Historian: Newton developed mathematical concepts and techniques that are fundamental to modern calculus. Leibniz developed closely analogous concepts and techniques. It has traditionally been thought that these discoveries were independent. Researchers have, however, recently discovered notes of Leibniz’s that discuss one of Newton’s books on mathematics. Several scholars have argued that since the book includes a presentation of Newton’s calculus concepts and techniques, and since the notes were written before Leibniz’s own development of calculus concepts and techniques, it is virtually certain that the traditional view is false. A more cautious conclusion than this is called for, however. Leibniz’s notes are limited to early sections of Newton’s book, sections that precede the ones in which Newton’s calculus concepts and techniques are presented.
In the historian’s reasoning, the two boldfaced portions play which of the following roles?The historian describes an argument made by several scholars and then criticizes that argument as too strong. The first boldface is part of the scholars’ evidence against the traditional view. The second boldface is the historian’s own judgment that the scholars’ conclusion is
too strong.
A. The first provides evidence in support of the general position that the historian defends; the second reports the doubts of others concerning that position.
This is incorrect. The first supports the scholars’ position, not the historian’s position. The second gives the historian’s own view, not the doubts of others.
B. The first states a conclusion drawn as part of an argument that the historian criticizes; the second is that conclusion.
This is incorrect. The first is not a conclusion; it is evidence used by the scholars.
C. The first is evidence that has been used to support a conclusion that the historian criticizes; the second is the judgment reached by the historian about that conclusion.
This is correct. The first supports the scholars’ claim that the traditional view is false. The second is the historian’s response:
that conclusion should be treated more cautiously.
D. The first identifies grounds for a potential objection to the conclusion of the argument; the second is the judgment reached by the argument concerning the accuracy of the finding.
This is incorrect. The first supports the scholars’ conclusion; it is not an objection to the historian’s conclusion.
E. The first is a claim, the explanation of which is at issue in the argument; the second brings evidence that has been used to support that explanation.
This is incorrect. The second is not evidence; it is the historian’s conclusion about how strong the scholars’ conclusion should be.
Answer: (C)