What it means to “explain” something in science often comes down to

What it means to “explain” something in science
often comes down to the application of mathematics.
Some thinkers hold that mathematics is a kind of
language—a systematic contrivance of signs, the
(5) criteria for the authority of which are internal
coherence, elegance, and depth. The application of
such a highly artificial system to the physical world,
they claim, results in the creation of a kind of statement
about the world. Accordingly, what matters in the
(10) sciences is finding a mathematical concept that
attempts, as other language does, to accurately describe
the functioning of some aspect of the world.

At the center of the issue of scientific knowledge
can thus be found questions about the relationship
(15) between language and what it refers to. A discussion
about the role played by language in the pursuit of
knowledge has been going on among linguists for
several decades. The debate centers around whether
language corresponds in some essential way to objects
(20) and behaviors, making knowledge a solid and reliable
commodity; or, on the other hand, whether the
relationship between language and things is purely a
matter of agreed-upon conventions, making knowledge
tenuous, relative, and inexact.

(25) Lately the latter theory has been gaining wider
acceptance. According to linguists who support this
theory, the way language is used varies depending
upon changes in accepted practices and theories among
those who work in a particular discipline. These
(30) linguists argue that, in the pursuit of knowledge, a
statement is true only when there are no promising
alternatives that might lead one to question it. Certainly
this characterization would seem to be applicable to the
sciences. In science, a mathematical statement may be
(35) taken to account for every aspect of a phenomenon it is
applied to, but, some would argue, there is nothing
inherent in mathematical language that guarantees such
a correspondence. Under this view, acceptance of a
mathematical statement by the scientific community—
(40) by virtue of the statement’ s predictive power or
methodological efficiency—transforms what is
basically an analogy or metaphor into an explanation of
the physical process in question, to be held as true until
another, more compelling analogy takes its place.

(45) In pursuing the implications of this theory, linguists
have reached the point at which they must ask: If
words or sentences do not correspond in an essential
way to life or to our ideas about life, then just what are
they capable of telling us about the world? In science
(50) and mathematics, then, it would seem equally
necessary to ask: If models of electrolytes or E = mc2,
say, do not correspond essentially to the physical
world, then just what functions do they perform in the
acquisition of scientific knowledge? But this question
(55) has yet to be significantly addressed in the sciences.

1. Which one of the following statements most accurately expresses the passage’s main point?

(A) Although scientists must rely on both language and mathematics in their pursuit of scientific knowledge, each is an imperfect tool for perceiving and interpreting aspects of the physical world.
(B) The acquisition of scientific knowledge depends on an agreement among scientists to accept some mathematical statements as more precise than others while acknowledging that all mathematics is inexact.
(C) If science is truly to progress, scientists must temporarily abandon the pursuit of new knowledge in favor of a systematic analysis of how the knowledge they already possess came to be accepted as true.
(D) In order to better understand the acquisition of scientific knowledge, scientists must investigate mathematical statements’ relationship to the world just as linguists study language’s relationship to the world.
(E) Without the debates among linguists that preceded them, it is unlikely that scientists would ever have begun to explore the essential role played by mathematics in the acquisition of scientific knowledge.



2. Which one of the following statements, if true, lends the most support to the view that language has an essential correspondence to the things it describes?

(A) The categories of physical objects employed by one language correspond remarkably to the categories employed by another language that developed independently of the first.
(B) The categories of physical objects employed by one language correspond remarkably to the categories employed by another language that derives from the first.
(C) The categories of physical objects employed by speakers of a language correspond remarkably to the categories employed by other speakers of the same language.
(D) The sentence structures of languages in scientifically sophisticated societies vary little from language to language.
(E) Native speakers of many languages believe that the categories of physical objects employed by their language correspond to natural categories of objects in the world.



3. According to the passage, mathematics can be considered a language because it

(A) conveys meaning in the same way that metaphors do
(B) constitutes a systematic collection of signs
(C) corresponds exactly to aspects of physical phenomena
(D) confers explanatory power on scientific theories
(E) relies on previously agreed-upon conventions



4. The primary purpose of the third paragraph is to

(A) offer support for the view of linguists who believe that language has an essential correspondence to things
(B) elaborate the position of linguists who believe that truth is merely a matter of convention
(C) illustrate the differences between the essentialist and conventionalist positions in the linguists’ debate
(D) demonstrate the similarity of the linguists’ debate to a current debate among scientists about the nature of explanation
(E) explain the theory that mathematical statements are a kind of language



5. Based on the passage, linguists who subscribe to the theory described in lines 21–24 would hold that the statement “The ball is red” is true because

(A) speakers of English have accepted that “The ball is red” applies to the particular physical relationship being described
(B) speakers of English do not accept that synonyms for “ball” and “red” express these concepts as elegantly
(C) “The ball is red” corresponds essentially to every aspect of the particular physical relationship being described
(D) “ball” and “red” actually refer to an entity and a property respectively
(E) “ball” and “red” are mathematical concepts that attempt to accurately describe some particular physical relationship in the world