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Comment
and Conclusion
Contrary to often expressed opinion the topic
of scientific discovery has not been a neglected one
in philosophy of science.
The above survey reveals that many
philosophers and scientists have addressed it with a
semantical approach using figures of speech.
But no application of a metatheory of
scientific theory development using a purely
semantical approach has yet succeeded in generating
a new and successful scientific theory in any
science, even though many noteworthy historic
scientific discoveries have resulted from the
intuitive use of such semantical devices as analogy
and metaphor. To
date the only metatheories that are sufficiently
practical to function as applicable procedures for
scientific discovery are those based on the
discovery-systems approach, and most of these have
been academic exercises involving the reconstruction
of existing or historical theories.
Only a few discovery systems have actually
been used to make new theories at the contemporary
frontier of a science.
Due to his semantical views Hanson had not
examined the use of figures of speech, and very few
discovery systems existed before his death in 1967.
But in his examination of historical episodes
in the history of science he recognized and
documented cases in which semantics has operated as
a constraint upon discovery, and he understood that this phenomenon
implies the need for a reconsideration of the nature
of scientific language, especially the language for
observation. However,
he himself had only suggested a metatheory of
semantical description in his discussion of the
semantics of Newton’s mechanics.
The following commentary is divided into five
topics: Firstly Hanson's attempt at a logic of
discovery with his wholistic gestalt
semantics is critiqued.
Secondly Hanson’s defense of the Copenhagen
interpretation with its duality thesis is considered
in the context of semantical change in science.
Thirdly Hanson’s principal criticism of
Bohm's hidden-variable thesis is viewed in
historical retrospect.
Fourthly some comments are given on Bohm's
and Hesse’s use of metaphor, and Wittgenstein’s
family-resemblance theory of meaning is critiqued.
And finally a semantical metatheory of
analogy, metaphor, and simile is set forth.
Consider firstly Hanson’s proposed logic of
scientific discovery, which took as its point of
departure Peirce’s investigations.
Peirce’s abductive (AKA retroductive) logic
of discovery does not conclude to a unique theory
from a given set of premises as deductive logic
concludes to a unique theorem.
And Hanson does not propose that there exists
a resolution for this indeterminacy, much less does
he supply one.
But Hanson adds something to Peirce, namely
the controlling role of logical syntax in the
determination of semantics, which in turn strongly
influences the selection of possible hypotheses
available for abduction.
Thus he says that the mathematical formalism
or syntax of the empirically adequate quantum theory
defines the conceptual possibilities for any future
development of microphysical theory, while
paradoxically he also maintains that it offers a
conceptual resistance to any future development of
an alternative microphysical having a different
formalism. This controlling role for syntactical
structure in statements and equations believed to be
true implies an artifactual thesis of the semantics
of language. But
in spite of the importance that Hanson places on
semantics, he never used or developed a systematic
philosophy of language.
His principal inspiration was Wittgenstein's Investigations, which is not without its insights but is an
aphoristic approach to philosophy of language.
In his discussion of "seeing"
Wittgenstein employed ambiguous drawings such as are
commonly used in texts on gestalt psychology, and Hanson developed a semantics of language
based on the idea of the conceptual gestalt.
Unfortunately Gestalt psychology is a very
blunt instrument for semantical analysis, because it
is a wholistic approach to semantical description.
Hanson's philosophy of scientific discovery
was greatly influenced by the physicist Paul Dirac.
Dirac had told Hanson that the Copenhagen
interpretation figured essentially in his
development of the formalism of his relativistic
quantum theory.
Hanson therefore took the position that the
Copenhagen interpretation (without Bohr's naive
epistemology based on forms of perception) is that
one, unique, and distinctive semantical
interpretation supplied by the formalism itself, and
is not merely some philosophical idea appended to
the formalism.
However, the gestalt semantics is not adequate to the defense of Hanson's view of
that Copenhagen interpretation is integral to the
formalism of the modern quantum theory.
Had Dirac said just the opposite of what
Hanson reports he said about the Copenhagen
interpretation's relation to the formalism of
quantum theory, then the gestalt semantics would have been neither more nor less serviceable
for a semantical analysis of quantum theory.
This is because the conceptual gestalt
is wholistic and does not enable the philosopher of
science to separate or even distinguish the
semantics that may in some way be integral to the
quantum theory's formalism, from that which may not
be integral to the formalism but is merely appended
to the formalism - what Hanson calls mere philosophy
and Bohm calls informal language.
