the speaker emits.
Each of these observable movements starts in precisely the same frame
of the film as does the beginning of a syllable, and ends in precisely
the same frame as does the end of a syllable. Some movements last for
only one syllable; others span several syllables. But each movement
starts in the same frame as does a syllable, and each ends in the same
frame as does a syllable. As Condon & Ogston put it,
| ... The body dances in time with speech. 3 |
B) BODILY MOVEMENTS AND LISTENING: INTERACTIONAL SYNCHRONY
As observed in sound movies using a time-motion analyzer, the bodily
movements of a person listening to a speaker occur in precise synchrony
with the syllabic structure of what the speaker says. Each movement
of the listener starts in the same frame as does the beginning of a
syllable of what the speaker says, and ends in the same frame as does
the end of a syllable.
... Metaphorically, the three interactants [in the filmed behavioral
sequence under discussion] looked like puppets being moved by
the same set of strings. 4
We interpret the small motions of a listener's interactional synchrony
with a speaker as an outward and visible sign of the process of
listening, of languaging. 5 |
Even the inclusive-sounding hyphenated terms we use to describe human
languaging turn out misleadingly discrete and isolating—whereas
the activities they refer to permeate, influence, and form a part of
just about everything we humans do. We find it almost impossible to
separate our activities—ranging from our largest, most central
ventures to the smallest and most trivial—from the ways we language.
We humans get born into a social (and that means cultural and linguistic)
context, grow up there, produce and raise offspring, engage in social
relations with our fellow-humans, and, after we die, the corpses get
buried, cremated, etc., in accord with the patterns given in the languaging
of our speech communities. Our languaging makes up the core of human
living, providing a central, supporting structure for our relations
with ourselves, with our fellows, with humans from other communities,
with members of other species, with the entire human species, and with
the biosphere as a whole.
However, our pictures, our perceptions of these processes and these
activities, have lacked opposition. No matter how many contrasting languages
we may have, we have had no contrast to those ways of languaging rooted
in the distant past. Our species has developed an almost incomprehensible
diversity of traditional patterns, but no alternative to the traditional.
And as a Taoist might tell us, this lack of opposition has limited what
of our matrix we could discern.
In the Western family of cultures, we have created a social institution
with the job of developing new oppositions, new perceptions. The exponents
of the social institution of science have not only gradually and progressively
generated new insights, new knowledge—and have done so at exponentially-increasing
rates—but also have led the rest of the human race to adopt these
innovations, and so to relinquish more traditional ways of doing things.
As Polanyi puts it,
| ... The discoveries of science have been achieved by the passionately
sustained efforts of succeeding generations of great men, who
overwhelmed the whole of modern humanity by the power of their
convictions. 6 |
But the exponential increase of Western scientific knowledge has occurred
only within a specific cultural and linguistic setting. The anthropological
linguist Benjamin Lee Whorf asserts that
| What we call "scientific thought" is a specialization of the
Western Indo-European type of language .... 7 |
And since we humans have had no contrasting alternative to science as
a specialization of the WIE type of language, we have remained unable
clearly to perceive the structure of presuppositions which our dependence
on the WIE type of language, and the grammar common to the WIE languages,
has entailed. For example, the WIE languages, and therefore the Western
cultures, grant a central place to the logical construct of
identity
(defined as "entire and absolute agreement or negation of difference"8):
These languages utilize this construct to 6generate the distinction
between the two main "parts of speech"—
nouns and
verbs—which
form the bulk of their vocabularies. 9 They treat any noun or noun-phrase
as subject to Aristotle's
Law of Identity, and therefore, as
identical with itself or
self-identical. Conversely, they treat
any verb or verb-phrase as not-subject to the Law of Identity—as
not-self-identical. 10
Then our classical scientists posit a "world" made up of distinct, discrete
"objects" or "things" with inherent "properties" or "attributes," which
enter into more or less transient "relations". Further, they treat the
"objects" and "attributes" as precisely suitable to represent by means
of self-identical noun-phrases, and treat the "relations" as precisely
suitable to represent by means of not-self-identical verb-phrases, combined
in agreed-upon patterns. In so doing, they
grant a privileged position
to the grammar common to the WIE discursive and formalized languages—and
thus to the at least partially unknown presuppositions encoded in that
traditional grammar. The
privilege which they grant amounts to
an unwillingness to recognize or acknowledge the presuppositions encoded
in that grammar, nor to allow themselves to question them, nor to permit
anyone else to do so.
