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"Could" can be used to say something is a possibility, which has a similar meaning to that of "might." The tense in the subordinate clause after "might" doesn't change. But when we use "could" in this sense, do we change the tense in the subordinate clause?

Example 1

The tense in the subordinate clause remains unchanged.

He has been doing lots of math recently. He might think that he will get good grades on the math exam tomorrow.

Example 2

What tense do we use when we use could here?

He has been doing lots of math recently. He could think that he will/would get good grades on the math exam tomorrow.

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    will in both cases. But bear this in mind: He could/might think that he would get good grades if he studied harder. Maybe this should be an answer...
    – Lambie
    Oct 3 at 14:25
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    Perhaps you're being misled by could in the second example, which can be used for both current and future possibilities. Compare He could be dead (now) and He could die (in the future). In your example, it seems to me that if we interpret he could think [something] as referring to what he might think now, the relevant thought is that he will do well (if he studies hard). But if we interpret could as referring to what he might think tomorrow (which is hypothetical irrealis "not present"), he would do well if he studied hard. Oct 3 at 16:28
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I think you're being misled by the fact that in some circumstances could functions as a past.

Historically, could was the past of can (and might was the past of may, incidentally). This still appears when we back-shift for indirect quotation:

He said "I can do it" -> He said he could do it.

But in modern English, as you note, could has other senses, expressing possibility or uncertainty. In these senses there's no past tense involved, and so no reason to alter the tense of the embedded sentence.

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