A NOTATIONAL PHYSICS WITH PHYSICISTS IN IT
C. A. Hilgartner
Hilgartner & Associates
254 Kensington Place
Marion OH 43302
Ronald V. Harrington
275 Susquehanna Road
Rochester NY 14618
Martha A. Bartter
Department of English
Ohio State University at Marion
1465 Mt. Vernon Avenue
Marion OH 43302
.PA
A NOTATIONAL PHYSICS WITH PHYSICISTS IN IT
C. A. Hilgartner
R. V. Harrington
M. A. Bartter
ABSTRACT
We hold that modern physical reasoning intrinsically depends on
the relations between two or more observers. Using an alternative
mathematics based on a derived grammar, we examine in detail the
situation of discovering a relativistic discrepancy, and accounting for
it. Our frame of reference systematically takes into account the
observer, and utilizes an explicit model for the apparently 'purposive'
activities of living systems; we use it to examine Walter Kaufmann as
he performs his 1901 study on the deflection of electrons by electric
and magnetic fields and the apparent mass of the electron. Thus we
consider not only the theoretical significance of his contribution, but
also the self-and-social components of his study. In our notation, we
describe a) The spatio-temporally ordered sequence of events; b) The
hierarchically-ordered roles Kaufmann plays in designing, performing
and reporting his experiment; c) The inter-personal and social
components of his career; and d) The consequences to Kaufmann and to
the scientific community. Our notational system, which cannot NOT take
the observer into account, confers two advantages: i) It yields
physical theory which systematically handles the relations of an
observer with himself and with other observers, and ii) It brings our
articulated physical knowledge and our articulated social knowledge
into a single rigorous symbol-system.
.PA
A NOTATIONAL PHYSICS WITH PHYSICISTS IN IT
C. A. Hilgartner
R. V. Harrington
M. A. Bartter
"Think in other categories!"
Coleridge
.HM1
.H1 -#-
.H2 A Notational Physics with Physicists
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INTRODUCTION
This paper forms the second installment in a series in which we
set out to scrutinize the theory of relativity to see how effectively
it manages to take the observer into account -- and what difference it
makes how well a theory does this, or even whether it does it at all.
To carry out this inquiry, we make use of a frame of reference which
does systematically takes the observer into account. Thus it provides
a suitable background against which to display the assumptions of older
theories (such as the theory of relativity) and to highlight the
significance of the assumptions that we disclose.
Historically, the earliest exponents of relativity (and quantum
theory) introduced a new distinction into human discourse, which they
expressed in terms of the construct of
.UL off
the observer, who gets either
included (taken into account) or eliminated from consideration.
Einstein and others developed the revolutionary precept and criterion
that prefers a physical theory which does take the observer into
account over any which does not. But by the latter half of his
lifetime, Einstein seemed mainly interested in the details of his
general theory of relativity, and he no longer made such a point of
that precept. Today's practicing physicists do account for the
observer in the ways that those early pioneers taught them to. But
they have reinterpreted that precept so as to tame it -- they take the
construct of the observer as if it had nothing to do with living
humans, observers. Consequently, they conduct their studies as if
divorced from any primary connections with actual humans, or from
effective concern for specifiable human values.
In our own frame of reference, we bracket the construct of taking
the observer into account: We present one array of logically general@
assumptions (centering about the explicit postulate of map-territory
non-identity) that, when held, allow one to account for the observer;
and disclose another, contrasting array of assumptions (centering about
the restricted and restrictive tenet of map-territory identity),
logically less general and usually tacitly held, which eliminate the
observer from consideration.@ These latter assumptions demonstrably
___________________
@ Criterion of logical generality
@ Null-A vs. traditional assumptions and "taking observer into
account"< (WHERE did we first lay out both sets of assumptions?????)
__________________
.PA
.PA
form a part of the premises encoded in the traditional grammar common
to the Western Indo-European (WIE) languages, both discursive (e.g.
Dutch, English, French, German, Greek, etc.) and formalized (e.g.
symbolic logic, set theory, analysis, topology, etc.).@ We suggest
that our science grants a privileged position to this WIE grammar. If
so, then even the best theories within WIE science include these
restricted and restrictive assumptions among their premises and so, in
some fundamental sense, on logical levels deeper than those ordinarily
examined, systematically eliminate the observer from consideration.
________________
@CAH, "Some Traditional Assumptions...") ________________
pa
A. FINDINGS OF OUR PREVIOUS STUDY
In Appendix 1, we summarize the findings of our previous study.
Succinctly stated, we find that:
In the period from about 1880 to about 1900 or 1910, workers
generated a body of perhaps two hundred experiments whose results cast
doubt on the tenets of Newtonian physics. We find that these
anomalies or relativistic discrepancies have a common structure, which
intrinsically depends on the relations between two or more observers.
Specifically, before a worker can make the kinds of observations which
logically precede and lead to one of the twentieth-century physical
theories which take the observer into account (such as the theory of
relativity), s/he has to rely on certain observations made by one or
more of her/his colleague(s) with the same kind of assurance with which
s/he relies on certain of her/his own observations. To discover an
anomaly, a worker compares two sets of observations, performed under
slightly different conditions; finds that they DON'T MATCH in some
crucial fashion; and takes this mismatch seriously enough to attempt to
account for the discrepancy -- or at least, to write it up and publish
it. These stages in the discovery of a relativistic discrepancy
comprise specific physical activities -- "doings" or "happenings" --
which observably occur at finite rates, in an ordered fashion.
1. In the theory of relativity, the notion of "taking the
observer into account" occurs mostly as verbal imagery and rhetoric;
whereas in the mathematical development, Einstein replaces this image
with the construct of a coordinate system, and spells out relations
between coordinate systems. To do so treats all observers as
interchangeable ('identical' -- the same in observational powers, in
methods and styles, in background and assumptions, etc.).
Consequently, for most of the anomalies, the theory of relativity
reconciles only those aspects of the observed discrepancy which one can
render by means of a coordinate system or the relations between
coordinate systems -- while ignoring those aspects of the discrepancy
not representable by a coordinate system, e.g. those which depend on
the human anatomy, physiology and the activities of an observer, on the
relations between the two observers, etc.@ Thus the theory of
relativity has two parts: the foreground, the explicit, visible theory;
and a more extensive, tacit background. Furthermore, it treats those
"doings" or "happenings" represented by the foreground AS IF they occur
at finite rates, in an ordered fashion; but as for those "doings" or
"happenings" represented only tacitly, in the background, it treats
them AS IF they take place in 'no time at all', in an non-ordered
fashion.
___________________
@Swanson, Marjorie
___________________
pa
Consequently, as judged by its own criteria, the theory of
relativity appears inconsistent. In our language, where it treats
aspects of an anomaly as if the "happenings" occur at finite rates --
as ordered-- it relies on map-territory non-identity and so takes into
account the observer. Where it treats aspects of an anomaly as if the
"happenings" occur in 'no time at all' -- as non-ordered -- it grants a
privileged position to the WIE grammar and so relies on map-territory
identity, eliminating the observer from consideration.
2. Any theory which eliminates the observer from consideration (by
relying on map-territory identity), even in part, guides its exponents
to create, to defend and to contribute to a mutilated science, one in
which its advocates prostitute the explanatory power of their theory to
local patriotism, economic interest, the power of the state, and the
like, for the sole benefit of some group smaller than the whole human
species. But when used for a narrow goal of that sort, a powerful
theory such as the theory of relativity guides the whole human species
into internecine strife and "war on nature." Furthermore, the
explanatory power of the theory expands these goals beyond previous
human experience, perhaps stretching the former limits of human
comprehension: When pursued with "weapons" which harness cosmic
forces, internecine strife becomes the prospect of species-suicide and
extinction; when conducted with the "tools" provided by the kind of
predictability yielded by the theory of relativity and quantum theory,
"war on nature" turns into the prospect of the annihilation of the
biosphere.
B. THE TASK OF THE PRESENT INSTALLMENT
With these findings as background, the authors now ask and answer
the following question: How can we humans use these insights into the
construct of taking the observer into account -- the topics of self and
the social -- so as to generate a self-consistent physical theory based
on map-territory non-identity?@
___________________
@We suggest that creating such a theory may stand as a crucial step
toward turning ourselves away from environmental devastation and
self-destruction, and toward celebrating and affirming the living,
including ourselves.
___________________
pa
In developing our answer to this question, we consider in detail
one historical example of the kind of experiment which discloses a
relativistic discrepancy. Walter Kaufmann (1871-1947) performed a
series of studies concerning the mass (or rather, charge-to-mass ratio)
of electrons. He reported the most significant of his observations in
a paper published in 1901. His findings did not match with the
predictions of Newtonian physics (nor with the results of some of his
own earlier studies), and so represented what we (along with Thomas
Kuhn) would call an anomaly. We use a rigorous model for the
apparently 'purposive' activities of living systems to account for the
"doings" by which Kaufmann designed, performed and reported this
experiment, In so doing, we focus on aspects of the experimenter's
activities crucial to his experimenting but traditionally left out of
account in the writings of physicists.
Where in the earlier paper in this series, we only mentioned our
alternative frame of reference and our non-standard notation (and
imported a few constructs from it), in the present paper we USE our
alternative framework.
a) Our notation relies on a novel "grammar" (pattern for what
constitutes a well-formed formulation) derived, by a small number of
explicit logical steps, from the non-aristotelian premises proposed by
the late Alfred Korzybski (1879-1950). By relying on mathematical
languages built up on a derived grammar, we gain an increase in logical
rigor.
b) It systematically takes into account the observer, thereby
eliminating that self-contradiction intrinsic to the structure of
relativity (and of quantum theory) which we disclose above (Hilgartner,
Harrington, & Bartter, 1989; Hilgartner & Di Rienzi (submitted for
publication)).
The present frame of reference subsumes the topics of "humans
studying physical "doings" or "happenings"," and of "the theories
humans generate to explain their findings."
Methodologically, we employ a procedure based on a careful
comparison between SAYING and DOING. We check (generate our own
reading of) the verbal or mathematical constructs which Kaufmann
actually used in his papers; and we infer that he MEANT what he SAID.
Likewise, we check what he DID (as reported by his biographers,
etc.). Then we compare (our picture of) what he said and of what he
did; we comment on the match between these two levels; and we account
for the disclosed congruences and/or discrepancies by means of the
non-standard notation which we have built up on our derived grammar.
The trouble with using our notation comes from two facts: that it
remains only partially published, and that, so far as we know, no one
outside our own research group has any familiarity with it at all.
We do not derive the new notation here. In Appendix 2, however,
we do give enough information about the notation so our readers can
make sense of what we say; and also give a glossary of notational
terms.
.PA
I. PRIMARY DATA
To provide an example for our study, we examine the life of Walter
Kaufmann (1871-1947), who in 1901 published a paper, "Die magnetische
und electrische Ablenbarkeit der Bequerelstrahlen und die schienbare
Masse der Elektronen," Nachrichten von der Gesellschaft der
Wissenschaften zu Gottingen, Math.-phys. Kl., 2:143-155 (1901). We
obtain the data from which we argue from the entry on Kaufmann in the
Dictionary of Scientific Biography (American Council of Learned
Societies, New York: Scribner's, 1970), from the essay on Kaufmann in
The World of the Atom, edited with commentaries by Henry A. Boorse &
Lloyd Motz (New York: Basic Books, 1966), and from the translation of
Kaufmann's paper which appears there, under the title of "Magnetic and
electric deflectability of the Becquerel rays and the apparent mass of
the electron."2
We shall consider a brief period in Kaufmann's life, during which
he did experiments on the mass of electrons.
Born in Elberfeld (Wuppertal), Germany, Kaufmann studied at
Munich, where he received his doctorate in 1894. In 1896-98, he began
research on the magnetic deflection of low-velocity cathode rays,
obtaining a first approximation to the ratio of electron charge to
mass.
