Very Incomplete Notes for 
The Aim and Structure of Physical Theory
by Pierre Duhem

What is the aim of a physical theory? Answer 1 (not Duhem): To explain a
group of laws which have been established by experiment. Answer 2 (Duhem):
To summarize and classify logically a group of experiment laws without
claiming to explain them. (7)

Cosmological schools (Aristotelian, Newtonian, atomistic, Cartesian) accuse
each other of appealing to "occult causes". (14)

"A physical theory is not an explanation.  It 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. (19)

The reduction of laws to theories is an "intellectual economy"; once a small
number of hypotheses are known, the laws can be deduced. (21)

Theory classifies laws, organizing them in a useful order.  "Order, wherever
it reigns, brings beauty with it.  Theory not only renders the group of
physical laws it represents easier to handle, more convenient, and more
useful, but also more beautiful." (24)

[Physical theory] never reveals realities hiding under the sensible
appearances; but the more complete [physical theory] becomes ... the more we
suspect that the relations it establishes among the data of observation
correspond to real relations among things, and the more we feel that theory
tends to be a natural classification." (26-27)

Duhem considers the question: "If theory is to be a natural classification
... is not the surest way to reach this goal to inquire first what these
realities are?" (31)

From Newton's Optics: "To tell us that every species of things is endowed
with an occult specific quality by which it acts an produces manifest
effects,  is to tell us nothing; but to derive two or three general
principles of motion from phenomena, and afterward to tell us how the
properties and actions of all corporeal things follow from those manifest
principles, would be a very great step in philosophy, though the causes of
those principles were not yet discovered; and therefore I scruple not to
propose the principles of motion above mentioned, they being of very large
extent, and leave their causes to be found out." (48)

A double economy of thought: 1. substituting a law for a multitude of facts
and 2. substituting a small group of hypotheses for a vast set of laws. (55)

Pascal: "There are, then, two kinds of minds: one kind, able to penetrate
quickly and profoundly the consequences of principles, we call the exact
mind; the other, able to comprehend a great number of principles without
confusing them, we call the geometrical mind." (57)

"Understanding a physical phenomenon is, therefore, for the physicists of
the English school, the same thing as designing a model imitating the
phenomenon; whence the nature of material things is to be understood by
imagining a mechanism whose performance will represent and simulate the
properties of the bodies.  The English school is completely committed to the
purely mechanical explanations of physical phenomena." (72)

"A physical theory will then be a system of logically linked propositions
and not an incoherent series of mechanical or algebraic models.  This system
will have for its object not the furnishing of an explanation but the
representation and natural classification of experiment laws, taken in a
group.  To require that a great number of propositions be linked in a
perfect logical order is not a slight or easy condition to satisfy [outside
of mathematics]." (107)

"The mathematical development of a physical theory cannot be welded to
observable facts except by a translation.... But translation is treacherous:
traduttore, traditore (to translate is to betray).  There is never a
complete equivalence between two texts where one is a translated version of
the other." (133)

"Whereas the contours of the drawing are fixed by a line of precise
hardness, the contours of the object are misty, fringed, and shadowy.  It is
impossible to describe the practical fact without attenuating by the use of
the word 'approximately' or 'nearly' whatever is determined too well by each
proposition; on the other hand, all the elements constituting the
theoretical fact are defined with rigorous exactness.  Whence we have this
consequence: An infinity of different theoretical facts may be taken for the
translation of the same practical fact." (134)

"A mathematical deduction is of no use to the physicist so long as it is
limited to asserting that a given rigorously true proposition has for its
consequence the rigorous accuracy of some such other proposition.  To be
useful to the physicist, it must still be proved that the second proposition
remains approximately exact when the first is only approximately true.  And
even that does not suffice.  The range of these two approximations must be
delimited; it is necessary to fix the limits of error which ca be made in
the result when the degree of precision of the methods of measuring the data
is known; it is necessary to define the probable error that can be granted
the data when we wish to know the results within a definite degree of
approximation....  But let us not be deceived about it; this 'mathematics of
approximation' is not a simpler and cruder form of mathematics.  On the
contrary, it is a more thorough and more refined form of mathematics." (143)

Two sorts of observation take place in the case of experiment.  The first
sort does not require any knowledge of physics; the second consists in the
interpretation of observed facts.  "An experiment in physics is the precise
observation of phenomena accompanied by an interpretation of these
phenomena; this interpretation substitutes for the concrete data really
gathered by observation abstract and symbolic representation which
correspond to them by virtue of the theories admitted by the observer."
(145-47)

"It would really be impossible to use the instruments we have in physics
laboratories if we did not substitute for the concrete objects composing
these instruments an abstract and schematic representation which
mathematical reasoning takes over, and if we did not submit this combination
of abstractions to deductions and calculations implying the assimilation of
theories." (153)

