#14 - Historian: Leibniz, the seventeenth century

[Administrator]

Complete Question Explanation


Assumption. The correct answer choice is (E)

The conclusion of the argument asserts that Leibniz and Newton each independently discovered
calculus, and in drawing the conclusion the author addresses the possibility Newton may have
influenced Leibniz, and then rejects that possibility. A review of the argument does not reveal any
conspicuous flaws, and so upon encountering the question stem, you should expect to see a Defender
answer. As such, do not spend time trying to prephrase an answer—just make sure you know the facts
of the argument.

Answer choice (A): The argument is about the independent discovery of calculus; the author makes
no assumption that Leibniz did not tell anyone else, and indeed the fact that Newton did tell Leibniz
is accepted by the author as not undermining the conclusion.

Answer choice (B): Negate the answer: “A third person independently discovered calculus prior to
Newton and Leibniz.” Would this negated answer attack the argument? No, the author would just
assert that three different parties independently discovered calculus.

Answer choice (C): The author cites Newton’s letter as evidence that Newton felt he had disclosed
ideas to Leibniz prior to Leibniz’s publication date. No assumption is made that Newton felt that
what was disclosed allowed Leibniz to learn something important. If you are uncertain of this
answer, negate the choice to see if it weakens the argument.

Answer choice (D): This is clearly not an assumption of the argument because the author discusses
Newton’s letter to Leibniz prior to Leibniz’s publication date.

Answer choice (E): This is the correct answer. The answer can be difficult because it is somewhat
similar to answer choice (B), which many people already eliminated by the time they reached this
answer. Answer (E) is different from answer (B) because it involves learning details from a third
source. This is important because the conclusion references the independent discovery of calculus,
and so the author must believe that neither Newton nor Leibniz learned anything substantial about
calculus from other sources.

This elimination of an idea that weakens the argument is the essence of a Defender answer choice.
To further confirm the answer, consider the negation of this answer choice (“neither...nor” becomes
“either...or”): “Either Newton or Leibniz learned crucial details about calculus from some third
source.” This negated answer undermines the assertion that Leibniz and Newton each independently
discovered calculus. Consequently, this is the correct answer.

[DlarehAtsok]

Hi! Why is A) wrong? If Leibniz informed Newton over what he was studying before publishing his version (thus possibly before Newton studied this matter on his private notebooks), would not this information hurt the argument? Thanks in advance!

[Dave Killoran]

Hey D,

The problem there is that the answer simply says "did not tell anyone," and that's incredibly broad (too broad for the author to be committed to it). For example, what if Leibniz told his sister about it the day before publishing? Would that undermine the argument? No, and since that would satisfy negating (A), it's not correct. So, while you raise a reasonable possibility, this answer choice doesn't align with that having to happen (it seems that you took the example to a point where it didn't have to go, which made it look more attractive to you). I'd also suggest that the test makers used "anyone" with intent there, knowing that how broad it was made it something the author didn't have to commit to.

Thanks!

[DlarehAtsok]

I see. I think I overlooked the fact that an Assumption answer must be a minimalistic one and A) goes well beyond. If it was a Strengthen question, probably A) would be correct, right?

[Dave Killoran]

Yes, if remade into a strengthen question, this would help the argument. Nice work!

[caroline222]

Is the negation of e that both Newton and Leibniz learned crucial details about calculus from some third source.

Thank you in advance!

[Rachael Wilkenfeld]

Close Caroline!

The negation of answer choice (E) is that either Newton or Leibniz (or both) learned calculus from a third source. That negation would weaken the conclusion that Newton and Leibniz BOTH independently discovered calculus.

Think of the neither/nor construction as being "not" to both terms. So if I say "Neither the Browns nor the Steelers will play in the Superbowl this year" I mean that the Browns won't play in the Superbowl and that the Steelers won't play in the Superbowl. To negate that idea, I only need one or the other to be true. So the negation of the neither/nor would be either the Browns or the Steelers (or both) play in the Superbowl.

Hope that helps

[JoshuaDEL]

I now understand why E is the answer but at first, I eliminated it because I didn't see "independently" as developed on their own in the complete absence of any help or source but rather as simply developing it on their own using whatever resources available.

Couldn't you still say that Newton and Leibniz developed independently with some third source? I mean, any discovery requires drawing ideas and application from different sources right? I'm worried because I'm not sure how I could have interpreted "independently" or any words like this as the question intended them to be.

Thanks in advance.

[Adam Tyson]

That's a bit tricky, JoshuaDEL! If the stimulus had said "independently of each other," then they could have done that while also relying on or with the aid of a third party. But to say that someone discovered something "independently" does mean that they did it on their own, without help. Negating answer E does ruin that claim, showing that neither of them discovered calculus on their own and disproving the conclusion. I think it's fair to say that "independently with the help of someone else" is a contradiction.