Download 6 Classical and non-classical science

6
Classical and non-classical science
"What is important, I believe, is that behavioral science should
stop trying to imitate only what a particular reconstruction claims
physics to be" (Kaplan, 1964, p. 11)
There is a difference between ’classical’ and ’non-classical’ physics. In the words of Pattee:
"In classical physics it is assumed that only the final results of measurement, that is, the numerical
values, are the relevant information one needs to explain and predict the behavior of the system.
(...) The measuring device itself is assumed to have vanishingly small physical interaction with the
system and, in contrast to quantum theory, the act of measurement is not recognized in the formal
model. (...) Quantum theory does not allow [the] precise conceptual distinction between laws and
measurements or between the objective structure being measured and the subjective agency of
measurement. (1979, p. 220)
A major difference between what I will call classical and non-classical science is that non-classical
science is qualified by an explicit admission of self-reference, both in calculations and in empirical
findings, whereas in classical science self-reference was ignored or even eschewed.
In this chapter I will maintain that classical science can be characterized as a combination of the realist
and nominalist discourses, a combination that became obsolete when self-reference became a more serious
issue of attention. Classical and non-classical science are understood as rooted in the realist-nominalist
controversy.
I will attempt to explain the integration of the realist and the nominalist discourses in terms of the
invention of ’classical science’, i.e. science in which the observer himself stays out of the domain of
study. I will maintain that in classical science the realist and nominalist discourses could be combined,
whereas in non-classical science they became no longer compatible due to the inclusion of self-reference.
Thus, we will find the following trade-off:
-
-
if self-reference is not allowed to occur in the objects of study, then the observer is permitted to
keep a detached, ’scientific’ position, from which objective, detached, observations are possible;
realist and nominalist positions can be combined into a ’classical solution’, which makes use of
models (meanings) as tools for performing abstract calculations about the dynamics of state
changes (essences) behind the empirical phenomena (appearances/symbols))
however, if self-reference is allowed to occur in the objects of study, then the observer cannot
maintain his detached position; realist and nominalist positions can no longer be combined; the
’classical solution’ breaks down, in favor of two separate, disjoint, modes of describing the
phenomena: one in terms of ’ideal’, unmeasured states, the other in terms of measured phenomena
A conclusion for the field of psychotherapy (section 6.3) will be that self-reference has survived only
within a realist tradition, as a mode of performance usually called ’introspection’, whereas in fact a nonclassical elaboration has been lacking so far.
86
87
6.1. Classical science: the integration of the two discourses
In classical science, i.e. the scientific tradition based upon the ideas and ideals of (among others) Galileo,
Descartes, Locke, Newton and Kant, a reciprocal relation can be recognized between observable (concrete)
and conceivable (abstract) terms: the abstract conceivable can be constructed out of the concrete
observable, and the latter can be deduced from the former. These two movements were symmetrical to
one another, and in fact became more relevant than the old opposition between realism and nominalism.
The introduction of calculus«239» in the natural sciences allowed the usage of formal terms without
the requirement that each step of the calculation corresponded to some state of the system«240».
The status of formal, abstract, terms thus became less relevant. These terms were usually considered to
refer to real, underlying entities, but at other times not to refer to anything, and to have the status of mere
auxiliary tools (for purposes of calculation or argumentation). The domain of empirical applications for
the new natural sciences itself became more and more of focal interest, and the controversy on the status
of universals faded.
More generally, through the construction of calculus present and past phenomena could be explained, and
future phenomena could be predicted (and controlled)«241». By means of calculus it was possible to
formulate general laws of nature and compute their implications. Thus, the tension between two questions
was overcome: the question about the source or foundation of phenomena and the question about the
attainment of a particular goal. Above in section 4.3.4 I qualified these two questions in terms of
’metaphysical explanation’ versus ’technological application’.
6.1.1. Content and form in classical science
In classical science, explanations and applications were recognized as based upon the same mechanisms,
which, formulated in terms of natural laws, could be calculated both forward and backward in time. This
required a partitioning of the world into states (also named phases, or conditions) and the dynamics that
239. I am emphasizing here calculus, such as for instance Descartes’ analytical geometry, and not so much ’scientific method’ (e.g.
as proposed by Descartes), because only calculus allows the computable connection between explanations in terms of backgrounds or
essences on the one hand, and on the other hand practical implications in terms of meanings assigned to empirical findings. The usage
of a scientific method is only a necessary condition to this computable connection. It is not a sufficient one, as is apparent from the
discipline of biology, where the classical scientific method is applied without rigorous results comparable to those in physics and
chemistry (cf. Rosen, 1985).
240. Cf.: "... that it is not necessary (even in the strictest reasonings) significant names which stand for ideas should every time they
are used, excite in the understanding the ideas they are made to stand for. (...) ... in algebra, in which though a particular quantity be
marked by each letter, yet to proceed right it is not requisite that in every step each letter suggest to your thoughts, that particular
quantity it was appointed to stand for." (Berkeley, 1970 (1734), p. 93)
Descartes (1954/1637) would not have agreed with this, since he took his calculations in geometry to concern issues that have
an already established (platonic or ideal) status ("If, then, we wish to solve any problem, we first suppose the solution already
effected..." (1954, p. 6/1637, p. 300)). Nevertheless he was also confronted with numbers that he called ’imaginary’: "Neither the true
nor the false roots are always real; sometimes they are imaginary(*); that is, while we can always conceive of as many roots for each
equation as I have already assigned, yet there is not always a definite quantity corresponding to each root so conceived of" (1954,
p. 175/1637, p. 380)
(*) translators’ footnote:"... This is a rather interesting classification, signifying that we may have positive and negative roots
that are imaginary. The use of the word "imaginary" in this sense begins here."
Cf. also: "If the circle neither cuts nor touches the parabola at any point, it is an indication that the equation has neither a true
nor a false root, but that all the roots are imaginary." (Descartes, 1954, p. 200/1637, p. 393). Thus, notwithstanding his own convictions,
Descartes seems to have accepted the notion of imaginary roots as abstract calculation tools!
241. Cf: "It was part of the incredible insight underlying Newton’s approach (...) to realize that where a particle is going to be must
be somehow entailed from where it is now." (Rosen, 1991, p. 91)
88
ruled the transitions between these states«242».
In a sense, classical science was of a realist signature. The abstract entities it dealt with were believed to
be really existing. But, taken this for granted, irrespective of ontological assumptions, these abstract
entities were also used as instruments for power, or prediction and control, as was for instance the case in
navigation maps (cf. Latour, 1988). Hence, at calculation time«243», also nominalist aspects were
present.
Abstract concepts were now related to concrete, empirically accessible observables in a twofold way: they
were both used as the calculation tools (or, appreciations, integrations, summaries, or models) of empirical
data, thus fitting in a nominalist tradition, and they were also considered as the latent entities behind the
manifest appearances, thus fitting in a realist tradition. In this way, the realist-nominalist distinction, as
introduced in section 4.3:
form:
content:
realist discourse:
essence/
agreed substance
appearance/
disagreed accident
nominalist discourse:
meaning/
disagreed accident
symbol/
agreed substance
integrated to:
classical science:
form:
essence = meaning
(abstract ideas)
content:
appearance = symbol
(concrete data)
The leading distinction became that between form and content, between the abstract and the concrete. The
ultimate elaboration of this came from Kant, in his treatment of the a priori - a posteriori distinction. But
also in Bacon we find already the ’modern’ tendency to arrange facts into abstract rules. The distinction
between substance and accident became less relevant. It became more of interest to those concerned with
epistemology than as a tool for the description and categorization of the world. This is different from the
medieval tradition of aristotelian science. Apart from this, the new leading distinction between form and
content entailed a disregard for rhetorics and in particular a rejection of argumentation based upon
authority or tradition. Issues of debate were established in classical science, at least in principle, in terms
of empirical findings and theoretical models; not in terms of a taxonomy of substances and accidents.
Agreement and disagreement between observers were not recognized to play a constitutive role (cf.
section 4.3) and instead were treated as a distraction from the objective study of Nature.
242. "As Wigner (...) has emphasized, Newton’s greatest accomplishment was not the discovery of the laws, but the discovery of the
crucial separation of the laws from the initial conditions that must be determined by measurements." (Pattee, 1992, p. 182; italics added)
More generally, these initial conditions constitute the system’s initial state, and the natural laws serve to calculate the various
possible changes of state over time.
Cf. also: "Newton’s Laws thus serve to transmute the initial dualism between system and evironment into a new dualism, that
between phase (states) and forces, or between states and dynamical laws. The states or phases constitute a description of system.
Environment, on the other hand, gets an entirely different kind of description; it is described in terms of the specific recursion rule it
imposes on states or phases. It is this dualism between states and dynamical laws that, more than anything else, has determined the
character of contemporary science. (Rosen, 1991, p. 95)
243. cf. Berkeley’s position, as in footnote 240 on page 87
89
The integration of the two discourses in classical science implied that the passage from essence to
appearance (and vice versa) and the passage from meaning to symbol (and vice versa) were considered
parallel movements. ’Appear’ and ’describe’, as well as ’found’ and ’interpret’«244» became
pairwise coupled. Thus, the relation ’appear’ could become an inversion of the relation
’interpret’«245».
abstract form (essence/meaning)
| ↑
analyze | | synthesize
(appear/ | | (found/
describe)| |
interpret)
| |
↓ |
concrete content (appearance/symbol)
We will find an illustration of this integration in section 8.4 in terms of the ’contaminations of the
nominalist discourse’ in psychiatric diagnosis. The combination of meaning and essence has in fact been
the respectable and sensible core mode of thinking in classical science.
