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.



The subjective beliefs of scientists referred to in the passage could be due to:

• A. Multiple scientists studying multiple phenomena and putting forth multiple hypotheses.
• B. Propositions offered by scientists being backed only by one's beliefs about their validity.
• C. Scientists presenting data selectively in support of their own favourite hypothesis over competing hypotheses.
• D. Scientists allowing their subjective opinions to bias their testing of hypothesis.

Hint:

A prior probability in the passage is a personal number a scientist starts with before evidence arrives, not something backed by data yet.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The passage refers to the subjective beliefs of scientists as the starting point of the whole discussion. We need to work out what the passage means by this, that is, where these subjective beliefs actually come from.

Step 2: Key Approach:
Trace the passage's own explanation of what a subjective belief is in this context: it is the prior probability a scientist gives to a hypothesis h before any new evidence arrives. Match this idea to the option that describes a proposition supported only by personal conviction rather than by an objective source.

Step 3: Detailed Explanation:
The passage explains that two scientists can start out disagreeing greatly about the probable truth of hypothesis h, and that this disagreement is resolved only later, once evidence comes in and both probabilities are scaled by the same objective rule. Before that evidence arrives, each scientist's number for h is simply their own degree of belief, not something derived from data or logic; the passage even says logic itself has nothing to say about where propositions come from. This means a scientist's belief in h is, at the start, backed by nothing except their personal sense that h might be true, which is a case of a proposition being supported only by one's belief in its validity. This differs from the ideas of selective data reporting or biased testing, since the passage keeps the testing process fully objective through Bayes' theorem; the only subjective piece is the number a scientist starts with.

Step 4: Final Answer:
The answer is option 2: propositions offered by scientists being backed only by one's beliefs about their validity. This is the subjectivity the passage is built around, sitting entirely in the prior probability, not in the later evidence based testing.