Logical Reasoning

PT113 · S3 · Q14 Historian: Leibniz, the seventeenth-century philosopher

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Historian: Leibniz, the seventeenth-century philosopher, published his version of calculus before Newton did.

Conclusion (Thus)

Leibniz and Newton each independently discovered calculus.

Evidence

Newton had a private notebook which showed he was using calculus ideas for at least a decade before Leibniz published his version of calculus (prior to Newton publishing any version).

Newton claims he showed these ideas to Leibniz in a letter shortly before Leibniz's publication.

But close examination of the letter shows that Newton's few cryptic remarks did not reveal anything important about calculus.

Evaluate

The story behind this argument is that Newton and Leibniz both published their own version of calculus, and the world kind of wonders,

One could build the case that Newton thought of calculus first and that Leibniz "stole" the idea and published first. After all, Newton has a notebook showing he was working on calculus for at least 10 years before Leibniz published. And Newton even disclosed some of his ideas to Leibniz in a letter shortly before Leibniz's publication.

But the author is saying,

Is that the only way to Explain the Curious Fact of who invented calculus?

Of course not. There are lots of possibilities: - L invented it, N stole it. - N invented it, L stole it. - L and N each separately invented it. - L stole it from X and N stole it from L. - N stole it from X and L stole it from N. - L and N both stole it from X. - L stole it from X, and N stole it from Y

The author is trying to shut down any story where Leibniz steals calculus from Newton. But that doesn't mean they both invented it.

Goal

The fact that this letter from Newton wouldn't have been enough for Leibniz to steal calculus from doesn't prove that Leibniz didn't steal calculus from Newton. Look for an answer ruling out some other way that Leibniz could have stolen the idea of calculus.

And even if we accept that Leibniz didn't steal calculus from Newton, that doesn't prove that they both discovered it independently. So we might see an answer ruling out some other possibility (like Newton did not steal it from Leibniz).

14.

Which one of the following is an assumption required by the historian's argument?

Leibniz did not tell anyone
Too Strong: told no one
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% picked this
No third person independently discovered
Too Strong: no one prior discovered
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% picked this
Newton believed that Leibniz was
Out of Scope: Newton's beliefs
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.
4% picked this
Neither Newton or Leibniz knew
Contradicted
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% picked this
Correct
Neither Newton nor Leibniz learned
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% picked this

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