In classical science it was assumed that the laws of nature were made of the same stuff as their formal
expressions«246». There was no need to distinguish explicitly between the two. Whenever a theory
proved to be incorrect, it could be dismissed; but when it proved to be correct, the description was
considered as the description of a law of nature. The classical investigator had the conviction that if a
particular mathematical relationship was confirmed by empirical findings, then his formula was apparently
the correct expression of ’how Nature works’. This still holds also for ’modern classical’ research until
now, up to the whole Artificial Intelligence culture that looks for algorithms and procedures«247»
according to which human intelligence works.
Theories were considered descriptions of mechanisms, and mechanisms were composed of structural
constituents that perform each a particular function. Thus, ’how Nature works’ could be decomposed into
structural parts such as each part to have a particular function. Structure could be expressed in terms of
states, and function in terms of dynamics, i.e.: changes of state. Hence, we find another way of saying
that between states (structure) there are particular dynamics (functions) at work.
Once it was believed that a particular mechanism was found according to which particular phenomena
were generated, this mechanism served both as the ground for explanation and as the tool for prediction of
new phenomena. This mechanism, then, was considered a particular Law of Nature (e.g. the second law of
thermodynamics). Such a mechanism was used as the tool for attaining the system’s next states, by
calculating its state transitions.
The mathematics that accompanied classical science were considered a language in which the various
Laws of Nature had been written and the formulations thus obtained were regarded as pertaining to the
states of the system under observation. These states were considered to be really existing. This was a
244. For a discussion of these terms see section 4.3.4, esp. the scheme on page 69. I am proposing ’synthesis’ and ’analysis’ here as
generic terms that encompass realist and nominalist connotations. Whereas realist relations are considered to be ’really existing’, and
thus of a causal (natural) variety, the nominalist relations are considered as performed by an actor, and thus of an artificial (symbol
processing) kind.
245. together forming the pair ’expression-impression’ (cf. section 4.3.4)
246. cf. section 6.1.3, also footnote 256 on page 94
247. or their "functional equivalents"
90
major assumption that underlay the usage of mathematics in classical science«248».
In particular, the axioms of euclidean geometry were regarded as corresponding to the physical world, and
for that reason they were taken as true. Furthermore, this truth could be extended to all theorems that
were derivable from the axioms, and this to the degree that the truth value of all theorems was considered
to be determinable.
If a theorem is true, then this truth should also be demonstrable. Conversely, if a theorem is deducible
from its axioms, then its truth can be said to be a property that is "hereditary" «249»from the
axioms. In terms of the two discourses that I introduced, this would look thus:
form:
content:
realist discourse:
essence:
’real’ truth
(axioms correspond
to empirical reality)
appearance:
theorem
nominalist discourse:
meaning:
proved truth
(theorem’s truth
as proof outcome)
symbol:
theorem
We thus find for classical mathematics an integration of the two discourses parallel to that of the classical
empirical sciences:
classical empirical science:
essence = meaning
classical mathematics:
real truth = proved truth
Notice that the assignment of the truth value ’T’ to a theorem is a particular case of meaning assignment
to a symbol. The meaning ’T’ thus assigned to a proved theorem coincides with the truth of the axioms,
which are taken to be in correspondence to reality. The theorem is regarded both a (realist) appearance of
these axioms and the (nominalist) symbol to which the proved truth is assigned.
Classical physics would take a system’s state«250» both as an underlying entity (essence) and as a
conceptual tool for calculations (meaning). The empirically observable phenomena are to be understood as
the products (appearances) of this essence, but also as the symbols to which the observer assigns a
meaning. Thus, in classical (Newtonian) mechanics a compression tank was assumed not only to have a
particular state which is a real entity and which is expressed in the system’s observable behaviors (as
248. Cf. also:"Pure mathematics, as synthetic knowledge a priori, is only possible because it bears on none other than mere objects
of the senses, the empirical intuition (of space and time), and can be so grounded because the pure intuition is nothing but the mere
form of sensibility which precedes the real appearance of objects" (Kant, 1783, §11/1971, p. 39-40)
and:
"Pure mathematics, and in particular pure geometry, can only have objective reality under the condition that it bears merely on objects
of the senses, in respect of which this principle holds good: that our sensible representation is in no way a representation of things in
themselves, but only of the way they appear to us. From this it follows that the propositions of geometry are not determinations of a
mere creature of our poetic fantasy which could not be reliably referred to real objects, but that they hold necessarily of space and hence
also of everything that may be encountered in space, because space is nothing other than the form of all outer appearances under which
alone objects of the senses can be given to us." (Kant, 1783, §13, note I/1971, p. 43)
249. I borrow this term from Nagel & Newman, 1958, p. 51.
250. See the first lines of my quotation from Jammer (1966) quoted below in section 6.2.2, on page 99, for a definition of the
concept of ’state’ in classical mechanics.
91
appearances); but also was such a state considered a qualification of these observables (as symbols), and
as such the state was a meaning assigned to them, a tool, indeed: a model, for calculating and controlling
the system’s features«251».
To take an example, let us regard a formulation on the observation of experimentally generated pain in
animals: "Cats also gave "pain suggestive" responses to stimulation in the superior and inferior colliculi"
(Milner, 1971, p. 168).
Here the laboratory animal’s pain seems to serve both as an abstract essence that is not at all immediately
obvious to the investigator. The investigator only seems to permit himself to observe the concrete
behaviors, in search of pain centers in the brain that could become manifest in particular loci of electrical
stimulation. Meanwhile, it seems, the animal’s behavioral responses are studied as possible manifestations
of pain. Here, the animal’s pain is used as an abstract construct, an essence, possibly situated at the top of
one’s electrode, and the source of behavioral manifestations. Furthermore, the term ’pain suggestive’ is
used in order to propose ’pain’ as a possible meaning that could be assigned to the behaviors observed.
"Is this to be qualified as pain?", the investigators must have been thinking, while watching the animal’s
responses. Here the meaning ’pain’ is the investigator’s way of dealing and relating with the essence
’pain’. Thus, in this example, ’pain’ is used in two ways: as an essence of the behavioral phenomena, and
as a meaning assigned to them.
6.1.2. The modeling relation in classical science
According to Rosen, the idea of a ’natural law’ contains the idea of a correspondence between a natural
system and a formal model of it. In the latter, formal inferences can be performed, that in a way
correspond to causal relations within the natural system. Thus, a ’modeling relation’ is possible, consisting
of a natural system and a formal system, between which the functions ’encoding’ and ’decoding’ hold.
A model is a formal system (F) that consists of a set of terms between which formal relations of inference
(3) hold. Furthermore, a model is related to a natural system, in two ways. First, there is a function of
encoding (2); second, there is a function of decoding (4). The inferential relations within the model are
meant to represent causal relations (1) within the natural system of which the model is made.
A model is said to commute (or: predictions are said to come out) if relation (1) leads to the same
phenomena as (2) + (3) + (4). That is, ’encodings’ (measurements) can be made, upon which some formal
inferences can be performed within the model, after which ’decodings’ (interpretations) can be made that
are indistinguishable from the outcome of some causal processes within the natural system (cf. Rosen,
1991, p. 60). In this way can inferential processes within F(ormal system) be a model of causal processes
within N(atural system):
251. Margenau discusses ’state’ as something that fits in with both discourses. The realist formulation is: "... valid states are real, for
they are verifacts. The state p,r of a particle is realized when it functions properly in an empirical circuit of verification (...). They do
not exist primarily because they are measurable, but because 1) they are satisfactory causal variables and 2) because they are linked to
sensation, i.e. observation, by statable rules of correspondence." (Margenau, 1949, p. 298)
and Margenau’s nominalist formulation:
"The postulate [of causality] requires that a state be a collection of observables suitably selected to insure predictability, or, more
carefully put, a state must comprise a "just sufficient" set of variables, or observables, so that it provides through them enough
information for rendering the solution of certain equations, called laws of nature, completely definite. This is, for example, why
momentum and position define the mechanical state of a particle, the laws of nature being Newton’s laws of motion" (ibid.)
92
The relations within F are considered to match those within N. They are parallel«252».
A prerequisite assumption in classical science was that the observer’s measurement activities did not
basically disturb the object of attention. If some impacts of observation were unavoidable, then they were
considered to be due to mechanisms that were unrelated to the mechanisms studied; in other words:
measurement was a matter different from the objects measured.
The same was true for control and manipulation: if a particular effect was looked for, e.g. shooting a
bullet from a cannon, then the acts of exactly positioning the physical cannon and installing its angular
directions, though of immediate influence on the bullet’s course, were considered physically independent
events, for which a separate model, disjoint from a model of the bullet’s course, could be given. Thus, to
implement the model’s computations was a matter different from applying the model. I will return to the
notions of application and applied science in section 9.1.1.
This means, in fact, that the functions ’encode’ and ’decode’ were considered to be separate and disjoint
parts, not interfering with the processes (3) of F, nor with those (1) of N! They could be subsumed under
the model as separate parts, representing the mechanisms of the measurement (or control) processes. They
could be added to the system modeled, as additional parts, and a model of them could be added to the
model of the system. For instance, in section 6.1.3 on Galileo we will notice that the processes related to
friction, taking place in the experimental setups for measuring gravitation, had to be considered as
complicating contaminants, as properties of the imperfection of the measurement configuration; not as part
of the natural system to be modeled!
The causal workings of the devices for measurement and manipulation were considered to be disjoint from
the causal workings of the object studied. Thus, given a model of a natural system, it was considered
always possible, at least in principle, to perceive a new natural system N’ that contains the devices for
measurement and control, and to construct a new model F’ that contains descriptions of the encode (2)
and decode (4) functions, so that, as a result, the remaining encode (2’) and decode (4’) functions, those
between the new model F’ and the natural system N’, were considered obvious and non-problematic in
classical science. No explicit understanding was required for performing them. In the terminology of our
chapter 3, they operated as tokens, as first order distinctions, through which the natural system could be
observed! In terms of James, they are the stream of consciousness’ transitive parts, the parts that remain
252. Cf.: "What can be defined in [classical] physical theory can be physically observed. And conversely, what can be physically
observed can be described and defined in physical theory" (Löfgren, 1992, pp. 136-7).