Particularly in the last couple of centuries, exponents of geometry,
logic, physics, etc., have framed "heretical" viewpoints which in certain
ways break with the WIE tradition. But even the non-euclidean geometers,
the modern set theorists and the exponents of relativity and quantum
theory still maintain tradition in a wider sense: by continuing to utilize
identity-based mathematical and logical languages in which to frame
their "heresies," they still grant a privileged position to the WIE
grammar.
One recent series of studies has systematically broken with tradition.
To date, it has yielded an alternative frame of reference which delivers
a revised world-view, an alternative grammar derived from known, non-traditional
premises, a non-standard notation of the "Let's keep track of what we
say" type built up on that derived grammar, and an axiomatized theoretical
system. These studies start with the work of Korzybski. In effect, Korzybski
makes a quick tour of the universe, asking, "In a cosmos which has human
observers in it, when and where may we LEGITIMATELY use the logical
construct of
identity? Where and when does the notion of
absolute
sameness in all respects, or negation of difference prove valid?
Under what circumstances does it apply?" His considered opinion: Never.
Under no circumstances does
identity survive scrutiny. 11 And
then Korzybski makes an outrageous suggestion: Since identity never
holds, he says, let's not RELY on it.
Korzybski proposes that we
reject identity—disallow it as
a valid "relation."
To state the matter in more general terms, Korzybski discloses that
there exist not one but two ways to handle the paired terms
identity
and
non-identity: a) One can "like"
identity as a foundation,
and "dislike"
non-identity (as our linguistic forbears did);
or else b) one can "like"
non-identity and "dislike"
identity.
Once a choice becomes possible, any human who uses this term-pair at
all must choose which way to use it. Korzybski himself takes a stand,
declaring himself one of the company—the first of the company—of
those who explicitly prefer non-identity.
Korzybski thus creates a choice with consequences—a fork in the
road, or a turning-point, for the human race—where no choice had
previously existed.
Furthermore, by way of taking his own suggestion, Korzybski develops
a coherent system or world-view, known as
general-semantics,
and reaches two end-points: a) He brings out into view, and states in
English, the fundamental (I might even say
metaphysical) premises
on which his system rests, including three
undefined terms and
three
non-aristotelian postulates (discussed in more detail below);
and b) he develops methods by which to enable others to USE the new
system, in their own living, rather than just to TALK ABOUT it.
In our own research project, we take non-identity seriously, relying
on Korzybski's non-aristotelian Postulate of Non-identity as our most
fundamental postulate. We deliberately generate an axiomatic system—an
alternative theoretical system radically different from the WIE frame
of reference; from any other traditional language or family of languages;
and from the "common-sense" of any traditional culture or family of
cultures.
Using this alternative frame of reference, we have developed unexpected
contrasts, new questions, new methods of analysis, unexpected insights
into the familiar. Of central importance here, we have disclosed two
opposing structures of assumptions: one which forms the basis for taking
the observer into account, as opposed to another which forms the basis
for eliminating the observer from consideration. Then, knowing how it
works, we systematically take the observer into account. In the present
study, we extend the construct of "taking the observer into account"
so as to make a new contribution to the knowledge of axiomatic systems,
human languaging, and also of the Gestalt viewpoint.
COURSE
OF THE ARGUMENT
In the remainder of this paper, we back up these claims by disclosing
a general and fundamental pattern which I call the
conventions for
symbolizing. We shall
- State the conventions for symbolizing in general terms, expressing
them as fundamental parts of any axiomatic system.
- Particularize this general pattern for WIE languages, e.g. for
written or spoken English and for written notational ("formalized")
languages such as the mathematical theory of sets.
- Particularize this general pattern for the non-standard notation
we have framed on the derived grammar we have generated.
AXIOMATIC
SYSTEMS
To facilitate making the comparison between the WIE frame of reference
and notation and our own, let us review the general outlines of what
we call an
axiomatic or
postulational system. One
difference shows up immediately: In the WIE view, an axiomatic system
"exists" as a
thing, independent of any observer, logician, or
other human. In contrast, what we call "an axiomatic system" "exists"
or "occurs" solely and exclusively as HUMAN ACTIVITIES—"something
someone does." Thus, someone (a
logician or "observer" or "organism")
chooses a) some
setting or other and b) a small number of
undefined
terms; s/he selects c) some
postulates, which s/he expresses
by means of the undefined terms; s/he arranges for d)
rules of inference,
and e)
standards of proof; etc. With these "pieces" in place,
s/he then derives and proves one or more
theorems, or formal
conclusions. In so doing, s/he satisfies our minimal criterion for the
"completeness" of an axiomatic system.
