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BOOK II
ERNST MACH AND PIERRE DUHEM ON PHYSICAL THEORY |
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Mach's Phenomenalism. Mach's Philosophy of
Science. Mach's History of Mechanics. Duhem
on Physical Theory and Metaphysics. Duhem's
Stratified Semantics for Physics. Duhem's
Philosophy of Science. Duhem's History of
Physics. The New Physics vs the Old Philosophy.
Comment and Conclusion.
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Ernst Mach (1838-1916) is a representative
figure of the early Positivist philosophy
of science in physics at the turn of the
twentieth century. He earned a doctorate in physics from the
University of Vienna in 1860, taught experimental
physics for most of his career at the University
of Prague (1867-1895), and then held the
chair of Inductive Philosophy at the University
of Vienna (1895-1901). He set himself the philosophical task of
implementing the phenomenalist philosophy
of David Hume in physics while Newtonian
mechanics still prevailed in physics, and
he made contributions to physics, psychology,
and education, as well as to philosophy.
Pierre Duhem (1861-1916), another important
early Positivist, studied physics at the
Ecole Normale in Paris, where he received
a doctorate in physics, and was a professor
of physics at the University of Bordeaux
for most of his career. His principal interest was physical chemistry,
where he aspired to recast the theoretical
foundations of chemical processes on the
basis of a generalized thermodynamics. Unlike Mach, Duhem accepted the Aristotelian
metaphysics, which he viewed as separate
from Positivist physics, and believed that
progress in physical theory asymptotically
approaches a "natural classification",
which he viewed as analogous to the cosmology
of Aristotle. Duhem’s philosophy differed from Mach’s philosophy
by the former’s acceptance of physical theory
as integral to physics, and his development
of a semantical metatheory to locate theory
in Positivist physics. This semantical metatheory served as the
basis for a general philosophy of language
in the contemporary Pragmatism, and retrospection
reveals that it has been his more lasting
philosophical contribution.
Mach's Phenomenalism
Prior to the contemporary Pragmatism philosophers
based their philosophies of science on one
or another metaphysical viewpoint. Though Positivists philosophers including
Mach were explicitly "antimetaphysical"
(Mach even denied that he was a philosopher),
they were actually advocating their own metaphysics
while labeling the views they opposed as
"metaphysical", and using the term
as a pejorative. Positivism is a philosophy that evolved in
reaction against the various Romantic philosophies,
and what the Positivists meant by "metaphysics"
was the metaphysics of the Romantics. Just as the views of the Romantics evolved
from the philosophical tradition of the Rationalists,
similarly those of the Positivists evolved
from the tradition of the Empiricists. Thus Mach's epistemology is very similar
to the views of the Empiricists Berkeley
and Hume, and he explicitly expressed indebtedness
to them in his works.
Mach's principal work setting forth his phenomenalist
philosophy is hisAnalysis of Sensations (1885), which went through five editions
in both German and English, although Mach
also discussed his epistemological views
in many of his other works. His epistemology postulates "elements"
such as individual sounds, temperatures,
pressures, spaces, times, and colors. When these elements are considered in relation
to one another, they are studied by the physical
sciences, and when they are considered in
relation to the human mind or rather the
nervous system of the human body, they are
called "sensations" and are studied
by psychology. One of the central theses of Mach's Analysis of Sensations is that the only difference between elements
and sensations is the aspect under which
they are viewed, and that physics and psychology
therefore have the same subject matter. The distinction between the physical and
the psychical is entirely a matter of convenience
or practicality, because everything is merely
a function of these elements. Everything is a mental construct consisting
of complexes of sensations.
All material things including our own bodies
and even the ego are nothing but complexes
of elements that have been constructed by
the human mind having some fixedness or constancy
in sense experience. A fundamental thesis of Mach’s philosophy
is that material bodies do not produce sensations,
but rather complexes of sensations are associated
together by the human mind to produce material
bodies. Ultimately all that is valuable in science
is the discovery of functional relations
of dependency of sensations upon one another. The constancies that enable our mental construction
of physical bodies have no privileged reality
status. This is even more so with such mental constructs
as the physicists' molecules and atoms, which
are mental constructs that unlike those of
physical bodies are not found in experience. The Positivist phenomenalist philosophy is
a nonrealist metaphysics, and if it is generously
said to have an ontology, the ontology consists
merely of the phenomenal elements or sensations.
Mach's Philosophy of Science
Aim of Science
Mach’s philosophy of science is rich enough
that it addresses all the four basic topics
conventionally considered in a philosophy
of science: the aim of science, explanation,
criticism, and discovery. He offers several statements of the aim of
science. One sets forth the "biological task
of science", which is to give the fully
developed human individual with as perfect
a means of orienting himself as possible. In a second statement he says that the aim
of all science is the representation of facts
in thought either for practical purposes
or for removing intellectual discomfort,
since every practical and intellectual need
is satisfied when our thoughts can represent
the facts of the senses completely. He adds that our knowledge of a phenomenon
of nature is as complete as possible, when
thoughts are set before the mind's eye such
that all the relevant sensible facts can
be regarded as a substitute for the phenomenon
itself. Then the facts appear to be familiar and
are not able to occasion any surprise. In a third statement he says that the goal
of science is the simplest and most economical
abstract expression of facts. The noted economy of science involves uncompleted
facts, judgments or laws. The last two statements of the aim of science
are essentially the same as Mach's theory
of scientific explanation, and do not represent
different aims for science. And unlike the first, the second and third
statements give an aim that is intrinsic
to science.
Scientific Explanation
Mach set forth his theory of scientific explanation
in many places including his Analysis of Sensations, his "The Economical Nature of Physical
Inquiry" (1882) and "On the Principle
of Comparison in Physics" (1894) reprinted
in his Popular Scientific Lectures (1898). He says that explanation is the economical
description of experience in terms of elements. When we examine facts for the first time
they appear confusing. In time we discover simple stable elements
out of which we can mentally construct the
entire factual domain, and when we have reached
the point where everywhere we can discuss
the same facts with other persons, then we
no longer feel lost and the phenomenon is
explained. The explanation offers a survey of a given
domain of facts with the least expenditure
of thought. The representation of all the facts of a
domain by some one single mental process
is economical. He adds that the greatest perfection in mental
economy occurs when science uses mathematics.
