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- 声望
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no5-3-1
The belief that art originates in intuitive rather than
rational faculties was worked out historically and phi-
losophically in the somewhat wearisome volumes of
Benedetto Croce, who is usually considered the orig-
inator of a new aesthetic. Croce was, in fact, express-
ing a very old idea. Long before the Romantics
stressed intuition and self-expression, the frenzy of
inspiration was regarded as fundamental to art, but
philosophers had always assumed it must be controlled
by law and by the intellectual power of putting things
into harmonious order. This general philosophic con-
cept of art was supported by technical necessities. It
was necessary to master certain laws and to use intel-
lect in order to build Gothic cathedrals, or set up the
stained glass windows of Chartres. When this bracing
element of craftsmanship ceased to dominate artists’
outlook, new technical elements had to be adopted to
maintain the intellectual element in art. Such were
linear perspective and anatomy.
17. The passage suggests that which of the following
would most likely have occurred if linear per-
spective and anatomy had not come to influence
artistic endeavor?
(A) The craftsmanship that shaped Gothic
architecture would have continued to
dominate artists’ outlooks.
(B) Some other technical elements would have
been adopted to discipline artistic inspi-
ration.
(C) Intellectual control over artistic inspiration
would not have influenced painting as it
did architecture.
(D) The role of intuitive inspiration would not
have remained fundamental to theories of
artistic creation.
(E) The assumptions of aesthetic philosophers
before Croce would have been invalidated.
18. The passage supplies information for answering
which of the following questions?
(A) Does Romantic art exhibit the triumph of
intuition over intellect?
(B) Did an emphasis on linear perspective and
anatomy dominate Romantic art?
(C) Are the intellectual and intuitive faculties
harmoniously balanced in post-Romantic
art?
(D) Are the effects of the rational control of
artistic inspiration evident in the great
works of pre-Romantic eras?
(E) Was the artistic craftsmanship displayed in
Gothic cathedrals also an element in
paintings of this period?
19. The passage implies that which of the following
was a traditional assumption of aesthetic
philosophers?
(A) Intellectual elements in art exert a necessary
control over artistic inspiration.
(B) Architecture has never again reached the
artistic greatness of the Gothic cathedrals.
(C) Aesthetic philosophy is determined by the
technical necessities of art.
(D) Artistic craftsmanship is more important in
architectural art than in pictorial art.
(E) Paintings lacked the intellectual element
before the invention of linear perspective
and anatomy
20. The author mentions “linear perspective and
anatomy” in the last sentence in order to do
which of the following ?
(A) Expand his argument to include painting as
well as architecture
(B) Indicate his disagreement with Croce’s
theory of the origins of art
(C) Support his point that rational order of
some kind has often seemed to discipline
artistic inspiration
(D) Explain the rational elements in Gothic
painting that corresponded to craftsmanship
in Gothic architecture
(E) Show the increasing sophistication of artists
after the Gothic period
(The passage below is drawn from an article published in 1962.)
Computer programmers often remark that com-
puting machines, with a perfect lack of discrimina-
tion, will do any foolish thing they are told to do. The
reason for this lies, of course, in the narrow fixation
of the computing machine’s “intelligence” on the
details of its own perceptions—its inability to be
guided by any large context. In a psychological
description of the computer intelligence, three related
adjectives come to mind: single-minded, literal-
minded, and simpleminded. Recognizing this, we
should at the same time recognize that this single-
mindedness, literal-mindedness, and simplemindedness
also characterizes theoretical mathematics, though to
a lesser extent.
Since science tries to deal with reality, even the
most precise sciences normally work with more or less
imperfectly understood approximations toward which
scientists must maintain an appropriate skepticism.
