The belief that art originates in intuitive rather than rational faculties was worked out historically and philosophically in the somewhat wearisome volumes of Benedetto Croce, who is usually considered the originator of a new aesthetic. Croce was, in fact, expressing 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 concept of art was supported by technical necessities. It was necessary to master certain laws and to use intellect 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 (linear perspective: 直线透视图) and anatomy.
17. The passage suggests that which of the following would most likely have occurred if linear perspective 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 inspiration.
(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 computing machines, with a perfect lack of discrimination, 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 mathematicians to learn that the Schrodinger equation (Schrodinger equation: [物]薛定谔方程) for the hydrogen atom is not a literally correct description of this atom, but only an approximation to a somewhat more correct equation taking account of spin, magnetic dipole (magnetic dipole: 磁偶极子), 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 situations. Thus, mathematicians depend on an intellectual effort outside of mathematics for the crucial specification 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 mathematicians 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 physicists 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 unknown