Not all descriptions are explanations; only
direct descriptions can be explanations,
while theories on the other hand are indirect
descriptions and are not explanations. Direct descriptions may be either complete
or incomplete. Description of what is
presently observed is a complete description. Incomplete description refers to what is
presently unobserved but observable and what
is associated by a law, as for example the
movement of a comet that is presently unobserved
or the body of a man who disappears behind
a pillar. The incomplete description can be completed
by the human mind by means of the associations
made by a scientific law. A direct description is one in which a single
feature of resemblance among facts is called
from memory, while a theory such as the description
of light as a wave motion is an appeal to
another description that had previously
been made elsewhere. A theoretical idea offers more than what
we actually observe in a new fact. It can be used to extend a fact and enrich
it with features, which we are firstly induced
to seek from its suggestions and, which are
often actually found. A theory may lead to discoveries, but the
adoption of a theory always carries a danger:
even the most fruitful theory may be an obstacle
to inquiry. By way of example Mach says the theory that
light is an undifferentiated straight line
of particles impeded the discovery of the
periodicity of light. The ideal of a given domain of facts is direct
description; such description accomplishes
all that the scientific investigator could
wish
Scientific Criticism
In the Analysis of Sensations Mach states that he has taken Hume as his
starting point, and this starting point is
reflected in his views on scientific criticism. The scientist like everyone else knows the
elements with complete certainty as sensations. But scientists and other persons also make
judgments that are laws or generalizations. Since the aim of science is the adaptation
of thoughts to facts, a new fact may require
a new adaptation, which finds its expression
in the operation of judgment. A judgment is the supplementing of a sensational
presentation, in order to represent more
completely a sensational fact. In the adaptation of thoughts to facts the
adaptation can be made only to what is constant
in the facts. Only the mental construction of constant
elements can yield economy. But our confidence in the constancy in our
judgments or generalizations rests entirely
on the supposition, which in a given case
has been substantiated by numerous trials,
that our mental adaptation is sufficient. And we must be prepared to find this supposition
contradicted at any moment.
Therefore empirical laws as well as theories
are provisional in Mach's view, but for different
reasons. The empirical generalizations are provisional,
because they impute constancies to an infinite
number of individual occurrences of sensations
while only a limited number have actually
been experienced. On the other hand theories postulate things
that have never been experienced; no one
for example has ever (in Mach's time) actually
seen atoms or molecules nor has anyone ever
experienced Newtonian absolute space or absolute
time. Mach did not seem to find the provisional
status of empirical laws to be very disturbing
and in fact he considered them to be necessary
for science to have its economy. But he considered the provisional status
of theories to be an unsatisfactory expediency
for science. His theory of scientific criticism includes
a phenomenalist criterion that rejects theories. Initially the Logical Positivists who followed
Mach were reluctant to accept Hume's skeptical
views on scientific criticism, and instead
accepted the idea of "verification",
the view the scientific laws or empirical
generalizations can be established in some
permanent sense, an idea that historically
had been definitive of truly scientific knowledge. But Carnap and the Logical Positivists moved
toward Mach’s acceptance of scientific laws
as provisionally true instead of permanently
true, even as they moved away from his phenomenalism.
Scientific Discovery
Unlike most other philosophers, Mach’s concept
of scientific discovery does not involve
the idea of theory development. In his "The Part Played by Accident
in Invention and Discovery" (1895) in
his Popular Scientific Lectures Mach notes the importance of accident in
invention and discovery, but maintains that
the inventor is not passive. In fact Mach compares the discoverer to the
artist. He says that no man should consider attempting
to solve a great problem unless he has thoroughly
saturated his mind with the subject and everything
else recedes into relative insignificance. Then the discoverer can detect the uncommon
features in an accidental occurrence and
their determining conditions. Mach believed that it is the idea that dominates
the thinking of the inquirer and not vice
versa. The movement of thought obeys the laws of
association, and in a mind rich with experience
every sensation is connected with so many
others that the course of thought is easily
influenced by apparently insignificant circumstances,
the accidental occurrence of which turn out
to be decisive.
Therefore there is a process of discovery, and Mach considered how this
process could be guided. He explicitly rejected any combinatorial
approach as too laborious and extensive. The man of genius in Mach's view consciously
or unconsciously pursues systematic methods,
and in his deliberate presentiment he omits
many alternatives and abandons others after
hasty trial, alternatives on which less endowed
minds would squander their energies. From the abundance of fancies that a free
and active imagination produces, there emerges
one particular configuration which fits perfectly
with a basic design or idea. Mach does not elaborate further upon this
process; and while he believes that it may
be guided, he does not propose any consciously
repeatable procedure. Perhaps he could go no further in this investigation,
because he also believed in gestaltqualities and accepted a wholistic view of
complexes of sense impressions. In any event his belief that the process
can be guided leads him to conclude that
genius may be regarded as only a small deviation
from the average mental endowment. He states that the way to discovery must
be prepared long beforehand, and that in
due course the truth will make it appearance
inexorable as if by divine necessity. Apparently therefore he rejected the heroic
theory of invention.
Mach's History of Mechanics
Mach's most popular work was his Science of Mechanics: A Critical and Historical
Account of Its Development (1883), also known as The History of Mechanics. This book went through nine editions both
in German and in English, seven of which
were published in Mach's lifetime. The physicists whose works Mach examined
were not phenomenalists, and he set out to
write a critical history of mechanics from
the perspective of his own phenomenalist
philosophy of science. As he stated in the introduction to the first
edition, the book's purpose is to clarify
ideas, reveal the real significance of the
matter, and to purge it of its metaphysics. For Mach this agenda amounted to purging
physics of theory. With this aim in mind he critiqued the contributors
of the past as he salvaged and reconstructed
what he found in their works to be of lasting
value. Even the achievements of the great Isaac
Newton did not escape his phenomenalist criticism
unscathed. Mach criticized Newton's principle of reaction,
his concept of mass, and his concepts of
absolute space and absolute time. Starting from his own view that all phenomena
are related, Mach concluded contrary to Newton
that all masses, all velocities, and all
forces are relative, a thesis known as Mach's
phenomenalistic relativity. And he proposes his own set of definitions
and empirical propositions to replace Newton's. The outcome of this criticism was to have
a large impact on the histories of both philosophy
of science and physics.
Mach's rejection of theory in physics resulted
in several lines of criticism of his philosophical
views. One was Duhem's, which is basically philosophical
in nature. This line involves a new philosophy of language,
and was eventually taken up into Pragmatic
philosophy of language of Willard Van Quine,
whose philosophy is examined separately. The second line of criticism evolved within
physics, and it evolved due to the two great
scientific revolutions in physics, the relativity
and quantum theories. It was eventually taken up into the Pragmatic
philosophy of science of the philosopher
Russell Hanson. This line of development is also examined
in greater detail separately. Thirdly both Einstein and Heisenberg, who
were initially Positivists, were led to reject
Positivism by reflection on their own work
in physics. Consider firstly Duhem's philosophy of science
and his distinctive semantical metatheory
of physical theory.
