Historian: Newton developed mathematical concepts and techniques that

Hey folks!

For Boldface questions, we need to understand not only the logic of the argument but also the roles of every statement and the relationships between the statements. Let us solve this question!




The argument presents an argument made by the historian. The question stem also asks us for the role of the two boldfaces in the historian’s argument.

So, as far as this argument goes, the historian is the author.

Historian: Newton developed mathematical concepts and techniques that are fundamental to modern calculus.

• This is a fact that seems to be setting the context for the argument.
• Fact: Newton developed mathematical concepts and techniques that are fundamental to modern calculus.

Leibniz developed closely analogous concepts and techniques.

• Another fact.
• Fact: Leibniz (another scientist/mathematician like Newton, actually!) developed concepts and techniques that were very similar to Newton’s concepts and techniques for calculus.

It has traditionally been thought that these discoveries were independent.

• Traditional Belief/Opinion: Newton and Leibniz discovered these similar concepts and techniques independently, i.e., one did not copy/get inspired by the other.
• Here, “these discoveries were independent” is a belief or opinion, not a fact.
• This is simply a third-party opinion at this point. We do not know at this point if the historian (author) shares the same belief.
• However, the overall statement is a fact. It is a fact that there is this traditional belief about the discoveries being independent.

Researchers have, however, recently discovered notes of Leibniz’s that discuss one of Newton’s books on mathematics.

• This line introduces a recent discovery.
• It is a fact. It is a fact that researchers have discovered these notes of Leibniz’s.
• It is also a fact that these notes 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,

• Fact: The book written by Newton includes a presentation of his calculus concepts and techniques. This is a fact.
• “since the book includes…”. The word “since” indicates that whatever is given next is the reasoning behind what the scholars are arguing for.
• This line introduces some people called scholars and introduces us to one of the reasons used by the scholars to make some point (we are yet to see what this point is).

and since the notes were written before Leibniz’ own development of calculus concepts and techniques,

• This statement builds on the previous statement.
• “and since” – indicates reasoning number two for what the scholars want to argue for. Reason number one was what we saw in the last statement, the fact that Newton’s book includes a presentation of his calculus concepts and techniques.
• Reasoning number 2: This is also a fact. These notes of Leibniz were written before Leibniz’ own development of calculus concepts and techniques.
• Think and Infer: Can we predict what the scholars’ argument would be even before reading the next statement? Yes.

o Leibniz’ notes discuss one of Newton’s books on mathematics.
o This book by Newton discusses his calculus concepts and techniques.
o Leibniz’ notes, which obviously came later (because they discuss Newton’s book), were written before Leibniz himself developed calculus concepts and techniques.
o Implication/Prediction: the scholars will argue that Leibniz’ work was derived from Newton (inspired/copied) i.e., the traditional view (both evolved independently) is incorrect.
• BF1:

o Factual statement.
o Reasoning #2 behind the scholars’ argument.

it is virtually certain that the traditional view is false.

• This is the conclusion being made by the scholars based on the reasoning highlighted above.
• This is a claim/conclusion made by the scholars (not a fact). This view challenges the traditional view that Newton and Leibniz developed calculus independently.
• So, as per the scholars, the two mathematicians/scientists did not independently develop calculus. Leibniz’ work was derived from Newton’s work.

A more cautious conclusion than this is called for, however.

• This is a claim/conclusion being made by the historian (author).
• This is the first claim made by the author. Before confirming if this is the main conclusion, we need to read the rest of the argument.
• Author/Historian’s claim: A more cautious conclusion than saying that the traditional view is false is needed. In other words, the historian(author) is claiming that the scholars’ conclusion is not cautious/careful enough. It is a criticism of the scholars’ conclusion.
• The word “however” is also a clue that this view is not in the same direction as the scholars’ view.

Leibniz’ 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.

• This statement is a fact.
• This statement provides the historian’s reasoning to support his/her conclusion above.
• We can now confirm that the last statement was the main conclusion.
• Author/Historian Reasoning for Conclusion:

o Leibniz’ notes only contain sections of Newton’s book that are before Newton introduces calculus concepts.
o Implication: Leibniz has not really referred to sections of Newton’s book that talk about calculus. So, we cannot be sure if Leibniz had knowledge of Newton’s calculus concepts. It is possible that Leibniz had no idea about the calculus aspects and arrived at calculus concepts independently.
• BF2:

o Factual statement
o Support for Main Conclusion

Let us understand the various claims and how they are supported in the argument.

