whether a sentence is truth-neutral or truth-committed often depends on factors other than the choice of verbal construction. In I’m surprised that your wife should object, the effect of the main verb is to cancel out the neutrality of the should + Infinitive construction, with the result that we clearly understand from this sentence that the wife does object. There is hence no logical difference, in many cases, between should + Infinitive and the simple Indicative form objects. This is not to say, however, that there is no difference in feeling. In I’m surprised that your wife should object, it is the ‘very idea of it’ that surprises me; in I’m surprised that your wife objects, I am surprised by the objection itself, which I take to be a known ‘fact’.
The meaning swings in the opposite direction (from truth-commitment to truth-neutrality) through the influence of verbs such as believe and suppose:
I believe (that) his mother is dead. | I suppose (that) you’re waiting for my autograph
Because of the essential element of uncertainty in the meanings of these verbs, a that-clause that would elsewhere be truth-committed becomes truth-neutral. The same applies to adjectives such as possible and likely.
We could go on to note that the primary modals (e.g. can, may, will) also express an element of uncertainty, and so belong to the truth-neutral category. However, they express more specific meanings, such as ‘possibility’ and ‘obligation’, whereas the forms with ‘theoretical’ meaning discussed here – the Infinitive, the Subjunctive and ‘putative’ should – express truth-neutrality in its most generalised form.
The difference between ‘arrangement’ and ‘intention’ is a very slight one; so be going to + Infinitive could be substituted for the Present Progressive in all these examples.
Be going to implies that the conditions for the future event already exist. However, will could replace be going to in these two examples with little difference of meaning.
Without an adverbial, a time in the near future rather than remoter future is generally intended: one could insert the adverb just or soon in these sentences to make the imminence explicit.
-- Leech, Geoffrey N. 2004. Meaning and the English Verb. Harlow, England: Pearson/Longman.
Do they indicate conditional (hypothetical) possiblities or factual possiblities in these examples?
I have come across them a lot in this book as well as in ELL answers. From my understanding, may or can is used a lot in such context of giving useful information.
I wonder if the preterite form makes these statements more tentative or informal or what.