"The physicist who complicates the theoretical representation of the
observed facts by corrections, in order to permit this representation to
come to closer grips with reality, is similar to the artist who, after
finishing the line sketch of a drawing, adds shading in order to express
better on a plane surface the profile of the model.... To allow a cause of
systematic error to remain in an experiment is to omit making a possible
correction which would increase the precision of an experiment ... it means
being content with a line sketch when we could make a shaded drawing." (158)

"If theoretical interpretation removes from the results of physical
experiment the immediate certainty that the data of ordinary observation
possess, on the other hand it is theoretical interpretation which permits
scientific experiment to penetrate much further than common sense into the
detailed analysis of phenomena, and to give a description of them whose
precision exceeds by far the accuracy of current language." (164)

"Such is not the case with the laws that a physical science, come to full
maturity, states in the form of mathematical propositions; such laws are
always symbolic.  Now, a symbol is not, properly speaking, either true or
false; it is, rather, something more or less well selected to stand for the
reality it represents, and pictures that reality in a more or less precise,
a more or less detailed manner." (168)

When several laws are equally appropriate to a physicist because they all
predict with a greater accuracy than can be detected by our instruments,
choice can be made on grounds of simplicity. (171)

"Any physical law, being approximate, is at the mercy of the progress which,
by increasing the precision of experiments, will make the degree of
approximation of this law insufficient: the law is essentially provisional."
(174)

"Physics does not progress as does geometry, which adds new final and
indisputable propositions to the final and indisputable propositions it
already possessed; physics makes progress because experiment constantly
causes new disagreements to break out between laws and facts, and because
physicists constantly touch up and modify laws in order that they may more
faithfully represent facts." (177)

Duhem/Bernard: Theory suggests experiment and is used to generalize it's
results, but "so long as the experiment lasts, the theory should remain
waiting, under strict orders to stay outside the door of the laboratory". 
Those who hold too strongly to their theories make poor observations. (181)

In physics, "it is impossible to leave outside the laboratory door the
theory that we wish to test, for without theory it is impossible to regulate
a single instrument or to interpret a single reading." (182)

"The physicist can never subject an isolated hypothesis to experimental
test, but only a whole group of hypotheses; when the experiment is in
disagreement with his predictions, what he learns is that at least one of
the hypotheses constituting this group is unacceptable and ought to be
modified; but the experiment does not designate which one should be
changed." (187)

"The only experimental check on a physical theory which is not illogical
consists in comparing the entire system of the physical theory with the
whole group of experimental laws, and in judging whether the latter is
represented by the former in a satisfactory manner." (200)

"In the course of its development, a physical theory is free to choose any
path it pleases provided that it avoids any logical contradiction; in
particular, it is free not to take account of the experiment facts.  This is
no longer the case when the theory has reached its complete development. 
When the logical structure has reached its highest point, it becomes
necessary to compare the set of mathematical propositions obtained as
conclusions from these long deductions with the set of experimental
facts.... This comparison between the conclusions of theory and the truth of
experiment is therefore indispensable, since only the test of facts can give
physical validity to a theory." (206)

"What are the conditions logically imposed on the choice of hypotheses to
serve as the base of our physical theory?  1. No self-contradictory
hypotheses.  2. No contradictory hypotheses.  3. "Hypotheses shall be chosen
in such a manner that from them taken as a whole mathematical deduction may
draw consequences representing with a sufficient degree of approximation the
totality of experimental laws.  In fact, the proper aim of physical theory
is the schematic representation by means of mathematical symbols of the
laws established by the experimenter; any theory of whose consequences is in
plain contradiction with an observed law should be mercilessly rejected. 
But it is not possible to compare an isolated consequence of theory with an
isolated experimental law.  The two systems must be taken in their
integrity: the entire system of theoretical representations on the one hand,
and the entire system of observed data on the other." (220)

The history of methods plays a role int he study of physics that it does not
in the role of geometry.  "In geometry, where the clarity of deductive
method is fused directly with the self-evidence of common sense, instruction
ca be offered in a completely logical manner.  It is enough for a postulate
to be stated for a student to grasp immediately the data of common-sense
knowledge that such a judgment condenses; he does not need to know the road
by which this postulate has penetrated into science.... [However, in
physics] it is forbidden to be purely and completely logical in teaching. 
Consequently, the only way to relate the formal judgments of theory to the
factual matter which these judgments are to represent, and still avoid the
surreptitious entry of false ideas, is to justify each essential hypothesis
through its history.  To give the history of a physical principle is at the
same time to make a logical analysis of it.  (269)