Except for the difference of opinion concerning the "locale" of an axiomatic
system, we expect that exponents of standard WIE axiomatic systems will
agree with this way of naming the "parts" that make up such a system.
However, we discern some key connections between these "parts" not previously
described. For example, in keeping with our views on the "locale" of
an axiomatic system,
- We regard the setting, and also the undefined terms, as human
"doings"—something someone DOES. Specifically, we hold that
each of these constructs operates as a special kind of postulate:
namely, as a silent postulate, the tenets of which the person
who relies on it cannot state in words. 12 S/he must, however, know
how to USE these constructs correctly.
- We posit a further connection between setting and undefined
terms, such that for one to occur requires the occurrence of
the other. In other words, we posit a polar relation between
them.
- In choosing a setting, our logician (to use a characteristically
WIE image) chooses the way in which her/his frame of reference
"slices up the world." 13
- In selecting undefined terms, our logician puts limitations
on the "slicing-up" process, so as to get "elements of the lexicon"—terms
or "words" or "sentence-parts" which will fit into the "slots"
of the template or grammar of the notation in question.
- In articulating the setting and the undefined terms, our logician
produces a version of the logic of opposites, which amounts
to a pattern for handling defined terms—in particular,
one which specifies the connections between a term or construct
and its opposite or contradictory or negation or complement.
14
- We maintain that our logician obtains the grammar by somehow inter-defining
the undefined terms.
Thus, taken together, setting and undefined terms specify the
conventions
for symbolizing.
COMPARING
THE PATTERNS
RHETORICAL
STANCE
From our point of view, anyone writing any text whatsoever (in any language)—even
a laundry list—takes a rhetorical stance: presumes a
speaker,
addresses an
audience, and posits a
dramatic situation.
When we use our alternative theoretical system, we take a rhetorical
stance different from that which we attribute to users of the WIE languages.
(A) INTERACTING:
WIE NOTATIONAL LANGUAGES
In general, texts written in a WIE language "posit" some dramatic situation
which centers about one or more "thing(s)"
interacting with one
or more "thing(s)." The term
interacting (modified from Dewey
& Bentley15), suggests a kind of "one-way causality":
| A causes B, and B causes C, and C causes ... |
As an example of the language of interacting, consider Newton's second
law of motion:
"Force," "mass" and "acceleration" exemplify the kind of "things" known
as
quantities, while "equals" and "times" or "multiplied by"
exemplify the kind of "interactions between things" known as
operations
or
relations. This famous equation describes the "motion" of
physical "bodies," in a world thought to consist of more or less discrete
objects ("bodies") of different sizes, which follow trajectories and
sometimes collide. Newtonian physicists regard the "happenings," the
interacting which this equation describes as taking place independent
of any observer. (The descriptions generated by Newtonian mechanics
turn out quite accurate, as long as the dimensions of the "bodies" or
"things" or "objects" examined remain within a few orders of magnitude
of the dimensions of a human body.)
One interpretation of (1) into English goes, "To exert a force f on
a mass m causes an acceleration a ."
(B) TRANSACTING:
OUR NON-STANDARD NOTATION
In our non-standard frame of reference, in general we posit "doings"
or "happenings" which consist of the two-way
transacting between
a human organism-as-a-whole and her/his environment, over a specific
period—as viewed by a particular observer, who writes out her/his
observations in our alternative notation. The term
transacting
(modified from Dewey & Bentley) suggests a kind of two-way interchange
between organism and environment which profoundly alters the living
system(s) involved, in some way that affects its/their further living.
For example, humans A and B meet as strangers, and have a conversation
which matters to each of them: Then they can never again meet as strangers.
Or consider the transacting between a weekend sailor and her/his sailboat,
before and after s/he takes a course on the physics of sailing—one
which includes applications of Newton's second law of motion. When we
humans learn how to use a tool skillfully, as Polanyi points out, we
come to handle it as a part of ourself. 16 Practicing what s/he has
learned in the course, our sailor improves her/his handling of her/his
tool, her/his sailboat. This obviously alters the sailor. That this
alters the environment as well—alters the way that wind and water
and channels, etc., occur for her/him—becomes apparent when a sudden
squall hits, and s/he brings the boat safely into a harbor in whose
dangerously narrow entrance a skipper with her/his previous degree of
skill would have wrecked the boat.
