CHAPTER 16 / PRACTICE TEST I 597
Directions:The following passage is an early
draft of an essay. Some parts of the passage
need to be rewritten.Read the passage and select the best answers
for the questions that follow. Some questions
are about particular sentences or parts of sen-
tences and ask you to improve sentence struc-
ture or word choice. Other questions ask you
to consider organization and development. In
choosing answers, follow the requirements of
standard written English.Questions 30–35 refer to the following passage.
(1)For thousands of years, philosophers have de-
bated whether humans discover mathematics or it is
something that has been invented. (2)Plato believed
that perceived mathematical objects like lines were
only vague shadows of abstract “ideals” that exist out-
side of human experience. (3)Circular objects or cir-
cles drawn on paper aren’t “really” circles. (4)Rather,
they are just a flawed approximation of the perfect
circular form. (5)So, in this sense, Plato believed that
mathematics was something revealed imperfectly to
humans, not invented by them. (6)Many students
surely wish that mathematics had not been invented
at all. (7)A position that opposes Plato’s idealism is
called mathematical intuitionism, which is the belief
that all mathematics is the product of human minds.
(8)There is one good way to understand the dif-
ference between idealism and intuitionism. (9)Look
at big numbers. (10)An idealist would say that all
numbers, no matter how large, truly exist, even if no
one has ever actually calculated them. (11)An intu-
itionist, on the other hand, might say that some num-
bers may be so big that they are physically impossible
to calculate or express in a meaningful way, and so do
not truly “exist.”
(12)Another point of view that is different from
these ones is one that says that it is a pointless thing to
ask the question as to whether mathematical objects
“really exist” or not. (13)This view simply regards
mathematics as a tool for interpreting information
from the world around us. (14)This view is essentially
a compromise between idealism and intuitionism.
(15) Although it acknowledges that mathematics
reaches beyond the mind of a mathematician, it also
denies that it has any meaning outside of the mind.
(16)The concept of a circle is not a reflection of an
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abstract “ideal,” and also it is not completely a human
invention. (17)Instead it is a concept that we form in
our minds after perceiving and thinking about many
circular objects in the world around us.- Which of the following is the best revision of
the underlined portion of sentence 1 (repro-
duced below)?
For thousands of years, philosophers have de-
bated whether humans discover mathematics or
it is something that has been invented.
(A) humans discover mathematics or
invent it
(B) humans so much discover mathematics
as they do invent it
(C) the discovery of mathematics is what
humans do or the invention
(D) humans discover mathematics or if it is
invented
(E) mathematics is something discovered or
if humans invent it - In context, which of the following is the most
logical revision of the underlined portion of
sentence 3 (reproduced below)?
Circular objectsor circles drawn on paper aren’t
“really” circles.
(A) Nevertheless, circular objects
(B) According to his reasoning, circular
objects
(C) Furthermore, circular objects
(D) Secondly, circular objects
(E) All the while, circular objects