This remark can be appreciated best if it is added that Löfgren takes ’observation’ to be a case of ’interpretation’ (this will be
dealt with more extensively in section 6.2.3), and ’definition’ to be a case of ’description’. His statement then amounts to: ’what can be
described in physical theory can be physically interpreted’, and vice versa. Hence, the two critical discourses, the realist and the
nominalist, are considered equally powerful, if not equivalent, for the case of classical physics.
93
beyond the scope of attention while thought was performed.
The model, therefore, was a description of a set of states and their interrelations, and as such it was built
within a nominalist discourse; it was a meaning assigned to the empirically obtained data. But qua
meaning, it referred to some underlying real state behind those data; and as such the model served to
maintain realist thinking!
In fact, what happened was that, due to the triviality (in principle) of encoding and decoding relations,
properties of the model were not distinguished unnecessarily from properties of the natural system. The
natural system (essence) and a model (meaning) were considered not only to match, as in Rosen’s
’modeling relation’, but in fact to coincide! The model is obscured by that which it expresses: the natural
system. We recognize here a phenomenon we discussed before«253» in terms of incorporation. For
it is the usage of a model as a tool for perceiving an essence behind observational data, that makes
invisible to its user that the model originally was a meaning that he assigned to his data. The formal
apparatus, in classical science, instead of being a mere representation of the natural system, has obtained a
status comparable to that of the blind man’s stick, through which the researcher touches for the natural
system that is of his interest! The model has become his way of dealing and relating with the natural
system.
This, I think, is why the opposition between realist and nominalist positions became of less importance, as
calculus developed as a tool for modeling nature. Whereas before they had been vigorously incompatible,
they now could become of mutual support. This was, of course, at the price of sticking to some
assumptions, especially those on the possibility to include the encode/decode relations in the model, as
separate, disjoint parts.
As long as the world was believed to be made up of mechanisms (even in the case of such difficult
subject matters as mind, embryogenesis, or acculturation, etc.) then there was no need to look for
properties of nature that could not be decomposed into disjoint units, and expressed in terms of
mechanisms, nor to look for the limits of formal descriptions. For instance, the need was not felt to look
for natural systems that contain a model of themselves, and to study the problems of encoding such
systems into models, and of decoding such models«254». This need, in fact, became felt only with
the rise of self-reference, both as a formal and as an experimental problem. When the encode and decode
relations became themselves of substantial interest to researchers, the tables turned and the issues of
classical science were no longer universal, but ’special cases’ of the issues of non-classical science.
253. section 4.2
254. This has been one of Rosen’s (e.g. 1978) ideas on the organization of living systems.
94
The shift from the realist-nominalist controversy towards a greater emphasis upon the abstract-concrete
dimension can be recognized par excellence in the work of Galileo (1564-1642). His major
accomplishment is the construction of what has become a prototype of modern empirical
science«255», one that uses "a methodology that provided a central place for mathematics in the
experimental manipulation of ordinary sensory experience" (Butts, 1978, p. 78). The realist-nominalist
dichotomy does not do justice to Galileo’s position. In fact his work can be taken as a point of departure
from this dichotomy. I will spend some words on this now, for the sake of illustration.
6.1.3. Galileo
Galileo is generally considered to be a mathematical realist, taking mathematical truths (of geometry and
arithmetics) as the language in which the book of nature has been written«256». Furthermore
according to his realism the mathematical forms are considered to be the essences of the observable
phenomena, and the latter are considered to be the imperfect appearances of those forms. Their
imperfection is due to all kinds of material impediments«257». Hence, the mathematics are
considered as the unattainable limits of experimental purity«258».
"[Galileo] wants to know what would happen if moving bodies of different weights were dropped
in a medium devoid of resistance. To find out, he tries a series of media of less and less resistance
and finds that difference in weight affects speed less and less until in the most tenuous medium
available, the difference is so small as to be almost unobservable. We may believe, he concludes,
"by a highly probable guess that in the void all speeds would be entirely equal."
This "asymptotic" method assumes that as the "impediments" are removed, nature is found to
act in a simpler and simpler way, closer and closer to the mathematically-expressed law that is
being proposed. The law is true of Nature, even though in vacuo fall does not occur in Nature. It is
true as a limit, departures from which (due to causal "impediments") can later be calculated and
allowed for." (McMullin, 1978, p. 233)
We recognize here, in the idea of the asymptotic method, a particular encoding relation (see section 6.1.2)
between a model and the physical reality it represents.
Of interest is also Galileo’s usage of the so called reasoning ex suppositione, i.e. arguments that assume
the real existence of the things spoken about«259» that he is talking about. Wallace (1978, p. 127)
considers this a major indication of Galileo’s realist attitude. Butts (1978, p. 83/footnote 4) compares
255. Cf.: "[Galileo’s free fall] law is simple and well-known: all physical bodies in a state of free fall (regardless of their differences
in weight, the property the Aristotelians had fastened attention upon) accelerate at the same rate in the direction of the surface of the
earth. The way in which Galileo arrived at this law is a classic case of ’deducting the material hindrances’. His own experiments with
rolling balls down inclined planes had shown him that according to normal commonsense observation (Aristotelian observation?) the law
of equal acceleration does not hold. The Aristotelians had concluded that the acceleration of a falling body depends upon its weight and
also upon the medium through which it is moving. Galileo’s insight consists in denying both Aristotelian points." (Butts, 1978, p. 79)
256. See for example Pitts (1992, p. 1) who starts his book on Galileo with a famous quotation in which Galileo calls the universe a
book, written in the language of mathematics.
257. "An "impediment" is not (...) something which prevents, or lessens the force of, the application of mathematics to nature.
Rather, it denotes a difficulty in realizing in the complexity of the material order the simple relations of the mathematical system. But to
the extent they are realized, mathematics can tell us what to expect." (McMullin, 1978, p. 230)
258. See also Garrison, 1986.
259. Reasoning ex suppositione was a realist tool of thought. The thing argued about is assumed to be really existing. On the other
hand, what the nominalists used was called reasoning ex hypothesi; the latter means that the thing argued about is introduced only for
the sake of argument, as a useful fiction (cf. McMullin, 1978, p. 250). This is how it was also useful for purposes of calculation.
Wallace (1976, p. 81) calls reasonings ex hypothesi "dialectical attempts to save the appearances - a typical instance would be the
Ptolemaic theories of eccentrics and epicycles."
95
Galileo’s realism with that of Descartes. Both Galileo and Descartes distinguished between the abstract
substance of a thing and the way it appeals to our senses«260».
However, a realist understanding of Galileo is criticized by McMullin (1978, p. 234ff.) who emphasizes
that Galileo’s usage of the reasoning ex suppositione is more ambiguous. McMullin’s point is that for
Galileo the ex suppositione reasoning became more and more hypothetico-deductive in character. Though
Galileo stuck to his claim that his mathematical descriptions of motion (a.o.) were in accordance with
reality, he also found a truth criterion in their mathematical character and their usefulness for prediction of
new phenomena. This, indeed, is what we would now call a model. Thus, according to McMullin (p. 223)
"in Galileo’s later works, "a truly novel relationship between experience and scientific reason appeared," a
new notion of explanation which "finds its true meaning in the anticipation of facts yet to be discovered,"
rather than in the description of causes"«261».
Pitt (1992)«262» even calls Galileo an instrumentalist (p. 62ff.), who gives priority to both
mathematics and the observable results that could be obtained using these mathematics. This
instrumentalism has roots in medieval nominalist schools, such as those of the ’calculatores’ (cf. Wallace,
1978, p. 124ff.), who took abstract concepts as mere tools for reasoning, first of all reasoning about
motion, without claiming that these notions corresponded to really existing entities or essences. But
Galileo’s conceptions are not identical to this nominalism. In fact, the realist-nominalist categorization
does not longer apply to Galileo:
"Thus, at the heart of Galileo’s most important scientific contribution we also find his most daring
methodological innovation. Galileo is claiming that the proof of the postulate needed in the
demonstration of the law of free fall will be the production of empirical truths. Now, if Galileo
were truly convinced that the structure of the world was mathematical, it would seem appropriate,
either here or later when those truths were produced, to argue for that claim using the empirical
proof of the necessary postulate as conclusive evidence. But he doesn’t. And, because he fails to
make that claim, it seems unreasonable to force any label on him" (Pitt, 1992, p. 50)
Butts gives a different emphasis:
"Galileo’s confidence in mathematics and in the efficacy of experimentation must be taken as a
philosophically unjustified confidence. In part the confidence is justified ex post facto by the
positive results of physics built upon his expectations, and such success was one of the outcomes
that Galileo trusted. But his mathematical realism had to wait for the philosophical justification he
himself had failed to provide." (Butts, 1978, p. 81)
In other words: Galileo may have believed in the realist status of his enterprise, and he may have argued
for it, but for his factual modes of performance the question of realism versus nominalism did not matter,
however he might have liked to have it otherwise. What mattered was that his formal descriptions were so
successful models, as to contribute to the onset of the classical tradition of science, where realist and
nominalist oppositions were fading out.
The classical integration of the two discourses, however, did not hold for those domains of research where
self-reference slipped into the operations of the researcher. Here classical science attained a limit, beyond
which essences and meanings did no longer coincide. This domain can been called non-classical science.
