Historian: Leibniz, the seventeenth-century philosopher

Answer choices

1. A

   Too Strong: told no one3% picked this

   Leibniz did not tell anyone about calculus prior to publishing his

   The author is assuming that Leibniz did not tell Newton about calculus prior to Newton's writing of his calculus notebooks, but that's it. She doesn't need to assume that Leibniz never told anyone about calculus prior to publishing his version of it. If we negate this and say, "actually, author, Leibniz did tell at least one person, his Mom, about calculus prior to publishing", that wouldn't weaken in the slightest.

   3%
2. B

   Too Strong: no one prior discovered10% picked this

   No third person independently discovered calculus prior to Newton

   This has the ruling-out "not/no" that Defender answers so often have. We slow down and negate to see if the negation would weaken. Does it hurt the argument if we say, "Yo, author -- there was a third person who independently discovered calculus prior to Newton and Leibniz?" Yes, it does hurt a little bit, because it creates some doubt -- it's possible that Newton and Leibniz (or at least one of them) learned calculus from this 3rd person, which would disprove the conclusion that they each independently discovered calculus. But who knows if this 3rd person had any contact with Newton or Leibniz? Maybe they lived 5,000 years earlier in Egypt. The correct answer, when negated, has a much sharper accusation that at least one of Newton / Leibniz did not independently discover calculus.

   10%
3. C

   Out of Scope: Newton's beliefs5% picked this

   Newton believed that Leibniz was able to learn something important about calculus from his

   The argument doesn't need to assume anything about what Newton believed to be true. The argument only cares about what is true. Did / didn't these two men independently discover calculus? If we said, "Hey, author, Newton didn't believe that Leibniz was able to learn anything important from the letter", that wouldn't weaken at all. In fact, it would align with the premise, which said that the letter didn't contain anything important.

   5%
4. D

   Contradicted17% picked this

   Neither Newton or Leibniz knew that the other had developed a version of calculus prior

   The issue isn't whether Newton or Leibniz knew that the other man also had a version of calculus. The issue is whether they each invented their own versions. The argument doesn't need it to be that neither man knew the other had a version of calculus. If we negate this and say, "Yo, author -- at least one of these guys knew that the other one had a version of calculus, prior to Leibniz's publication", that would not weaken. They could be each independently discovering calculus while still being aware that the other person was also discovering something very similar. In fact, given that the author tells us that Newton showed Leibniz some ideas from his version of calculus "shortly before Leibniz's publication" contradicts this answer.

   17%
5. E

   Correct65% picked this

   Neither Newton nor Leibniz learned crucial details about calculus from some

   Why this is right

   If we negate this answer, it's saying that "Newton, Leibniz, or both learned crucial details about calculus from some third source". That badly weakens. Whichever of them learned crucial details about calculus from some third source (possibly both of them) cannot be said to have independently discovered calculus. Since those learned details were crucial, that would mean that Newton's or Leibniz's discovery was dependent on third source. This answer is a good reminder that we need to be flexible while considering answers (because most students don't consider the exotic objection that Newton / Leibniz stole calculus from some heretofore unmentioned third party). In particular, when we're doing Necessary Assumption, we should be very charitable to answers that are ruling out ideas. They are often surprising answers. The easiest way to like them is to ask yourself if the negation would weaken.

   Skill tested: Necessary Assumption · how this choice captures the argument's function is the move to repeat next time.

   65%