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During this period a controversy arose over whether electrons,
believed to be the ultimate constituents of matter, could have
"apparent" mass in addition to "real" (material) mass. Apparent
mass would be the "electromagnetic mass" gained from the
interaction of the moving charge with its own field. (Dictionary
of Scientific Biography, p. 263).
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We take the above comment as expressing Kaufmann's experimental focus
(fragestellung).
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During the Gottingen years, 1899-1902, Kaufmann conducted
research on the magnetic and electric deflection of radium
emanations -- then known as Becquerel rays. From the Curies he
obtained several radioactive particles of radium chloride and set
about measuring the [charge/mass (epsilon/mu)] ratio. Since
these newly discovered rays had velocities approaching the speed
of light, it was assumed that the maximum possible
electromagnetic charge was imparted to them. On the basis of his
initial epsilon/mu measurements in 1901, Kaufmann asserted that
the apparent mass was appreciably larger than the real mass -- by
an estimated magnitude of at least three to one. (Dictionary of
Scientific Biography, p. 263)
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Thus the results which Kaufmann obtained from his 1901 experiment
did not match with his earlier findings.
The essay in Boorse & Motz (1966) clearly sets the overall
theoretical context for Kaufmann's study.
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With the discovery that cathode rays consist of negatively
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charged particles (electrons, as they came to be called),
physicists began an intensive study of the properties of these
particles; one of the most interesting and important questions
dealt with their mass. With the equipment that was available
immediately after the electron had been discovered, only the
ratio of its charge to its mass could be measured directly. Only
after Millikan had measured the charge on the electron first with
charged water drops in 1909 and then with his famous oil-drop
experiment in 1910-11 was it possible to obtain a precise value
for the mass of the electron.
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Although the electronic mass could not be measured directly,
some important observational conclusions could be drawn,
particularly since the various applicable theories pointed to
some unusual properties of the mass. The problem that arose in
connection with the mass of the electron is essentially the
following one.
Since an electron has an electrostatic field surrounding it
because of its own charge, we must picture this field as moving
along with the electron. Moreover, if the electrostatic field is
set moving, it should, in principle, be accompanied by a magnetic
field according to Maxwell's electromagnetic theory. Indeed,
Rowland in 1878 had demonstrated experimentally that a moving
charge is accompanied by a magnetic field whose lines of force
form concentric circles about the line of motion of the charge.
From this we can see at once that setting an electron in motion
requires a greater push than setting an uncharged particle in
motion, if we consider the situation in terms of Newton's laws of
motion and Maxwell's electromagnetic theory.
Let us consider an electron and an uncharged particle of the
same mass at rest, and let us accelerate these particles by
applying the same force to both of them. According to Newton's
second law of motion, the force applied to either of these
particles, divided by the acceleration imparted to this particle
by the force, is the mass of the particle. In the case of the
uncharged particle, this ratio (that is, the way a particle
responds to a force) was referred to as the "true" mass of the
particle.
The situation for the charged particle is much more
complicated because of the electrostatic and the magnetic field.
The same force that imparts a given acceleration to the uncharged
particle cannot impart the same acceleration to the electron
because, to begin with, the entire electrostatic field of the
electron must also be set moving. Moreover, the moving electron
immediately finds itself surrounded by a magnetic field that
(according to the laws of induction) is always so directed as to
oppose the force acting to accelerate the electron. In other
words, the electron behaves as though it were more massive when
it is set moving than when it is at rest. When Kaufmann
undertook his experiments on the variation of the mass of an
electron with velocity, physicists differentiated between what
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they called the "true" mass and the "apparent" mass of the
electron. The "true" mass referred to the mass of the electron
when it was not in motion and the "apparent" mass to its mass in
virtue of its motion. (Boorse & Motz (1966), pp. 502-3)
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Since Kaufmann had no high-energy accelerators to obtain
electron speeds sufficiently high to show an appreciable increase
of the mass, he used Becquerel rays, the electrons emitted by
radioactive atoms, now called (beta)-rays. These were much more
energetic than the cathode rays that were available to him. In
the first few paragraphs of his paper, he gives arguments in
support of the belief that Becquerel rays are the same as cathode
rays despite their much higher speeds. Then he outlines his
experiment and describes his apparatus. The theoretical aspects
of the experiment are discussed in terms of the arrangement of
Fig. [34-1] taken from Kaufmann's paper.
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FIGURE [34-1] ABOUT HERE
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We shall use this figure for a brief description of his
experiment. A speck of radium bromide was placed at A , just
below a pair of closely spaced and electrically insulated square
metal plates K . A difference of potential of about 7,000 volts
could be applied to the plates to produce a strong electric
field. The whole region represented by Fig. [34-1] could also be
subjected to a uniform magnetic field generated by an
electromagnet, the field direction being perpendicular to and
into the plane of the paper. The vertical line x1x2 determined
by A and a fine circular opening at B , terminates on a
photographic plate lying in the xy plane at C . In the
absence of the electric and magnetic fields (beta)-rays
(electrons) from the radium bromide source could reach the
photographic plate only along x1x2 . Thus C on the
photographic plate was a reference point for the undeflected
rays. When only the magnetic field was applied electrons of the
proper velocity initially directed along x1 were forced along
the circular arc ABQ of radius (rho), by the action of the
field. When both electric and magnetic fields were applied
simultaneously, the path of all the electrons that could get
through the hole B , terminated on the curve CP on the
photographic plate. Thus the point P lying on the yz plane
has coordinates y0 and z0 . From his measurements Kaufmann
deduced values of (epsilon/mu) for electrons of five different
velocities. These values are listed in Table [34-1]. It is
clear that as the velocity of the electrons increased, the value
of (epsilon/mu) decreased, thus showing that since the
electronic charge (epsilon) is constant, the mass of the
electron increased with velocity. If the ratio M+m0.(eta)/M
+m0 is calculated from Kaufmann's data for his given values of
v and plotted against the corresponding values of (beta)=v/c,
the open circles shown in Fig. [34-2]
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FIGURE [34-2] ABOUT HERE
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result. This figure appears at the end of the paper. It is
evident that the mass of the electron is tending to very large
values as v approaches the speed of light. For reference, the
full line in this figure is the graph of the Lorentz-Einstein
relation. The dots on the lower part of the curve are the values
of m/m0 found by Bucherer in his experiments eight years later.
(Boorse & Motz (1966), pp. 504-5)
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II. APPARENTLY 'PURPOSIVE'
We systematize these primary data using the resources built into
our notation. For example, our notation presupposes the construct of
directively correlated (DC) (Hilgartner & Randolph, 1969a; Ashby,
1962; Sommerhoff, 1950; Singer, 1946). In other words, we consider the
"doings" of any organism in its environment in general, or Kaufmann's
in his environment in particular, as apparently 'purposive'.
SP <DCk> {<HCTe, HFTe>
{.:k <.:h <f(HCTe)f, g(HCTe)f>
{psi(f(HCTe)f, g(HCTe)f)g} OhOt>
{Saj <HFTe>
{HOci} OhOt}j OhOt}k OhOt} O . (2)
The construct of directively correlated consists of the following
four terminological parts:
a) Coenetic terming (CT), signifying "exigencies (of both
organism and environment) which require behavior" -- e.g., in this
situation, "initial conditions that affect both Kaufmann and his
environment";
b) Focal terming (FT), signifying "criteria for what would
constitute a 'favorable' outcome for Kaufmann";
c) Negotiations (e.g. .:, f(CT), g(FT), (psi)) between Kaufmann
and his environment initiated by the coenetic terming; and
d) Outcome (Oc) , which either does or does not satisfy the
criteria of the focal terming.
We show these parts as related in the following ways:
i. Coenetic and focal terming: we regard these as mutually
necessary, "complementary or polar-opposite."
(nu) <CT> {FT} OpOs (3)
.PA
(This says: Our organism's polar-opposed termings (nu), specified
as: background, CT; figure, FT; polar and synchronous ordering.)
ii. Coenetic terming (CT) and negotiations (psi): we regard these
as ordered spatio-temporally (Ot) and hierarchically (Oh) .
iii. Negotiations and outcome (Oc): we regard the outcome Oc as a
particularizing PZ of the negotiations (psi) (e.g. the transactings
between Kaufmann and his environment), namely, that which we select as
the terminus, "the ending of the story."
PZ <psi> {Oc} O (3a)
iv. Outcome and focal terming: we regard the outcome as an
empirical terminus and the focal terming as the logical standard set up
to judge it by.
To facilitate translating expression (2) into English, we print it
again here, with the various parentheses indexed with left
superscripts:
SP 4<DCk> 4{3<HCTe, HFTe>
3{.:k 2<.:h 1b<f(HCTe)f, g(HCTe)f>
1b{psi(f(HCTe)f, g(HCTe)f)g} OhOt>
2{Saj 1f<HFTe>
1f{HOci} OhOt}j OhOt}k OhOt} 4O . (2a)
Expression (2) says: The specifying of our organism, spelled out
as: 4background, the construct of DC, directively correlated; 4figure,
a compounded expression, specified as: 3background, the coenetic term
CT , along with the focal term, FT , for our organism at time e;
3figure, the compounded expression that at time k, from the
background follows the figure, specified as: 2background, the
compounded expression that at time h, from the background follows the
figure, specified as: 1bbackground, happenings f (consequential to the
CT for our organism at time e ) at time f; 1bfigure, the happenings
psi (consequential to the happenings f along with the happenings g
), at time g ; 2figure, the compounded expression that the figure
satisfies the background, specified as: 1fbackground, the focal terming
for our organism at time e ; 1ffigure, the outcome for our organism at
time i .
We can express Kaufmann's coenetic terming as deficit of
orienting (Df(Or)) . (We can particularize this as his fragestellung,
"What charge/mass ratios do I obtain by deflecting Becquerel rays by
means of magnetic and electric fields?") Here we use the construct of
orienting (Or) to signify that combination of motoric and neural
activities (e.g. attending (At) and interest (In) (Hilgartner &
Randolph, 1969a, pp. 303-8)) by which an organism increases its
sensitivity to and awareness of its immediate environment. Think of a
dog "cocking an ear" at an unexpected, unexplained sound, or of a human
"getting his bearings" so as to avoid falling off the edge of the Grand
Canyon, or down a flight of stairs. We also use the term orienting to
designate longer-term, more elaborate human "doings." For example, the
social institution of science serves as one way for the human species
as a whole to orient more accurately or more comprehensively
(Korzybski, 1921; see also Einstein, 1955, p. 1). Kaufmann, as he
prepares to perform his 1901 experiment, has oriented himself to
Newton's mechanics and Maxwell's field theory (and the most recent
permutations of these), and has made himself aware of the evidence
explained by postulating cathode rays and Becquerel rays (or
electrons), and has made himself competent to study them. In other
words, in the midst of his excellent general orientation, he
experiences a deficit of orienting: he feels curious.
Further, we can express Kaufmann's focal terming as obtaining an
answer to his fragestellung, which we could express in notation as the
'awareness' (Aw) of an aspect of his environment (Y) , or Aw(Y) .
If the outcome of his experiment gave a definite answer -- the
photographic plate showed a line or an arc, or a patterned array of
discrete spots, as the trace produced by the deflected electrons --
that would, in effect, relieve his deficit of orienting. If, however,
the photographic plate showed only a blur, that would not permit
Kaufmann to answer his fragestellung, but instead would suggest that he
had framed his key question wrongly.
III. COMPONENTING
Our viewpoint leads us to component the information concerning
Kaufmann's life into two mutually-necessary themes, which we call
'self' and 'other'.
A. Kaufmann's 'other': fast vs. slow electrons
In dealing with his 'other', which he called electrons (fast vs.
slow), Kaufmann showed a high degree of skill in handling all the
facets needed to experiment successfully.