260. Cf. the quotation from Descartes in section 4.3.2 on page 64.
261. McMullin quotes here from M. Clavelin, The natural philosophy of Galileo. Cambridge (Mass.): MIT Press, 1974.
262. He returns partially from an earlier opinion: on an earlier occasion (Pitt, 1978, p. 193) he explicitly called Galileo ’a realist, not
an instrumentalist’.
96
6.2. Non-classical science and self-reference in the researcher’s operations: the
realist-nominalist controversy revisited
As paradigms of non-classical science are to be considered the works of Gödel, Bohr, and perhaps also
William James. More recent non-classical research programmes«263» can be found in Pask (e.g.
1975), Rosen (e.g. 1991) and Kampis (e.g. 1991). In non-classical science the encoding and decoding
functions cannot be added to the model as separate units, as they cannot be performed as operations that
are disjoint, in principle, from the natural system to which they are applied. Hence, it became more
troublesome to distinguish between the model and the reality modeled, as the encoding or decoding itself
became non-trivial and of substantial interest. The models in non-classical science were models of
encoding or decoding functions as well as of the things encoded/decoded. As a result, such models did no
longer claim to be complete; they were partial models, especially when the model pertained to how it had
been encoded, or to how it should be interpreted«264». Hence, the distinction between the execution
of a set of formal operations (the application of a model) and its decoding (the implementation of the
model’s outcomes) were no longer as clear as they had been in classical science.
Hence, the idea that all performances of a system could be caught in strict descriptions, and eventually be
programmed on computers in terms of calculations, lost a major claim, viz. that of its universality (the so
called Church-Turing thesis). This claim has been a leading idea in Artificial Intelligence. Rosen (1991,
pp. 203-4) discusses its limitations in terms of the impossibility to describe semantic relations in terms of
mechanist (and hence: effectively computable) models (cf. also Rosen, 1962). Rosen and Kampis,
however, argue for some limitations to the validity of this thesis. Rosen uses Gödel’s famous idea (cf.
Nagel & Newman, 1958) of the unprovability of a particular self-referential, but true, statement. In a
similar vein, according to Rosen, it is possible that a particular materially realized (physical) system
contains aspects of self-reference, and for that reason cannot be represented and decomposed in terms of a
step by step procedure (’effective computation’). Living beings are such systems. A device that operates
by means of a program, however complicated, cannot be a proper model for a living being, which is selfreferentially organized. Kampis (1991, p. 472ff) gives an extensive treatment of these problems,
maintaining that "thinking and processual logic (...) can be creative and can cross all algorithmic barriers
and enable humans to indeed transcend the Gödelian limits that bound computers." (p. 480)
One of the most pertinent properties of classical science had been specified as a prohibition (Whitehead &
Russell, 1910-1913) of self-referential forms (e.g. paradoxes) to occur in logical expressions«265».
If this rule is violated and self-reference is allowed to enter into a scientific procedure, then it becomes
impossible to keep a rigorous bookkeeping between properties of the object studied, and properties of the
research process.
Nonclassical science took self-reference explicitly. It was no longer possible to combine realist and
nominalist assumptions, but instead a renewed split arose. The pivotal characteristic of non-classical
science is that some aspects of the object of study have become indistinguishable from the researcher’s/
observer’s own operations. Furthermore, the impact of the researcher/observer upon his object of study
becomes substantial to the extent that the outcome of the research efforts are ineradicably changed by
these very efforts. I will illustrate this in terms of Gödel’s famous undecidable proposition, and in terms
of some of Bohr’s ideas on complementarity.
263. Maturana & Varela (e.g. 1980) do not express their ideas in terms of models of natural systems; Maturana’s (1987a) theory of
the observer would certainly count as non-classical, as would Varela’s work with Thomson and Rosch (1991). Varela’s work in
cognitive science, on the other hand (e.g. 1989), tends more to classical approaches.
264. Cf. Lögren, 1990; see also section 6.2.3.
It is the impossibility to construct a complete formal (mechanist) model of the circularity of the living organization, that brings Rosen to
propose a comparison with semantics:
"In fact, it is not too far wrong to say that an organism (...) is itself like a little natural language, possessing semantic modes of
entailment not present in any formal piece of it that we pull out and study syntactically." (1991, p. 248)
265. Russell is said to have been delighted when the prohibition of self-referentiality was finally proved to have been incorrect
(Spencer Brown, 1972).
97
6.2.1. Gödel’s formal undecidability: the proof process mixes up with the contents of the proof
Hofstadter (1979, pp. 420ff.) discusses Cantor’s so called ’diagonal argument’, which has been used to
prove the impossibility to assign a unique positive integer number to each element of the set of real
numbers. In classical mathematics, the mathematician’s procedure itself would remain beyond the scope of
theorizing, but in Cantor’s diagonal argument this was no longer the case. Now the act of encoding
became substantial.
One of the outcomes of the crisis of mathematics that developed during the turn of the 19th century, was
that the blend of the two discourses was made undone. Among other things, this was an impact of the
discovery of the so called non-euclidean geometries. Once it was accepted that the axioms of a
mathematical system did not necessarily correspond to nature, their truth was no longer a matter of
correspondence, but rather one of arbitrary choice. Formal axiomatic systems were now primarily
considered as a matter of definition of terms, not as descriptions of Nature, and the definitions of axioms
and other mathematical terms became regarded primarily as pertaining to their use in calculations, not as a
reference to something in empirical Nature. This culminated in the quest for a complete formalization of
mathematics, so that all mathematical truths were to be made mathematically provable. As a result, it was
attempted that mathematics was to lose all its apparent reference to any reality, and to gain an absolute
rigor. This was David Hilbert’s programme.
Instead of the correspondence question, the formalization of mathematics required that the axioms of a
particular mathematical system, if not true in themselves due to a correspondence to the physical world,
were at least consistent with one another«266». This, in fact, led to a search for criteria to decide
the consistence of systems of axioms, and it is with respect to this search that we find Gödel’s famous
proof of the necessary incompleteness of axiomatic systems in the field of arithmetics. His proof amounts
to the rejection of the idea that a system of axioms can be proved to be complete. This is to say that for
any axiomatic system of arithmetics there will be at least one true proposition that, though formulated
according to the proper syntax, cannot be proved true or false within this axiomatic system. It is called
’undecidable’. A statement that maintains its own undecidability, then, may be true yet (and: therefore)
undecidable. The truth of such a statement is beyond the domain of formalization of the axiomatic system.
The crucial property of such an uncanny proposition is that it pertains to its own provability. This is what
the famous sentence constructed by Gödel says«267». Here the predicate of provability itself is
mapped, in an intricate way, to the contents of the sentence to be proved. As a result, a paradox is
constructed which effectively impedes the assignment of a truth value to the sentence (and this is
precisely what the sentence is maintaining). Henceforth it was considered impossible to attain the rigor of
complete formalization in mathematics. The question remained: if the truth of the sentence cannot be
formalized, then what is it?
As we are faced with the existence of true propositions that cannot be assigned a truth value within an
axiomatic system, we are brought to the core of the matter: a split has emerged between what is true with
respect to an axiomatic system on the one hand, and on the other hand what can be proved within it. In
the words of Wang (1988):
"I believe that [Gödel’s] idea is that his [incompleteness] theorem presses upon us the need for
’assumptions essentially transcending arithmetic’ even for solving problems in arithmetic, just as
we use physical laws that transcend sense perception. G[ödel] then says that, of course, under these
circumstances mathematics may lose a good deal of its ’absolute certainty’" (p. 315)
and:
"The contrast between formal systems and the axiomatic method (as G appears to understand them)
may be seen as a fundamental aspect of what might be called G’s dialectic of the formal and the
266. cf. Nagel & Newman (1958, p. 14)
267. Lucid discussions of his famous 1931 paper can be found in Nagel & Newman (1958) and Hofstadter (1979).
98
intuitive.
(...)
His incompleteness theorems are a spectacular result of his application of the dialectic between the
intuitive concept of arithmetic truth and the more precise concept of formal provability as revealed
by concrete instances of formal systems. (...) The dialectic is especially transparent in the process
of G’s discovery. He first saw that arithmetic truth is not definable in arithmetic. Then he noticed
that provability (in a formal system) is definable, and constructed a proposition that is true and
expressible in the system, but not provable in it." (p. 201)
In classical mathematics this difference did not exist. But now that a split between ’real’ truth and proved
truth has emerged, the former does not, as before, pertain to empirical reality. Instead, it is often
considered to pertain to some ideal, platonic, reality«268».
For our present purposes it is relevant to notice that a major element of Gödel’s proof was the translation
of meta-mathematical statements (such as about the consistency of a particular axiomatic system) into
number theoretical propositions. In other words, it was the formulation of statements which were about
number theory, in terms of propositions about numbers. In the case of Gödel’s proof, it was a statement
about the absence of a particular proof process itself that was reformulated in terms of numbers. Thus, a
statement about a proof process became treated as if it were ’just’ a matter of numbers, and the contents
of the proof were mixed up with a numerical translation (the so called ’Gödel-numbering’) of the proof
process itself.
The outcome of the proof process is that the sentence constructed is not decidable. This is precisely what
the sentence itself says. Its truth, therefore, exists as the impossibility to prove it«269» within the
confines of the axiomatic system in which it has been formulated! It is this circumstance that elevates the
truth of Gödel’s sentence above the truth qua provability that exists within an axiomatic system. The truth
of the Gödel sentence concerns the proof process itself, and hence the computational acts of the
mathematician. Thus the sentence describes an act of assignment of a meaning (’undecidable’), such that
among the symbols to which this meaning is assigned, the very meaning to be assigned has been encoded.