OVERVIEW
OF THE WIE PATTERNS
In our frame of reference, we regard the obvious "structural" features
of a symbolic system such as a grammar as evidence which manifests what
the speakers/writers of this symbol system
assume.
As noted above, a WIE discursive language such as English has a vocabulary
composed mostly of two main categories of terms, known respectively
as
nouns and
verbs. Between them, these two categories
make up some 70 to 80 percent of the entries in a big dictionary. Furthermore,
we distinguish between the two categories relationally, by regarding
and treating the nouns as "identical with themselves" and the verbs
as "not-identical with themselves." In so doing, we define the binary
relation of
identical with as signifying "entire and absolute
agreement or negation of difference."
Identical with itself,
then, comes out meaning "permanent" or "persisting" or "really existing"
or (as little as we may like to admit it) "unchanging."17 To form a
complete sentence, we place at least one noun—or, better,
noun-phrase—next to at least one verb-phrase:
A WIE formalized language such as a symbolic logic or one of the mathematical
theories of sets also has a vocabulary composed of two main classes,
which we variously call
things and
relations (
between
things), or
quantities and
operations, etc. Again,
we tell the classes apart by regarding and treating the
things
or
quantities, etc.—the terms which substitute for nouns—as
"identical with themselves," and the relations or operations—substitutes
for verbs—as "not-identical with themselves." To generate a
well-formed
formulation, then, we place at least one noun-substitute next to
at least one verb-substitute:
A. MAP-TERRITORY
IDENTITY
The WIE grammar makes no provision for distinguishing between "map"
and "territory." For example, it includes no mandatory prefix, suffix,
infix, no special grammatical forms, etc., by which a speaker/writer
can keep track of this distinction. Of course, a speaker/writer CAN
arrange to differentiate "map" from "territory," by secondary means,
whenever s/he wants to (or remembers to)—but underneath such locutions,
the primary structure of the WIE grammar still does not make this distinction.
By analogy, a video tape record of an "event" SUGGESTS the past "existence"
or "occurrence" of that
event. But the structure of English,
or set theory, provides no built-in way to distinguish between the taped
"event" and the actual
event (if any).
In our frame of reference, the construct of "does not distinguish between"
appears equivalent to "holds or treats as identical with." In other
words, where by presupposition the WIE grammar provides a speaker/writer
with no primary means to distinguish between "map" and "territory,"
by that presupposition it constrains this speaker/writer to hold that
"the territory"—ultimately, "the world" or "the Universe" or "the
Cosmos"—has a structure which precisely matches that of the WIE
grammar. "The world," it says, REALLY DOES consist of (a) static-and-unchanging
"objects," precisely suitable for anyone to represent in "language"
by means of self-identical noun-phrases; and of (b) more or less transient
"relations between objects," precisely suitable for anyone to represent
by means of not-self-identical verb-phrases.
In WIE mathematical terms, we can express this tenet by means of the
construct of an exhaustively complete, entirely accurate one-to-one
relation, such that every point of "the territory" or "the world" gets
represented by one and only one point of our speaker/writer's "map"
of "the world," and that our speaker/writer's "map" contains no extraneous
points (no points which do NOT represent or refer to points of "the
world").
We designate this presupposition as
map-territory identity or
tacit identity. Elsewhere, we have demonstrated that this (silent)
postulate of tacit identity underlies the standard logical sense(s)
of the term
identity (or the relation of
identical with).
We designate this latter construct as
explicit identity.
Our frame of reference and notation contrast sharply with the WIE discursive
and formalized languages at precisely this point. The WIE frame of reference
and the various WIE notations include among their premises some kind
of postulate of tacit identity, the construct of explicit identity,
and either Aristotle's Law of Identity or the modern Logical Axiom of
Identity. Hence we refer to these languages as
identity-based
or as
generically Aristotelian. Our frame of reference and notation
stem from a central premise known as Korzybski's Postulate of Non-identity,
which
rejects (disallows as valid)
the construct of identity
in any guise or form, explicit or tacit. Hence we refer to these
languages as
non-identity based or
generically non-aristotelian.
WIE LANGUAGES
AS AXIOMATIC SYSTEMS
We regard English as a traditional discursive language of the Western
Indo-European family. It did not arise as a deliberately generated axiomatic
system. For example, no one consciously chose a setting or undefined
terms or postulates for it, or otherwise specified its "antecedents."
