Choice of (should / could / would / might) in the "so that" clause

Question

He used a false name so that no one should discover his secret. source

I refused an invitation so that I might spend Sunday with you. source

She burned the letters so that her husband would never read them. source

I close my eyes so that I could stop missing you. (from internet)

The dictionaries just provide definitions for each modal-verb in these examples.

Any difference in meaning or usage?

I think they are just ordinary meanings here. Why do the dictionaries list them separately as standalone entries? Just because they are used in the "so that" clause?

Answer 1

In American English, "should" and "might," in this context, are not idiomatic. A native speaker of American English would not use either one in the sentence unless they were pretending to be (1) pretentious or (2) British, or unless they are part of a fixed phrase or construction that has preserved this archaic idiom: "I should think not!", for example.

As a native American English speaker, I would use "would" or "could." They do have slightly different meanings, but in context, the differences are unlikely to be important.

In the sentence:

He knew that no one would ever discover his secret

the speaker is talking about whether a thing will happen. In:

He knew that no one could ever discover his secret

the speaker is talking about whether a thing is possible. In practice, they are more or less interchangeable. If you want to understand the difference, consider this sentence.

The smartest man in the world knew that no one would, because no one could, ever solve his devious puzzle.

Here, the speaker makes this distinction expressly: it will not happen, because it is not possible.

In my understanding, "might" is a British, and possibly archaic, variant with roughly the same meaning as "could," and "should" is a British, and possibly archaic, variant with roughly the same meaning as "would."

Answer 2

so that here indicates the purpose of doing something in the first clause. I'll wear an overcoat so that I don't feel cold. As I said, so that here is used to show the purpose. I don't want to feel cold and that is why, I'll wear an overcoat.

Now your sentences. Each of them has a particular purpose and that's why those modal-verbs are used that way.

He used a false name so that no one should discover his secret - He's very much concerned about hiding his identity. So, no one should know that.

I refused an invitation so that I might spend Sunday with you - The person who refused is still not sure of spending Sunday with whosoever that 'you' is (but mind it, he has all the plan for that).

She burned the letters so that her husband would never read them - She does not want her husband to read them in future.

I close my eyes so that I could stop missing you (from internet) [looks a bit off to me* but still] - talks more about the capability to stop missing whoever that 'you' is.

None of these verbs are interchangeable as doing so will change the meaning though quite a little.

For instance,

I close my eyes so that I might stop missing you - here, it'd change the meaning and will say that if you close your eyes, you might (may be, possibly) stop missing whoever that 'you' is whereas originally closing the eyes enhances the capability of stop missing whoever that 'you' is.

Also,

I refused an invitation so that I should spend Sunday with you - Here, it completely removes the doubt or probability (which is in the original sentence) and puts (moral?) responsibility or compulsion (on the person who's refusing) to meet whosoever that 'you' is.