Indeed, a divergence has occurred between a ’real’ (platonic) truth (viz. the incompleteness of axiomatic
systems and the undecidability of self-referential Gödel-sentences) and a proved (formalized) truth (such
as the truth of other, non-selfreferential theorems within an axiomatic system). Notice also that the
difference between the proof process and its subject matter has become less clear.
As has been said above, a ’real’ truth is something that is maintained within a realist discourse; a proved
truth occurs in a nominalist discourse, where it can be assigned to a theorem as a meaning to a symbol.
The self-reference of Gödel’s sentence, therefore, is one that occurs within a nominalist discourse. The
qualification ’undecidable’ is assigned to this sentence as a final meaning, after attempts to prove it true
or false have failed. More precisely, the qualification ’undecidable’ pertains to these failures. Hence, its
truth is that of the necessity of failure of proving this sentence within the axiomatic system within which
it has been formulated. This truth, therefore, pertains to the limits of provability. Though Gödel
considered this as a ’real’ truth, we may notice at this place that it does pertain to (the limits of) the
mathematician’s operations. It is the self-reference of these operations that turns out to be self-defeating.
268. Cf.: "Classes and concepts may, however, also be conceived as real objects, namely classes as "pluralities of things" or as
structures consisting of a plurality of things and concepts as the properties and relations of things existing independently of our
definitions and constructions.
It seems to me that the assumption of such objects is quite as legitimate as the assumption of physical bodies and there is quite
as much reason to believe in their existence. They are in the same sense necessary to obtain a satisfactory system of mathematics as
physical bodies are necessary for a satisfactory theory of our sense perceptions and in both cases it is impossible to interpret the
propositions one wants to assert about these entities as propositions about the "data", i.e., in the latter case the actually occurring sense
perceptions." (Gödel, 1990 (1944), p. 128)
Wang (1988, p. 188) refers to Gödel’s position as a ’conceptual realism’.
269. shadows of a ’via negativa’, cf. chapter 7
99
More about the limitations of self-referential operations will be said in chapter 7«270». First I will
turn now to a comparable situation of self-referential operations which can be found in the domain of
measurement of quantum phenomena.
6.2.2. Bohr’s understanding of complementarity in quantum mechanics: the measurement process
mixes up with the contents of the measurement
Bohr’s commitment was to find a new conceptual framework that could account for the anomalies he
encountered within the framework of classical physics. His ’principle of complementarity’ was introduced
to this purpose. His (e.g. 1934) topic of concern was that during quantum measurements an interaction
occurred, inevitably and necessarily, between the measuring device itself and its object. The measured
properties of this object then could no longer be conceived as existing irrespective (and independent) of
the measuring device.
Though it is possible to define a quantum particle’s development in time (e.g. according to the so called
Schrödinger wave equation«271») and describe its course in terms of causally determined changes,
this course of the particle remains inaccessible to empirical observation. We can either (obtrusively)
observe the system’s spatiotemporal state, or we can describe (unobtrusively) the system’s abstract causal
development. But we cannot integrate the two into one coherent representation.
Jammer summarizes Bohr’s position on complementarity:
"The "state of a system," as understood, for example, in ordinary mechanics, is the set of all the
(position) coordinates and the momenta of the constituent parts and implies the possibility of using
these data for the prediction (or retrodiction) of the structural properties of the system. Prediction
(or retrodiction), however, is possible only if the system is closed, that is, unaffected by external
disturbances. For an open system, strictly speaking, no "state" can be defined. Now, the evolution
of the structural properties of the system is governed by the law of causality; their progress in time
is the causal behavior of the system. But according to the quantum postulate, in atomic physics,
any observation of the system implies a disturbance. In other words, a system, if observed, is
always an open system. A space-time description, however, presupposes observation. Hence,
concluded Bohr, the claim of causality excludes spatiotemporal description and vice versa. The
usual causal space-time description, that is, the simultaneous use of complementary descriptions, is
made possible in classical physics, argued Bohr, merely because of the extremely small value of
the quantum of action "as compared to the actions involved in ordinary sense perceptions.""
(Jammer, 1966, p. 352)
Thus, what we could measure, according to Bohr, was no longer indicative of the (conceived) state of the
system before measurement! Clearly, such a situation does not fit with the assumption, held by classical
science, that a system’s state qua essence coincides with its state qua meaning«272». We meet here,
therefore, a renewed divergence of the two discourses. We recognize this divergence in Bohr’s opposition
of ’definition’ and ’observation’:
"On one hand, the definition of the state of a physical system, as ordinarily understood, claims the
elimination of all external disturbances. But in that case, according to the quantum postulate, any
observation will be impossible, and, above all, the concepts of space and time lose their immediate
sense. On the other hand, if in order to make observation possible we permit certain interactions
with suitable agencies of measurement, not belonging to the system, an unambiguous definition of
270. The reader may be reminded of the distinction I made in section 4.3.4 between realist relations ’appear’ and ’found’ versus
nominalist relations ’interpret’ and ’describe’. The latter were associated with the actions of an observer, the former not. The selfreference of Gödel’s sentence is one of nominalist relations.
271. Though Bohr (1928, p. 589) does mention Schrödinger’s work, the reference to his wave equation has become conventional
since von Neumann (1932, p. 5).
272. See section 6.1.2, esp. footnote 252.
100
the state of the system is naturally no longer possible, and there can be no question of causality in
the ordinary sense of the word. The very nature of the quantum theory thus forces us to regard the
space-time co-ordination and the claim of causality, the union of which characterises the classical
theories, as complementary, but exclusive features of the description, symbolising the idealisation
of observation and definition respectively." (Bohr, 1928, p. 580/Collected Works VI, p. 148)
The realist discourse is the one in which causal laws are expressible that are valid for the undisturbed
object, the nominalist discourse is the one in which spatiotemporal measurements are obtained, those that
can be used for (statistical) prediction and control«273», but which do not allow a precise account
of the causal development of individual quantum objects«274».
What impedes the possibility of an all-encompassing formulation in line with the classical solution, is the
transition from the causally determined flow of events to the a-causal situation during and after the
measurement interaction. This transition itself cannot be measured, whereas, furthermore, each
measurement disturbs the object measured in an unpredictable way. It is precisely at the encounter
between the measured system and the measurement device that a discontinuity is created in the quantum
system’s state (a so-called ’collapse of the wave function’)«275». This discontinuity is what
separates here the realist from the nominalist discourse.
Thus, we can compare mathematics and physics with respect to the split between realist and nominalist
discourses:
mathematics
physics
realist discourse:
essence
’real’ truth’
unmeasured state,
causally developing
nominalist discourse:
meaning
proved truth
spatiotemporally describable
state, tool for statistical
prediction
The crux of the matter is that it is impossible to measure the things that happen when a measurement
device interacts with a quantum object and disturbs it. Dependent on the measurement arrangement used,
and dependent of features of the measurement interaction itself (that cannot be measured) the wave
function collapses in one way or other. Different measurement arrangements lead to measurement results
273. i.e., in terms of chance distributions of measured events
274. A modern elaboration of this has been given by Pattee. This author concludes from Bohr’s results that complex phenomena
require an approach in which two complementary languages are required, one concerned with (dynamic, physical) laws and one with
(static, symbolic) constraints or (computational) rules. Laws and constraints, according to Pattee, can never be reduced to one another,
and together they constitute two complementary modes of description of empirical reality:
"In order to justify the need for a complementary mode of description we must look for significant situations where one mode
of description fails, and fails in such a fundamental way that it cannot be patched up by adjustments of parameters or functional forms.
Such situations are well known in dynamical descriptions. They are called singularities by mathematicians and instabilities by
physicists." (Pattee, 1978, pp. 198-9)
Furthermore, according to Pattee, a measurement is to be seen as a transition between these two modes of description: "Since
(...) both laws and computation are universal, there appears to be an ambiguity in where lawful description should end and
computational description should begin. Measurement is, by definition, the process that separates the two" (Pattee, 1992, p. 183)
Notice that measurement, thus understood, occurs at the transition from a dynamic to a symbolic domain, not at the reverse
transition. According to Pattee, Bohr wanted to explain the measurement process in uniquely causal terms, and hence was faced with an
infinite regress, whereas in fact he needed a mode of description that was complementary to the language of causal (dynamic) processes
(cf. Pattee, 1992, p. 183).
It is interesting to notice that to Pattee’s two complementary modes of description (’laws’ and ’constraints’) correspond to the
realist and nominalist discourses respectively. The former mode enables explanations; the latter enables descriptions in terms of
information processing.
275. During this transition the system’s state parameters collapse from complex values to real values, cf. Penrose (1989, p. 250)
101
that cannot be combined into one representation. The properties measured are not compatible (such as:
wave and particle) or cannot be measured simultaneously (such as: position and momentum). As a way of
dealing with this uncommon situation, Bohr proposed to take into account how an experimental
phenomenon had been obtained«276», and, furthermore, "that we must, in general, be prepared to
accept the fact that a complete elucidation of one and the same object may require diverse points of view
which defy a unique description."«277». This conception of complementarity is called by von
Weizsäcker (1955, p. 522) ’parallel complementarity’.
The compilation of these diverse points of view is a task within the realist discourse, which is fit for
reconciliating the diverging varieties of appearance with respect of one single underlying entity. In this
discourse Bohr’s term ’definition of the state of the system’«278» is understood as pertaining to the
essence behind the empirical phenomena, and as such it aims to provide a description of the ’pure’,
undisturbed state of the system; a description, that is, of a side of the system that cannot be approached
empirically.