In fact Hanson's gestalt
semantics does not even offer him a basis for his
distinction between the Copenhagen interpretation
and the Bohr interpretation.
The wholistic character of the conceptual gestalt makes it impossible to partition the semantics of the
quantum theory into parts, to identify those parts
that are integral to the formalism and those parts
that are not, or those parts that are properly
called the Copenhagen interpretation and those parts
that are distinctive to the Bohr interpretation.
In Patterns of Discovery Hanson had a brief flirtation with the idea
that the meanings of terms contain each other as
parts, but he failed to explore the idea.
Had he done so, he would have found that
semantics can be as analyzable as the syntax of any
semantically interpreted and empirically warranted
text.
The wholistic character of the conceptual gestalt
also thwarts Hanson's attempt to explain scientific
discovery. On the one hand the conceptual gestalt offers conceptual resistance to any change to a new gestalt
and therefore to any new theory.
In other words it is an impediment to the
semantical change integral to scientific discovery.
On the other hand it is also a guide to
scientific discovery, because it informs the
scientist of the kind of hypothesis that may satisfy
the retroductive logic of scientific discovery.
Semantics may function in both of these
contrary ways, but the gestalt
psychology cannot explain how.
More specifically in connection with the
modern quantum theory, the
gestalt psychology does not explain why Hanson
should be defending the Copenhagen interpretation as
a guide instead of attacking it as an impediment to
the discovery of a new and more empirically adequate
quantum theory.
The reason for this problem is the basic fact
that the wholistic gestalt cannot function in a logic of scientific discovery or in any
other application of logic, because its wholistic
character deprives the retroductive logic of any
procedural character. Retroduction can only describe the conditions that the new gestalt
must satisfy after it has been hit upon, which is to
say that it is a statement of a scientific problem
that the discovery must solve rather than a
procedure for obtaining a solution.
On the
gestalt view the discovery itself is a
transition that does not admit to a procedure, just
as the transition from one interpretation of an
ambiguous drawing to another does not admit to a
procedure. Just as there could never be a logical or mathematical
formalism to describe the transition occurring in a
change of a substantial form described in
Aristotle's physics, so too there could never be a
logical formalism to describe the change in a change
of a gestalt form in modern physics.
In both cases the transition from one form to
the other is a substitution, which is instantaneous,
whole and complete, and with no intelligible
continuity to warrant calling it a process instead
of a simple replacement.
Turn next to the second topic, Hanson's
defense of the Copenhagen interpretation and his
view that the formalism of the equations and
statements of the theory necessarily imply it.
The central question is whether the semantics
of physical theory is exhaustively specified by the
equations of the theory together with the statements
describing the measurement apparatus and procedures
used to obtain the measurement data related by the
equations, or whether additional discourse is
involved characterizing the domain of the equations
and measurements.
Hanson rejects any semantical role in
scientific explanation for any discourse other than
the equations of the theory and the statements
required for experimental description and
measurement procedures. Accordingly he maintains
that the wave-particle duality, which is the
distinctive characteristic of the Copenhagen
interpretation, is not some semantics added to the
formalism of the quantum theory by those statements
that he calls mere philosophy, but rather is an
ontological claim that is expressed by the formalism
due to the formalism’s control of the semantics of
the theory. His
motive for stating this position is Dirac's
statement made personally to Hanson that the
wave-particle duality is integral to the formalism,
and that it was strategic in Dirac’s development
of his own relativistic quantum theory.
And it is built into the syntax of Dirac’s
operator calculus.
There are physicists who disagree with
Hanson’s view.
Some disagree because they do not recognize
the occurrence of semantical change.
Hanson illustrates the phenomenon of
semantical change in the first chapter of his
Concept of the Positron, where he gives a brief
historical overview of the wave and particle
theories of light.
He notes that Newton did not have a semantics
for the terms “wave" and "particle"
making the concepts dichotomous or mutually
exclusive, when Newton proposed his theory of fits.
Only later did these concepts assume their
dichotomous implications, when the experiments of
Foucault, Frenzel, and Young were believed to have
the force of crucial experiments that persuaded the
physicist that they must decide between one and the
other characterization.
Thus the concepts of wave and particle had
undergone semantical change with the advance of
physical experiment and theory. By the twentieth century the wave-particle dichotomy had
become very well established even though the
discoveries of Planck’s quantum constant in 1900,
Einstein’s equation for the photoelectric effect
for light in 1905, Compton’s equation for his
Compton effect for light in 1922, and de Broglie’s
relation for matter waves in 1924 enabled physicists
to express the wave-particle duality mathematically
prior to development of the modern quantum theory by
Heisenberg and Schrödinger. Interestingly in his Conceptual Development of Quantum Mechanics (1966) Max Jammer
observed that Bohr had come to his complementarity
principle by consideration of these earlier
equations, and he references a four-page postscript
to a paper written by Bohr in 1925.
