For anyone claiming to write a history of a science of which reasoning

Question

For anyone claiming to write a history of a science of which reasoning forms the very essence, the question of the logic is of paramount importance. For example, a modern western account of any historical period in mathematics would, as a matter of course, show a detailed proof justifying each and every mathematical result discussed. Despite this obvious fact, general histories of Chinese mathematics rarely show concern for this issue. They insist above all on presenting only the mathematical results, the logical underpinnings of which are unclear, and rarely do they provide the reader with any semblance of a proof. While this approach to the history of mathematics is naturally a result of various causes, one which probably plays an essential role is the fact that most Chinese mathematical works themselves contain no logical justifications: according to this worldview, apparently it was enough to state authoritatively that something was true—it was completely superfluous to demonstrate why it was true.

There is one major exception to this general pattern, namely a set of Chinese argumentative discourses which has been handed down to us from the first millennium A.D. We are referring to the commentaries and sub-commentaries on the Jiuzhang Suanshu  , the key work which inaugurated Chinese mathematics and served as a reference for it over a long period of its history. This fact, which was long unrecognized, means that we are now in a position to know a lot more about the logical construction of mathematics in China than, for example, in Egypt, Mesopotamia, or India.   1 
1/ What distinguishes the commentaries on the Jiuzhang Suanshu from almost all other works of Chinese mathematical history is that the authors of the former

A made clear exactly what theorems are true
B spent time justifying their qualifications as authorities
C did not fully disclose all the results in the fields discussed
D provided explicit proofs for the mathematical results presented
E had influence over a large portion of Chinese history

2 
2. The author is primarily concerned with:

A discussing the most effective way to elucidate the history of science
B explaining how one ancient work conforms to our modern expectations for logical transparency
C arguing for a change in the methodology used in studying the history of mathematics
D demonstrating that ancient Chinese mathematics was far more advanced than that of other ancient civilizations
E providing an example of how authors making clear their own qualifications enhances the respectability of the work as a whole

3 
3/ The author implies all of the following except:

A The ancient mathematical texts of Mesopotamia do not provide explicit proofs for all their results.
B The first Western scholars studying the history of Chinese mathematics were unaware of the proofs available in the commentaries and sub-commentaries on the Jiuzhang Suanshu

C Proofs are a method of demonstrating the logical arguments underlying a mathematical result.
D The majority of important Chinese mathematicians between 1000 and 1500 would have known of the Jiuzhang Suanshu
E The authors of the Jiuzhang Suanshu do not make any claim justifying their own authority.

goforgmat · Answer

This fact, which was long unrecognized, means that we are now in a position to know a lot more about the logical construction of mathematics in China than, for example, in Egypt, Mesopotamia, or India.  we can infer form this that logical construction wasn't available for their mathematical construction. Hence A can be inferred.

Using the same excerpt above - this fact was long unrecognised- this fact here refers to the westerners who didnt know of this one exception. Hence B can be inferred.

Hope its clear.

sambit66 · Answer

Hi, Thanks for your reply. But i still have some confusions. How can we infer we can infer from this that logical construction wasn't available for their mathematical construction. ? The author has mentioned This fact, which was long unrecognized, means that we are now in a position to know a lot more about the logical construction of mathematics in China than, for example, in Egypt, Mesopotamia, or India. . "the logical construction of mathematics in China than, for example, in Egypt, Mesopotamia, or India" more logical construction in China than in Mesopotamia doesnt mean "The ancient mathematical texts of Mesopotamia do not provide explicit proofs for all their results." . The words "do not" arent they too strong ? I mean how can we outrightly infer "do not".

Talayva · Answer

This is an "EXCEPT" question. We expect that the passage clearly implies four of the answers, and for the last, it either implies something else or simply is not clear on that point. This last one, the one not clearly implied, is the right answer. 
In the last sentence, the passage clearly says we know more about the logical reasoning in Chinese math because of this one work that shows proofs. If we know less about the logical reasoning in ancient Mesopotamian math, it's because those works don't show proofs. Choice (A) is clearly implied, so it is not the answer to the EXCEPT question. 
The passage clearly says "This fact, which was long unrecognized, …" --- in other word, the first folks studying this did not realize that the commentaries and sub-commentaries on the Jiuzhang Suanshu provided proofs. Choice (B) is clearly implied, so it is not the answer to the EXCEPT question. 
The passage clearly says that proofs "justify" mathematical results, and explain why it is true. In other words, proofs "demonstrate the logical argument underlying a mathematical result". Choice (C) is clearly implied, so it is not the answer to the EXCEPT question. 
The passage clearly says that the Jiuzhang Suanshu "served as a reference for   over a long period of its history." Therefore, it is quite reasonable to infer that most Chinese mathematicians between 1000 and 1500 would have known about it. Choice (D) is clearly implied, so it is not the answer to the EXCEPT question. 
The passage talks about "justification" in terms of the logical justification a mathematical proof implies. Nowhere does it discuss people justifying themselves. Choice (E) is not implied, so this is the correct answer to the EXCEPT question.