Duhem on Physical Theory and Metaphysics
Duhem was influenced by Mach, and he called
his own philosophy of science Positivist. But there were other intellectual influences
in his thought, and as a result Duhem differed
from Mach in at lease two important respects:
firstly Duhem accepted scientific theory
as a valid and integral part of science,
and secondly he reserved a place in human
knowledge for metaphysics. Mach's philosophy is often called "scientistic",
by which is meant the view that only science
offers valid knowledge and that no nonphenomenalist
discourse, which is summarily called "metaphysical",
is valid. While Mach was a physicist, philosopher,
historian of science, and atheist, Duhem
was a physicist, philosopher, historian of
science and believing Roman Catholic. Like Mach, Duhem rejected the mechanistic,
atomistic physics although for very different
reasons than Mach. But unlike Mach, Duhem wished to retain the
natural philosophy and cosmology of the Aristotelian
and Scholastic philosophies upon which had
been built the theology of his religion since
Thomas Aquinas.
The outcome of these differences between
Mach and Duhem is a complex philosophy of
science that affirms and protects the autonomy
of physics from any encroachment by metaphysics,
while conversely affirming and protecting
the autonomy of metaphysics from any encroachment
by physics. This mutual isolation of physics and metaphysics
is due to Duhem's view that metaphysics,
natural philosophy, and cosmology on the
one hand pertain to realities that are hidden
and that underlie the phenomenal appearances
accessible by the senses, while physics on
the other hand pertains only to observed
phenomena. Furthermore and contrary
to Mach, Duhem maintained that theories are
integral to physics and are valid science. The only criterion for scientific criticism
of a theory, unlike a phenomenal description,
is the theory’s ability to make predictions
that are correct with a sufficient degree
of approximation, i.e. correct within the
range of indeterminacy produced by a degree
of measurement error that always exists in
experimental data. Thus when Duhem rejected mechanism, one reason
that he gave is that no mechanical atomic
theory has been found to be sufficiently
accurate, when judged by his purely scientific
criterion for the criticism of theories. But his principal reason for saying that
the autonomy of physical theory is protected
from the metaphysical thesis that physics
must be mechanistic, is that physical theory
has a special semantics that forbids interpreting
the hypothetical postulates realistically,
even if a proposed mechanistic hypothesis
were scientifically adequate. Physical theory in Duhem's view can never
be given a realistic semantics. No metaphysical or cosmological philosophy
may be called upon to supply theoretical
physics with its axioms. For this reason Duhem denies that physical
theory has any explanatory function in science;
only metaphysics is able to “explain”, and
metaphysics has no place in physics. The distinctive semantics of physical theory
is a very strategic part of Duhem's philosophy
of science. His religious and other intellectual influences
may have operated in his developing this
distinctive philosophy of science, but his
stratifying the semantics of the language
of science into the realistic and the nonrealist
has as its basis reasons that are entirely
integral to his concept of empirical science
itself. These reasons are semantical, and must be
examined before attempting an exposition
of his philosophy of science.
Duhem's Stratified Semantics for Physics
As mentioned above, the second respect in
which Duhem differs from Mach is the former's
views on physical theory, and the difference
is the most distinctive aspect of Duhem's
philosophy of science. Mach had rejected theory as "metaphysical",
meaning nonphenomenalist, and he maintained
that ultimately in the ideal state of science
all theory would be eliminated from science. Duhem's alternative view is set forth in
his Aim and Structure of Physical Theory (1906). In this work as well in other works he not
only recognized a valid metaphysics distinct
from science, but also considered theory
to be characteristic of science in its highest
state of development. Over and above the economy that Mach saw
in the empirical laws of science, Duhem furthermore
saw an additional economy offered by theory. Theory is a hypothetical axiomatized system
of equations that orders the multiplicity
of experimental laws by means of a symbolic
structure, which is not identical with the
empirical laws but which "represents"
them in a parallel language.
This symbolic structure consisting of the
axiomatized mathematical system which constitutes
the theory is a distinctive language in science. It is different from all other language of
science including the realistic semantics
of common discourse, the nonmathematical
generalizations of descriptive sciences such
as physiology, and the phenomenalist semantics
of mathematically expressed empirical laws
of science such as Kepler's laws. The language of theory is distinctive from
nontheory language, because the nontheory
language has a semantics that describes either
the phenomenal or real world, while the language
of theory does not have these semantics. Instead the semantics of theory language
is called "symbolic", which means
that its meaning is a sign of the meanings
of the nontheory language. Thus the semantics of science in Duhem's
philosophy is stratified into two levels,
in which one represents the other.
The basis for Duhem's distinguishing the
semantics of theory language from that of
all other language is the existence of a
numerical indeterminacy caused by the fact
that measurements, which may occur in the
equations of theory, are always approximate. There are two reasons for the indeterminacy
between the equations of theory and the nontheoretical
language. The first reason is simply the approximate
character of all measurements. When measurements are made, a "translation"
must also be made from what Duhem called
a “practical” fact to a “theoretical” fact. The practical fact describes the observed
phenomena and circumstances of the experiment;
the theoretical fact is the set of mathematical
data that replaces the practical fact in
the equations of the theory. Duhem calls the method of measurement the
dictionary that enables the physicist to
make this translation.
For any practical fact there is always an
infinity of potential theoretical facts,
even though the degree of indeterminacy
is reduced with improved instruments and
measurement procedures. So long as the one or several equations of
a theory are correct, the numbers that are
the solution set for the equations will fall
within the range of measurement indeterminacy. Duhem illustrates the semantical duality
caused by this numeric indeterminacy in his
discussion of the different meanings of the
phrase "free fall.” One meaning is contained in a phenomenal
description given by any person who knows
nothing about physical theory. And a second meaning occurs in the physical
theory that includes the idea of uniform
acceleration. These are two distinct meanings; the former
may be either a realist or phenomenalist
meaning, while the latter is called the symbolic
meaning. The latter is a sign of the former, so long
as the theory is accurate enough to be accepted
as true.