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... His research was marked by great proficiency in
experimentation, especially in the techniques for obtaining the
high vacuums necessary for cathode ray discharge tubes. His most
notable contributions to this art was the construction of the
first rotary high-vacuum pump; it was very artfully made of
loops of glass tubing through which separate columns of mercury
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forced trapped volumes of gas out of the vacuum space. Although
the pump was extremely fragile, unwieldy, and temperamental,
Kaufmann used it with great success in his celebrated electron
mass research. (Boorse & Motz (1966), p. 505)
.PA
B. Kaufmann's 'self':
Although few references explicitly discuss the topic of Kaufmann's
(or any other experimenter's) 'self', we consider this topic central to
our investigation (cf. below, sections V, VI). Among other topics, we
shall consider Kaufmann's (a) acts of affiliation, (b) self-esteem, (c)
trustworthiness and ability to trust others, and (d) the sense of
having an audience.
IV. SPATIO-TEMPORALLY ORDERED STORY
In discussing the study in question, let us start with the
Kaufmann who has everything ready to go -- and for the first time
starts the two-day experiment.
CT: Our organism (Kaufmann) has mastered the relevant theory
(theories), framed his hypothesis, designed the experiment, developed
the new tools he needs, assembled the equipment (he has the radium in
place, the orifice in place, the field generators in place, the
photographic plate in place, etc.), and so on.
FT: Our organism intends to USE the equipment, CARRY OUT the
experiment, TEST the hypothesis, and JUDGE the theory (theories).
HO <CP1 <CT0> {Df(Or)0} O>
{CP2 <FT0> {Aw(Y)} O} OpOs (4)
This says: Our organism at moment 0, specified as including:
background, a compounded expression, namely: background, our organism
generating the first component (CP1) of a term at moment 0, specified
as: background, the construct of our organism's coenetic terming (CT)
at moment 0 ; figure, our organism's deficit of orientation (Df(Or)) at
moment 0 ; figure, our organism generating the second component (CP2)
of a term, specified as: background, the construct of focal terming
(FT) at moment 0 ; figure, our organism's awareness of some Y (Aw(Y))
at a subsequent unspecified moment; polar and synchronously ordered.
Expectings Ex at instant t0 derived from past experiencing:
We shall not spell these out in our alternative notation at this point,
because we have not yet developed what Kaufmann brings to bear on this
experiment. As the remainder of our text, we shall develop a
vocabulary and a way of talking/writing which allows us to get specific
about Kaufmann's background.
"Alerted": As he enters his laboratory to begin his experiment,
Kaufmann appears fully alert -- attending to (At) and interested in
(In) his experimental system (Sy) .
.PA
O-1 <At1 In1 , Sy1> {Aw(Sy1)2)} OhOt (5)
This says: Our organism abstracting (theta), specified as:
background, our organism attending (At) and interested (In) at moment 1
along with his experimental system (Sy) at moment 1 ; figure, our
organism's awareness of his-experimental-system-of-moment-1 (Aw(Sy1))
at moment 2 ; hierarchically and spatio-temporally ordered.
Our organism motors (M*) over so as to approach (Ap) the
three-way vacuum stopcock (Stk) , and closes (Cls) it.
O-3 <M*(Ap(Stk))3> {Cls(Stk)4} OhOt (6)
This says: Our organism abstracting at moment 3, specified as:
background, our organism motoring so as to approach the stopcock at
moment 3 ; figure, our organism closing the stopcock at moment 4 ;
hierarchically and spatio-temporally ordered.
Our organism motors over to the vacuum pump off/on switch (Von)
and turns it on (Ton) .
O-5 <M*(Ap(Von))5> {Ton(Von)6} OhOt (7)
This says: Our organism abstracting at moment 5 , specified as:
background, our organism motoring so as to approach the vacuum pump
off/on switch at moment 5 ; figure, our organism turning on the off-on
switch at moment 6 ; hierarchically and spatio-temporally ordered.
After a suitable interval, our organism "motors" over to the
off/on switch for the electric/magnetic fields (Mon), and turns it
on.
O-7 <M*(Ap(Mon))7> {Ton(Mon)8} OhOt (8)
This says: Our organism abstracting at moment 7, specified as:
background, our organism motoring so as to approach the off/on switch
for the electric/magnetic fields at moment 7 ; figure, our organism
turning on the switch at moment 8 ; hierarchically and
spatio-temporally ordered.
In a similar fashion, he motors to the photographic plate and
uncovers it. Then, at intervals during the two-day experiment, our
organism reads the meters concerning the performance of the equipment,
and records his readings.
After two days, our organism (a) stops the vacuum pumps, (b) turns
off the electric and magnetic fields, (c) opens the stopcock to release
the vacuum, (d) removes the photographic plate, and (e) develops it.
Since these "doings" closely resemble those already described in
notation, we will not write out further notational sentences to
describe them.
Subsequently, our organism makes his measurements on the
photographic plate, producing a table of numbers (Table 1).
Kaufmann's paper gives the details of his mathematical
computations. Table 1 (Boorse & Motz, 1966) presents the first results
of his measurements. Here z0 signifies the magnetic deflection of
the electrons, y0 signifies the electric deflection, (rho) signifies
the radius of curvature of the deflected trajectories, s1 signifies
the projection of half the path traversed in the electric field, s2
signifies the projection of the path from the fine circular opening to
the photographic plate, v.10-10 signifies the velocity of the
electrons, and (epsilon)/(mu).10-7 signifies the charge-to-mass ratio.
TABLE 1*
_______________________________________________________________________
z0 y0 (rho) s1 s2
v.10-10 e/m.10-7
_____ ______ __________ _____
_______ _______
0.271 0.0621 15.1 0.888 2.02 2.83
0.63
0.348 0.0839 11.7 0.888 2.03 2.72
0.77
0.461 0.11758.9 0.889 2.06 2.59
0.975
0.576 0.15657.1 0.889 2.09 2.48
1.17
0.688 0.198 6.0 0.890 2.13 2.36
1.31
_______________________________________________________________________
* All numbers in absolute units.
(Boorse & Motz, 1966, p. 509)
Our organism translates these "results" into "findings" (Cs) .
O-11 <".:10 <O-3, O-5, O-7>9
{Table 1}10 Oh10Ot10>
{Cs11} Oh11Ot11 (9)
This says: Our organism abstracting at moment 11, specified as:
background, a compounded expression that from the background follows
the figure (.:) at moment 10 , specified as: background, our organism
abstracting (theta) as of moment 3 along with that as of moment 5 along
with that as of moment 7, at moment 9 ; figure, table 1; hierarchically
and spatio-temporally ordered as of moment 10; figure, our organism's
consciousness as of moment 11; hierarchically and spatio-temporally
ordered as of moment 11 .
Our organism repeats the experiment during the interval t12-22 .
Our organism reaches "conclusions": (Gt) .
.PA
O-24 <Cs11, Cs22>
{.: <Gt23>
{"The mass of electrons increases with increasing
velocity. As velocity approaches c , mass
approaches
infinity. This conflicts with Newton's dm/dv = 0
."24}
OhOt} Oh24Ot24 (10)
This says: Our organism abstracting as of moment 24, specified as:
background, our organism's consciousness as of moment 11 along with
that as of moment 22 ; figure, a compounded expression that from the
background follows the figure, specified as: background, our organism's
Gestalt or generalization as of moment 23 ; figure, the English
paragraph, "The mass of electrons increases with increasing velocity.
As velocity approaches c , mass approaches infinity. This conflicts
with Newton's dm/dv = 0 ." as of moment 24; hierarchically and
spatio-temporally ordered; hierarchically and spatio-temporally ordered
as of moment 24.
Our organism writes his ms.
Our organism drops his ms into the delivery system, so that it
will go to the journal for possible publication.
V. HIERARCHICALLY-ORDERED STORY
Let us continue discussing the study in question.
In addition to and synchronous with the spatio-temporal story, we
discern also a hierarchically-ordered story, that spells out Kaufmann's
expectings Ex involved in his doing his experiment. In effect,
Kaufmann expects of himself that he function on a number of different
levels: instrument-handler, instrument-maker, experiment-designer,
hypothesis-framer, and theory-writer.
1. Instrument-handler
In order to perform his experiment, Kaufmann has to gather the
required parts, assemble them into a functioning experimental
apparatus, and manipulate it so as to do the experiment.
In so doing, he operates in a directively correlated sequence in
which he monitors and interacts with both 'self' and 'other.' As
preconditions, Kaufmann shows high self-esteem (Hilgartner &
Harrington, 1984) and high skill with his chosen tools, which he has
earned through his previous experience.
.PA
1O-0 <1Gt-1> {1Ex0} Oh0Ot0 (11)
This says: The first-ordered abstracting of our organism at
moment 0 , specified as: background, the first-ordered Gestalt derived
from past experiencing (1Gt-1) at moment -1; figure, the expectings
based on the Gestalt (1Ex0) at moment 0; hierarchically and
spatio-temporally ordered.
.RR L-----------------------------------------------------------------R
"His successful measurements apparently were made possible
by his experimental apparatus, which attained a more complete
vacuum than other experimenters could produce in their vacuum
tubes."
(Dictionary of Scientific Biography, 1970, p. 263d)
.RR----!---------------------------------------------------------------R
These measurements also entail high skill in handling, assembling,
etc., the parts which make up Kaufmann's experimental apparatus.
(Alternatively, if Kaufmann had low self-esteem as an
instrument-handler and KNEW it, he could depend on someone else to
handle the instruments; if he had low self-esteem and DENIED it, he
could do the job himself in a bungling fashion.)
2. Instrument-maker
In order to design and build an instrument that he feels confident
will accomplish a certain task, an instrument-maker has to have had
experiences with instruments that DIDN'T do the job, and with
instruments that DID.
In designing and building a new instrument (such as a high-vacuum
pump made of glass and mercury) to do a new job, Kaufmann operates in a
directively correlated sequence in which he monitors and interacts with
both 'self' and 'other' on a higher logical level than that discussed
in the previous section. As preconditions, Kaufmann shows high
self-esteem as an instrument-maker and high skill with the chosen tools
of instrument-making.
2O-0 <2Gt-1> {2Ex0} Oh0Ot0 (12)
This says: The second-ordered abstracting of our organism at
moment 0, specified as: background, the Gestalt derived from past
experiencing (2Gt-1) at moment 0; figure, the second-ordered expectings
based on the Gestalt (2Ex0); hierarchically and temporally ordered.
Success in designing and building an instrument to do a certain
task increases the instrument-maker's skill on the lower level -- as an
instrument-handler.
(Alternatively, he could belong to the Lumpy School of
Glass-Blowing, and clumsily make his own instuments, or could depend on
someone else to make his instruments for him.)
3. Experiment-designer
In order to design an experiment that uses the given instruments,
Kaufmann has to
a) Intuit how he might arrange to make the physical "happenings"
predicted by the hypothesis/theory detectable by his senses.
b) Intuit how he might relate this sensing of the physical
"happenings" to logically-distinct alternatives, so he can make the
judgment, "Hypothesis disconfirmed/not-disconfirmed."
In so doing, he operates in a directively correlated sequence in
which he monitors and interacts with both 'self' and 'other' on a
higher logical level than that discussed in the previous section. As
preconditions, Kaufmann shows high self-esteem as an
experiment-designer, and high skill with the tools of
experiment-design.
3O-0 3Gt-1 3Ex0 Oh0Ot0 (13)
This says: The third-ordered abstracting of our organism at
moment 0 , specified as: background, the third-ordered Gestalt derived
from past experiencing (1Gt-1) at moment -1; figure, the
third-ordered expectings based on the Gestalt (1Ex0) at moment 0;
hierarchically and spatio-temporally ordered.
Success in designing an experiment which uses given instruments
increases the experiment-designer's skill on the lower levels.
(Alternatively, Kaufmann could depend on someone else to design
the experiment, could design it poorly, etc.)
4. Hypothesis-framer
In order to frame a hypothesis (derived from theory) which one
could design an experiment to test, Kaufmann has to have
a) A working knowledge of what the available equipment can and
cannot do;
b) A working familiarity with the available theory (or the rival
theories) and some of its (their) implications;
c) Awareness of a topic on which his preferred theory says, "Yes,"
and some rival theory says, "No." (Or on which the whole spate of
current theories don't express an opinion.) "Are Becquerel rays and
cathode rays the same thing, except the Becquerel rays are going
faster?"