It is interesting to make here a comparison with Galileo’s idea of mathematics as describing a reality that
is freed from the material ’impediments’ that make up the imperfections of physical phenomena. This
reality, according to Galileo, can only be approximated in experimental arrangements«279», but not
really attained in its purity. There is, however, one important difference between Bohr and Galileo. As we
saw, the issue of realism versus nominalism (the reality of the pure mathematical forms) was for Galileo’s
scientific practice not too vital. His experimental approximation of the pure forms was considered a matter
of degree, and the degree he needed was ruled by the prospects of prediction. In the quantum situation, on
the other hand, empirical approximations of the pure form were no longer thinkable, since the pure form
was severely disturbed by the measurements. Here the realist versus nominalist controversy regained its
virulence. For what is it the mathematical notions (such as those of Schrödinger’s wave equation) refer
to? Were they really existing entities, and if so, how should we understand the difference between
complex (and imaginary) values and real values?
A strong case in favor of a realist interpretation of Bohr’s position has been given by Folse (1992, p. 52).
Bohr’s way of thinking, according to Folse, remains compatible with a kantian framework, in which the
existence of the ’object behind the phenomena’ is also presupposed«280». This in itself
unperceivable object is regarded the subject matter of what Bohr calls ’definition’, whereas ’observation’
pertains to a mode of description in terms of the empirically accessible spatiotemporal properties. But
there is an ambiguity in Bohr’s usage of the term ’definition’. For it may mean either that its subject
matter is a kind of thing in itself, the essence of the phenomena observed, or that it is a concept, not a
real thing. This is the old opposition between real and nominal definitions«281».
276. Cf.: "While, within the scope of classical physics, the interaction between object and apparatus can be neglected or, if
necessary, compensated for, in quantum physics this interaction forms an inseparable part of the phenomenon. Accordingly, the
unambiguous account of proper quantum phenomena must, in principle, include a description of all the relevant features of the
experimental arrangement." (Bohr, 1963, p. 4, as quoted by Folse, 1992, p. 61).
277. Bohr, 1934, p. 96/Collected Works VI, p. 212. Because the English text of 1934 is, qua translation, considered not entirely
successful (Kalckar, 1985, p. 195), I include here and at other places, when available, a German translation additional to the citations
from the English version:
"Wir müssen im allgemeinen darauf gefaßt sein, dass eine allseitige Beleuchtung eines und desselben Gegenstandes
verschiedene Gesichtspunkte verlangen kann, die eine eindeutige Beschreibung verhindern" (Bohr, Collected Works VI, p. 205)
278. Bohr, 1928; see the quotation from Bohr on page 100 above.
279. cf. section 6.1.3
280. In particular, Folse (1992, p. 59) points at the following passage: "We are aware even of phenomena which with certainty may
be assumed to arise from the action of a single atom, or even of a part of an atom. However, at the same time as every doubt regarding
the reality of atoms has been removed and as we have gained a detailed knowledge even of the inner structure of atoms, we have been
reminded in an instructive manner of the natural limitation of our forms of perception." (Bohr, 1934, p. 103)
281. ’definitio realis’ and ’definitio nominalis’ in scholastics
102
On the other hand, if the subject matter of a definition is regarded as an abstract concept, then we find
ourselves in a nominalist discourse, which deals with the interpretation of symbols. In fact, Bohr often
expresses himself in terms of the empirical description of experiences as well as in terms of the ordering
of these experiences«282». Indeed, there are in Bohr’s writings many passages in which he takes a
firm nominalist position«283».
It is the language of classical physics that he considers to be necessary to order the experimentally
obtained quantum phenomena, but he also considers the language of classical physics to be basically
insufficient to this purpose«284». For example, the quantum objects are qualified by states in a
complex space, i.e. complex numbers are used for the description of these states. The classical framework
does not permit a clear representation of these states. More important, however, is the fact that the
classical framework does not permit a description of the interaction processes between the measured
object and the measurement device. Bohr was particularly interested in these interaction processes, which
he would have liked to formulate in the conceptual framework of classical science (i.e.: using the classical
combination of causality and spatiotemporal descriptions).
Hence, when Bohr found himself challenged by an impossibility to adequately measure the interaction
between object and measurement device and account for it in the classical (causal plus spatiotemporal)
terms, he took this as evidence for the necessity of finding a proper conceptual framework for interpreting
the new empirically obtained experiences«285». It was thus that Bohr was concerned with "an
investigation of the conditions for the proper use of our conceptual means of expression"«286».
That is, given his quest for measuring the interaction processes during measurement, his emphasis shifted
from a causal description of these processes to the conditions for understanding them in causal terms. The
problem ’why can the causal processes that take place during measurement not be measured?’ changed
into: ’why are our conceptual tools inadequate for understanding quantum measurements in causal terms?’.
The fact that the empirically obtained spatiotemporal descriptions did not fit in with the conceptual
(causal) frameworks, which the observer has already available, triggered a rethinking of these
frameworks«287». I will return to this change of emphasis, from the object studied to the
conceptual framework in section 7.2, when discussing the limits of observing self-reference. For the
present moment it suffices to notice that, as a result of his efforts, Bohr turned his attention towards his
instruments, i.c. his tools for conceptualization. This, indeed, can be seen as a transition opposite to that
of incorporation. We might call it ’excorporation’.
282. Bohr, 1934, p. 92/Collected Works VI, p. 208 (German: "Einordnung der Erfahrungen"; Collected Works VI, p. 203)
283. E.g.: "... a subsequent measurement to a certain degree deprives the information given by a previous measurement of its
significance for predicting the future course of the phenomena. Obviously, these facts not only set a limit to the extent of the
information obtainable by measurements, but they also set a limit to the meaning which we may attribute to such information. We meet
here in a new light the old truth that in our description of nature the purpose is not to disclose the real essence of the phenomena but
only to track down, so far as it is possible, relations between the manifold aspects of our experience." (Bohr, 1934, p. 18/Collected
works VI, p. 296)
284. "... it is decisive to recognize that, however far the phenomena transcend the scope of classical physical explanation, the
account of all evidence must be expressed in classical terms. The argument is simply that by the word "experiment" we refer to a
situation where we can tell others what we have learned and that, therefore, the account of the experimental arrangement and of the
results of the observations must be expressed in unambiguous language with suitable application of the terminology of classical
physics." (Bohr, 1949, as quoted by Holton, 1970, p. 1018)
and:
"... only with the help of classical ideas is it possible to ascribe an unambiguous meaning to the results of observation." (Bohr, 1934,
p. 17/Collected Works VI, p. 295)
285. "The main point to realize is that all knowledge presents itself within a conceptual framework adapted to account for previous
experience and that any such frame may prove too narrow to comprehend new experiences." (Bohr, 1958, p. 67; as quoted by Honner,
1982, p. 25)
286. Bohr (1958, p. 2); quotation cited by Honner (1982, p. 24)
287. See Honner (1982, p. 23) on Bohr’s interest in the "general limits (or conditions) for the possibility of forming unambiguous
concepts."
103
Bohr’s thinking led to a fully nominalist discourse! If the term ’definition’ pertains to a concept, then it is
concerned with the way in which this concept can be used for interpreting empirical experiences and
observations«288». A definition of a concept, then, becomes a prescription of its usage when
empirical data are to be interpreted.
The conception of complementarity that is implied here, is different from the ’parallel complementarity’.
Here the scientist’s own conceptual framework is of focal interest. Von Weizsäcker (1955, p. 524) calls
this ’circular complementarity’, and he considers it to be Bohr’s own conception of complementarity. The
major difference with parallel complementarity is that two modes of description are not, as in parallel
complementarity, considered mutually complementing, but that one mode of description is regarded as
instrumental for making descriptions in the other mode. Thus, the best example: through thinking in
causal terms we attempt to interpret the spatiotemporal descriptions of our empirical observations.
Bohr recognizes a tension between the definition of a concept (such as causality) and its actual usage for
dealing with empirical information. The usage of a concept impedes a full detachment from it, and, on the
other hand, the analysis of a concept (and the act of defining it) impedes fully using it for observations in
the mean time«289». The conceptual tools that we use as instruments for ordering our observations
cannot be analyzed while being used. When analyzed, there are other conceptual tools required, which
escape being analyzed at that very same time.
There is some evidence«290» that, as to these ideas on the limitations of our conceptual
frameworks, Bohr has been inspired by the ideas of William James on the stream of consciousness and
the impossibility of introspectively observing its transitive parts without turning them into substantive
parts«291». Indeed, we find ourselves back on familiar ground: the tension between the usage of a
(conceptual) instrument and its analysis, which is the issue of Bohr’s circular complementarity, is similar
(and probably inspired by) William James’ relation between substantive and transitive parts, and it returns
at several places in his work in terms of the relation between subject and object«292».
The following comparison can be made between some of James’ and Bohr’s core notions:
288. A concept, thus understood, is a dynamic process, to which the term ’interpretation’ would also be appropriate. It is this
dynamic conception of ’concept’ that has been elaborated extensively by Pask in his monumental conversation theory (e.g. Pask, 1975).
I leave this vast topic beyond the scope of the present text, though I do recognize that many issues presented here could be unfolded in
terms of conversation theoretical notions.
289. "... the nature of our consciousness brings about a complementary relationship, in all domains of knowledge, between the
analysis of a concept and its immediate application" (Bohr, 1934, p. 20/Collected Works VI, p. 298)
290. Von Weizsäcker (1955, p. 525) recalls as a personal experience with Bohr that "the only occidental philosophers whom I heard
often and emphatically being cited by Bohr, were Socrates and William James". Folse (1992) suggests a more indirect connection via
the Danish philosopher Ho/ffding. See also Holton (1970, p. 1031ff.) and Jammer (1966, pp. 178/9) for discussions of the relation
between Bohr and James.
