XAT 2014 Question 17

Instructions

Analyze the following passage and provide appreciate 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’.

Question 17

The statement, “The relations between probability and experience are still in need of clarification” implies that:



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