PrepTest 113, Section 3, Question 14
Historian: Leibniz, the seventeenth-century philosopher, published his version(73 more words not shown)
Which one of the following(8 more words not shown)
- ALeibniz did not(11 more words not shown)
- BNo third person(8 more words not shown)
- CNewton believed that(14 more words not shown)
- DNeither Newton nor(15 more words not shown)
- ENeither Newton nor(10 more words not shown)
Reading the argument
Publishing first doesn't necessarily mean discovering first. Newton's older notebooks establish that he had worked on the ideas earlier, but what if Leibniz also had earlier unpublished work? So far, we shouldn't treat publication dates as a complete history of discovery.
Then comes the letter. Newton says he disclosed the ideas to Leibniz, but its actual contents don't reveal anything important about calculus. That undermines this proposed route for passing along the ideas. Does it rule out every route?
Perhaps there was another letter or a conversation. Perhaps information traveled in the other direction. Or imagine a third person, Bob, who worked out crucial ideas and told one or both of them. Those are alternatives to investigate, not historical claims we're adding. Examining this one letter doesn't eliminate them.
What we’re looking for
The necessary assumption should protect the claim that each made an independent discovery against one of those possibilities. I'd look for a denial of an alternative way they could have learned the crucial ideas, rather than a claim about who published first.
Working the answers
- A
Leibniz could have developed calculus independently and then told a friend about it before publication. Sharing a discovery after making it wouldn't show that it wasn't his discovery. The historian doesn't need to deny every earlier conversation Leibniz had with anyone.
- B
Someone else could have discovered calculus earlier without either Newton or Leibniz ever learning about that person's work. That would affect a claim that they were the first people ever to discover it, but the conclusion is that each discovered it independently. An unknown earlier discovery doesn't automatically undermine that claim.
- C
Newton's belief about what Leibniz could learn from the letter doesn't establish what Leibniz actually learned. Newton could have overestimated how informative his remarks were. Or he could have known they revealed little. Either possibility leaves the letter's actual contents and the independence of discovery as separate questions.
- D
Knowing that someone else has developed calculus isn't the same as learning the crucial details from them. Two people could know about each other's work while independently arriving at their own ideas. D denies even that awareness, which is more than the historian needs. The passage doesn't require us to declare D either true or false.
- ECorrect
If one of them learned crucial details from a third source, the historian's claim of independent discovery would be undermined. E rules out that possibility, just as we'd wanted to rule out Bob supplying the essential ideas.
It doesn't say a third person never worked on calculus. It says neither Newton nor Leibniz learned crucial details from a third source. That distinction matters: independent work elsewhere can coexist with their independence; receiving the crucial ideas from elsewhere cannot support the historian's account of how they discovered them.
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