If someone holds (as we do) that English does have a postulational structure,
with "antecedents" or "premises" and "consequents," s/he has made an
assumption not shared by the speech community as a whole. In contrast,
each of the WIE mathematical languages, e.g. each of the various mathematical
theories of sets, does stand as a deliberately generated axiomatic system,
whose innovators do specify undefined terms and—after 1902, the
date of Russell's paradox concerning sets which do not belong to themselves,
18 a setting, etc., for it. However, lacking a contrasting system, each
of those innovators relies in an unquestioning fashion on the grammar
common to the WIE languages (both discursive and formalized). None examines
that grammar for "conventions for symbolizing" or other assumptions,
nor characterize such conventions in general terms (as we do here).
Thus the antecedents we outline here occupy a "position" logically prior
to any of the antecedents discussed by WIE logicians and linguists.
By analogy with the revised pattern for axiomatic systems laid out above,
let us now frame English or set theory as that kind of axiomatic system.
To do that, we infer the missing "parts," and then fit them into place.
In the process, we account for (or at least incorporate) the features
of WIE languages mentioned above, in our overview of the identity-based
WIE pattern.
- Setting: As noted, we regard setting and undefined terms
as human "doings", silently postulated by the person who relies
on them. The setting for a WIE language, in our view, consists of
a distinction—a pair of opposites, an "empty" dichotomy which
we may indicate generically as x and not-x.
- Undefined terms: As undefined terms, we propose noun,
verb, and the copula (e.g. 'is').
- Interconnections between setting and undefined terms: The
interconnections in question generate the conventions for symbolizing
of WIE languages such as English or set theory.
- (a) Slicing-up: Someone who chooses the above
setting thereby "slices up the world" into two "KINDS"—into
the "empty" dichotomy mentioned above, x and not-x
. Or, to use an image that begs fewer questions, s/he CREATES
two disparate "kinds." In any case, s/he treats them as polar;
or in other words, treats her/his "process of slicing" or "process
of creating" as if it necessarily generates both "kinds." Further,
s/he utilizes this process of "slicing in two" over and over
again within the grammar of a WIE language, on various logical
levels, producing a dichotomously branching logical (or grammatical)
"tree."
- Putting on constraints: Someone who chooses the above
undefined terms (noun, verb, and 'is') thereby puts constraints
on the "process of slicing" just described. S/he treats one
of the two "kinds" (say, x ) as in some sense "the domain
of words," and subdivides it into noun and verb
(where noun 'is' noun and it is not the case
that verb ("not-noun") 'is' verb). In the same
breath, s/he treats the other "kind" (say, not-x) as
in some sense "the domain of not-words," and subdivides it into
two sub-classes, one of which s/he treats as precisely suitable
to represent by means of self-identical noun-forms or
noun-phrases, and the other of which s/he treats as precisely
suitable to represent by means of not-self-identical
verb-forms or verb-phrases.
These arrangements not only yield terms or "words" or "sentence-parts"
which will fit into the "slots" in the template or "grammar"
of the notation or discursive language in question—they
also support the conviction that there "really exist" two disparate
domains: one which has something to do with "words" or "language,"
and another which seems somehow "non-verbal," e.g. a "reality"
or "world" that "exists" "out there," independent of any "speaker"
or "observer" or "organism," and also independent of any "words"
the "speaker" may utter. Finally, these arrangements support
the conviction that these "sentence-parts" uniquely "represent"
this non-verbal "reality".
- Logic of opposites: As noted, the logic of opposites
amounts to a pattern for handling defined terms (in a WIE language,
nouns or noun-substitutes), one which specifies the connections
between the noun-phrase in question and its negation (or other
polar-opposite). The WIE tradition has included at least two
distinctly different versions of the logic of opposites, commonly
known as undelimited and delimited.
- Undelimited The undelimited version of the WIE
logic of opposites utilizes two key terms, namely, some
(defined) noun-substitute x and its negation, not-x . When
expressed in a discursive language, this version of the
logic of opposites contrasts "a thing" (e.g. day)
against its negation (not-day), 19 which eventually
consists of "everything else." Combined with the discursive
language example, a simple Venn diagram makes this relationship
clear:
FIGURE 1 ABOUT HERE
Critics point out that the construct of "everything else"
proves unsatisfactory, undefinable—for the term day,
it not only includes "night," but also "pollywogs," "foreign
policy," "Cantor's transfinite cardinal numerals," etc.
