XAT 2014 — VARC Question 18
Analyze the following passage and provide appropriate answers for the questions that follow.
Ideas involving the theory probability play a decisive part in modern physics. Yet we will still lack a satisfactory, consistence definition of probability; or, what amounts to much the same, we still lack a satisfactory axiomatic system for the calculus of probability. The relations between probability and experience are also still in need of clarification. In investigating this problem we shall discover what will at first seem an almost insuperable objection to my methodological views. For although probability statements play such a vitally important role in empirical science, they turn out to be in principle impervious to strict falsification. Yet this very stumbling block will become a touchstone upon which to test my theory, in order to find out what it is worth. Thus, we are confronted with two tasks. The first is to provide new foundations for the calculus of probability. This I shall try to do by developing the theory of probability as a frequency theory, along the lines followed by Richard von Mises, But without the use of what he calls the ‘axiom of convergence’ (or ‘limit axiom’) and with a somewhat weakened ‘axiom of randomness’ The second task is to elucidate the relations between probability and experience. This means solving what I call the problem of decidability statements. My hope is that the investigations will help to relieve the present unsatisfactory situation in which physicists make much use of probabilities without being able to say, consistently, what they mean by ‘probability’.
Author has talked about the two tasks in the above passage. Choose the best option from the following statements relevant to the tasks.
Answer & solution
- A
The first task is sufficient to become the touchstone for the author to test his theory.
- B
The second task is sufficient to become the touchstone for the author to test his theory.
- C
Either of the tasks is sufficient for the author to test his theory.
- D
None of the tasks is sufficient for the author to test his theory.
Both the tasks would be important for the author to test his theory.
The author's theory aims to come up with “a satisfactory, consistent definition of probability” while clarifying the “relations between probability and experience”. The two tasks he mentions in the passage - “to provide new foundations for the calculus of probability” and “to elucidate the relation between probability and experience” are both essential in accomplishing the goals of the author's theory. In no manner, does the author indicate a precedence of one task over the other. Therefore, option 5 is the most suitable choice.
Hence, the correct answer is option 5.