In so doing, he operates in a directively correlated sequence in
which he monitors and interacts with both 'self' and 'other' on a
higher logical level than that discussed in the previous section. As
preconditions Kaufmann shows high self-esteem as a hypothesis-framer,
and high skill with the tools of hypothesis-framing.
In effect, he must solve the problem of deriving from theory a
hypothesis which one could TEST with the available equipment.
Scientists credit the person who frames the hypothesis with
authorship of the study.
.RR L-----------------------------------------------------------------R
It was during his period at Gottingen that [Kaufmann] did
his most important experimental work, in particular the
experiment which yields the dependence of the mass of the
electron on its speed, a classic investigation that after sixty
years is still cited in the textbooks of modern physics. (Boorse
& Motz, 1966, p. 505; italics ours)
.RR----!---------------------------------------------------------------R
4O-0 4Gt-1 4Ex0 Oh0Ot0 (14)
This says: The fourth-ordered abstracting of our organism at
moment 0 , specified as: background, the fourth-ordered Gestalt derived
from past experiencing (1Gt-1) at moment -1; figure, the
fourth-ordered expectings based on the Gestalt (1Ex0) at moment 0;
hierarchically and spatio-temporally ordered.
Success in framing a hypothesis (derived from theory) that one
could design an experiment to test increases the hypothesis-framer's
skill as an experiment-designer.
(Alternatively, Kaufmann could depend on someone else to master
the theory and frame the hypothesis, or could frame it imprecisely,
etc.)
5. Master Scientist and Theorist
The theories which humans generate start out in principle
implicit; scientists seek to make theirs explicit, and to subject them
to testing. While functioning only at the logical level of
hypothesis-framer, a scientist can depend on someone else's theory or
theories, which he masters and uses as the basis for the hypotheses he
frames. A master scientist and theorist, however, generates his own.
To develop his theory far enough to make it accessible to testing,
Kaufmann has to
a) Know the previous relevant work in the field;
b) Select a problem to solve (the predicted dependence of the mass
of the electron on its velocity).
c) Solve it, and derive a hypothesis.
d) Test the hypothesis experimentally.
e) From his findings, draw inferences, spell out implications, and
so modify the theory (theories) he started with.
.PA
At the beginning of his experiment, Kaufmann shows high
self-esteem in the domain of theorist, but he has not yet demonstrated
high skill with the tools of theory-writing. Instead, he has depended
on others to provide the articulated theories which guide him in
selecting which "phenomena" to consider "interesting": He has
functioned as a disciple of Thompson, Searle, Lorentz, et al. --
Kaufmann's own theory appears inarticulate (embedded in his experiment,
but not clearly stated as HIS theory.) After he completes his
experiment, Kaufmann then makes his own theory explicit:
"dm/dv --> infinity as v --> c ."
In so doing, he operates in a directively correlated sequence in
which he monitors and interacts with both 'self' and 'other' on a
higher logical level than that discussed in the previous section.
By the time he has performed his experiment, interpreted his
results, and submitted his ms for publication, Kaufmann has
demonstrably become a master scientist/theorist.
5O-0 5Gt-1 5Ex0 Oh0Ot0 (15)
This says: The fifth-ordered abstracting of our organism at
moment 0 , specified as: background, the fifth-ordered Gestalt derived
from past experiencing (1Gt-1) at moment -1; figure, the
fifth-ordered expectings based on the Gestalt (1Ex0) at moment 0;
hierarchically and spatio-temporally ordered.
Success in theory-writing increases the master
scientist/theorist's skill in framing hypotheses.
(In Section IV above, under the rubric of Expectings, we brought
up the topic of "Expectings Ex at instant t0 derived from past
experiencing," but deferred considering the details. Now, we would go
back and write in 1Ex0, 2Ex0, 3Ex0, and 4Ex0 -- but, for Kaufmann
at the beginning of his experiment, we would NOT write in 5Ex0 .)
VI. INTER-PERSONAL AND SOCIAL STORY
Besides these immediate spatio-temporally and hierarchically
ordered "doings," an adequate discussion of Kaufmann's experiment
requires considering more remote "doings."
In performing his experiment and accounting for his results,
Kaufmann displays consequences of past choices, inter-personal and
social.
.PA
PZ <FT> {As} O (16)
PZ <FT> {So} O (17)
This says: (16) Our organism particularizing a term, specified
as: background, the construct of focal terming (FT); figure, the
construct of forming an associating with
self-and-other-member(s)-of-the-species (As); ordered. (17) Our
organism particularizing a term, specified as: background, the
construct of focal terming (FT); figure, the construct of continuing
the associating (So); ordered.
A. Apprenticeship (cf. Polanyi, 1964, pp. 206-9)
i. Affiliating1 (as a student)
At some (probably early) age, Kaufmann said (we conjecture)
something like "When I grow up, I'm going to be a scientist" -- and
subsequently, he progressively affiliated himself with the company of
scientists. As Polanyi (1964, pp. 216-7) points out, from the current
self-selected group of applicants, the company of scientists selects
its own successors.
PZ <FT> {1As} O (16A)
PZ <FT> {1So} O (17A)
This says: (16A) Our organism particularizing a term, specified
as: background, the construct of focal terming (FT); figure, the
construct of affiliating oneself with a community. (17A) Our organism
particularizing a term, specified as: background, the construct of
focal terming (FT); figure, the construct of self-selecting as a
candidate for membership in a community (accepting apprenticeship).
ii. Fostering/emulating (as a student)
In undertaking apprenticeship, a human credits certain other
humans as having mastered that which he aspires to practice, and he
voluntarily submits to their authority.
In accepting him as an apprentice and undertaking to teach him,
these humans engage in fostering (Fo) . This term subsumes a sequence
of inferences: The fostering organism affirms (-|) that another
human (Pe) (who might imitate (Im) his "doings") does actually
exist, and further affirms that should this person's "doings" or
"happenings" imitate his own, the outcomes of this person's "doings"
will satisfy (Sa) this person's focal termings (fundamental needs or
goals).
SP <Foi> {<Pei, Pc(Pei)i+1>
"{O-|(.:) <Im <Hi> {Pei+j} OhOt>
{Sa <PeFTi> {PeOci+k} OhOt} OhOt}"i+1 OhOt} O . (18)
This says: our organism specifying a term, specified as:
background, the construct of fostering at moment i; figure, a
compounded expression, specified as: background, our organism
recognizing a person at moment i, along with our organism's conscious
projecting with respect to this person-at-moment-i at moment i+1;
figure, our organism affirming that from the background follows the
figure, specified as: background, a compounded expression that the
figure imitates the background, specified as: background, our organism
at moment i ; figure, the person at moment j ; hierarchically and
spatio-temporally ordered; figure, a compounded expression that the
figure satisfies the background, specified as: background, the focal
termings for the person at moment i ; figure, the outcome for the
person at moment i+k ; hierarchically and spatio-temporally ordered at
moment i+1 ; hierarchically and spatio-temporally ordered; ordered.
This seems equivalent to saying that one of the focal terms of the
fostering organisms gets satisfied when the relevant focal terms of the
apprentice get satisfied.
SP <HFoi> {<HFTi>
{Sa <PeFTm> {PeOcn} OhOt}i O. (19)
This says: Our organism specifying a term, specified as:
background, our organism fostering at moment i ; figure, the compounded
expression that the figure satisfies the background, specified as:
background, the person's focal terming at some moment m ; figure, the
person's outcome at some subsequent moment n ; hierarchically and
spatio-temporally ordered; ordered.
The apprentice, in submitting to authority, engages in emulating
(Et). This term also subsumes a sequence of inferences: The emulating
organism affirms that there actually exists another human (whose
"doings" he would imitate), and further affirms that should his own
"doings" imitate those of this person, the outcomes of his own "doings"
will satisfy his own focal termings.
SP <Eti> {<Pei, Pc(Pei)i+1>
{-|(.:) <Im <Hi+j> {Pei} OhOt >
{Sa <HFTi> {HOci+1} OhOt} OhOt"i+1 OhOt} O . (20)
This says: Our organism specifying a term, specified as:
background, the term emulating at moment i ; background, the construct
of emulating at moment i ; figure, a compounded expression, specified
as: background, our organism recognizing a person at moment i along
with our organism engaging in conscious projecting with respect to this
person-at-moment-i at moment i+1 ; figure, a compounded expression that
our organism affirms that from the background follows the figure,
specified as: background, a compounded expression that the figure
imitates the background, specified as: background, our organism at
moment i+j ; figure, the person at moment i ; hierarchically and
spatio-temporally ordered; figure, a compounded expression that the
figure satisfies the background, specified as: background, our
organism's focal terming at moment i ; figure, our organism's outcome
at moment i+k; hierarchically and spatio-temporally ordered;
hierarchically and spatio-temporally ordered at moment i+1 ; ordered.
The fostering organism holds the results (Rsl) obtained
initially by the emulating organism as less important than the skills
(Skl) he may develop while performing the procedures. In other words,
in the Gestalt of the fostering organism, the emulator's skills occupy
the figure, while his results occupy the background.
FoO- <PeRsl> {PeSkl} OhOt (21)
This says: The abstracting of the fostering organism, specified
as: background, the person's results; figure, the person's skills;
hierarchically and spatio-temporally ordered.
When the apprentice emulates the teacher and finds that the
outcomes of his "doings" satisfy his relevant focal terms, the teacher
finds his own focal terms satisfied. This amounts to saying that the
apprentice fosters the teacher (on the next logical level). In other
words, any fostering/emulating entails mutual fostering,
[HFo(Pe), PeFo(H)]
"[HFo(Pe), PeFo(H)] <Sa <HFTm> {HOcn} OhOti> {PeFT} OhOt
| | | |
| | | |
<Sa <PeFTm> {PeOcn} OhOt}i> {HFT }(22)
This says: Our organism fostering the person along with the person
fostering our organism, specified as two parallel compounded
expressions; background1, the figure satisfies the background,
specified as: background, our organism's focal termings at some moment
m ; figure, our organism's outcome at some subsequent moment n ;
hierarchically and spatio-temporally ordered; background2, the figure
satisfies the background, specified as: background, the person's focal
terming at some moment m ; figure, the person's outcome at some
subsequent moment n ; hierarchically and spatio-temporally ordered at
moment i ; figure1, the person's focal terming; figure2, our organism's
focal terming; hierarchically and spatio-temporally ordered.
iii. "Graduating" (a "rite of passage")
Kaufmann, once a novice, learned how to use the relevant tools by
emulating skilled tool-users committed to fostering. The standards or
criteria concerning how to use the tools which he mastered don't
"exist" "OUT THERE," independent of humans, but rather, they became
manifest when someone in some sense or other said to him, with a
particular attitude and in a particular tone which we might call the
fostering voice, "Do it this way, and don't do it that way."
Eventually he made the fostering voice his own, and used it with
himself.
The performances of our novice with his tools elicited judgments
from teachers and peers on his skill. Furthermore, he incorporated the
judgments on his skill and other aspects of the esteem of others into
self-esteem, and came to assess the degree of his skill. In the
process, he also judged the degree of skill of his predecessors,
teachers and peers.
When both Kaufmann and his teachers considered that his degree of
skill surpassed some minimum standard, he graduated from the role of
apprentice. Thereafter he associated with the community of scientists
as a peer.
B. Functioning as a peer
i. Affiliating2 ("continuing the associating")
After his graduation, Kaufmann answered inquiries about his
occupation (we conjecture) with something like, "I am a physicist." As
a member of the peerage, he began taking part in the process of
training and selecting his own successors.
PZ <FT> {2As} O (16B)
PZ <FT> {2So} O (17B)
(For rough translations, cf. (16), (17), (16A), and (17A).
Consider 2As as signifying "accepting a person as a student," and
2So as signifying "engaging in teaching this person."