But that makes "everything else" unsuitable as a basis for
a mathematics capable of generating "secure" inferences.
- Blank delimited: This version of the WIE logic
of opposites utilizes three key terms, namely, a delimited
domain D , within which "exists" the noun-substitute x and
its negation not-x . Here not-x comprises "everything else
within the domain D ". No one has yet modified a WIE discursive
language so as to make use of the blank delimited version
of the logic of opposites, so we have examples only from
WIE notational languages. 20 A Venn diagram displays these
relationships clearly:
FIGURE 2 ABOUT HERE
In this version of the WIE logic of opposites, not-x proves
readily definable, avoiding most of the logical difficulties
of the earlier version.
- Grammar: The pattern for a "complete sentence" or "well-formed
formula," requires someone to place at least one noun-phrase or
noun-substitute next to at least one verb-phrase or verb-substitute.
But since any noun 'is' 'identical with' itself, this grammar consists
precisely of the undefined terms inter-defined.
- Postulates: The postulates of the WIE frame of reference
include (for the undelimited version of the logic of opposites)
the "Laws of Thought" of Aristotle of Samos (384-322 BC). Aristotle
called them laws of thought; today, it becomes clear that
they spell out the rules for naming or "nouning":
- The law of identity: Whatever is, is.
- The law of contradiction: Nothing can both be, and not be.
- The law of excluded middle: Everything must either be, or
not be.
For the delimited version of the logic of opposites, replace the
"Law of Identity" with the modern Logical Axiom of Identity:
For all x which belong to the delimited domain D ,
x º x . |
- Rules of inference, and
- Standards of proof: We have little to add to the traditional
characterization of these topics.
WHAT WE CAN TALK ABOUT IN THIS LANGUAGE:
"Things" interacting with "things".
In a larger sense, the frame of reference here consists of a dualism,
e.g. framed as 'mind' vs. 'matter', where the "words" (which belong
to 'mind') stand for or represent "things" (which belong to 'matter'),
with perfect accuracy.
OUR NOTATION
AS AN AXIOMATIC SYSTEM
As noted above, we treat the constructs of
setting and
undefined
terms as designating human activities: "something someone does."
- Specific delimited setting: We can express the setting
for our non-standard notation by means of a run-on phrase, such
as "One particular human-organism-as-a-whole-dealing-with-her/his-environment-at-a-date."
More succinctly, we can express it by means of single terms such
as "transacting" or "contacting" or "living." With the Gestalt therapists
Perls, Hefferline & Goodman, we say,
| We speak of the organism contacting the environment, but
it is the contact which is the first and simplest reality.
21 |
This makes "I" and "it," or "I" and "thou," into INFERENTIAL "ENTITIES"
on our specific delimited setting, rather than into "the Really
Real."
- Undefined terms: As undefined terms, we follow Korzybski's
example and choose structure, order, and relation.
22 In our non-standard notation, we signify these by means of S
, O , and R . When we write these in English, we treat them as verb-forms:
(to) structure, (to) order, (to)
relation.
- Interconnections between setting and undefined terms: When
dealing with the present non-standard notation, the image of "slicing
up the world" has seriously misleading implications. It suggests
an already-existing dualism, e.g. a dichotomy between "the world"
and "the one who slices." Such a construct works well as an image
for an identity-based WIE frame of reference; it does not work for
the present one. Instead of regarding "organism" and "environment"
as separate, disparate "things" which occasionally collide with
each other, the present frame of reference treats "the environment"
as the other side of the organism's skin, and treats "the
organism" as the other side of the environment's skin.
- Creating a pattern: When we choose the above specific
delimited setting, we thereby create the main pattern which
the non-standard notation expresses. By adopting this non-standard
notation, a user thereby restricts her/himself to a single point
of view. S/he then can discuss "doings" or "happenings" solely
and exclusively from a standpoint of this created pattern, which
we can indicate by some run-on phrase such as the one stated
above concerning organism-and-environment, or by a single
term such as transacting.
- Putting on constraints: When we choose the above undefined
terms, we thereby put constraints on the pattern generated by
the setting. In particular, when we use an undefined term, we
designate, or postulate, some example of "a transacting" or
of "the dealings of an organism-as-a-whole with its environment
at-a-date."