However, the numerical indeterminacy that
occasions the semantical distinction between
practical facts and theoretical facts is
not unique to the variables occurring in
the equations of theories, the equations
that are the conclusions drawn from the hypotheses
which are the postulates of the theory. It
also occurs in the variables occurring in
the equations of empirical laws, the equations
that are developed by experimental or other
observational judgments. This creates
another occasion for numerical indeterminacy,
one which exists between the values of the
variables in the equations of theory and
the values of the corresponding variables
in the equations of the empirical laws that
a theory orders. Duhem discusses this numerical indeterminacy
and the semantical duality to which it gives
rise, when he criticizes Newton's claim that
his theory of gravitation is not based on
hypotheses. The basic question is whether or not Newton's
theory was or could be developed empirically
by generalizing from Kepler's laws. Duhem argues that Newton had actually created
hypotheses, because the mathematical deduction
from these hypotheses produces conclusions
that formally contradict Kepler's observational
laws. In other words the solution set for the empirical
law and that for the theory are not the same. But
Kepler's laws are approximate, and therefore
admit to an infinity of small deviations. The measurements by Tycho Brahe permit the
theorist to choose a variation of Kepler's
laws which is also produced by deduction
from Newton's theory. Just as there must be a translation from
practical facts to theoretical facts resolving
the indeterminacy in measurements, so too
there must be a translation from empirical
laws such as Kepler's laws to "symbolic"
laws such as Newton's dynamics. Here again the numeric indeterminacy causes
a semantic duality, and a translation is
made in which the new symbolic formulas derived
from Newton's hypotheses, are substituted
for the old realistic formulas, which are
Kepler's observational laws.
Having shown that there are different semantics
for theory and nontheory language in science,
Duhem then gives two ways in which the meanings
of the symbols in theory language differ
from the meanings in all the other language
of science. The first way, which is most important to
him, is that the semantics of theory language
is neither realistic nor phenomenalist; it
does not describe the world of phenomena
as does the semantics of empirical laws,
nor the real world as does the semantics
of common sense discourse. When Duhem states, therefore, that theories
represent laws, he means to be taken literally;
he means that theories do not represent the
world but instead represent the empirical
statements which in turn represent the phenomenal
world. Thus he cannot be called an instrumentalist
in the sense that he denies that theory language
has any semantics. He has stratified the semantics of science
such that theory has its own higher level
semantics.
He also states that when a theory agrees
with experimental laws to the degree of approximation
corresponding to the measuring procedures
employed, and furthermore when the theory
predicts the outcome of an experiment before
the outcome has occurred, then there is reason
to believe that the theory is not merely
an economical representation of the experimental
laws. Such a theory is also a natural classification
of these laws in which the logical order
in which the theory organizes the experimental
laws is a reflection of the metaphysician’s
ontological order that underlies the physicist’s
phenomenal order. However, professionally the physicist cannot
pass judgment on this analogical apprehension
of the underlying ontological order, because
this order is the proper subject only of
metaphysics or natural philosophy.
The second way in which the meanings of the
symbols in theory language differ from those
in the other language of science is that
the meanings of theory are determined by
their context, by the statements that constitute
the theory itself. Therefore, according to whether the physicist
adopts one or another theory, the variables
in the symbolic law change their meaning,
so that the law may be accepted by one physicist
who admits one theory while it may be rejected
by another physicist who admits an alternative
theory. Duhem illustrates this contextual determination
of meaning in theory language in his discussion
of Kepler's observational laws and the symbolic
laws of Newton's theory. The formulas that constitute Kepler's laws
refer to orbits, but when they are replaced
by the symbolic formulas that are deduced
from Newton's dynamics, the symbolic law
contains variables referring to forces and
masses also. The translation from Kepler's laws into symbolic
laws presupposes the physicist's prior adherence
to the hypotheses of the theory. The contextual determination of the meanings
of theories is Duhem's wholistic concept
of theory, a concept that is strategic to
his views about scientific criticism of theories. With his wholistic view he says theoretical
physics is not like a machine but is more
like an organism.
Finally it should be noted that although
the higher level semantics of theory language
is relatively remote from the phenomena described
by the semantics of the nontheory language,
nevertheless theory is not remote from the
experimental situation. He states that an experiment in physics is
not simply the observation of a phenomenon,
but is furthermore the theoretical interpretation
of it. And this theoretical interpretation is not
just a technical language, but one that makes
possible the use of instruments. He illustrates this distinction between observation
and interpretation in physical experiment
by offering two descriptions of an experimental
apparatus in a laboratory. One description is given in the vocabulary
of the physicist who understands the theory
of electricity, and the other description
is given in the observational language of
the observer innocent of such theoretical
understanding. The experimenting physicist actually has
two distinct representations of the instrument
in his mind. One is the phenomenal image of the concrete
instrument that he manipulates in reality. The other is a schematic model of the same
instrument constructed mentally with the
aid of the symbols from the theories that
the physicist accepts. Without knowing the theories that the physicist
regards as established and that he uses for
interpreting the facts he observes, it is
impossible for anyone to understand the meaning
he gives to his statements. And when a physicist discusses his experiments
with another physicist, who accepts an alternative
theory, it is necessary for the two physicists
to seek to establish a correspondence between
their different ideas and then to reinterpret
the experiment. Twenty years before the development of the
quantum theory Duhem cited as an example
the two alternative theories of light: Newton's
emission theory and Frensel's wave theory. He maintained that the observations and experiments
interpreted in the concepts of one theory
can be translated into the concepts of the
other theory. In his philosophy this
is possible, not because he anticipated quantum
theory, but because he was a Positivist,
who believed that the two theories can be
related to a common theory-neutral phenomenalist
semantics.
Duhem's stratification of the semantics of
the language of theoretical science is central
and strategic to his philosophy of science. It is not surprising he stated that the approximate
fit between measurements and theory creates
a semantical difference, although it might
seem more correct were he to have said that
the resolution of the indeterminacy in measurement
by the calculated value for a variable in
a theory actually resolves a semantic vagueness
instead of saying, as he does, that it creates
two distinct meanings. But it is surprising to find him concluding
that the distinct meaning of the symbol in
the theory is a "sign" of the phenomenal
meaning defined by the experimental measurement
method. It is this latter position that stratifies
the semantics of science, so that theory
cannot be given a realistic or phenomenalistic
interpretation. Nonetheless Duhem has a reason for taking
this position. In his "The Physics of a Believer",
an appendix to Aim and Structure of Physical Theory, he reports that earlier in his career after
attempting unsuccessfully to conform to Newton's
methods set forth in the "General Scholium",
he concluded that physical theory is neither
a metaphysical explanation nor a set of general
laws, whose validity is established, but
rather that theory is an artificial construction
manufactured with the aid of mathematical
magnitudes, and that the relations of the
magnitudes to the abstract notion emergent
from experiment, is that of sign to thing
signified. The key concept seems to be the idea of artificial
construction. The artificial nature of theory gives it
an artificial semantics, and this artificial
semantics is of a different kind than the
natural semantics of language that describes
the phenomenal world.