1. Traditional belief: Newton and Leibniz came up with calculus independently.

a. No support presented

2. Scholars’ conclusion: The above belief is false (against traditional view). (Leibniz’ work is derived from Newton). Based on these points -

a. Leibniz’ notes discuss one of Newton’s books on mathematics.
b. This book by Newton discusses his calculus concepts and techniques.
c. Leibniz’ notes which obviously came later (because they discuss Newton’s book), were written before Leibniz himself developed calculus concepts and techniques.

3. Author’s Conclusion (Main Conclusion): A more cautious conclusion than above is called for (we cannot just say the traditional view is false)- against scholars’ conclusion. Supported by -

a. Leibniz’ notes only contain sections of Newton’s book that are before Newton introduces calculus concepts.

A. The first provides evidence in support of the overall position that the historian defends; the second is evidence that has been used to support an opposing position.
Incorrect:

BF1 -> BF1 provides evidence in support of the scholars’ position, which the historian attacks (not defends). Hence, BF1 is incorrect.
BF2 -> BF2 provides evidence in support of the main conclusion. “Opposing position of the position the historian defends” cannot be the main conclusion because the main conclusion is obviously the position that historian defends. The only opposing position is the scholars’ argument, which has nothing to do with BF2. Hence, BF2 is incorrect.

B. The first provides evidence in support of the overall position that the historian defends; the second is that position.
Incorrect:

BF1 -> BF1 provides evidence in support of the scholars’ position, which the historian attacks (not defends). Hence, BF1 is incorrect.
BF2 -> BF2 is a fact, not a position/claim. Hence, BF2 is incorrect.

C. The first provides evidence in support of an intermediate conclusion that is drawn to provide support for the overall position that the historian defends; the second provides evidence against that intermediate conclusion.
Incorrect:

BF1 -> The only issue is “provide support for.” In reality, the first provides evidence in support of an intermediate conclusion (scholars’ view) that goes against the traditional belief (which the historian defends) and is challenged by the main conclusion. The intermediate conclusion here (the scholars’ conclusion) does not provide support for the overall position taken by the historian at any level. Hence, BF1 is incorrect.
BF2 -> The second provides evidence to support the main conclusion. In the argument, BF2 is not used as evidence against the scholars’ conclusion, only as support for the main conclusion. Hence, BF2 is incorrect.

D. The first is evidence that has been used to support a conclusion that the historian criticizes; the second is evidence offered in support of the historian’s own position.
Correct:

BF1 -> The first is factual evidence, used as reasoning to support the scholars’ conclusion, which the historian indeed criticizes/challenges. Refer to our prethinking. BF1 is correct.
BF2 -> The second is factual evidence offered in support of the main conclusion, which is indeed the historian’s own position. Hence, BF2 is also correct.

E. The first is evidence that has been used to support a conclusion that the historian criticizes; the second is further information that substantiates that evidence.
Incorrect:

BF1 -> The first is factual evidence used as reasoning to support the scholars’ conclusion, which the historian indeed criticizes/challenges. Refer to our prethinking. BF1 is correct.
BF2 -> The second BF does not further substantiate/support the evidence presented in BF1. In fact, it weakens the point made by using that evidence. Hence, BF2 is incorrect.

1. Even in Boldface question, we should understand the core logic of the argument. This makes the identification of roles and relationships of each Boldface easier.
2. Focusing on keywords (However, since, etc.) is useful to understand the logical flow of the argument.
3. We need to be extremely careful with option choice analysis in Boldface questions.


Warm Regards,
Harsha

Hi E-GMAT,

Please find my analysis below,

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’ 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’ 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’ 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


A. The first provides evidence in support of the overall position that the historian defends; the
second is evidence that has been used to support an opposing position.
B. The first provides evidence in support of the overall position that the historian defends; the
second is that position.
C. The first provides evidence in support of an intermediate conclusion that is drawn to provide
support for the overall position that the historian defends; the second provides evidence
against that intermediate conclusion.
D. The first is evidence that has been used to support a conclusion that the historian criticizes;
the second is evidence offered in support of the historian’s own position.
E. The first is evidence that has been used to support a conclusion that the historian criticizes;
the second is further information that substantiates that evidence.