- Logic of opposites: As noted above, the logic of opposites
amounts to a pattern for handling defined terms. In our non-standard
frame of reference, this pattern consists of five points:
- Our incompletely-informed and inaccurately-informed (symbolic)
'organism'
- Consists of spatio-temporally ordered "doings" or "happenings"
which occur within a (specific, delimited) setting known
as transacting.
- By her/his abstracting, our 'organism' elaborates a 'gestalt'
composed of
- a 'figure' which focally interests the 'organism'
- specified against a 'background' which does not (at
present) interest her/him.
- Any 'gestalt' further consists of two 'components'
- one of which tells about the 'environment', and
- the other tells about the 'organism' who elaborates
the 'gestalt'.
- In negating a 'gestalt', our 'organism' interchanges
the 'figure' and the 'background', and alters none of the
other considerations listed here.
Please note that when we negate a 'gestalt', and then re-negate
it, that does not bring us back exactly to our starting-place.
| EXAMPLE: Consider the positive degree of an ordinary
English adjective vs. its negated negation: not
unhappy does not qualify as an exact synonym for happy. |
- Grammar: We obtain the grammar of our notational system
by inter-defining the undefined terms. For example, where we designate
or posit a structuring S , that already gives us a "bridge" from
the non-verbal to the verbal. Whenever we want to give more details
about that S , we use the other two undefined terms. For instance,
we can specify the structuring S in terms of two relationings
R ordered O somehow, namely,
SRRO .
Or, equally comfortably, in terms of two orderings O
relationed R somehow, namely,
SOOR . |
By similar 'reasoning,' when we use R or O as the bridge from the
non-verbal to the verbal, that gives two more pairs of possible
expressings composed of undefined terms, or a total of six
such expressings:
SRRO or
SOOR or
ORRS or
OSSR or
ROOS or
RSSO. |
Where we use an undefined term twice in an expressing, we intend
that no one take the two usages as 'identical'.
- Postulates: In a formal presentation of an axiomatic system,
one uses the undefined terms to state the postulates. Here, for
the sake of intelligibility, we state Korzybski's non-aristotelian
postulates in terms of the map-territory analogy, which holds
that to say that an organism lives means that it makes some
kind of maps of (or guesses about) that territory
composed of "what goes on in and around our organism"—and then
it guides its "doings" or "choosings" by these maps. Stated colloquially,
then, these postulates become:
- Non-identity: The map is not the territory it stands
for.
- Non-allness: The map represents not all of the aspects
of the territory.
- Self-reflexiveness: Any map contains some kind of representation
of the map-maker (organism).
- Rules of inference: For the present purposes, it suffices
merely to name the rules of inference of the non-standard notation:
Generalizing, Particularizing, Componenting, and Specifying.
- Standards of proof: Again, for the present purposes, it
suffices to say that to "prove" an expressing, one demonstrates
that s/he can both derive (particularize) it from an expressing
composed solely of undefined terms, and can "decompose" (generalize)
it back into an expressing (or a number of expressings) composed
solely of undefined terms.
WHAT WE CAN TALK ABOUT IN THIS LANGUAGE:
"An observer observing the observed," as viewed by another observer
("logician"), who writes down her/his observations. 23
DISCUSSION
The present findings, or creations, extend and in a sense complete the
revised world-view delivered by our alternative frame of reference.
They summarize the accomplishments to date of what I might call
non-identity
'
reasoning', and (as mentioned above) offer a new domain for
the construct of
taking the observer into account.
TIME-BINDING
As noted above, Korzybski opens the way to the revised world-view by
making a quick tour of the universe, asking self-reflexive questions
concerning humans and how they—we—fit into the observable
scheme of things. His procedure contrasts with that of Western philosophers
and other workers, who for thousands of years have asked certain self-reflexive
questions, e.g. "What IS man?" In conformity with the presuppositions
encoded in the WIE grammar, they have framed their queries so as not
to distinguish between "map" and "territory"—so these queries lead
not to testable hypotheses, but rather to answers which presuppose and
so conform to the fixed, culturally-determined views of the asker. In
the Western cultures in particular, two answers to such questions have
predominated. As Korzybski puts it,
| One of the answers is biological—man is an animal, a certain
kind of animal; the other answer is a mixture partly biological
and partly philosophical—man is a combination or union
of animal with something supernatural. An important part of my
task will be to show that both of these answers are radically
wrong and that, beyond all things else, they are primarily responsible
for what is dismal in the life and history of humankind. 24 |
In the course of his own inquiry, Korzybski re-frames the self-reflexive
questions so that they yield disconfirmable answers, in the process
questioning the shared "map" and so distinguishing between "map" and
"territory". He designs his answers for us to examine in the light of
evidence and observation. He asks, in effect, "What do we humans DO
that distinguishes us from other living organisms?" His query centers
on a kind of dimensional analysis:
| To know anything that is to-day of fundamental interest about
man, we have to analyze man in three coordinates—in three
capacities; namely, his chemistry, his activities in space, and
especially his activities in time; whereas in the study of animals
we have to consider only two factors: their chemistry and their
activities in space. 25 |
Korzybski finds that we humans function "in time" as a
time-binding
class of life—we accumulate human knowledge (in the form of
disconfirmable guesses that we test), at rates that depend on how much
knowledge we already have. We gain our living in the biosphere by cooperating
to apply what we know, in the process coming to know more.