Throughout most of the history of philosophy,
philosophers believed that while the multiplicity
of languages argues for the existence of
a conventional aspect in human language,
still, as Aristotle said, while men speak
different languages, they have the same cognitive
experiences. This is the thesis of a naturalistic semantics;
all men have the same cognitive experience
when in the presence of the same reality,
because there is a natural relation between
knowledge and reality. Mach’s theory of sensations and of their
identification with elements of the phenomenal
world is a variation of this thesis. But Duhem could not fit this thesis to the
language of physical theory, even while he,
like Mach, maintained it for the language
of observation. He viewed physical theory as so artifactual,
that its meanings could not be natural but
had to be artificial. Therefore the
language of theory does not describe either
the real or the phenomenal world, the world
of nature. At the same time he was not led to conclude
that theory is meaningless. Thus his reconciliation strategy was to make
the artificial semantics of theory language
describe or represent the language of science,
which is not a phenomenon of nature but rather
is an artifact.
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ON PHYSICAL THEORY
Duhem's Philosophy of Science
The Aim of Science
Duhem's statement of the aim of science is
similar to Mach`s: the aim of science is
economy of thought. Like Mach, Duhem believes that experimental
laws contribute an intellectual economy,
because they summarize a large number of
concrete facts. But unlike Mach, Duhem furthermore says that
theories also contribute to the realization
of the aim of science. The economy achieved by the substitution
of a law for concrete facts is redoubled
for the mind, when the mind substitutes theories
for the numerous experimental laws. A theory is a system of mathematical propositions
deduced from a small number of principles,
which aim to represent as simply, as completely,
and as exactly as possible, a set of experimental
laws. Its aim in other words is economy of thought
by schematically representing and logically
organizing experimental laws.
Scientific Criticism
Duhem developed a sophisticated theory of
scientific criticism, and it is central to
his philosophy of science. He is very emphatic in defending the autonomy
of empirical science from any encroachment
by metaphysics or natural philosophy. Metaphysics pertains to realities that underlie
the phenomenal appearances that are hidden
by the phenomena, while science pertains
to these appearances. Consequently whatever may be the criteria
and procedures for criticizing a metaphysical
thesis, they are not relevant to empirical
science. In empirical sciences that are nonmathematical,
the generalizations such as "all men
are mortal" may be accepted or rejected
as simply true or false. But in mathematical physics the equations
both of the empirical laws and of the hypothetical
theories are not simply regarded as true
or false, but are approximate. The amount of indeterminacy due to the approximate
nature of the values of the variables in
these equations will be reduced as experimental
and measurement techniques improve. These improvements in theory occur because
instruments are improved. And because instruments depend on physical
theory, the improvement of instruments occurs
in turn due to the improvement in theory. As
the range of this indeterminacy becomes smaller,
the equations of either the empirical laws
or the hypothetical theories that represent
the laws may no longer be able to predict
values for their variables that fall within
the smaller range. When this happens,
the equations are no longer satisfactory. Duhem is very emphatic in his thesis that
the only criterion that may validly operate
in scientific criticism is the ability of
the law or theory to make accurate predictions. This exclusion of all prior ontological or
metaphysical criteria from scientific criticism
has been carried forward into the contemporary
Pragmatist philosophy of science. It shows up for example as Quine’s rejection
of all “first philosophy.”
In his theory of scientific criticism Duhem
rejected the use of so-called crucial experiments
as a means of establishing the validity of
a theory. His thesis is that if the physicist is confronted
with several alternative theories, the rejection
of all but one cannot imply the establishment
of the remaining one. As an example he cites the two alternative
theories of light: one theory is the hypothesis
that light is a stream of high speed projectiles,
and the other is the hypothesis that light
consists of vibrations whose waves are propagated
in an ether. This is not an anticipation of the Copenhagen
duality thesis; Duhem is thinking of the
wave and particle theories as alternative
theories. His position is that the choice is not mutually
exclusive, because no one can ever enumerate
completely all of the various hypotheses,
which may pertain to a determinate group
of phenomena. He thus maintains that several alternative
theories may fall within the range of indeterminacy
of the measurement data and experimental
laws, so that more than one theory may be
satisfactory. This represents a pluralistic thesis about
science, and in the crucial experiment discussion,
it means that even if all hypotheses could
somehow be enumerated, elimination could
not leave but one to be considered as established. More generally his pluralism means that the
indeterminacy in measurement, laws, and theories
produces indeterminacy in scientific criticism. This pluralism is another aspect of his philosophy
of physical theory that has been carried
forward into the contemporary Pragmatist
philosophy of science.
His theory of scientific criticism also reflects
his wholistic or organic view of theories. This wholistic view not only makes the meanings
of the mathematical symbols mutually determined
by the context consisting of the equations
of the theory, it also necessitates testing
the theory as a whole together with all the
hypotheses used in the experiment including
assumptions about the measuring instruments. If the prediction in the test is wrong, not
only may the proposition being tested be
at fault, but also the whole theoretical
scaffolding used by the physicist. The physicist can never subject an isolated
hypothesis to experimental test, but only
a whole group of hypotheses. The only thing that the experiment reveals
is that among all the theoretical propositions
used to predict the phenomenon, there is
at least one error. Thus the failure of the prediction does not
inform the physicist where the error lies
or reveal which hypothesis should be modified. In Duhem's view physics is not like a machine
which lets itself be disassembled; the physicist
cannot test each piece in isolation and then
make adjustments to the isolated part found
wanting. Duhem compares physics to an organism in
which one part cannot be made to function
except when the parts that are most remote
from it are called into play. When there is a malfunction felt in the organism,
the physician must ferret out through its
effects on the entire system, the organ that
needs to be remedied or modified without
the possibility of isolating the organ and
examining it apart. Duhem says that the physicist confronted
with a failed prediction is more like a physician
than a watchmaker.