Now lets break this argument.

Historian: Newton developed mathematical concepts and techniques that are fundamental to
modern calculus....FACT1
. Leibniz developed closely analogous concepts and techniques.FACT2

It has traditionally been thought that these discoveries were independent. HISTORIAN OPINION....intermediate conclusion.

Researchers have,however, recently discovered notes of Leibniz’ that discuss one of Newton’s books on
mathematics. Researchers Opinion

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’ own development of calculus concepts and techniques, SCHOLORS OPINIONS


it is virtually certain that the traditional view is false. Historians Opinions..... MAIN CONCLUSION.


A more cautious conclusion than this is called for, however.
Leibniz’ 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. Historion Opinion.

So as per the above understanding, First Bold face is the explanation to support the main conclusion.

and Second Bold Face as it mention However. I though i should be against the main conclusion.

With this understanding I'm able to eliminate all the choice but I'm not able to understand why in option D,second bold face statement support the main conclusion.

Thanks

Nitin Singh

Hi Nitin,

Thanks for sharing detailed analysis. In this way, I'll be able to point exactly where all you faltered:

Historian: Newton developed mathematical concepts and techniques that are fundamental to
modern calculus....FACT1 - Correct
. Leibniz developed closely analogous concepts and techniques.FACT2 - Correct

It has traditionally been thought that these discoveries were independent. HISTORIAN OPINION....intermediate conclusion. - It's not an intermediate conclusion. A conclusion needs to be supported by some reasoning. Which statement supports this? It is only traditional opinion.
Researchers have,however, recently discovered notes of Leibniz’ that discuss one of Newton’s books on
mathematics. Researchers Opinion -Incorrect. It's a discovery. So, it needs to be a FACT.

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’ own development of calculus concepts and techniques, SCHOLORS OPINIONS -Incorrect - Both the parts following "Since" are facts. They are presented as information or facts.


it is virtually certain that the traditional view is false. Historians Opinions..... MAIN CONCLUSION. -Incorrect. This is scholars' opinion and it's their conclusion, not Historian's


A more cautious conclusion than this is called for, however.
Leibniz’ 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. Historion Opinion. - Incorrect. Historian opinion is limited to " A more cautious conclusion than this is called for". The rest of the sentence is a fact. Since, this is the only historian opinion in the argument, this is also the main conclusion.

Now, given my above comments, would you like to re-evaluate the option statements?

Thanks,
Chiranjeev

Hi my honorable experts AaronPond, RonPurewal, MartyTargetTestPrep, jennpt, AjiteshArun, ccooley, DmitryFarber, GMATNinja, egmat, generis, VeritasKarishma
Whose part the highlighted part is, actually? Is it author's side or the OTHER SIDE?
Thnaks__

It is the view of several scholars.

Several scholars have argued that
since the book includes a presentation of Newton’s calculus concepts and techniques, - scholars' premise
and since the notes were written before Leibniz’ own development of calculus concepts and techniques, - scholars' premise
it is virtually certain that the traditional view is false - scholars' conclusion

Thank you so much for your feedback.
Answer option D says:
support a conclusion that the historian criticizes---> What (conclusion) does the historian criticize here?

The historian (the person from whose viewpoint the argument is presented) criticises this "traditional view is false". Several scholars believe the traditional view is false because of first bold statement (and other things) but our historian says that "a more cautious conclusion than this is called for, however." and then proceeds to give his reasons in the second bold statement.

Hi GMATNinja,

Could you please help in explaining the argument and how to arrive to correct answer for this argument.

GMATNinja VeritasKarishma AndrewN
I have a specific query. Although i chose correct answer D, i could not convince myself with one read. I wouldn't deny that the word 'criticize', found it too extreme, in D didn't hinder me choosing D, making me look at C and thus spending almost a minute to decided between them. However, i would leave it.

I had apprehension In C for it mentions 'intermediate conclusion' which i understand is not right, however, i didn't eliminate it right away. So, the question is - Would i be right in saying that an 'intermediate conclusion' must go in similar direction as that of main conclusion?
I ask so because here, at best, the contender for 'intermediate conclusion' is 'it is virtually certain that the traditional view is false' but this is opposed by the author who makes the main conclusion hence 'it.. false' can't be 'intermediate conclusion'. There's no 'intermediate conclusion' that author makes to reach his/her final conclusion in this passage.