.PA
ii. Fostering/emulating (as a teacher)
Functioning as a teacher, Kaufmann treated the skills developed by
his students by performing procedures as figure, and the results they
may obtain as background. (cf. (21))
Regarded as a researcher, Kaufmann and his peers treated
Kaufmann's results as figure, and the skills required to produce the
results as background. In effect, he acted on the assumption that "The
group (guild) will take me and my result seriously."
HO- <HSkl> {HRsl} OhOt (23)
This says: Our organism's abstracting, specified as: background,
our organism's skills; figure; our organism's results; hierarchically
and spatio-temorally ordered.
iii. Mastery (a "rite of passage")
Most of what scientists do and publish fills in details of the
dominant paradigms of the time. Occasionally, however, a member of the
community, using available equipment and acceptable methodology applied
with high skill, gets results which do not fit with these paradigms.
At the point when this scientist acknowledges his results as
anomalous, and judges that since the experiment meets his criteria his
results merit his own trust, he becomes a master scientist. In writing
up his results and submitting them for publication, he asserts his
mastery, and invites his community to scrutinize his results from
logical and theoretical viewpoints, to replicate his experiment, and in
general to put his findings to use. We can see how this worked for
Kaufmann: According to the Dictionary of Scientific Biography (1970,
pp. 263d, 264a,b), Lorentz and Bucherer subsequently discussed the
topic of the mass of electrons; Abraham and Planck and Einstein
specifically discussed Kaufmann's 1901 results, and Einstein in 1907
fitted Kaufmann's findings into the special theory of relativity.
VII. CONSEQUENCES
A. Changes brought about in the guild
A scientist expects the universe (both non-living and
inter-personal) to foster him in his scientific work. In the process
of the dialogue between theory and experiment, he improves his
orientation in his directively correlated efforts toward individual and
species survival.
With respect to the non-living, Kaufmann's 1901 experiment yielded
findings which Newtonian physics could not account for. Contemporary
physicists used it to argue in favor of revising Newtonian dogma.
.PA
.RR L-----------------------------------------------------------------R
As early as 1901 Kaufmann reviewed the history of electron
theory in his address "Die Entwicklung des Elektronenbegriffs,"
delivered at the seventy-third Naturforscher Versammlung at
Hamburg. He noted the fruitless efforts in the past to reduce
electrical phenomena to mechanical phenomena and advocated
reversing the process by attempting to reduce mechanics to
electrical principles. Acknowledging the contributions of
Lorentz, J. J. Thompson, and W. Wien in this direction, Kaufmann
reasoned that if atoms consisted of conglomerates of electrons,
then their inertia resulted as a matter of course. (Dictionary
of Scientific Biography (1970), p. 264 b,c)
.RR----!---------------------------------------------------------------R
As for the inter-personal aspects, physicists do not customarily
describe, or even acknowledge, the effects on the experimenter or on
other physicists produced by performing any particular experiment. But
to write up results and submit them for publication comprises a SOCIAL
act, with SOCIAL consequences. The following expression states the
relation of "continuing the associating between our organism H and a
person Pe ", So(H,Pe), as " H abstracts so as to generate a gestalt
Gt ("publishable findings") from his outcome Oc ("results"); and the
person Pe takes in the (transmitted, e.g. published) gestalt Gt so
as to generate an 'awareness' Aw ."
So(H,Pe) <HO- <HOcg>
{HGth} OhOt>
{PeO- <HGti>
{PeAwj} OhOt} OhOt (24)
This says: Continuing the associating between our organism and a
person, specified as two compounded expressions: background, a
compounded expression that our organism abstracts, specified as:
background, an outcome for our organism at moment g ; figure, our
organism's Gestalt or generalization at moment h ; figure, a compounded
expression that the person abstracts, specified as: background, our
organism's Gestalt at moment i ; figure, our person's awareness at
moment j ; hierarchically and spatio-temporally ordered; hierarchically
and spatio-temporally ordered.
In keeping with custom, Kaufmann focussed on the inanimate and
left un-discussed the possible personal and social effects of
performing and publishing his 1901 experiment.
As it turned out, the social aftermath of this experiment included
the personal growth which Kaufmann underwent in the process of
designing, performing and reporting this experiment (cf. above, V 5),
and the attention subsequently paid to Kaufmann by the theorists
mentioned above. The entry on Kaufmann in the Dictionary of Scientific
Biography (1970) backhandedly acknowledges his originality, as
follows:
.RR L-----------------------------------------------------------------R
The significance of Kaufmann's experimental evidence that
electron mass varied with velocity, coupled with his belief that
mass could be expressed as essentially electromagnetic phenomena,
has rarely been recognized. He outlined a major pathway along
which research in twentieth-century physics would be directed.
(Dictionary of Scientific Biography, p. 264a)
.RR----!---------------------------------------------------------------R
In short, Kaufmann's study entails expectations concerning the
inanimate, which he makes quite explicit. These expectations got
tested and not-disconfirmed, and so yielded an advance in articulated
physical knowledge. The cognate Newtonian tenets did get disconfirmed.
Kaufmann's study also entails expectations concerning self and the
social. However, Kaufmann did not make these explicit at all. Hence
he provided no way to disconfirm these expectations. He may have
erred, but he had no protocol, no way of ESTABLISHING whether he did or
not. Hence his study provided no explicit advance in articulated
SOCIAL knowledge.
B. Eliminating vs. including the observer
As just noted, in his 1901 experiment Kaufmann failed to make
explicit his expectations concerning self and the social. By so doing,
he continued to associate himself with the Newtonians, who, in their
theorizing, SYSTEMATICALLY eliminate the observer (or self) and the
relations between self and other humans from consideration.
1. The structure of "eliminating the observer"
The Newtonians never SAID (prior to 1900-1905) that they eliminate
the observer from consideration (Hilgartner & Harrington, 1984a).
Instead, they never discussed the topic of the observer -- of how a
physicist builds up his picture of the physical happenings which occur
in and around him -- at all.
In accounting for this omission, we attribute to the Newtonians a
special, restricted and restrictive assumption which has the effect of
eliminating the observer from consideration -- namely, a tacit form of
"absolute certainty." Furthermore, we attribute to the quantum
theorists and relativists and Newtonians alike still another hidden
assumption, distinguishable from the one disclosed in Newtonian physics
by the early quantum theorists and relativists, which also has the
effect of eliminating the observer from consideration by failing to
consider the hierarchically-ordered relations of an experimenter with
himself and with other scientists -- another tacit form of "absolute
certainty" (Hilgartner & Harrington, 1984).
Still further, we say: If in his theorizing a human relies on some
special assumption which eliminates from consideration a crucial aspect
of the situation, or certain facets thereof -- e.g. the self-component
or observer -- he unavoidably leaves out of account some crucial aspect
of the environmental component of the situation as well.
.PA
CP <ZF> {SfF OtF} O (25)
and likewise,
CP <O-F> {(sigma)F (rho)F} O (26)
This says: (25) Our organism componenting a term, specified as:
background, left-out-of-account aspect of organism's map (ZF); figure,
left-out-of-account self-component (SfF) along with left-out-of-account
other-component (OtF); ordered.
(26) Our organism componenting a term, specified as: background,
left-out-of-account aspect of organism's abstracting (O-F); figure,
left-out-of-account self-referential abstracting ((sigma)F) along with
left-out-of-account hetero-referential abstracting ((rho)F); ordered.
In other words, like the early quantum theorists and relativists,
we impute to the Newtonians (including Kaufmann) at least one
fundamental theoretical error concerning self-and-environment -- and
to the quantum theorists and relativists themselves, another. On the
topic of such errors, Perls, Hefferline & Goodman (1951) lay out the
crucial issues trenchantly:
.RR L-----------------------------------------------------------------R
Fundamental theoretical errors are invariably
characterological, the result of a neurotic failure of
perception, feeling, or action. (This is obvious, for in any
basic issue the evidence is, so to speak, 'everywhere' and will
be noticed unless one will not or cannot notice it.) A
fundamental theoretical error is in an important sense given in
the experience of the observer; he must in good faith make the
erroneous judgment; and a merely 'scientific' refutation by
adducing contrary evidence is pointless, for he does not
experience that evidence with its proper weight -- he does not
see what you see, it slips his mind, it seems irrelevant, he
explains it away, etc. Then the only useful method of argument
is to bring into the picture the total context of the problem,
including the conditions of experiencing it, the social milieu
and the personal 'defenses' of the observer. That is, to subject
the opinion and his holding of it to a Gestalt-analysis. A basic
error is not refuted -- indeed, a strong error, as St. Thomas
said, is better than a weak truth -- it can be altered only by
changing the conditions of raw experience.
Then, our method is as follows: We show that in the
observer's conditions of experience he must hold the opinion, and
then, by the play of awareness on the limiting conditions, we
allow for the emergence of a better judgment (in him and in
ourselves). We are sensible that this is a development of the
argument ad hominem, only much more offensive, for we not only
call our opponent a rascal and therefore in error, but we also
.RR----!---------------------------------------------------------------R
charitably assist him to mend his ways! Yet by this unfair
method of argument, we believe, we often do more justice to an
opponent than is common in scientific polemic, for we realize
from the start that a strong error is already a creative act and
must be solving an important problem for the one who holds it.
.RR L-----------------------------------------------------------------R
(Perls, et al., 1951, pp. 243-4)
.RR----!---------------------------------------------------------------R
The opinion rigidly held by Kaufmann centers about the way he
linguistically "cut[s] nature up [and] organize[s] it into concepts"
(to use Whorf's (1956, p. 213) phrase), and the degree of reliability
he attributes to this arbitrary, linguistically-determined pattern.
Kaufmann symbolically cuts up nature into two distinct and disparate
realms, namely, "the objective" vs. "the subjective," which he
maintains in "logic-tight compartments" (Cartier, 1963). As we have
already shown, Kaufmann treats his expectations concerning the
inanimate, e.g. electrons, as hypothetical and tentative, and subjects
them to experimental testing -- the most devastating kind of criticism
yet devised. And his findings violate the predictions of Newtonian
theory -- mass, he finds, increases with velocity. In contrast, by not
making explicit his expectations about self and the social, Kaufmann
treats them as NOT in any way hypothetical or tentative, but rather as
beyond scrutiny or criticism -- as "The way things REALLY ARE."3 Since
he does not subject his expectations in this domain to scrutiny, he
tacitly assumes that they reach "absolute certainty." Or, stated in
logical terms, Kaufmann TREATS his picture or map of self and the
social as identical with the territory referred to -- he attributes
absolute certainty to unscientific views in that arena. Absolute
certainty logically precludes any role for the observer.
In the end, by adhering to a fundamental theoretical error, each
member of the Newtonian guild denies to his unscientific expectations
concerning self and the social the scrutiny he gives to his disciplined
expectations concerning the inanimate -- and in so doing, represents
his most fundamental needs as insatiable and his self as dissociated
(Hilgartner & Randolph, 1969a,b,c,d; Perls, Hefferline & Goodman, 1951;
Whyte, 1949).
SP <OGtd>i
__
{.: <O -|>i {OPr}j OhOt }
| |
| |
{.: <OIr(O -|>i {OSv}j OhOt }
| |
| |
{.: <OSv}j > {OIr(O -|}k OhOt} (27)
This says: Our organism specifying a term, specified as:
background, our organism's dissociative Gestalt at moment i ; figure,
an expression composed of three compounded expressions taken in
parallel, namely, figure1, our organism's Gestalt that from the
background follows the figure; background, our organism's affirming at
moment i ; figure, our organism's total destruction
(not-preservation-and-growth) at moment j ; hierarchically and
spatio-temporally ordered; figure2, our organism's Gestalt that from
the background follows the figure, specified as: background, our
organism interrupting his affirming at moment i ; figure, our
organism's bare survival at moment j ; hierarchically and
spatio-temporally ordered; figure3, our organism's Gestalt that from
the background follows the figure, specified as: background, our
organism's bare survival at moment j ; figure, our organism
interrupting his affirming at moment k ; spatio-temporally and
hierarchically ordered.