This is one year before Heisenberg reports
that Bohr had developed his complementarity
principle.
Yet in
spite of having been led by these considerations to
conclude that wave and particle are alternative
manifestations of the same physical reality, the
inconsistent concepts were retained by Bohr, because
he retained the classical concepts of wave and
particle in his complementarity principle and
relegated mathematical formalism to an
instrumentalist status, even as he affirmed the
wave-particle duality.
His complementarity principle is a
contradiction resulting from his belief in the
naturalistic philosophy of perception, which in turn
implies that like all classical concepts, those of
wave and particle cannot be changed.
And the complementarity principle is an
example of the philosophical discourse defining the
semantics in a way that is inconsistent with the
semantics defined by acceptance of the
mathematically expressed theory.
After some weeks of disagreement with Bohr,
Heisenberg concluded that he could accommodate
Bohr's complementarity thesis by accepting the idea
that the wave-particle duality is expressed by the
uncertainty principle, save that the mathematical
formalism of the uncertainty principle is consistent
while the complementarity principle is inconsistent.
Heisenberg made this accommodation, because
he accepted Bohr's naturalistic philosophy of
perception. Yet
in so doing, he was himself philosophically
inconsistent, since unlike Bohr, he did not construe
the formalism instrumentally.
Instead by accepting Einstein’s admonition
that the theory decides what the physicist can
observe, Heisenberg let his theory decide what the
physicist observes, and furthermore following
Einstein's precedent applying scientific realism to
the concept of time in relativity theory, Heisenberg
likewise attempted to construe his indeterminacy
relations realistically.
The only way the Copenhagen wave-particle
duality thesis can be affirmed consistently is to
let the equations control the semantics of the terms
"wave" and "particle", as these
terms relate to the descriptive variables in the
mathematically consistent formalism. Accepting this
mathematical context produces a semantical change in
the meanings of the terms with the result that they
no longer stand for classical concepts and are
therefore no longer antilogies.
The empirical adequacy of the quantum theory
demonstrated after testing enables its equations to
function as definitions.
This amounts to using the equations of the
theory in a functionally a priori manner and as pattern statements, as Hanson said, and to
letting the theory decide what is observed, as
Einstein said.
Heisenberg may have been approaching the
recognition of the semantical change, when in his
"Questions of Principle" (1935) he said
the restrictions on classical concepts as enunciated
in the uncertainty relations acquire their
“creative value” only by making them questions
of principle, such that they can have the freedom
necessary for a noncontradictory ordering of
experience. In the light of his autobiographical
description of his development of the uncertainty
relations, his phrase “creative value” may be
taken to refer to the role of the mathematical
equations in defining the semantics, when the
concepts of the formalism are used for observation
as in the case of his reconsideration of the tracks
in the Wilson cloud chamber.
In other words he recognized that the
formation of a new semantics is integral to the new
scientific discovery.
In this paper Heisenberg also states that the
system of mathematical axioms of quantum mechanics
entitles the physicist to regard the question the
simultaneous determination of position and impulse
values as a false problem, just as Einstein's
relativity theory makes the question of absolute
time a false question in the sense that they are
devoid of meaning.
Clearly the reason Heisenberg said such
questions become devoid of meaning, is that the
meanings of the variables have been changed by the
in-principle maneuver of giving semantical control
to the new theory.
Hanson reiterates Heisenberg's in-principle
approach. In
the chapter "Elementary Particle Physics"
in his Patterns of Discovery he states that one cannot maintain a
quantum-theoretic position and still aspire to the
day when the difficulties of the uncertainty
relations have been overcome, because this would be
like playing chess and yet hoping for the day when
the difficulties of having but one king piece will
have been overcome.
But Hanson proceeds beyond Heisenberg.
Heisenberg's explicit and systematic theory
of semantical change, his doctrine of closed-off
theories developed under the influence of Bohr, was
not only intended to explain semantical change, but
was also intended to explain semantical permanence
for classical concepts used for observation.
In contrast Hanson said that the uncertainty
principle is built into every observation of every
fruitful experiment since 1925.
In Hanson's explicit and systematic
philosophy of science, unlike Heisenberg's, the
theory controls even the semantics of the language
used for description of observed phenomena.