Scientific Discovery
Duhem also has a philosophy of scientific
discovery. Unlike Mach's view on discovery and invention
in science, Duhem's is not principally a
theory of perception. He anticipates later philosophers including
the Logical Positivists with his emphasis
on the language of science. For him scientific discovery is not reduced
to noticing what had previously been overlooked
in perception; for him discovery is also
the construction of theoretical hypotheses. The construction of a theory involves four
successive operations: Firstly certain physical
properties are taken as simple, so that other
things are combinations of these simple properties. These properties are not simple in any absolute
sense like Mach's elements, but are taken
as simple for purposes of the theory only. The simple properties are measured, and the
magnitudes are assigned to symbolic variables. Secondly the magnitudes are connected by
propositions that are hypotheses, and that
serve as postulates of the deductive system. Thirdly the postulates are not realistic
or phenomenalist, but are freely created;
using them requires only that the logic of
algebra be correctly applied for making deductions. Fourthly
the conclusions drawn from the postulates
are compared with the experimental laws that
the theory is intended to represent.
If the conclusions agree with the laws within
the degree of approximation corresponding
to the measurements taken in the experiments,
then the theory is said to be a good theory. Such acceptable theory may in turn be used
for the further development of measuring
instruments used in experiments, as well
as constituting the final product of the
scientific endeavor with its maximum economy. Improved theory produces improved instruments,
which in turn produce better measurements. These better measurements reduce the range
of the indeterminacy in the numerical data,
which may cause the theories to fail in their
predictions. This failure will occasion two types of responses. The initial response is to modify the theory
with corrections, which will enable the predictions
made with the theory to fall within the smaller
range of indeterminacy produced with improved
measurements. But these corrections also complicate the
theory, and in due course "good sense"
may lead some physicists to decide to refrain
from adding more complicating corrections,
and instead attempt to revise the hypothetical
postulates of the symbolic schema, the whole
theory itself. The accomplishment of such a revision is
the work of the genius. But Duhem does not subscribe to the heroic
concept of invention; history creates the
genius as much as the genius creates history. The physicist does not choose the hypotheses
on which he will build a new theory; the
theory germinates within him. This germination is not sufficiently explained
by the contemplation of the experimental
laws that the theory must represent. It is a larger cultural development. In due course when the cultural process that
he calls universal science has prepared minds
sufficiently to receive a theory, it arises
in a nearly inevitable manner. Often physicists who do not know one another
and who are working great distances from
one another, generate the same theory at
the same time. In the course of his studies the historian
of science according to Duhem often observes
this simultaneous emergence of the same theory
in countries far from one another.
Scientific Explanation
On Duhem’s philosophy theories do not explain
the laws nor do the laws explain the facts. Explanation is proper only to metaphysics
and not to science. In the opening sentence
of the introduction to his Aim and Structure of PhysicalTheory, Duhem says that he offers a simple logical
analysis of the method by which physical
science makes progress. While affirming the autonomy of physics with
his thesis that agreement with experiment
is the sole criterion of truth for a physical
theory, Duhem has a distinctive concept of
scientific progress, which he elaborates
in the appendices to the book. He says that there are two types of development
in physics that are occurring simultaneously. One is what today would be called the revolutionary
type of development consisting of a succession
of alternative theories, in which one theory
arises, dominates the scene for the moment,
and then collapses to be replaced by another
theory. The other is an evolutionary progress in
which constantly more ample and more precise
mathematical representation of the phenomenal
world is disclosed by experiment. When the progress of experimental science
goes counter to a theory and compels the
theory to be modified or transformed, the
purely representative part enters nearly
whole into the new theory, bringing to it
the inheritance of all the valuable possessions
of the old theory, while the hypothetical
part falls away in order to give way to another
theory. The first type is identified with the mechanistic
physical systems including Newtonian physics
as well as Cartesian and atomic physics. The second type is identified with general
thermodynamics, which Duhem believes will
lead physical theory toward its goal. He envisioned this goal as the convergence
toward an analogy with Aristotle's physics. He concludes in his discussion of the value
of theory, that the physicist is compelled
to recognize that it would be unreasonable
to work for the progress of physical theory,
if theory were not the increasingly better
defined and more precise reflection of a
metaphysics. He thus concludes his book with the thesis
that belief in an order transcending physics
is the metaphysical justification of physical
theory.
Duhem's History of Physics
Just as Mach had written a history of physics
viewed through the lenses of his philosophy
of science, so too did Duhem. However, Duhem's effort was relatively monumental;
it is a work originally intended to be twelve
volumes of which ten were actually written
before its author's death in September 1916. This magnum opus was his System of the World: A History of Cosmological
Doctrines from Plato to Copernicus. The central thesis of this work is summarized
in a much smaller book begun earlier, To Save the Phenomena: An Essay on the Idea
of Physical Theory from Plato to Galileo (1908). The thesis is that the hypotheses of physics
and especially the heliocentric hypothesis
in astronomy are mere mathematical contrivances
for the purpose of saving the phenomena.
Pope Urban VIII condemned Galileo in 1633
for maintaining that Copernicus' heliocentric
theory is not merely a mathematical contrivance,
but is rather a description of the real world. Formerly Cardinal Bellarmine, the Pope maintained
that regardless of how numerous and exact
may be the confirmations of a theory by experience,
these confirmations can never transform a
hypothesis into a certain truth that can
be taken realistically, since this transformation
would require that the experimental facts
should contradict any other hypotheses that
might be conceived, a requirement that cannot
logically be satisfied. Galileo, on the other hand, maintained that
because Copernicus's theory saved the phenomena
more adequately than any alternative hypothesis,
the Copernican theory had to be a realistic
one. Contemporary Pragmatists agree with Duhem's
rejection of any prior ontological criteria
for the criticism of scientific theory, but
contrary to Duhem they furthermore agree
with Galileo's practice of scientific realism. Contemporary Pragmatists are realists, who
let the most empirically adequate theory
decide the ontology. Galileo's argument for realism is the same
as Quine's doctrine of ontological relativity,
and Feyerabend calls it the Galileo-Einstein
tradition of realism. And Heisenberg invoked this tradition, when
he referenced Einstein's realistic interpretation
of relativistic time in the relativity theory,
and then used it as a precedent for his own
realistic interpretation of the quantum theory's
duality thesis, notwithstanding Bohr's instrumentalist
complementarity principle. Duhem, however, denied that science is realistic,
and he construed Galileo's argument as a
case of the fallacy of the crucial experiment. He
argued that it is impossible to enunciate
all the possible hypotheses, and establish
the truth of one by elimination of all others. The accomplishment that Duhem credits to
Kepler and Galileo is the rejection of Aristotle's
view that celestial and terrestrial physics
are fundamentally different, and that hypotheses
of physics must save all the phenomena of
the inanimate world.