aragonn · Answer

official Explanation for Q2 
The author talks about our modern mathematical standards (show a proof for everything), then talks about how most traditional Chinese works do not do this, but one, the commentaries on the Jiuzhang Suanshu, does. This latter work follows the same standards we keep in modern times. The credited answer is (B), because this one ancient work conforms to our modern standards of showing proofs for mathematical results. The term "logical transparency" simply means: showing the logical basis for something; explaining logically why something is true, which is precisely what a proof does.

The author is not discussing the history of science in general --- that's a much much broader topic. The author is very specifically focused on this one ancient Chinese work. Choice (A) is not correct.

The author makes clear the methodology used to study the history of mathematics, and voices no objection to it whatsoever. The author does make clear that most ancient Chinese writers did not follow the standards of our modern methodology, but that does not constitute an argument against this methodology. Choice (C) is not correct.

Choice (D) is tricky. At the end, the passage definitely says that we know more about mathematical reason in China than we know in the other civilizations. Does this mean Chinese math was more advanced? Not necessarily. We just know about it better. Choice (D) is not correct.

The passage talks about "justification" in terms of the logical justification a mathematical proof implies. Nowhere does it discuss people justifying themselves. Choice (E) is not correct.

aragonn · Answer

official Explanation for Q3 
This is an "EXCEPT" question. We expect that the passage clearly implies four of the answers, and for the last, it either implies something else or simply is not clear on that point. This last one, the one not clearly implied, is the right answer.

In the last sentence, the passage clearly says we know more about the logical reasoning in Chinese math because of this one work that shows proofs. If we know less about the logical reasoning in ancient Mesopotamian math, it's because those works don't show proofs. Choice (A) is clearly implied, so it is not the answer to the EXCEPT question.

The passage clearly says "This fact, which was long unrecognized, …" --- in other word, the first folks studying this did not realize that the commentaries and sub-commentaries on the Jiuzhang Suanshu provided proofs. Choice (B) is clearly implied, so it is not the answer to the EXCEPT question.

The passage clearly says that proofs "justify" mathematical results, and explain why it is true. In other words, proofs "demonstrate the logical argument underlying a mathematical result". Choice (C) is clearly implied, so it is not the answer to the EXCEPT question.

The passage clearly says that the Jiuzhang Suanshu "served as a reference for   over a long period of its history." Therefore, it is quite reasonable to infer that most Chinese mathematicians between 1000 and 1500 would have known about it. Choice (D) is clearly implied, so it is not the answer to the EXCEPT question.

The passage talks about "justification" in terms of the logical justification a mathematical proof implies. Nowhere does it discuss people justifying themselves. Choice (E) is not implied, so this is the correct answer to the EXCEPT question.

aragonn · Answer

official Explanation for Q1 
Most Chinese mathematical works stated results only, without the proofs justifying the results. The commentaries on the Jiuzhang Suanshu are different in that they contain both the results and the proofs. In other words, they provide "explicit proofs for the mathematical results presented", which is precisely what choice (D), the credited answer, says.

The majority of Chinese mathematical works did not include proofs, but they all said what was true. Both the commentaries on the Jiuzhang Suanshu and the other works "made clear exactly what theorems are true", so this does not distinguish them. Choice (A) is not correct.

The passage talks about "justification" in terms of the logical justification a mathematical proof implies. Nowhere does it discuss people justifying themselves. Choice (B) is not correct.

Choice (C) sounds awfully fancy, but it's not 100% clear what it even means. The authors of the commentaries on the Jiuzhang Suanshu "did not fully disclose all the results in the fields discussed"(??) Well, the only "field discussed" is mathematics. The verb "disclosed" is particularly odd, because it implies that someone was keeping secrets by withholding information, something not mentioned in the passage at all. As stated in answer choice (A), all Chinese mathematical works stated "results", i.e. what was true; only the commentaries on the Jiuzhang Suanshu also showed the proofs, i.e. why things were true. In that sense, the commentaries on the Jiuzhang Suanshu showed (disclosed?) more than the other works. Insofar as this choice says anything meaningful, it contradicts the passage. Don't be fooled by fancy wording. Choice (C) is not correct.

