meaning - Should vs. Shouldn't

They believe this.

1. Should they?



2. Shouldn't they?

Do the both replies mean the same?

Answer

Both questions are asking for a normative statement in response to somebody's belief. However, there is a difference in emphasis.

As I said in an answer to the question "'should They?' or 'should they be?'?":

These are actually both fine, but they have a different emphasis.

They believe this. Should they?

This is stating they believe something but then questioning if it's appropriate. In other words, there is doubt being expressed.

It could be rephrased as:

They believe this. But why do they believe it? Isn't is strange that they do?

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They believe this. Shouldn't they?

This is stating that they believe it but then questioning why it should be questioned. Here, there isn't doubt in the appropriateness of the belief itself but puzzlement as to why somebody might think it should be otherwise.

It could be rephrased as this:

They believe this. Is there some reason to think their belief is wrong?

You can ask either Should they? or Shouldn't they? and get the same general answer in response. But which wording you use, as well as the tone of voice associated with it if it's asked in conversation rather than writing, will determine if you, as the questioner, are more critical or supportive of the belief.