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 says that argument goes too far. The first boldface is one piece of evidence the scholars use: Newton’s book contained calculus material. The second boldface is the scholars’ conclusion: the traditional view of independent discovery is almost certainly false.
The historian criticizes that conclusion because Leibniz’s notes discuss only earlier sections of the book, not the sections containing
Newton’s calculus concepts.
A. The first is a claim that has been advanced as a hypothesis in arguing for the position the historian rejects; the second is that position.
This is incorrect. The first boldface is not a hypothesis; it is presented as evidence used by the scholars.
B. The first is evidence that has been used to support a conclusion that the historian criticizes; the second is that conclusion.
This is correct. The first boldface supports the scholars’ conclusion, and the second boldface states that conclusion. The historian then criticizes it as too strong.
C. The first provides evidence in support of an intermediate conclusion drawn in order to support the position that the historian defends; the second is that intermediate conclusion.
This is incorrect. The first supports the scholars’ position, not the historian’s defended position.
D. The first provides evidence in support of the position that the historian defends; the second provides evidence to support that position.
This is incorrect. Both boldfaced portions belong to the scholars’ argument, not to the historian’s own position.
E. The first is the position taken by the argument; the second is evidence that has been used to support that position.
This reverses the roles. The first is evidence, and the second is the conclusion drawn from it.
Answer: (B)