Logically speaking, dissociating the self and eliminating the
observer follow from a single hidden untenable assumption (a tacit form
of "absolute certainty"), and so seem equivalent. Furthermore,
developmentally speaking, when a human generates the dissociative
Gestalt (Gtd), he imparts to his experiencing an affect
.UL on
ive tone which
we call the sense of isolation (ORe-).
__
.: <Gtd> {ORe} OhOt . (28)
This says: Our organism generating the Gestalt that from the
background follows the figure, specified as: background, the organism's
dissociative Gestalt (Gtd); figure, the organism's sense of isolation
(ORe); ordered.
2. Consequences of eliminating the observer
A human or group that tacitly regards its views as absolutely
certain (and thus eliminates the observer), and that encounters another
human or group whose views do not exactly match its own, manifests
counter-fostering of that human or group by defending the rightness of
its own views. In other words, it perpetuates an ethos of
power-struggle. This in turn has serious consequences, which we
discuss in detail in the next installment of this series.
3. The structure of including the observer systematically
We humans can eliminate the fundamental theoretical errors and the
underlying untenable assumption discussed above by treating our
expectations concerning self and the social as also hypothetical and
tentative, and subjecting them to experimental testing. In so doing,
we distinguish between our pictures of self-and-the-social and what our
pictures represent.
POSTULATE 1:
Non-identity: 1=_/ <oZ> {eHeY} OhOt
(29)
This says: Our organism (first-ordered) non-identifying (=_/),
specified as: background, our organism's (object-leveled) map (OZ);
figure, the (event-leveled) self-component (eH) along with the
other-component (eY) of the environment; hierarchically and
spatio-temporally ordered.
That means that we explicitly regard our pictures in principle
both as incomplete and inaccurate, and as containing some kind of
representation of the human who generates the pictures.
POSTULATE 2:
Non-allness:(rho) <v0> {y0} OhOt
___
(rho) <v0> {y1} OhOt
___
(rho) <v1> {y0} OhOt
___
(rho) <v1> {y1} OhOt (30)
POSTULATE 3:
Self-reflexiveness:(sigma) <u0> {h0} OhOt
_____
(sigma) <u0> {h1} OhOt
_____
(sigma) <u1> {h0} OhOt
_____
(sigma) <u1> {h1} OhOt (31)
A human who operates from these premises does not represent his
self as dissociated; he represents his transacting with his environment
as directively correlated, and as competent to satisfy the fundamental
needs of organism and group. In other words, he shows an attitude
which we call O-|i , affirming.
SP <O-|>i {OPrj} OhOt (32)
This says: Our organism specifying a term, specified as:
background, our organism affirming at moment i; figure, our organism's
preservation-and-growth at subsequent moment j; hierarchically and
spatio-temporally ordered.
.PA
Logically speaking, affirming of self-and-other and taking the
observer (or self) into account appear equivalent. Furthermore,
affirming imparts to the experiencing of a human who does it an
affective tone which we call the sense of relatedness-in-a-field,
(ORei).
.: <O-|i>: {ORej} OhOt (33)
.: <(29), (30), (31)> {ORe} OhOt (34)
This says: (33) Our organism generating the Gestalt that from the
background follows the figure, specified as: background, our organism
affirming at moment i ; figure, our organism's sense of
relatedness-in-a-field, at moment j ; hierarchically and
spatio-temporally ordered.
(34) Our organism generating the Gestalt that from the background
follows the figure, specified as: background, the premises (sentences
(29), (30) and (31)); figure, our organism's sense of
relatedness-in-a-field.
4. Consequences of including the observer systematically
To date, not many workers explicitly operate from theories which
systematically include the observer. Instead, most subscribe to
theories which posit absolute certainty in some arena (most often, that
of self and the social), and so surround themselves with a dissociated
setting which endorses counter-fostering in an ethos of power-struggle.
Therefore, the consequences of including the observer remain as yet
inadequately experienced.
From our preliminary assessment of this topic, it appears that
systematically taking the observer into account eliminates the basis
for dissociating one's self, and for the inter-personal transactings we
could call
.UL off
institutionalized counter-fostering in general and
power-struggle in particular.
We parochial humans have grown up in a dissociated social
environment, characterized by an ethos of power-struggle. When we hear
of a practicable way toward an alternative ethos, we feel stunned.
Somehow we can't quite imagine what it would look like.
The present frame of reference provides guidance in our endeavors
to develop such an alternative ethos. Our non-standard notations
cannot NOT take the observer into account. Hence our mathematics makes
the crucial relations clear, and shows us when we have left out some
central factor of our relations with self-and-other. The third paper
in this series will discuss some of the implications for physics of
this frame of reference.
.PA
FOOTNOTES
1. At the current stage of development of our notation, we use a total
of five ordering terms: Besides spatio-temporal and hierarchical, we
utilize synchronous with Os ("occurring along with, as viewed from a
specified position"), co-ordered with Oc ("occupying one and only one
position in an ordering on abstracting"), and polar to Op ("mutually
necessary, opposing").
2. We quote at length from these sources for at least three reasons:
.RR L-----------------------------------------------------------------R
a) Few readers, we expect, will find themselves fully conversant
with the details;
b) It takes special care to reconstruct the setting for
Kaufmann's experiment convincingly; and
c) The "fit" between our integrative framework and the details
presented in these sources makes one of the most striking
features of our framework which our study discloses. If we
should paraphrase instead of quoting, we would deprive our
readers of their opportunities to sense this "fit."
.RR----!---------------------------------------------------------------R
3. One might excuse Kaufmann from any necessity to deal with such
expectations, on the grounds that they lie outside the field of
physics, or that he does not claim competence in such areas. To do so
not only begs the questions we raise, but also endorses eliminating the
observer.
.PA
REFERENCES
Ashby, W. Ross (1962): "The Set Theory of Mechanism and Homeostasis."
Technical Report No. 7, Electrical Engineering Research
Laboratory, University of Illinois, Urbana, IL.
Boorse, Henry A. & Lloyd Motz (1966): The World of the Atom. New York:
Basic Books.
Cartier, Francis (1963): "Three Misconceptions of Communication." ETC.:
A Review of General Semantics 20:135-145
Dictionary of Scientific Biography (1970): American Council of Learned
Societies, New York: Scribner's.
Hilgartner, C. A. (1978f): "'International' or 'One-World' Languages:
"You Can't Get There From Here"." Eco-logos: A Magazine of
One-World Environmental Concepts, Vol 24, No. 90, Appendix V.
Hilgartner, C. A. (1978g): "The Method in the Madness of Western Man."
Communication 3:143-242.
Hilgartner, C. A. (1979a): "A Complete Severance from Traditions."
Presented at the Centennial Conference on General Semantics, New
York City, 27 October 1979. Printed in the General Semantics Bulletin
No. 47, 112-9 (1980).
Hilgartner, C. A. & Ronald V. Harrington (1984): "Relativity Revisited:
The Case for Hierarchical Ordering" (Submitted for publication.)
Hilgartner, C. A. & John F. Randolph (1969a,b,c,d): "Psycho-logics: An
Axiomatic System Describing Human Behavior. 1. A Logical Calculus of
Behavior." Journal of Theoretical Biology 23:285-338. "2. The
Structure of 'Unimpaired' Human Behavior." Journal of Theoretical
Biology 23:347-374. "3. The Structure of Empathy." Journal of
Theoretical Biology 24:1-29. "4. The Structure of 'Impaired' Human
Behavior." (Submitted for publication.)
Kaufmann, Walter (1901): Nachrichten von der Gesellschaft der
Wissenschaften zu Gottingen, Math.-phys Kl., 2:143-155.
Korzybski, Alfred (1921): Manhood of Humanity. New York: Dutton. Second
edition (1950), Lakeville CT: Institute of General Semantics.
Korzybski, Alfred (1933): Science and Sanity: An Introduction to
Non-Aristotelian Systems and General Semantics. Chicago:
International Non-Aristotelian Library Publishing Co. Fourth edition
(1958), Lakeville, CT: Institute of General Semantics.
Perls, Frederick S., Ralph Hefferline & Paul Goodman (1951): Gestalt
Therapy: Excitement and Growth in the Human Personality. New York:
Julian Press.
Polanyi, Michael (1964): Personal Knowledge: Toward a Post-Critical
Philosophy. Chicago: University of Chicago Press, 1958. Torchbook
edition, New York: Harper & Row.
Singer, E. A. (1946): "Mechanism, Vitalism, Naturalism." Philosophy of
Science 13:81-99.
Sommerhoff, G. (1950): Analytical Biology. London: Oxford University
Press.
Whorf, Benjamin Lee (1956): Language, Thought, and Reality. John B.
Carroll, editor. New York: Wiley/MIT Press.
Whyte, Lancelot Law (1950): The Next Development in Man. New York:
Henry Holt, 1948. Paperback edition (1950), New York: Mentor Books
(New American Library).
.PA
GLOSSARY OF TERMS
In general, treat each of these terms as some kind of a
verb-form.
-| Affirming HOur (human) organism
Rsl Results InInterest
Ap Approach M*Motor
At Attend MonOff/on switch for the
electric/magnetic fields
Aw Aware
OOrder
CP Component
OcOutcome
Cs Consciousness
PZParticularize
CT Coenetic term
PePerson
Cls Close
ReRelatedness
Df Deficit
SaSatisfy
DC Directively correlated
SklSkill
Et Emulate
SoContinue the associating
Ex Expect
SPSpecify
FT Focal terming
StkStopcock
Fo Foster
TonTurn switch on
Greek letters:
SySystem
Theta (Overall) abstracting
VonVacuum pump off/on switch
Rho Hetero-referential
abstracting. YEnvironment
Sigma Self-referential ZMap or representation
abstracting
Psi In DC, the interacting of f(d) and g(d).
Gt Gestalt
Gtd The dissociative Gestalt
.PA
APPENDIX 1
A. SUMMARY OF PREVIOUS PAPER
In the first paper of this series,@ we utilize our frame of
reference to look at how the theory of relativity does the job of
taking the observer into account. To make our first point, we use
selected ones of our own constructs (mainly the undefined term
ordering) to see how much of the theory of relativity fits within our
theory, as a kind of special case. In the process, we differentiate
between those aspects of the theory of relativity which amount to
taking the observer into account and those aspects which do not.
___________________
@Criterion of logical generality
@Null-A vs. traditional assumptions and "taking observer into account"
(WHERE did we first lay out both sets of assumptions?????)
@"Anomalies Generated by Contemporary Physics"
___________________
pa
A) Using the special case of spatio-temporal ordering, we
account, with considerable economy of means, for some of the positive
accomplishments of the theory of relativity. Our constructs handle
with particular ease the dispute over relativity, manifested in the
well-known opposing tenets: the one attributed to Newtonian mechanics,
a) that light travels from one point to another in 'no time at all',
vs. the one Einstein offers, b) that light travels at a finite
velocity which remains constant for all observers, regardless of their
motion relative to each other or relative to the light source. The
complex of relations which Einstein's tenet makes it possible to handle
provides the grounds for saying that his theory of relativity takes the
Observer into account.
B) Using the special case of hierarchical ordering, we examine the
process of discovering the kind of anomaly (also known as a
relativisitc discrepancy) which logically precedes and leads to the
theory of relativity. We find that the discovery of an anomaly or
relativistic discrepancy hinges on key relations with self and the
social. Moreover, our examination discloses certain previously
unnoticed assumptions within the theory of relativity, specifically,
tacit assumptions concerning how an investigator deals with self and
the social. In detail, we find that these anomalies have the following
common structure:
a) Observer B makes some observations;
b) B takes in some observations made (under slightly different
conditions) by Observer A; or else B considers observations that B
made at a different date, and under slightly different conditions;
c) B finds that the two sets of observations DON'T MATCH in some
crucial fashion; and
.PA
d) B takes seriously (eventually, takes on the job of accounting
for) this mismatch, this anomaly.