Hanson states how a theory has its creative
value in ways that Heisenberg actually used and
chronicled in his development of the uncertainty
principle, but which Heisenberg did not incorporate
into his explicit and systematic philosophy, his
doctrine of closed-off theories.
Heisenberg was inconsistent when he viewed
the semantics of the variables in the mathematical
quantum theory as classical concepts with restricted
applicability for observation.
One problematic and indeed controversial
outcome of the semantical change resulting from
giving semantical control to the formalism of the
theory, as Hanson advocates, is a complication in
the problem of how empirical control is also
exercised over the theory in scientific criticism,
such that independent evidence enabling empirical
decidability is possible and tautology is prevented.
This is a problem that still vexes those
contemporary Pragmatists who employ a wholistic
thesis of the semantics of language.
Hanson could have called upon his thesis of
theory-independent phenomenalist seeing as an
observation language.
But he never invokes this idea to defend the
empiricism of science, even while he never doubts
either the empirical decidability of science or the
theory-laden character of observation language.
Instead he regrettably invokes Wittgenstein's
idea of the multiple uses of language with theory
language having a concept-defining function for
observation only in some uses and a testing function
in others. This
seems no better than Heisenberg’s inconsistency.
Letting the consistent mathematical formalism
of the theory control its semantics and thus the
ontology its semantics describes, enables the new
theory to supply a new semantics and ontology.
But recognition of semantical change does not
resolve the central ontological issues associated
with the quantum theory.
In fact there is no compelling evidence
either from experiment or from the formalism of the
quantum theory for the Copenhagen ontology.
Whether the wave and particle are two
alternative manifestations of the same entity, as
Bohr and Heisenberg say, or whether they are
copresent but separate entities, as de Broglie and
Bohm say, or whether the particle is the only real
entity, as Lande says, or whether the wave is the
only real entity, as Schrödinger says - are all
different ontological commitments that cannot be
decided by reference to the mathematical syntax,
because mathematics does not reference entities, or
in Carnap’s phraseology it is not a “thing
language”. The
mathematical syntax does not express instantiation
in things or entities like the syntax of the
Aristotelian categorical logic, the Russellian
predicate calculus, or ordinary language.
In the mathematical equations the
semantically interpreted calculus expresses the
universal claim, when no numeric measurement values
are assigned to the descriptive variables.
And the claim is made particular when any of
the variables are assigned numeric values either by
measurement actions of the experimenter or by
calculation with the equation from measurement
values assigned to other descriptive variables in
the equation. The
individual measurement action is the referenced
instance at a specific place and time, and no claim
is made about instantiated entities.
In categorical logic on the other hand
entities are explicitly referenced by the subject
term, which is quantified, and their existence is
claimed by the copula, a form of the verb “to
be”, when the considered categorical statement is
proposed as true.
Similarly in the Russellian predicate
calculus quantified (or bound) variables also
reference entities, although in the Russellian
predicate calculus ontology and quantification are
commingled so that the syntax implies nominalist
ontology, such that one may blithely ignore such
subtleties as simple or personal supposition, and
say with Quine that in the Russellian predicate
calculus to be is to be the value of a variable.
In ordinary substantive discourse reference
to entities is often implicit, but can be made
explicit with terms such as “thing” or
“entity”.
In order for any mathematically expressed
theory to make ontological claims about entities, it
is necessary to supplement its mathematical language
with additional thing-language discourse having the
syntactical categories that enable reference to
entities. This
could be as elementary as a statement of a
measurement procedure in terms of counting certain
types of entities, such as members of a population.
Even if the mathematics were set theory, it would be
necessary to add information identifying which sets
have elements as entities.
Thus there is merit in Bohm’s thesis that
the interpretation of a mathematical formalism is
something that is in the informal language and not
in the measurements or the equations themselves.
And he was furthermore correct in maintaining
that the informal language contains philosophical
assumptions, because the statements of test design
used to make quantum-theory measurements do not
describe the microphysical entities adequately to
decide between the various ontological
interpretations. Thus any discourse purporting to describe the one or more
microphysical entities in terms of wave and particle
attributes must be relegated to what Hanson called
mere philosophy. In this respect whether or not Bohm’s hidden-variable
interpretation is the correct interpretation, he
seems to have been philosophically correct in
stating that the interpretation is in the informal
language, and that the discourse is philosophical,
because that informal discourse is not yet
empirically testable.
Thus it is not yet empirically decidable -
and the ontological debate goes on.
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