THE STRUCTURE
OF INCREASES IN KNOWLEDGE
Increases in knowledge, in this alternative view, occur in the setting
of a shared linguistic and cultural viewpoint; and they occur by a process
of making new distinctions—ultimately, of distinguishing between
"map" and "territory," at some point where the shared viewpoint previously
available does not distinguish between the two. In other words, increases
in knowledge come about by a process of eliminating usages of tacit
identity. For example, consider how Newton, in devising his construct
of universal gravitation, changes what he himself assumes.
| His first Gestalt in the relevant sequence of "doings" has as
its background the traditional view, which tacitly assumes map/territory
identity; and has as its figure, a questioning of the traditional
view, which in effect means distinguishing between map and territory:
What if the commonly held view amounts to only a surmise, instead
of expressing 'the way things really are'? This Gestalt then
becomes the background of the next Gestalt encoded in Newton's
insight. In expressing its figure, Newton devises an alternative
map: What if the ball (or apple) and the Moon BOTH fall—and
the apple reaches the surface of the earth whereas the Moon doesn't.
How would I account for that?26 |
Newton completed this sequence by using his new theory of fluxions (or
as we now call it, the calculus) to compute the centripetal and centrifugal
forces on the moon, and compute the value for the period of the moon
which would make these forces equal. His first rough calculation gave
a period close to the true value, about 27.25 days. 27 Thus a procedure
which hinged on eliminating a usage of tacit identity led to a major
gain in the ability of physical theory to deliver accurate predictions.
Our view holds that any usage of an undefined, or defined, term designates
or postulates some example of "a transacting between knower (organism)
and known (environment)." Consequently, it treats any "increase of knowledge"
as having two components: It not only models and so makes explicit some
aspect of the environment of the human organism who tests (and fails
to disconfirm) her/his hypothesis, but also makes explicit some aspect
of her/his own "doings." With Newton's second law of motion, the construct
focuses on and models the "behavior," the trajectories, of physical
"bodies"; but it also models the behavior of organisms capable of using
eyes, muscular system and nervous system to track and perhaps move so
as to intercept physical bodies.
ACCOUNTING
FOR VS. ELIMINATING THE OBSERVER
At the turn of the twentieth century, the revolutionary physicists,
notably Einstein and the quantum theorists, introduced to the human
race the construct of "Taking the observer into account." As noted above,
the alternative frame of reference discloses two opposing structures
of assumptions: the one which underlies taking the observer into account,
in contrast to the one which underlies eliminating the observer from
consideration.
- We know only one route to taking the observer into account: to
distinguish between "map" and "what the map refers to," to postulate
map/territory non-identity. This manifests itself in remembering
to treat the map as more or less tentative and approximate, as incomplete,
and as created from one's own point of view for one's own purposes;
in remaining willing to test it for accuracy; and in holding oneself
in readiness to revise it at need. These locutions stand as shorthand
for "relying on the non-aristotelian postulates as one's most fundamental
presuppositions." But to treat one's "maps" as created from one's
own point of view for one's own purposes amounts to "taking
the observer into account."
- In order to eliminate the observer from consideration, one need
only assume map/territory identity. Let us express this in terms
of an exhaustively complete, entirely accurate one-to-one relation
between "map" and "territory." If every point of my "map" represents
one and only one point of the "territory," no point of the "territory"
gets left out, and and my "map" contains no extraneous points, then
there exists no "room" in my "map" for any kind of representation
of the map-maker. In other words, such a "perfect" map eliminates
the observer from consideration.