Thus, for instance, it may come as a shock to mathe-
maticians to learn that the Schrodinger equation for
the hydrogen atom is not a literally correct description
of this atom, but only an approximation to a some-
what more correct equation taking account of spin,
magnetic dipole, and relativistic effects; and that
this corrected equation is itself only an imperfect
approximation to an infinite set of quantum field-
theoretical equations. Physicists, looking at the
original Schrodinger equation, learn to sense in it the
presence of many invisible terms in addition to the
differential terms visible, and this sense inspires an
entirely appropriate disregard for the purely technical
features of the equation. This very healthy skepticism
is foreign to the mathematical approach.
Mathematics must deal with well-defined situa-
tions. Thus, mathematicians depend on an intellectual
effort outside of mathematics for the crucial specifica-
tion of the approximation that mathematics is to take
literally. Give mathematicians a situation that is the
least bit ill-defined, and they will make it well-defined,
perhaps appropriately, but perhaps inappropriately.
In some cases, the mathematicians’ literal-mindedness
may have unfortunate consequences. The mathema-
ticians turn the scientists’ theoretical assumptions, that
is, their convenient points of analytical emphasis, into
axioms, and then take these axioms literally. This
brings the danger that they may also persuade the
scientists to take these axioms literally. The question,
central to the scientific investigation but intensely
disturbing in the mathematical context—what
happens if the axioms are relaxed?—is thereby
ignored.
The physicist rightly dreads precise argument, since
an argument that is convincing only if it is precise
loses all its force if the assumptions on which it is
based are slightly changed, whereas an argument that
is convincing though imprecise may well be stable
under small perturbations of its underlying
assumptions.
21. The author discusses computing machines in the
first paragraph primarily in order to do which of
the following?
(A) Indicate the dangers inherent in relying to a
great extent on machines
(B) Illustrate his views about the approach of
mathematicians to problem solving
(C) Compare the work of mathematicians with
that of computer programmers
(D) Provide one definition of intelligence
(E) Emphasize the importance of computers in
modern technological society
22. According to the passage, scientists are skeptical
toward their equations because scientists
(A) work to explain real, rather than theoretical
or simplified, situations
(B) know that well-defined problems are often
the most difficult to solve
(C) are unable to express their data in terms of
multiple variables
(D) are unwilling to relax the axioms they have
developed
(E) are unable to accept mathematical
explanations of natural phenomena
23. It can be inferred from the passage that scientists
make which of the following assumptions about
scientific arguments?
(A) The literal truth of the arguments can be
made clear only in a mathematical
context.
(B) The arguments necessarily ignore the
central question of scientific investigation.
(C) The arguments probably will be convincing
only to other scientists.
(D) The conclusions of the arguments do not
necessarily follow from their premises.
(E) The premises on which the arguments are
based may change.
24. According to the passage, mathematicians
present a danger to scientists for which of the
following reasons?
(A) Mathematicians may provide theories that
are incompatible with those already
developed by scientists.
(B) Mathematicians may define situation in a
way that is incomprehensible to scientists.
(C) Mathematicians may convince scientists
that theoretical assumptions are facts.
(D) Scientists may come to believe that
axiomatic statements are untrue.
(E) Scientists may begin to provide arguments
that are convincing but imprecise.
25. The author suggests that the approach of physi-
cists to solving scientific problems is which of
the following?
(A) Practical for scientific purposes
(B) Detrimental to scientific progress
(C) Unimportant in most situations
(D) Expedient, but of little long-term value
(E) Effective, but rarely recognized as such
26. The author suggests that a mathematician asked
to solve a problem in an ill-defined situation
would first attempt to do which of the following?
(A) Identify an analogous situation
(B) Simplify and define the situation
(C) Vary the underlying assumptions of a
description of the situation
(D) Determine what use would be made of the
solution provided
(E) Evaluate the theoretical assumptions that
might explain the situation
27. The author implies that scientists develop a
healthy skepticism because they are aware that
(A) mathematicians are better able to solve
problems than are scientists
(B) changes in axiomatic propositions will
inevitably undermine scientific arguments
(C) well-defined situations are necessary for the
design of reliable experiments
(D) mathematical solutions can rarely be
applied to real problems
(E) some factors in most situations must remain
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