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User 'jlovegren' : 'Might' is the preterite form of 'may', and both can be used as present tense modals. It originally meant "to be strong, to have power".

Source: p 123, Line 660; Antigone, Oedipus the King, Electra; by Sophocles, E Hall et al

TUTOR [to the chorus]. Might I inquire of you if I have come
To the royal palace of the lord Aegisthus?

Is the use of might here right? The Tutor's question isn't past in any way; so why would you use the preterite might, as per the grey above? I also read this.

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Might + present tense and could + present tense can be used to express a possibility of something in the present tense. May and can are present tense only.

@zerohedge is right, might sounds a bit more polite (when asking) than may, and both sound much more polite than can or could.

I may go to the park.

I might go to the park.

Can I go with Bobby?

Could I go with Bobby?

You could substitute any of the words in any of those sentences and say the same thing.

When might and could are used to express a past possibility that no longer applies now, might and could are always followed by have + past participle.

I might have gone to the park, but it was raining.

He could have gone with Bobby, but he ended up not going.

You cannot use can or may here, or might/could + present tense.

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At least in today's English, might and may have simillar usages, and while one may/might seem a little more suitable in certain situations, neither would be wrong.

The usages of might instead of may in the question you quote is entirely about the extra1 politeness it adds to the request.

1 "may I" is already polite (surely more than "can I")

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It is true "might" is a past form, but theoretically it can be past tense indicative and past tense subjunctive. Even today I'not sure whether it is possible to find uses where "might" is indicative and referring to past time.

Normally "might" is past subjunctive and though this is grammatically a past tense, the subjunctive does not refer to past time, but to present time.

This discrepancy between grammatical tense and time referred to can clearly be seen in sentences such as

  • Could* you lend me your bike?
  • Would* you like to go to the cinema?
  • Might* I ask where you come from? (The * marks the subjunctive form).
  • You should* stop smoking.

In these four examples the time referred to is not past time, but present time. http://www.grammaring.com/past-subjunctive

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