[DBP]

M56:
In his chapter on modal auxiliaries in The English Verb, Michael Lewis lists what he thinks are the basic semantic meanings for each. I cite those meanings below and ask if you agree with them.

Please remember, we are talking about the basic semantic meaning. In context, these auxiliaries take on wider meanings, but it is the basic meaning I want to discuss.


Paraphrased.

Can = I assert that it is possible that ...
Could = I assert that it is "remotely" possible that ...

I don't think that "assert" fits very well here because 'can/could' can be epistemically very weak. This is especially notable in speech where intonation strengthens or weakens 'can/could'.

That caaaaaan happen. OR That cooooould happen.

Also, while 'could' is used to discuss remote/impossible events, it can also be used as a near equivalent of 'can'.

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May = If I have anything to do with it, it is possible that ...
Might = If I have anything to do with it, it is "remotely" possible that ...

I wonder why Mr Lewis has prefaced all these, eg. "If I have anything to do with it". I'd say that 'may' and 'might' have a discernible range of possibility, so they don't simply mean "it's possible that" and "it's remotely possible that".

Those are more the meanings of 'can' and 'could', which only express "possibleness" but don't express any discernable range of possibility.

'may' & 'might' express how certain a speaker is. They don't simply address that the speaker thinks something is possible.

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Must = I assert that it is necessary that ...

Is 'must' never used to relate another's assertion? An equal core concept for 'must' is epistemic 'must'.

Based on the available information, my logical deduction is that such and such is the case.

That must be the plumber.

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Will = Given my perception of the immediate situation, it is inevitable that ...

Would = Given the (hypothetical) situation which I perceive at the moment of speaking, the action described is also inevitably true.

These two, 'will' & 'would', like can/could are not always distinctly different. Rather than disjointed, I feel it's better to look at them as occupying the same scale.

Certainly, 'would' covers the unreal/impossible end of this scale/spectrum and 'will' the real/possible end but they meet in the middle and sometimes it's possible to use one or the other with virtually no difference in meaning.

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Shall = According to my perception of the present situation, it is, if it's anything to do with me, inevitable that ...

I'd say that 'shall' and 'will' share this meaning and others and intonation and context would/will fill us in as its strength.

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Should is dealt with separately as it is a far more complex auxiliary and has many meanings.

I don't understand the distinction that is being made here by Mr Lewis. All the other other modals have epistemic and deontic meanings just as 'should' does. 'should' equates to probably/likely as regards epistemic meaning and I suggest that this level of epistemic strength gives it its deontic strength, occupying a level below 'must'.
{From The English Verb by M Lewis. LTP 1986.}