The New Physics vs. the Old Philosophy
The history of philosophy of science has
been greatly influenced by the history of
physics. As twentieth-century physicists found themselves
departing farther and farther from Newtonian
physics, they also found themselves departing
farther and farther from the Positivist philosophy
notwithstanding the Positivists’ criticisms
of Newtonian physics. At the beginning of
the century Positivism was not merely the
academic philosophy it later became. It was for a time the working philosophy
for many physicists including those who produced
the revolutionary relativity and quantum
theories. It achieved ascendancy in academia during
the first half of the century, where it evolved
into Logical Positivism with the introduction
of the symbolic logic, which made it nearly
completely irrelevant to the practice of
basic research in physics. But long before academia recognized Positivism
as a kind of latter-day decadent scholasticism
in the second half of the century, it had
fallen into disrepute in the eyes of the
physicists who encountered its fundamental
inadequacy for the new physics.
In his "Autobiographical Notes"
in Schilpp's Albert Einstein (1949) Einstein stated that Mach's History of Mechanics had exercised a profound influence on him
when he was a student. He related that all physicists of the last
century saw in classical mechanics a firm
and final foundation not only for all physics
but also for all natural science, and that
it was Ernst Mach who with this book shook
his dogmatic faith. At sixty-seven years of age, when he was
writing these autobiographical notes, Einstein
saw Mach's greatness in the latter's incorruptible
skepticism and independence, even though
Einstein himself had since rejected Mach's
philosophy. Einstein was specifically influenced by Mach's
critique of the Newtonian concept of absolute
space, time and motion, ideas that are also
rejected in Einstein's relativity theory. Initially Mach seemed to support Einstein's
views. But Mach and Einstein were fundamentally
working at cross purposes: Mach attacked
the Newtonian concepts of absolute space,
time and motion as part of his critique of
all theoretical physics, while Einstein discarded
these Newtonian ideas as a means for developing
a new theoretical physics.
Another influence on Einstein was a thought
experiment that Einstein reports he imagined,
when he was sixteen years of age. In this thought experiment Einstein wondered
what would happen if an observer traveled
at the speed of light, riding on a beam of
light. The light would then be at rest relative
to the rider, but Einstein concluded that
the idea of a light beam at rest is self-contradictory. This thought experiment was imagined many
years before Einstein was introduced to Mach's
book by his friend Besso, while they were
students at Zurich, and Einstein reports
that it contributed to his forming the idea
that the velocity of light in a vacuum is
constant in all reference systems. From the Positivist view the constancy of
light is no less objectionably absolute than
the concepts of absolute space or time. Mach's phenomenalist relativity states that
all sensations are dependent on all other
sensations, while Einstein's relativity theory
states that the velocity of light in a vacuum
is independent of other phenomena.
Throughout Mach's lifetime Einstein continued
to view his relativity theory as a continuation
of Mach's philosophy, and in his obituary
on Mach in 1916 Einstein expressed the opinion
that Mach would have come across the theory
of relativity, if when Mach was younger the
constancy of the velocity of light had been
accepted by physicists. In 1921 Mach's son published his father's Principles of Physical Optics. The preface of the book is dated July 1913,
and in it Mach opposes Einstein's relativity
theory and rejects the idea that he was a
forerunner of relativity theory. As it happens, in June of 1913 Einstein had
sent Mach a preliminary draft of the general
theory of relativity, which uses non-Euclidian
geometry. But in the 1912 edition of his Science of Mechanics Mach had introduced a lengthy footnote (Ch. IV, Sec IV, 9) opposing Minkowski's
use of four-dimensional geometry in physics
and stating that the space of sight and touch
is three-dimensional. It is unlikely, therefore, that Mach was
pleased when he received Einstein's 1913
correspondence, and it may have provoked
Mach's footnote comments in the 1913 preface
to the book on optics. Eventually Einstein accepted the existence
of basic differences between his relativity
theory and the philosophy of Mach, and he
ultimately rejected Mach's philosophy.
Einstein's general theory of relativity departed
even further from Mach's philosophy than
did the special theory of relativity, because
in the general theory it is not possible
to restrict the equations to relations among
observable magnitudes. But as the theory became accepted among physicists,
the Positivists who followed Mach did not
want to reject it, and instead they modified
their philosophy. These later or "Logical" Positivists,
as the Positivists of the Vienna Circle came
to be known, replaced Mach's rejection of
theories with the less restrictive idea. They said that the language of science may
contain theoretical terms referring to nonobservable
entities and magnitudes, on condition that
statements referring only to observables
could logically be related to those that
contain these theoretical terms referring
to the nonobservable magnitudes or entities. This later Positivist program is considered
below in the discussion of the Logical Positivists
and particularly of Rudolf Carnap. Mach accepted Einstein's relativity theory,
and persuaded Moritz Schlick, founder of
the Vienna Circle and successor to the chair
of inductive philosophy held by Mach at Vienna,
to accept Einstein's theory also. With this acceptance of Einstein's relativity
theory one of the basic theses of the Positivist
philosophy was changed.
Positivism was not without some influence
on the contributors to the new quantum physics,
whose views became known as the "Copenhagen
interpretation.” Adherents to this interpretation included
Niels Bohr, Werner Heisenberg, and Wolfgang
Pauli. Its opponents included Albert Einstein, Erwin
Schrödinger, Max Planck, Louis de Broglie
and David Bohm. The member of Bohr’s Institute for Theoretical
Physics in Copenhagen, Denmark, who was initially
influenced by the Positivist philosophy,
was Werner Heisenberg. In his Physics and Beyond (1971) Heisenberg relates how Mach's philosophy
operated in his own thinking. In the chapter titled "Understanding
in Modern Physics (1920-1922)" he described
his Positivist views during the years that
preceded his development of his matrix mechanics. At that time he believed that true understanding
in physics consists in using only language
that refers to direct sense perceptions,
and that while the ability to make correct
predictions is often a consequence of this
Positivist kind of understanding, nonetheless
making correct predictions is not the same
as having true understanding. Because he accepted the Positivist philosophy
of science, Heisenberg rejected Bohr’s hypothesis
of electron orbits, since the orbits are
not observable, but unlike Mach he admitted
the existence of the electron itself due
to the observable tracks produced by the
free electron in the Wilson cloud chamber
experiments.