The discovery of a relativistic discrepancy requires, and signals
the presence of, a new level of trust between the scientists involved
-- a trusting of themselves and of each other. If, like the
traditional Newtonians, Observer B should seek to invalidate and
discredit the findings of Observer A which don't match with her/his own
observations/conclusions, then s/he could never discover a relativistic
discrepancy in the first place. The trusting must precede the
discovering. The increase in predictability delivered by the theory of
relativity (and quantum theory), then, follows from this increase in
intra-personal and interpersonal trusting.
As noted, Einstein takes into account certain aspects of
spatio-temporal ordering in human experiencing -- e.g. the finite
velocity of light, and thus the finite interval it takes for Observer
A's observations to reach Observer B. But by neglecting to discuss the
specific patterns of dealings with self and the social -- e.g. the
nervous system activities by which B makes her/his observations --
Einstein tacitly REPRESENTS observable physical "happenings" which
occur at finite velocities AS IF they occurred in 'no time at all'.
That, however, involves a chain of implications which Einstein himself
first disclosed: It treats ordered activities as non-ordered -- and in
the process, eliminates the Observer from consideration.
Thus we demonstrate that, within a limited arena, the theory of
relativity does effectively deviate from the tenets concealed in the
WIE grammar so as to rely on map-territory non-identity, and so does
take the observer into account; whereas, elsewhere throughout the
theory, it still grants a privileged position to the WIE grammar and so
relies on map-territory identity, and so systematically eliminates the
observer from consideration.
As the second point of our previous paper, we address the question
of what difference it makes whether one takes the observer into
account, or does not. We show the importance of this issue in terms of
the role which the practice of science plays in species-survival.
In the largest perspective, we humans practice science in order to
increase human knowledge and our ability to predict accurately, so we
can increase the likelihood that individual, group and species will
survive.
Today, however, when we humans generate and apply new knowledge --
when we practice science -- we bring the human species closer and
closer to species suicide and extinction (and in the process, push the
rest of the biosphere toward annihilation too). The authors hold that
the disjunction between what we see going on around us -- the headlong
rush toward species suicide, extinction and pan-biocide -- and the
reason we humans practice science in the first place constitutes an
anomaly. It represents "findings which we must take seriously, that
current theory cannot adequately account for."
In order to account for the current anomalies, we start with the
supposition that humans expect or assume. Then what one DOES follows
from what one ASSUMES, as theorems follow from premises. We hold that
every human transacts with her/his environment -- s/he continuously
undergoes two-way interchanges with her/his environment, which leave
both participants fundamentallly and profoundly altered, in some sense
that affects the further living of the living system(s) involved.
Furthermore, every human transacts AS IF from some theory or other,
some structure composed of assumptions, which we call a lived theory --
whether s/he notices or not. Still further, we regard it as possible,
feasible and desirable for any human to make her/his lived theory
explicit, and to subject it to scrutiny, revising it as needed.
Lived theories have a creative aspect, functioning like
self-fulfilling prophecies. As we humans transact on the basis of
lived theory, our "doings" remake everything involved in the
transacting into a closer approximation to the pictures of "what goes
on" in the theory which we live. For example, a lived theory which
tacitly posits map-territory identity and so systematically leaves out
of account the observer also systematically leaves out any transacting
between organism (observer) and environment, and thus in turn leaves
out the environment. Such a theory thus provides the symbolic means to
represent only inanimate mechanisms, e.g. those that maximize a single
variable (e.g. power, or status, or profits). In general, when we
humans live a theory which systematically leaves out of account the
observer -- ourselves-in-our-environments -- we transform the
environment so that it becomes more hospitable to mechanisms and less
hospitable to living systems, while we transform ourselves so we more
resemble the types of mechanisms depicted in the theory --
machine-tending machines, or businessmen, etc. -- than we do persons
engaging in mutually-altering transacting.
Conversely, a theory which explicitly posits map-territory
Non-identity and so systematically takes the observer into account --
in her/his dealings with self, with the non-living environment, with
other humans and with other species -- provides the symbolic means
adequately to represent living systems transacting with
themselves-and-their-environments. So far, we humans have few worked
examples of this kind of theory to consider. But in principle, when we
live such a theory, we provide ourselves with the possibility of
transforming our environments so as to make them more diverse, more
hospitable to transacting persons; and of transforming ourselves so we
resemble not mechanisms, but rather, transacting persons --
participants in an ecology -- (co-)operating on a people-centered,
life-centered basis.
In this light, we find that although, historically speaking, the
theory of relativity served as the focus for introducing the construct
of taking the observer into account, for the most part its exponents --
in company with the rest of the practitioners of WIE science -- still
grant a privileged position to the WIE grammar, and so maintain their
tacit reliance on map-territory identity. This reliance leads them
both to keep the doctrines they hold concerning self and the social
concealed, and to protect those concealed doctrines from scrutiny and
revision. Even the advocates of the very best of the scientific
theories of the WIE tradition, then, split their science into two
components: In the foreground part, the exponents operate from
disciplined observing/inferring from shared explicit assumptions which
they acknowledge, question and test, while defining as 'favorable' any
outcome which increases knowledge. In the background part, they
operate from secretly shared tacit assumptions which they do not
acknowledge, question or test, while treating as 'favorable' any
outcome which both keeps those tacit assumptions concealed and
maintains or increases the power or prestige or profits of some
specified group (at the expense of other groups), for the sole benefit
of the specified group.
Thus scientists and non-scientists alike have cooperated in
exploiting modern science, including modern physics, with no concern or
responsibility for the welfare of the human species in its environment,
and with no concern for the internal structure of science itself, its
logic and ethics. In the process, we have created a mutilated
science,@ committed to maintaining certain hypotheses, views, opinions,
beliefs or guesses as hidden, tacit, unrecognized, unexamined and
untested. We have subjugated our advances in explanatory power to
local patriotism, economic interest, the power of the state, and the
like. Thus we have created a social institution of "science" with a
different, darker goal: To use the explanatory power of modern
science, especially modern physics, to produce physical power in the
service of power struggle, for the sole benefit of some group smaller
than the entire human species. By so doing, we have created the modern
anomalies, and so threaten ourselves with species-suicide,
self-inflicted extinction.
In conclusion, we assert that:@
The currently-dominant forms of human knowledge -- standard-brand
Western logics, mathematics, sciences, philosophies, jurisprudences,
religions, along with the lived theories of their exponents -- appear
incompatible with species-survival. And in their present stages of
development, none of our Western scientific theories -- in "natural
science or psychology," as Einstein puts it -- shows us how to arrange
our personal lives and our social systems so as to replace the
non-viable pattern of power struggle with some alternative, viable
pattern. None rigorously accounts for how the terrible dangers which
constitute the modern anomalies can arise out of modern physics.
We summarize our findings as follows:@
.RR L-----------------------------------------------------------------R
In casting about for a way to talk about our current
species-suicidal impasse, the authors... explore [the]
possibility ... [t]hat, as organisms who guide what we DO by the
assumptions encoded in the theories we hold, we humans HAVE DONE
exactly what the currently dominant assumptions have told us to
-- to our immediate peril -- and that we can change what we do
ONLY by changing our assumptions.
As our considered opinion, the authors suggest that the
assumptions encoded in our currently dominant theories include at
.RR----!---------------------------------------------------------------R
least one now-disclosed tacit assumption which directs us humans
in self-defeating, self-eliminating, suicidal directions. We
further suggest that we now have the resources -- alternative
assumptions and the beginnings of an alternative scientific frame
of reference based on them -- with which to reject and replace
this dangerous tacit assumption. We hold that the time has come
for us humans to revise our traditional premises.
________________
@Polanyi
@Anomalies, p. 138b
@"Anomalies...", p. 139a,b
________________
.HM3
.HM1
.H1 APPNDX2.TNL October 28, 1990 at 8:40
.H2 PM
.PA
October 23, 1990 at 11:54 AMOctober 23, 1990 at 12:32 AM10/17/90 at
23:41:0910/16/90 at 22:18:5510/15/90 at 23:47:0110/15/90 at
15:33:31heWORKOVR7 10/15/90 at
13:48:1410/13/90 at 00:05:0610/12/90 at 21:59:5610/12/90 at
12:05:3810/10/90 at 10:41:2810/09/90 at 20:41:27heAPPNDX2.TNL 10/09/90 at 11:56:3310/08/90 at
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16:43:5010/03/90 at 10:01:0110/03/90 at 01:30:5210/02/90 at
22:30:1410/01/90 at 23:13:5509/30/90 at 23:01:07APPENDIX 2
.RR-----!--!----!----!----!----!----!----!----!----!----!----!----!----R
In this Appendix, we give enough information about our
non-standard notation so our readers can make sense out of what we say
with it. However, here we do NOT undertake to derive the notation in
any formal sense.
As noted in the text, we have embarked on the task of generating
physical theory which systematically takes the observer into account.
The present non-standard frame of reference and notation started out as
a deliberately generated axiomatic system. It arises out of an ongoing
study aimed at exploring the consequences of taking Korzybski's
non-aristotelian premise of Non-identity seriously. To that end,
elsewhere we have already generated a frame of reference and a notation
based on map-territory non-identity as our most fundamental postulate.@
In the current series of papers, we begin develping the constructs we
believe necessary to elaborate a physical theory that cannot eliminate
the observer from consideration. The main limitation on the growth of
this non-standard notation has come from its unfamiliarity.
___________________
@Elsewhere
___________________
pa
In approaching our non-identity-based notation, almost everyone
trained in WIE science will do so expecting the formalized expressings
in our text to work somewhat the way the equations or formulae of the
familiar identity-based WIE notational languages do.
They don't. They have their own pattern, radically different from
that of the formalized or discursive WIE languages. Let's start with
two main examples of expressings from our non-standard notation, with
interpretations in English; then, for those who want more details, we
compare the pattern of the WIE languages with that of our own, so as to
highlight both the differences and the similarities between them.
1. A NON-STANDARD NOTATION
From our point of view, any written text (in any language) -- even
a laundry list -- presumes a speaker, addresses an audience, and posits
a dramatic situation.
(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 &
Bentley@), suggests a kind of "one-way causality." Consider, for
example, Newton's second law of motion:
f = ma (1)
"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. Moreover, this famous equation describes the "motion" of
physical "bodies," in a world thought to consist of more or less
discrete objects of different sizes, which follow trajectories and
sometimes collide. (The descriptions it generates prove quite
accurate, as long as the dimensions of the "bodies" or "things"
examined remain within a few orders of magnitude of the dimensions of a
human body.)
(b) Transacting: Our non-standard notation
In our 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.
___________________
@Dewey & Bentley, 1949
___________________
pa
Our demonstration consists of four parts, ending up with an
expressing which corresponds roughly to an English-language
characterization of our non-standard theoretical system as "An
accounting for how humans account for human accounting."
(1) For our purposes, we consider the topic of what our observer
regards as the kind of primary, first-order transactings by which our
organism accounts for and deals with what goes on in and around
her/himself. In generic terms, our observer designates this kind of
accounting by the defined term abstracting, which s/he symbolizes with
O- .
O- . (2a)
To interpret (2a) in English: "Our organism abstracting."
Put into idiomatic English: "Our organism accounting for and
dealing with what goes on in and around her/him."
(2) Given that our observer wants to say more about what s/he sees
going on than just O- , "our organism abstracting": S/He spells out
more details using a kind of topic-comment "template," which has four
"places" within it.
1O- <HY> {Z} OhOt (2b)
(i) In the first of these places, the "topic" term (e.g. O- ,
abstracting) expresses the organism's "doings" or "happenings" of the
moment, in context, as viewed by our observer.
In the remaining three terms our observer specifies a "comment" on
this topic, framed as a Gestalt. To do this, s/he writes a
"background" term set off by French brackets < > , followed by a
"figure" term set off by braces { } , followed by a term which spells
out how the background and figure terms hang together.
(ii) In the second place, the "background" term <HY> , our
observer refers to what s/he regards as the "territory" which our
organism accounts for, and includes H , a designation for the "doings"
or "happenings" occurring within our organism, and Y , a designation
for the "doings" or "happenings" occuring in the vicinity of our
organism.
