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

The passage opens by talking about the subjective beliefs of scientists, and then explains, through Bayes' theorem, how a scientist's prior probability for a hypothesis h is a personal number they start out with before seeing new evidence. The question asks what kind of thing could actually cause these subjective beliefs to exist in the first place.

1. Multiple scientists studying multiple phenomena and putting forth multiple hypotheses: This just describes that science involves many scientists and many hypotheses in general. It does not explain why any one scientist's belief in a hypothesis is subjective rather than objective.
2. Propositions offered by scientists being backed only by one's beliefs about their validity: This matches the passage closely. The whole discussion of prior probabilities is about a scientist assigning a probability to h before any confirming evidence forces a specific number. That prior number is not derived from an objective rule; it comes from the scientist's own sense of how likely h is to be true. In other words, the proposition h is initially supported only by personal conviction, which is exactly what makes it subjective.
3. Scientists presenting data selectively in support of their own favourite hypothesis over competing hypotheses: This describes a form of bias in reporting evidence, but the passage never mentions scientists cherry picking data. It only talks about differing prior probabilities before evidence comes in.
4. Scientists allowing their subjective opinions to bias their testing of hypothesis: This assumes the testing process itself is corrupted by opinion, but the passage's whole point is that the testing process, applying Bayes' theorem to new evidence, is objective. It is only the starting probability, not the test, that is subjective.

Since the passage roots subjective belief in the personal probability a scientist assigns to a hypothesis before evidence, and not in biased testing or selective reporting, option 2 fits best.

Let's summarize:

• The passage's Bayesian method is objective once a prior is set, but the prior itself is a personal degree of belief, not an objectively derived number.
• Nothing in the passage supports selective data presentation or biased testing as the source of subjectivity.

The correct answer is option 2.