In the chapter titled "Quantum Mechanics
and a Talk with Einstein (1925-1926)"
Heisenberg relates that on the day that he
presented his matrix mechanics to the Physics
Colloquium at the University of Berlin, Einstein,
who was present in the assembly, expressed
interest and invited Heisenberg to talk with
him at his home that evening. The matrix mechanics does not postulate the
existence of electron orbits around the nucleus
of the atom, and when Einstein questioned
Heisenberg about his Positivistic views that
evening, Heisenberg replied that he did not
believe that postulates about orbits are
appropriate, because the orbits are not observable. Heisenberg affirmed the view that the physicist
should consider only observable magnitudes,
and for that reason he developed the matrix
mechanics, which treats only of the frequencies
and amplitudes associated with the lines
in the spectrum of the atom. Heisenberg also stated that he was using
the same philosophy that Einstein had used,
when the latter had rejected the concept
of absolute space and time in developing
relativity theory. Einstein then replied that he no longer accepted
the Positivist view, because it is the physical
theory that describes what the physicist
can observe. This idea that theory determines what is
observed is philosophically very strategic,
because it contradicts the underlying Positivist
assumption that there is a dichotomous distinction
between the descriptive language about what
is observable on the one hand, and the theoretical
language about what is not observable on
the other hand. When this dichotomy is denied, the Positivist
program of building science on firm foundations
of observation is rendered untenable.
In the chapter titled "Fresh Fields
(1926-1927)" Heisenberg describes the
arguments between Niels Bohr and Erwin Schrödinger
concerning the issue of the wave verses the
particle views in microphysics and of the
statistical approach taken by Max Born in
1927. Born maintained that Schrödinger's wave function
can be construed as the measure the probability
of finding an electron at a given point in
space and time. Heisenberg accepted Born's probability interpretation,
but there still remained a problem in Heisenberg's
mind: Born's interpretation did not explain
how the trajectory of an electron in the
cloud chamber could be reconciled with the
wave mechanics. Trajectories did not figure in the quantum
mechanics, and wave mechanics could only
be reconciled with the existence of a densely
packed beam of matter if the beam spread
over areas much larger than the diameter
of an electron. With this problem in mind Heisenberg remembered
his conversation with Einstein the previous
year, specifically Einstein's statement that
it is the theory that determines what the
physicist can observe. Einstein's discussion with Heisenberg on
the day that Heisenberg had first presented
his matrix mechanics in 1926 in Berlin led
Heisenberg to recognize in 1927, that it
was the classical theory that led him to
think that the tracks in the Wilson cloud
chamber represent the movement of a particle
as having a definite position and velocity
that defined its trajectory. Recognition of the interpenetrating of theory
and observation led Heisenberg to reconsider
what is observed in the cloud chamber. He then rephrased his question about trajectories
in terms of the quantum theory instead of
the classical theory; he asked: Can the quantum
mechanics represent the fact that an electron
finds itself approximately in a given place
and that it moves approximately at a given
velocity? In answer to this new question he found that
these approximations could be represented
mathematically, and he called this mathematical
representation the "indeterminacy principle",
also known as the “uncertainty relations.” On this principle the limit of accuracy with
which both position and momentum can be known
is defined in terms of Planck's constant. In the view of Heisenberg and those who advocate
the "Copenhagen interpretation"
this necessary degree of approximation is
not merely a measurement inaccuracy, but
is imposed by the nature of the universal
quantum of action. Einstein's semantical principle, that theory
decides what the physicist can observe, became
one of the corner stones of the post-Positivist
philosophy of science as articulated both
by Karl Popper and by the contemporary Pragmatists;
it led the contemporary philosophers to reject
the Positivist separation of theory and observation.
Heisenberg also describes his thought processes
in this discovery experience in his chapter
on the history of quantum theory in his Physics and Philosophy (1958). There he says that he turned around a question:
instead of asking how the known formalism
of Newtonian physics could be used to express
a given experimental situation, he instead
asked whether or not only such experimental
situations can arise in nature as can be
expressed in the mathematical formalism of
the matrix mechanics. This recounting of his thinking gives greater
emphasis to the ontological commitment that
characterizes the "indeterminacy principle",
according to which there does not simultaneously
exist in reality both a determinate position
and a determinate momentum for the electron.
As it happens, Einstein was never willing
to accept the ontology of the Copenhagen
interpretation, even though Heisenberg attempted
to do the same thing with his matrix mechanics
that Einstein did with the Lorentz transformation,
when the latter interpreted the Lorentz equation
in terms of actual time instead of apparent
time and redefined the concept of simultaneity. Einstein maintained that a more "complete"
microphysical theory is needed, which would
satisfy his own ontological criteria for
physical reality. In imitating Einstein, Heisenberg was practicing
scientific realism according to which ontological
commitment is extended to the most empirically
adequate theory. The Pragmatist philosophy
of language implies this practice, in which
it might be said that a carte blanche metaphysical realism is presumed, while the
ontology describing reality is supplied by
empirical science; it is a realism which
is a blank check for which scientific theory
specifies its cash value, and for which empirical
criticism backs its negotiability.
Heisenberg did not escape the influence of
Positivism, even though he had departed from
it in a very fundamental way to develop the
indeterminacy relations. Another influence upon his thinking was Bohr’s
philosophy of knowledge. Bohr did not explicitly embrace Positivism,
but in his view classical physics is permanently
valid and must serve as the language of observation,
in which all accounts of evidence in physical
science must be expressed. Heisenberg's
attempt to reconcile the influences of Einstein
and Bohr resulted in his developing his semantical
theory of "closed-off theories.” This is his attempt at a systematic philosophy
of language for science. It is different from the Logical Positivist
philosophy, but due to Bohr’s influence it
is more like Positivism than the contemporary
Pragmatism. Einstein and Heisenberg had made very insightful
criticisms of Positivism, but neither produced
a new systematic philosophy of language adequate
to their insights, however portentous these
insights have turned out to be. The portended Pragmatist philosophy of language
and science was as great an intellectual
revolution in philosophy as the revolutions
in physics which they themselves produced.
Comment and Conclusion
This chapter examined two variations on Positivism
formulated by two turn-of-the-nineteenth-century
physicists, and previewed the story of Positivism’s
rejection by the physicists who made the
two great scientific revolutions in twentieth-century
physics. This story will be given in greater detail
below in the chapter describing Heisenberg’s
philosophy of quantum theory. But to appreciate these developments more
adequately, it is helpful firstly to have
examined the development of the Pragmatist
philosophy of language. Therefore the next chapter describes the
extension of Machian Positivism by Carnap
in response to Einstein’s development of
the theory of relativity, and then Quine’s
critique of Carnap with Duhem’s philosophy
of physical theory, which Quine transformed
into a general philosophy of language, the
contemporary Pragmatist philosophy of language.
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