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

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For anyone claiming to write a history of a science of which reasoning [#permalink]

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New post 12 Jan 2018, 14:36
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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 Nine Chapters on the athematical Art"], 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/ 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. 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/ 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.

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Re: For anyone claiming to write a history of a science of which reasoning [#permalink]

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New post 12 Jan 2018, 20:25
chesstitans wrote:
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 Nine Chapters on the athematical Art"], 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/ 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. 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/ 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.




Ans
DBE.
Took 7 minutes to do the passage.
Good One.


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Re: For anyone claiming to write a history of a science of which reasoning [#permalink]

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New post 14 Jan 2018, 18:46
Excellent RC!

6 mins 58 seconds.
D/B/E- Answers

Please post the OE for each of the questions! Would love to see if my reasoning for eliminating the wrong answers was right or not!
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Re: For anyone claiming to write a history of a science of which reasoning [#permalink]

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New post 14 Jan 2018, 23:26
Can anyone please explain Answer to Q3?
How can we eliminate option 1 and Option 2. ?
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Re: For anyone claiming to write a history of a science of which reasoning [#permalink]

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New post 14 Jan 2018, 23:27
csaluja wrote:
Excellent RC!

6 mins 58 seconds.
D/B/E- Answers

Please post the OE for each of the questions! Would love to see if my reasoning for eliminating the wrong answers was right or not!

Please Explain Answer to Q3? How did you eliminate option 1 and 2?
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For anyone claiming to write a history of a science of which reasoning [#permalink]

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New post 15 Jan 2018, 06:32
sambit66 wrote:
csaluja wrote:
Excellent RC!

6 mins 58 seconds.
D/B/E- Answers

Please post the OE for each of the questions! Would love to see if my reasoning for eliminating the wrong answers was right or not!

Please Explain Answer to Q3? How did you eliminate option 1 and 2?



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.
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Re: For anyone claiming to write a history of a science of which reasoning [#permalink]

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New post 15 Jan 2018, 10:59
1
goforgmat wrote:
sambit66 wrote:
csaluja wrote:
Excellent RC!

6 mins 58 seconds.
D/B/E- Answers

Please post the OE for each of the questions! Would love to see if my reasoning for eliminating the wrong answers was right or not!

Please Explain Answer to Q3? How did you eliminate option 1 and 2?



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.


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". :-(
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Re: For anyone claiming to write a history of a science of which reasoning [#permalink]

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New post 05 Jun 2018, 23:24
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 [Chinese mathematics] 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.
Re: For anyone claiming to write a history of a science of which reasoning   [#permalink] 05 Jun 2018, 23:24
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