Among the speculative questions which arise in connection with the stu

Question

Among the speculative questions which arise in connection with the study of arithmetic from a historical standpoint, the origin of number is one that has provoked much lively discussion, and has led to a great amount of learned research among the primitive and savage languages of the human race. A few simple considerations will, however, show that such research must necessarily leave this question entirely unsettled, and will indicate clearly that it is, from the very nature of things, a question to which no definite and final answer can be given. Among the barbarous tribes whose languages have been studied, even in a most cursory manner, none have ever been discovered which did not show some familiarity with the number concept. The knowledge thus indicated has often proved to be most limited; not extending beyond the numbers 1 and 2, or 1, 2, and 3. At first thought it seems quite inconceivable that any human being should be destitute of the power of counting beyond 2. But such is the case; and in a few instances languages have been found to be absolutely destitute of pure numeral words.

These facts must of necessity deter the mathematician from seeking to push his investigation too far back toward the very origin of number. Philosophers have endeavoured to establish certain propositions concerning this subject, but, as might have been expected, have failed to reach any common ground of agreement. Whewell has maintained that “such propositions as that two and three make five are necessary truths, containing in them an element of certainty beyond that which mere experience can give.” Mill, on the other hand, argues that any such statement merely expresses a truth derived from early and constant experience; and in this view he is heartily supported by Tylor.

But why this question should provoke controversy, it is difficult for the mathematician to understand. Either view would seem to be correct, according to the standpoint from which the question is approached. We know of no language in which the suggestion of number does not appear, and we must admit that the words which give expression to the number sense would be among the early ords to be formed in any language. They express ideas which are, at first, wholly concrete, which are of the greatest possible simplicity, and which seem in many ways to be clearly understood, even by the higher orders of the brute creation. The origin of number would in itself, then, appear to lie beyond the proper limits of inquiry; and the primitive conception of number to be fundamental with human thought.    1 
 1. What is the primary purpose of the passage?

(A) To outline the history of mathematics 
(B) To discuss the origin of numbers 
(C) To resolve a dispute about the use of numbers 
(D) To critique the ancient tribes for use of numbers 
(E) To discuss the effects of numbers on society

2 
 2. The author of the passage would most probably agree with each of the following EXCEPT:

(A) Almost all primitive societies were using some form of numbers.
(B) Mathematicians are divided in their views about the origin of numbers.
(C) Numerical words were part of ancient languages.
(D) The concept of numbers finds its origin in barbarous tribes.
(E) The issue of the origin of numbers should not be a controversial one.

3 
 3. The mathematicians consider the debate on the origin of numbers as:

(A) Enlightening 
(B) Essential 
(C) Obligatory 
(D) Compulsory 
(E) Unnecessary

4 
 4. What does the line, in the third para, ‘primitive conception of number to be fundamental with human thought’ mean?

(A) Numbers are an inevitable creation of every language.
(B) Numbers have been a conscious creation of every language.
(C) Numbers have been interpreted differently by different tribes.
(D) There is a perennial debate over the origin of numbers.
(E) Numbers were incorporated strategically by the primitive tribes.

Sajjad1994 · Answer

Official Explanation

4. What does the line, in the third para, ‘primitive conception of number to be fundamental with human thought’ mean?

Explanation

Inferred from  para 3 , the author talks of how numbers have always been a part of the language skills of all primitive tribes researched till date. This is especially noted by all that even if the counting included only numbers 1, 2 and 3, the tribes were using it advantageously. Hence, option  (A)  is the correct answer.

(B)  The word ‘conscious’ is misleading since the inclusion of the numbers was instinctive rather than planned.

(C)  The passage never states or implies this.

(D)  While this may be true, it does not have any reference to the context here.

(E)  Same as B.

Answer: A

Sajjad1994 · Answer

Official Explanation

2. The author of the passage would most probably agree with each of the following EXCEPT:

Explanation

The author has concluded the passage on the line that numbers are to be considered ‘a part of human thought’ rather than an experience or intentional inclusion in the language. Hence,  (D)  is the correct answer.

(A)  Can be inferred from the first para

(B)  Can be inferred from the second para

(C)  Can be inferred from the first and the third paras

(E)  Can be inferred from the first sentence of the last para

Answer: D

Among the speculative questions which arise in connection with the stu

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Among the speculative questions which arise in connection with the stu

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