(iii) In the third place, the "figure" term {Z} , our observer
refers to what s/he regards as the "map" which our organism generates
in the process of "accounting for what goes on in and around her/him"
at present.
(iv) In the fourth place, the "ordering" term OhOt , our observer
spells out how the background and figure terms relate to each other. Here, Oh , hierarchically ordered, means "One term (here, the figure)
occupies a position in a hierarchical order one logical "level" higher
than does the other (the background)." Likewise, here Ot ,
spatio-temporally ordered, means "One term (here, the figure) occurs
later and/or in a different location than does the background."
To interpret (2b) in English: Topic, our organism abstracting:
background of the Gestalt, the "doings" or "happenings" occurring in
and around our organism; figure, our organism's map of these "doings";
ordering, the figure (map) occurring one logical level higher than does
the background, and also occurring later and/or in a different location
than does the background.
Put into idiomatic English: "Our organism accounting for what
goes on in and around her/himself."
(3) In expressing (2b), our logician focuses on "the map" or "the
accounting" which our organism generates, and relegates "what goes on
in and around our organism" -- the details that the map represents or
refers to -- to the background. S/He can reverse this stance, treating
HY as figure and Z as background, which allows focusing on "what
goes on in and around our organism" instead of on "the map of what goes
on in and around her/him."
1O- <Z> {HY} OhOt (2c)
Our logician defines this process of reversing the positions of
figure and ground as negating -- s/he produces (2c) by negating (2b).
(4) Finally, in this notation we can nest expressings to make
compounded expressings. For example, in place of a single term used as
background or as figure, we can insert a whole well-formed expressing,
e.g.
... <O- <HY> {Z} OhOt> ....
.PA
This makes it possible to deal with some of the complexities of human
behaving-and-experiencing which otherwise escape our efforts to account
for them.
The process of nesting produces expressings of considerable
complexity. In order to keep track of the way we terms in our
notation, we can index any term T in various ways, for example, by
means of right and left superscript and right and left subscript. For
example, our logician uses the left superscript, aT , to spell out the
logical level of that term (position in a hierarchical ordering,
relative to the positions of the other terms or expressings present).
With the right superscript, Tb , s/he spells out the position of that
term in a spatio-temporal ordering (relative to the positions of the
other terms present). With the right subscript, Tc , s/he
individuates that term (relative to the other terms present), e.g. O
signifies some ordering term (in a generic sense), but does not
particularize a specific one; whereas the indexed Oh signifies one
particular ordering, namely, hierarchical ordering; while Ot
signifies another, namely, spatio-temporal ordering.@
___________________
@Footnote 1 (5 ordering terms)
___________________
pa
Sometimes it appears necessary, or at least useful, to index terms
in an ordinary English sentence. The characterization, above, of our
non-standard theoretical system in particular might profit from such
indexing, yielding the compounded construct of "3Accounting for how
humans 2account for human 1accounting." Expression (2d) gives a
notational version of this compounded construct.
To produce (2d), we treat our expressing for 1accounting (viz.
(2b)) as the background. Then a similar expressing for 2account,
indexed as occupying a second logical level, makes up the figure. Then
the construct of 3accounting, the main expressing, indexed as occupying
a third logical level, expresses our organism's main activities of the
moment, as viewed by our logician.
3O- <1O- <HY> {Z} OhOt> {2O- <HY> {Z} OhOt} OhOt (2d)
To interpret (2d) in English: Main topic, our organism abstracting:
main background, the nested expressing (12b): <1sub-topic, our organism
abstracting (first-ordered or occurring on the "lowest" logical
"level"); background, the (mainly non-verbal) "doings" or "happenings"
occurring in and around our organism; figure, our organism's
first-ordered (mainly non-verbal) "map" of those (mainly non-verbal)
"doings" or "happenings"; ordering, the figure (map) occurring one
logical level higher than does the background, and occurring later than
does the background>; main figure, the nested expressing (22b):
{2sub-topic, our organism abstracting (second-ordered or on a
"middle" logical "level"); background, the first-ordered "doings" or
"happenings" represented by (12b), the process by which our organism
generates a first-ordered "map" of mainly non-verbal "doings" or
"happenings"; figure, the second-ordered "map" of those "doings" or
"happenings," the process by which our organism accounts for
first-ordered accounting; ordering, the figure (map) occurring one
logical level higher, and later, than does the background}; main
ordering, the figure occurring one logical level higher, and later,
than does the background.
Put into idiomatic English: "Our organism 3accounting for how
humans 2account for human 1accounting."
These remarks probably do not contain enough detail to enable our
readers to WRITE in the non-standard notation; but, like a
foreign-language phrase-book, (when coupled with the Glossary of Terms)
they should make it possible for you to read the notational sentences
in the text.
For those who want more background, the following section compares
the pattern of symbolizing within WIE languages such as the
mathematical theory of sets with the pattern of symbolizing within the
present non-standard notation.
2. COMPARING THE PATTERNS OF WIE AND NON-STANDARD NOTATION
A. OVERVIEW OF THE WIE PATTERN
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 exponents of this symbol system assume.
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."@ To form a complete
sentence, we place at least one noun -- or, better, noun-phrase -- next
to at least one verb-phrase:
The cat grinned.
___________________
@Webster's Second, 1961, p. 1236
@CAH, "Some Traditional Assumings" -- GSB 1977/78, p. 140-1
___________________
pa
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 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:
Not-A .
x [element of] A .
1. MAP-TERRITORY IDENTITY
The WIE grammar makes no provision for distinguishing between
"map" and "territory," or alternatively, between "a word" and "that
which the word represents or stands for." 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.
But 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 an exponent with no primary means to distinguish
between "map" and "territory," by that presupposition it constrains
this exponent 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 exponent's "map" of "the
world," and that our exponent'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.
___________________
@CAH, "Some Traditional Assumptions ..."
___________________
pa
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 stem from tacit
identity, from explicit identity, and either from Aristotle's Law of
Identity or from 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.
B. AXIOMATIC SYSTEMS
To facilitate making the comparison between the WIE and our own
non-standard frames of reference and notations, 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 our non-standard view, 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 prove one or more theorems, or formal
conclusions. In so doing, s/he satisfies our minimal criterion for the
"completeness" of an axiomatic system.
___________________
@Note on Euclid and Russell -- construct of setting.
___________________
pa
Except for the difference of opinion concerning the "locale" of an
axiomatic system, we expect that exponents of standard WIE axiomatic
systems would 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,
1) 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.
2) 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.
(a) 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."
.PA
(b) 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.
(c) 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.
3) 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 of the notation in question.
heWORKOVR8 10/22/90 at 16:03
10/18/90 at 00:26:0710/17/90 at 10:12:0310/17/90 at 00:43:07 C. 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 for it. The WIE mathematical languages,
e.g. the various mathematical theories of sets, stand as axiomatic
systems, but the innovators who generated them grant a privileged
position to the WIE grammar and so tacitly rely on its conventions for
symbolizing -- rather than questioning and disclosing these conventions
and characterizing them in general terms, as we do here.
By analogy with the pattern laid out in B above, let us now infer,
and then supply, the missing "parts," and so frame English or set
theory as a version of an axiomatic system. In the process, we shall
account for (or at least incorporate) the features of WIE languages
mentioned above, in our overview of the identity-based WIE pattern.
1) Setting: As noted, we regard setting and undefined terms as
human "doings", silent postulates of an exponent. 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 .
2) Undefined terms: As undefined terms, we propose noun, verb,
and the copula (e.g. 'is').
3) 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) Someone who chooses the above setting thereby "slices up the
world" into two "KINDS." 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 dichotomizing over and
over again within the grammar of a WIE language, on various logical
levels.
(b) Someone who chooses the above undefined terms thereby puts
constraints on the "process of slicing" just described. S/he
subdivides one "kind" into noun and verb, where noun 'is' noun, while
she does NOT hold that verb ("not-noun") 'is' verb . In the same
breath, s/he subdivides the other "kind" 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 "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".
(c) 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.
(i) 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),@ which eventually
consists of "everything else." In addition to 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.
___________________
@We Westerners treat opposing terms as somehow separable, "unrelated."
Watts remarks on this attitude, and calls it an "illusion":
.PA
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 ture of both its Christian and secular, technological
phases. Here, or hereafter, our ideal is a world iln which "there
shall be no more death, neither sorrown, nor crying, neither shall
there be any more pain; for the former things are passed away."
(Revelations 21:4) (Watts, Alan W.: The Two Hands of God: Myths of
Polarity. New York, Brazillier. Paperback edition, 1969, Collier
Books, p. 48)
____________________
pa
(ii) 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 delimited
version of the logic of opposites, so we have examples only from WIE
notational languages.@ 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.
___________________
@Some discursive languages outside the WIE family routinely utilize a
delimited version of the logic of opposites. Sino-Tibetan languages,
for example Mandarin, treat term-pairs, e.g. buy and sell, as defined
on a common domain. As Chu puts it,
.RR L-----------------------------------------------------------------R
... Ideas are often denoted [in Mandarin] by compound expressions
composed of antonyms: for examples, "buy-sell" for "trade,"
"advance-retrea" for "movement," "rule-chaos" for "political
condition," etc. The antonyms are not thought of as
irreconcilable opposites but as being united to form a complete
idea. One of the most important concepts in Chinese philosophy
is expressed in a compound of antonyms, yin1yang2. These two
terms denote two opposing but complementary forces in the
universe, the interaction of which produces all things and the
unity of which reposes in the Ultimate. (Chu, Yu-Kuang:
Interplay between language and thought in Chinese. ETC.: A
Review of General Semantics 22:307-329 (1965), p. 316.)
.RR----!---------------------------------------------------------------R
___________________
pa
4) 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.
5) Postulates: So far as we know, no one within the WIE tradition
has exhaustively characterized the postulates of the WIE frame of
reference. These postulates 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 =_ x .
6) Rules of inference, and
7) 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" stand
for or represent "things," and both follow the same patterns, both
follow the same grammar.
rm 72heWORKOVR9 October 28, 1990 at 6:39
PMOctober 27, 1990 at 1:56 PMOctober 27, 1990 at 9:48 AMOctober 25,
1990 at 10:50 AMOctober 24, 1990 at 2:41 PMOctober 23, 1990 at 2:25 PMD. THE PRESENT NOTATION AS AN AXIOMATIC SYSTEM
As noted above, we treat the constructs of setting and undefined
terms as designating human activities: "something someone does."
1) 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.
2) Undefined terms: As undefined terms, we follow Korzybski's
example and choose structure, order, and relation (Korzybski, 1943).@
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.
3) 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 might work well as an image for a
WIE frame of reference -- which makes it inappropriate 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.
(a) When we choose the above 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, and 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, or by a
single term such as transacting.
(b) 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."
(c) 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, it consists of five points:
1. Our incompletely-informed and inaccurately-informed (symbolic)
'organism'
2. Consists of spatio-temporally ordered "doings" or "happenings"
which occur within a (specific, delimited) setting known as
transacting.
3. By her/his abstracting, our 'organism'elaborates a 'gestalt'
composed of
a) a 'figure' which focally interests the 'organism'
b) specified against a 'background' which does not (at present)
interest her/him.
4. Any 'gestalt' further consists of two 'components'
a) one of which tells about the 'environment', and
b) the other tells about the 'organism' who elaborates the
'gestalt'.
5. In negating a 'gestalt', our 'organism' interchanges the
'figure' and the 'background', and alters none of the other
considerations listed here.
.PA
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.
4) Grammar: We obtain our grammar 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.
Wheneverf we want to give more details about that S , we use the other
two undefined terms, as follows:
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.
5) 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).
6) Rules of inference: For the purposes of this appendix, it
suffices merely to name the rules of inference of the non-standard
notation: Generalizing, Particularizing, Componenting, and Specifying.
7) Standards of proof: Again, for the purposes of this appendix,
it suffices to say that to "prove" an expressing, one demonstrates that
s/he can both derive it from an expressing composed solely of undefined
terms, and can "decompose" 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.
.PA