291. "The unavoidable influence on atomic phenomena caused by observing them here corresponds to the well-known change of the
tinge of the psychological experiences which accompanies any direction of the attention to one of their various elements." (Bohr, 1934,
p. 100/Collected Works, VI, p. 216) ("Die unvermeidbare Beeinflussung der atomaren Erscheinungen durch deren Beobachtung
entspricht hier der wohlbekannten Änderung der Färbung des psychischen Geschehens, welche jede Lenkung der Aufmerksamkeit auf
ihre verschiedenen Elemente begleitet." (Collected Works VI, p. 206))
and:
"... the unavoidable influencing by introspection of all psychical experience, that is characterized by the feeling of volition, shows a
striking similarity to the conditions responsible for the failure of causality in the analysis of atomic phenomena." (1934, p. 23-4/
Collected Works VI, p. 301-2)
292. E.g. Bohr (1928, p. 590).
104
James:
Bohr:
substantive parts
transitive parts
concepts (subject matter of definitions)
use of concepts (for ordering experiences)
By using an instrument, Bohr maintains, one cannot perceive that instrument. As an example Bohr (1934,
p. 99) speaks of a stick that, when grasped firmly, can be used as an instrument for touching objects in
the environment. The tactile sensations in the hand then escape from attention, and instead the distal edge
of the stick takes the quality of a tactile organ. It is there, at this distal site, where the person observes the
object he is touching with his stick; no longer is the palm of the hand the boundary of the person as a
sensing unity, but the edge of the stick. Conversely, if the stick is held loosely, it cannot be used as an
instrument of touch, and it appears to the observer as a stick, i.e., as an independent object, sensed in the
hand. In fact I discussed this phenomenon already in section 4.2 in terms of ’incorporation’«293»,
and in section 2.3.4 , esp. footnote 65, page 36, one the usage of words as instruments to bring forth
objects. Likewise, other tools, such as concepts, can be taken as an object of study only when ’holding it
loosely’, i.e. at the price of not using the concept for arranging empirical data. The complementarity
between observation and definition which Bohr mentions several times in his Como paper (1928), then
arises as one between the usage of the instrument versus its analysis. This is entirely a nominalist affair,
concerned with the study of the limits of arranging empirical data.
To finish this section, let me quote from Honner (1982, p. 22), who gives a bright remark on Bohr’s
position:
"In my view, then, the following uncompromising schema for Bohr’s underlying train of thought
must be adopted. First, the situation in quantum physics and the situation with respect to the
discussion of consciousness both entail similar instances of the one argument. Secondly, this one
argument rests on the analysis of the conditions for the possibility of unambiguous communication
about processes at and beyond the boundaries of human experience."
In chapters 10 and 11 we will find opportunity to discuss comparable ’similar instances’, when discussing
how a psychotherapist may develop a particular self-experience, when involved in particular encounters
with patients.
6.2.3. Löfgren’s ’linguistic complementarity’
It is the mixture, within the nominalist discourse, of process (proof process or measurement process) with
the outcome of the process (proof or measurement) that is the locus of confusion. Löfgren has focused
upon this.
Löfgren, from a point of view of mathematical automata theory, elaborates the thesis that within a
language (e.g. a computer language) it is impossible to give a complete description of the way in which
the sentences of the language are to be interpreted«294». He uses the term ’linguistic
complementarity’ for this impossibility. The concept of linguistic complementarity comprises that it is
impossible for any language, provided it is sufficiently rich, to contain such a complete description of its
own interpretation processes, i.e. a description of the processes and functions that convert the sentences of
this language into fully operative interpretations (e.g.: running computer programs or calculation
293. It is interesting to notice that Merleau-Ponty (1945, p. 167, see section 4.2 above) used a similar metaphor. Both for Bohr and
for Merleau-Ponty this metaphor illustrates that we cannot simultaneously pay attention both to an object and to the method by which,
or the instrument through which, it is perceived.
294. ’Interpretation’ and ’description’ as defined in section 4.3.4.
105
processes)«295».
interpretation
^
|
|
|
interpretation |
|
description
processes
|
|
processes
|
v
description
If a description would exist that specifies the way in which it should be interpreted, then the interpretation
of this description would coincide with the interpretation process required for it.
Equivalent to this is to say that, within a formal system, the meaning (interpretation) of a description
cannot coincide with the interpretation processes. In a functioning system (computer), the interpretation
processes are not interpretations of the description (e.g. a program in Pascal), but they are the
interpretations of a description in a meta-language (e.g. a description of the operating system, given in
machine language).
Now this idea is applied by Löfgren to Bohr’s circular complementarity. In particular, Löfgren maintains
that there is a self-reference implied in the idea of measuring the interactions by the measuring device and
the object to be measured. In order to know the object as it was before measurement, it would be
necessary to know in detail the precise ways in which this object interacts with the measurement
instrument and how it has been influenced. Precisely this is impossible, as it would require a measurement
of the very measurement process, which would entail an infinite regress«296». In order to avoid
that, a self-referential measurement would be required, one that registers its own process as it takes place.
But this would get stuck on (circular) complementarity: we cannot observe the instrument while using it
for our observations. Let us note, in passing, that such self-referential ’measurement’ is only possible for
immediate experiences, at a more elementary level than object perception, and at the price of losing the
object qua perceivable entity. I will discuss that in chapter 7.
The impossibility of self-measurement, Löfgren maintains, is not due to a limitation of classical physics or
its causal language. It is a feature of languages in general that self-reference cannot be expressed fully (cf.
Löfgren, 1990). His major step, then, is to reduce Bohr’s ideas on (circular) complementarity to his
concept of linguistic complementarity.
Löfgren points at a similarity between the works of Gödel and those of Bohr. Both authors were
concerned with self-reference: Gödel with self-reference of arithmetic propositions, Bohr with selfreference of measurements. In quantum physics, unlike in classical physics, there is a limitation to what
can be observed, comparable to the limitations of what can be proved in mathematics.
295. As an example of this we may think of a computer program written in a particular language, say Pascal. It is then impossible
to have the program also contain a set of (Pascal) instructions for the computer as to how to interpret the Pascal statements into
computer actions. A program for reading and executing Pascal statements (either a so called ’interpreter’ or a ’compiler’) is presupposed
to be already installed on the computer before it can transform the Pascal lines into actions. This auxiliary program that performs the
transformation (Löfgren calls this the interpretation process) should itself also be written in a language already available on the
computer (such as machine language). The computer should ’know’ the language before it can process a program written in it; the
program itself cannot provide its own ad hoc interpreter or compiler.
Any (fancy) program that would accomplish that, would be self-referential in that it says how to interpret its own lines,
including the lines that prescribe the interpretation process!
See also Löfgren (1992, p. 116).
296. cf. Löfgren (1989, p. 302ff.); Pattee (1992, p. 183)
106
self-reference of operations in:
mathematics
physics
undecidable proof process
unmeasurable measurement process
Both authors also hit upon the impossibility to arrive at a particular goal: the incompleteness of
formalization of arithmetics and the incompleteness of description of quantum measurements. Löfgren
(1988, p. 144) claims that the linguistic complementarity is the crucial link between these domains of
mathematics and physics, since it pertains to all languages (and hence is valid both for physics and
mathematics).
Löfgren’s work, I think, is to be considered the most parsimonious elaboration of this notion of
incompleteness that is present both in the work of Gödel and of Bohr. I will use Löfgren’s insights,
especially his concept of ’linguistic complementarity’, in the next chapter, when describing the limitations
of realist and nominalist discourses (section 7.1, especially 7.1.2). The linguistic complementarity is to be
understood as the ultimate formulation of self-reference, within the confines of a nominalist discourse.
To end this section, I will make some terminological comments that can easily be skipped for the course
of my argument.
6.2.3.1.
Remarks on terminology
Löfgren (e.g. 1992, pp. 145-148) translates in terms of this linguistic complementarity the quantum
mechanical measurement problems, especially the impossibility of self-measurement«297».
It is remarkable that Löfgren, in order to justify this step, understands measurement not as something
applied to physical reality, but to descriptions of physical reality! Measurement and observation, then, are
reduced by Löfgren to (linguistic) operations of interpretation of these descriptions«298». An
adequate theory of quantum physics, according to Löfgren, should contain a description of how the
measurements should be performed. But if measurements are reducible to interpretations, then such a
theory is reducible to a description of how it should be interpreted«299». The impossible case of
self-measurement in quantum mechanics is thus presented by Löfgren as reducible to the impossible case
of formulating a sentence that describes its own interpretation processes.
It is thus that Löfgren de facto imposes a nominalist discourse upon Bohr’s ideas on complementarity,
where a more natural way to recognize a nominalist discourse in Bohr is overlooked. Löfgren expresses
Bohr’s tension between ’observation’ and ’definition’ in his own terms, i.e. as a tension between
’interpretation’ and ’description’ respectively. This is somewhat curious, since, as we saw, Bohr’s notion
of ’definition’, being concerned with the arrangement of experiences, is a more likely candidate to be
translated as Löfgren’s ’interpretation’; likewise, ’observation’, which is for Bohr a matter of
297. "It is in recognizing the quantum mechanical measurement problem as self-referential, with the measurement process, as
interpretation process, itself belonging to the quantum physical domain, that we encounter a phenomenon of language for which the
linguistic complementarity takes the form of Bohr’s primary view." (Löfgren, 1992, p. 145) [’primary view’: i.e., that of Bohr’s Como
paper, 1928]
298. "... that observation by measurement is how to interpret the state symbols of the formalism" (Löfgren, 1992, p. 148). Cf. also
Löfgren, 1992, p. 136; 1991, p. 64; 1989, p. 298.
299. "The measurement process is in quantum mechanics part of the quantum mechanical domain. Thus, with measurement regarded
as interpretation, a description of quantum mechanics must contain a description also of how it is to be interpreted." (Löfgren, 1989,
p. 310)
107
administrating the data, might fit in Löfgren’s notion of ’description’«300».
