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.



Scientists' beliefs which differ at the outset are related to:

• A. Different outcomes only.
• B. Different hypotheses only.
• C. Different hypotheses about different outcomes.
• D. Differences in explanatory power of competing hypotheses.

Hint:

A 'belief' in the passage always pairs a hypothesis with the outcome it predicts; think about what differs between two such pairs.

Answer 1

The Correct Option is C

The question asks what exactly is different between two scientists when the passage says their beliefs differ at the outset. To answer this we need to be precise about what a Bayesian belief actually is in this passage: it is a probability assigned to a hypothesis that predicts some outcome.

1. Different outcomes only: A belief in the passage is not just about an outcome by itself; it is about how likely a hypothesis is, which in turn predicts an outcome. Reducing it to outcomes alone drops the hypothesis half of the picture.
2. Different hypotheses only: This drops the outcome half. A hypothesis in this passage always exists in relation to what it predicts, so talking about the hypothesis alone, without reference to what it is meant to explain, is incomplete.
3. Different hypotheses about different outcomes: A belief, as the passage frames it, is a probability tied to a specific hypothesis h that predicts a specific outcome e. When beliefs genuinely differ at the outset, in the broad sense the passage is building its argument around, they differ because they concern different hypothesis-outcome pairs, that is, different hypotheses tied to different outcomes, before any evidence has forced them into line. This keeps both halves of the belief, the hypothesis and what it predicts, in the picture, which matches how the passage defines belief throughout.
4. Differences in explanatory power of competing hypotheses: The passage never compares how well hypotheses explain things; it only tracks probability values assigned to a hypothesis and how those probabilities shift with evidence. Explanatory power is not part of this discussion.

Because a belief in this passage is always a probability attached to a hypothesis and the outcome it predicts, and differing beliefs at the outset means differing on both of these together, option 3 is the accurate description.

Let's summarize:

• A belief here is not a bare number; it is a probability tied to a specific hypothesis and its predicted outcome.
• Differing beliefs therefore mean differing on the hypothesis-outcome pairing, not on just one half of it.

The correct answer is option 3.