Question

Read the following passage and answer the question that follows.

Attempting to understand science and scientific reasoning in terms of the subjective beliefs of scientists would seem to be a disappointing departure for those who seek an objective account of science. Howson and Urbach have an answer to that charge. They insist that the Bayesian theory constitutes an objective theory of scientific inference. That is, given a set of prior probabilities and some new evidence, Bayes' theorem dictates in an objective way what the new, posterior, probabilities must be in the light of that evidence. There is no difference in this respect between Bayesianism and deductive logic, because logic has nothing to say about the source of the propositions that constitute the premises of a deduction either. It simply dictates what follows from those propositions once they are given. The Bayesian defence can be taken a stage further. It can be argued that the beliefs of individual scientists, however much they might differ at the outset, can be made to converge given the appropriate input of evidence. It is easy to see in an informal way how this can come about. Suppose two scientists start out by disagreeing greatly about the probable truth of hypothesis h which predicts otherwise unexpected experimental outcome e. The one who attributes a high probability to h will regard e as less unlikely than the one who attributes a low probability to h. So P(e) will be high for the former and low for the latter. Suppose now that e is experimentally confirmed. Each scientist will have to adjust the probabilities for h by the factor P(e/h)/P(e). However, since we are assuming that e follows from h, P(e/h) is 1 and the scaling factor is 1/P(e). Consequently, the scientist who started with a low probability for h will scale up that probability by a larger factor than the scientist who started with a higher probability for h. As more positive evidence comes in, the original doubter is forced to scale up the probability in such a way that it eventually approaches that of the already convinced scientist. In this way, argue the Bayesians, widely differing subjective opinions can be brought into conformity in response to evidence in an objective way.



Strictly following the idea put forward in the article, which one of the following is a logical possibility:

• A. The idea that astrologers can predict stock market movements better than economists, if astrologers' hypothesis (h) is more consistently followed by outcomes (e) than that of economists.
• B. The fact that stock-market movements are in sync with the movement of the heavenly bodies; both (h) and (e) contained in the same statement.
• C. That certain astrological phenomena can influence thinking of humans (e) which is manifested in stock-market booms and crashes (h).
• D. None of these.

Hint:

Check whether each option keeps h as the single hypothesis and e as the single, separate predicted outcome, the way the passage's own example does.

Answer 1

The Correct Option is D

This question asks us to apply the passage's structure strictly: a hypothesis h predicts a distinct outcome e, and confirming e raises belief in h through an objective, evidence based rule. We need to find which option correctly keeps h and e as two separate, clearly defined things related by prediction, without breaking the passage's own logic.

1. The idea that astrologers can predict stock market movements better than economists, if astrologers' hypothesis (h) is more consistently followed by outcomes (e) than that of economists: This compares two different hypothesis-outcome systems, astrologers versus economists, rather than applying the passage's single h-predicts-e structure to one hypothesis being tested. It borrows the language of h and e but does not actually set up one clean hypothesis being confirmed or denied by one outcome, the way the passage describes.
2. The fact that stock-market movements are in sync with the movement of the heavenly bodies; both (h) and (e) contained in the same statement: The passage needs h and e to be separate. h is the hypothesis, e is the outcome it predicts, and the two are then compared through probability. Folding both into a single statement, as this option does, removes the very structure the passage relies on, so it cannot be a valid instance of the idea.
3. That certain astrological phenomena can influence thinking of humans (e) which is manifested in stock-market booms and crashes (h): Here the labels are swapped from how the passage uses them. h is supposed to be the hypothesis that predicts e, but here the human thinking is called e and the market outcome, which should logically follow, is called h. This scrambles the roles the passage assigns to h and e.
4. None of these: The first three options each break the passage's structure in a different way, one blends two separate hypothesis systems, one merges h and e into one statement, and one mislabels which is the hypothesis and which is the outcome. Even the remaining option in the original paper, which chains two outcomes off one hypothesis, does not fit the passage's simple h to e model either. None of the options actually gives a clean case of one hypothesis h making one clear, testable prediction e in line with the passage's description. So none of them work.

Since every option distorts the passage's h-predicts-e structure in some way, either by comparing two systems, merging h and e, or mislabelling them, the only honest choice is that none of them is a valid application of the passage's idea.

Let's summarize:

• The passage's logic needs one hypothesis h making one prediction e, checked by evidence in an objective way.
• Each option breaks this setup differently, so none of them is a correct instance of the idea.

The correct answer is option 4: none of these.