Also, can i say, in general, that intermediate conclusion, if it is there, will always precede main conclusion?

Please help..
Thank you.

Hello, unraveled. We seem not to be crossing paths as much as we used to (under our former names, in fact). I am glad to hear that you arrived at a correct conclusion, speaking of those. At the same time, each of your queries raises a caution flag in my mind, and, in hopes of assisting you and the larger community, I would like to express my reservations, one by one. I will do so in-line below.


Do not worry about landing on the one true answer in one read. I often make two passes of the answer choices. The first one is just to burn off what I am next to positive are incorrect answers; the second one is where I dig into the details of the passage and compare against the language of the answer choices that are left. Yes, criticizes in (D) warrants pause and further consideration, but that is what a second pass is for.


Be careful. The first part of (C)—right through intermediate conclusion—is absolutely correct. Notice that the answer indicates that the first boldface portion provides evidence for an intermediate conclusion, not that it is that conclusion itself. That conclusion, rather, is the part that follows the boldface, just as you said: it is virtually certain that the traditional view is false. Choice (C) runs into trouble when it seeks to qualify that that intermediate conclusion provides support for the overall position that the historian defends. The historian does not indicate that the traditional view of the independent discoveries of calculus is false, as the last two lines of the passage make clear. Hence, we can eliminate (C) before we even hit the semicolon.

So, you ask, can you say that an intermediate conclusion must go in the same direction as that of the main conclusion? No, you cannot. This passage presents conclusions that are at loggerheads, even if they are not the two boldfaced portions. You can almost see the passage as presenting two opposing points of view. If the author of the passage mentions such an opposing view to advance an eventual argument, then perhaps you might think of the first conclusion as an intermediate conclusion, but not one that the author has put forth.


I like the in general part, but not the always. Sure, maybe nine times out of ten or even every single example you can find of this type of question in the OG will adhere to such a format, but creating an ironclad rule out of the pattern may be misguided. By comparison, consider that a passage with a single conclusion often builds up the premises from line to line and then delivers that conclusion at the end, but sometimes the conclusion is given as the first line instead. I urge caution and critical reasoning over blind adherence to rules that may be based on false assumptions.

I hope that helps. Thank you for thinking to ask me about the question.

- Andrew

Let’s understand the details provided in the historian’s argument.

Newton developed mathematical concepts and techniques that are fundamental to modern calculus.
2) Leibniz developed closely similar concepts and techniques.
Traditional view: these discoveries were independent.

HOWEVER,

Researchers recently discovered notes of Leibniz’s that discuss one of Newton’s books on mathematics.

Scholars’ argument

since the book includes a presentation of Newton’s calculus concepts and techniques
2) and since the notes were written before Leibniz’ own development of calculus concepts and techniques,

Scholars’ Conclusion

it is virtually certain that the traditional view is false.

Historian

A more cautious conclusion than this is called for, however. - Historian’s opinion/conclusion about the scholars’ argument

Leibniz’ 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. - premise/data/evidence used to support his conclusion.


If you have been able to identify each of the viewpoints and the viewpoint of the historian, the job is almost done.

Option A- The first provides evidence in support of the overall position that the historian defends; the second is evidence that has been used to support an opposing position.

The first does not provide evidence in support of the overall position the historian defends; rather it provides evidence in support of the scholars’ conclusion that the historian criticizes- Eliminate A

Option B- The first provides evidence in support of the overall position that the historian defends; the second is that position.

Same as A- Eliminate B

Option C- The first provides evidence in support of an intermediate conclusion that is drawn to provide support for the overall position that the historian defends; the second provides evidence against that intermediate conclusion.

The intermediate conclusion is not drawn to provide support for the overall position that the historian defends. The historian criticizes the intermediate/ the scholars’ conclusion- Eliminate C

Option D- The first is evidence that has been used to support a conclusion that the historian criticizes; the second is evidence offered in support of the historian’s own position.

The first is evidence drawn by scholars to support their conclusion that the historian criticizes. The second is the evidence used to support his conclusion. Option D is the correct answer.

Option E- The first is evidence that has been used to support a conclusion that the historian criticizes; the second is further information that substantiates that evidence.

The second is not information that substantiates the evidence used by the scholars. Instead, the second is in favor of the historian’s conclusion- Eliminate option E.

Vishnupriya
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