We know the commentaries on the Jiuzhang Suanshu "had influence over a large portion of Chinese history" because they "served as a reference for it over a long period of   history." Does this make the commentaries on the Jiuzhang Suanshu different from other works of Chinese mathematics? Do we have the grounds, based on the passage, to conclude that absolutely no other work of Chinese mathematics had any influence over the course of China's long history? Hmm. That seems like a stretch. The passage only talks about the influence of the commentaries on the Jiuzhang Suanshu, and says zilch about whether other works had a long influence. We just don't know. Choice (E) is not correct.

auradediligodo · Answer

Hi everyone,
Took 7:30 minutes and got all correct. Took 3:20 minutes to read, write down paragraphs summaries and main point.

P1: Generally Chineses don't prove their results
P2: And old document may help understand the logic behind Chineses' computations.

MP: Discuss Chineses results in relation with and old document explaining the methodology followed

------------------------------------------------------------------------------------------------------------------------------------------------------
  
 1/  What distinguishes the commentaries on the Jiuzhang Suanshu from almost all other works of Chinese mathematical history is that the authors of the former

Pre-thinking:
 Explained the reasoning behind the results

A made clear exactly what theorems are true
 The author is clear about the methodology used to drive at results. Hence incorrect

B spent time justifying their qualifications as authorities
 These are the current Chineses. The author is clear about the methodology used to drive at results. Hence incorrect

C did not fully disclose all the results in the fields discussed
 The author is clear about the methodology used to drive at results. Hence incorrect

D provided explicit proofs for the mathematical results presented
 In line with pre--thinking. Hence correct

E had influence over a large portion of Chinese history
 The author is clear about the methodology used to drive at results. Hence incorrect

------------------------------------------------------------------------------------------------------------------------------------------------------

2.  The author is primarily concerned with:

Pre-thinking:
 Refer to main point above.

A discussing the most effective way to elucidate the history of science
 Too general while the passage is specific about Chineses' results. Hence incorrect

B explaining how one ancient work conforms to our modern expectations for logical transparency
 The ancient work described helps understanding the logic of Chineses'computations. In the first lines it is written that the logic factor is extremely important to understand results.Overall the specific examples present in the passage are used to the point made in the first lines. Hence correct

C arguing for a change in the methodology used in studying the history of mathematics
 No such intention is present in the passage. Hence incorrect

D demonstrating that ancient Chinese mathematics was far more advanced than that of other ancient civilizations
 No such comparison is made. Hence incorrect

E providing an example of how authors making clear their own qualifications enhances the respectability of the work as a whole
 The respectability factor is not discussed. Hence incorrect

------------------------------------------------------------------------------------------------------------------------------------------------------

3/  The author implies all of the following except:

Pre-thinking:
 Let's have a look at the answer choices since we cannot make inferences here.

A The ancient mathematical texts of Mesopotamia do not provide explicit proofs for all their results.
 Look at this portion:"This fact, which was long unrecognized, means that we are now in a position to know a lot more about the logical construction of mathematics in China than, for example, in Egypt, Mesopotamia, or India."

It means that the logical construction of mathematics ofMesopotamia is not clear.
Hence this is incorrect

B The first Western scholars studying the history of Chinese mathematics were unaware of the proofs available in the commentaries and sub-commentaries on the Jiuzhang Suanshu
 Read the same portion of the passage mentioned in the previous answer choice. Focus on the word  now . It means that before scholars were unaware of the proofs. Hence incorrect

C Proofs are a method of demonstrating the logical arguments underlying a mathematical result.
 can be inferred from the first lines of P1. Hence incorrect

D The majority of important Chinese mathematicians between 1000 and 1500 would have known of the Jiuzhang Suanshu
 "has been handed down to us from the first millennium A.D. " If it has been handed down from 1st millennium it makes sense to infer this option choice. Hence incorrect

E The authors of the Jiuzhang Suanshu do not make any claim justifying their own authority.
 This aspect cannot be inferred from the information given. Hence correct

------------------------------------------------------------------------------------------------------------------------------------------------------

It is a good day to be alive, cheers!

VerbalBot · Answer

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For anyone claiming to write a history of a science of which reasoning

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