Bohr’s concepts:
Löfgren’s concepts:
my understanding:
definition
observation
description
interpretation
interpretation
description
The usage of ’interpretation’ and ’description’ that I am proposing is more in line with the terminology of
Pattee. His (e.g. 1992) concept of ’measurement’ is comparable to what Löfgren calls ’description
process’. Furthermore, for Pattee measurement is an operation in which a time dependent (dynamic)
process is transposed to a time independent (static) description. For Löfgren, to the contrary, measurement
is an operation through which a static description comes to time dependent processes (the ’interpretation’,
’meaning’ or ’model’)«301».
Instead of Löfgren’s reduction of self-measurement to self-interpretation, one might venture to think, it
could make better sense to translate the idea of impossible self-measurement as an impossible selfdescription, i.e. as the impossibility to describe in a description the very description processes required for
writing down that description. Likewise, the impossibility to write down the interpretation process that is
required for interpreting the very same description, parallels the impossibility to analyze a conceptual tool
(a definition, cf. section 6.2.2) while using it; it also resembles the impossibility to think the (transitive)
processes that lead to a (substantive) thought. The terminology Löfgren uses in order to reduce Bohr’s
concept of (circular) complementarity to his own concept of linguistic complementarity, therefore, seems
to be not maximally plausible, even though this reduction itself, I think, is very valuable for recognizing
the nominalist discourse in Bohr’s thoughts.
Finally, we may extend the comparison between the concepts of James and Bohr (see the diagram on page
104) with those of Löfgren:
James:
substantive parts
(empirical Me)
Bohr:
concepts
(subject matter of
definitions)
Löfgren:
interpretations
(e.g. automatic
calculation)
transitive parts
(judging Thought, I)
use of concepts (for
ordering experiences)
interpretation
processes
empirical findings
empirical phenomena
descriptions (e.g.
computer program)
300. However, it must be acknowledged that Bohr’s usage of the term ’definition’ is not always consistent. For example, in the
following fragment this term is used as ’description’ or ’measurement’:
"The reciprocal uncertainty which always affects the values of these quantities is, as will be clear from the preceding analysis,
essentially an outcome of the limited accuracy with which changes in energy and momentum can be defined, when the wave-fields used
for the determination of the space-time co-ordinates of the particle are sufficiently small." (Bohr, 1928, p. 583/Collected Works VI,
p. 151).
301. cf. footnote 213 (p. 80)
108
6.3. Psychotherapy and self-reference
The nominalist discourse easily affords the formulation of a principle of complementarity between
observing process and observed object, whenever it is attempted to self-referentially describe a system. On
the other hand, in the case of self-reference the realist discourse would straightforwardly claim the identity
of the observing process and the object of observation (as in the cartesian Cogito).
realist discourse:
nominalist discourse:
self-reference:
self-transparence (of the Cogito to itself)
complementarity (between the observed and the
act of observation)
It is precisely here that we recognize a renewed split between the nominalist and realist discourses. Since
the realist discourse deals with self-reference in a way entirely different from the nominalist discourse,
their classical integration is no longer possible.
This integration consisted of the primacy of the analysis-synthesis pair of operations«302», so that
abstract conceptions were related to concrete perceptions, disregarding the allocation of substance and
accident to form and content. Classical science, as an integration«303» of realist and nominalist
discourses, could not include self-reference as a topic of study without losing its ground, i.e. this
integration.
When psychology as a newly developing discipline dealt with self-reference, traditional realist approaches
were opposed by nominalist ones (like William James opposing the realism of the ’Hegelians’ and
’Fichteans’«304», but also like Sartre opposing the realism implicit in Husserl’s transcendental
ego«305»), etc. The self-transparent Cogito was thus opposed by a complementarity between ’I’
(pour-soi) and ’Me’ (ego), between the processes of observation and their outcomes, the things observed.
Likewise, psychotherapy, to the extent that self-reference is involved, has not succeeded in finding a way
to continue the classical combination of realist and nominalist discourses. Mostly it became realist,
emphasizing essences (self-transparent Cogito, self-consciousness, self-observation, self-insight, etc.).
Psychoanalysis, as a paradigm, has become an enterprise into the depths of the patient’s mind, assuming
the idea of full self-accessibility in principle. To the extent self-reference has become a topic of interest, it
has been so at the price of a certain vagueness. Also an appeal to the reader’s sympathy was and still is
typical for those studies on therapeutic techniques in which the therapist’s own subjective feelings are
302. cf. section 6.1.1
303. It is also the loss of this integration that characterizes modern developments in the field of science studies, where emphasis is
given more to the observational (meaning assigning) history of science than to foundational issues (which are more about formal a priori
matters, and hence have more of an essentialist look). The latter are regarded as outdated themes stemming from a past era, viz. the
Enlightenment (e.g. Rorty, 1979). Instead of rethinking the relation between realist and nominalist discourses, now that the
Enlightenment solution has broken down upon self-reference and other issues, these science studies stick to a (nominalist) emphasis on
historical observation of scientific developments, without any claim of ’getting into’ them and contributing to them substantially. As if
by doing so one would hopelessly be trapped by some of the old realist assumptions of Enlightenment!
304. e.g.: "... Transcendentalism is only Substantialism grown shame-faced, and the Ego only a ’cheap and nasty’ edition of the
soul. All our reasons for preferring the ’Thought’ to the ’Soul’ apply with redoubled force when the Soul is shrunk to this estate. The
Soul truly explained nothing; the ’syntheses,’ which she performed, were simply taken ready-made and clapped into her as expressions
of her nature taken after the fact; but at least she had some semblance of nobility and outlook. She was called active; might select; was
responsible, and permanent in her way. The Ego is simply nothing: as ineffectual and windy an abortion as Philosophy can show. It
would indeed be one of Reason’s tragedies if the good Kant, with all his honesty and strenuous pains, should have deemed this
conception an important outbirth of his thought.
But we have seen that Kant deemed it of next to no importance at all. It was reserved for his Fichtean and Hegelian successors
to call it the first Principle of Philosophy, to spell its name in capitals and pronounce it with adoration, to act, in short, as if they were
going up in a balloon, whenever the notion of it crossed their mind." (James, 1890, p. I-365)
305. cf. section 5.3.1, esp. footnote 223
109
considered of pivotal importance. This vagueness and this appeal are apparent both in psychoanalytic
literature and in writings on client-centered and experiential therapy. They are in sharp contrast to the
objectivist phraseologies of the behaviorists.
On the other hand, vigorous nominalist trends, like behaviorism, hardly dealt with self-reference, as this
was considered too often a matter of (reprehensible) introspection. Behavior therapy, as a major
nominalist trend in psychotherapy, has even obtained its successes, at least for a long time, due to an
explicit disregard of the therapeutic (interactional) processes themselves. Instead, behavior therapy focuses
nearly exclusively upon the proper formulation of techniques and procedures«306». I will return
upon this issue in chapters 8 and 9.
Thus, whereas in the exact sciences self-reference became a topic most fruitfully«307» dealt with
within a nominalist environment, in psychotherapy the reverse seems to have happened: self-reference has
survived as introspection only within a realist environment; within a nominalist environment it has been
replaced by a behavioral technology, one that requires an external controller (however benevolent) of the
person under observation. In experimental contexts the latter has been the research subject, in
psychotherapeutic contexts this has been the patient.
At stake in modern psychotherapy is the reciprocal relation between the (realist) postulation of latent
(mental) essences behind manifest (behavioral) appearances on the one hand, which require a considerable
amount of introspection and other ’cogitations’ to be unearthed, and on the other hand the (nominalist)
assignment of (therapist’s) meanings to (patient’s behavioral) symbols (which hardly allow for selfreferential formulations). Or, in other words, at stake is the relation between explanation, the convergent
search for unifying underlying principles on the one hand, and on the other hand the divergence of the
various pragmatic implications that can be assigned to a (behavioral) symbol.
psychotherapy:
realist discourse:
nominalist discourse:
-excavation of essences
-behavior as appearances
-theoretically oriented
-diagnosis as explanation
-self-reference as introspection
-assignment of meanings
-behavior as symbols
-practically oriented
-diagnosis as tool
-self-reference ignored
Here realist and nominalist discourses mix up without integrating. Explanations and practical solutions to
problems are independent of one another, if not incompatible. At best they alternate, but do not integrate
as they did in the classical way. A non-classical approach has been missing thus far.
When a discipline, such as psychotherapy, or, to take a point of departure, psychiatric diagnosis, is not
successful in connecting the two discourses, then it might be prudent to look for a new kind of
interconnection between them and to question the tenability of the classical solution as interconnection.
Or, in other words, when a discipline is not successful in relating the explanatory principles that underlie
empirical research phenomena to the practical implications that are to be assigned to the research data,
then not so much the quality of these data is to be improved by means of (more and more) sophisticated
statistical and psychometric tools (which is what is usually done in psychology), but rather are the
relations between essences and meanings, between explanations and applications, to be reconsidered
(which is usually overlooked). But what could be an alternative way of relating essences and meanings?
I will deal with this question in two steps. First, I will make a rather formal point in chapter 7, where I
will describe the limitations imposed upon us by the usage of the two discourses in which critical objects
306. This is not at all to say that these are performed rigorously and without respect for the unique circumstances of the patients.
307. see the motto of this chapter
110
can be formulated. There, self-reference will be situated beyond the two critical discourses. Second, in
chapters 8 and 9 I will explore how a reappreciation of naive discourse can help us to relate essences and
meanings. Chapter 8 will focus on the field of psychiatric diagnosis and how the two critical discourses
do not permit a classical solution, and chapter 9 will focus on psychotherapy in general and the selfreferential structure of exploration processes.