English grammar - Modal forms and use of ‘can' and ‘may'

Extract

[...] To understand the importance of contexts, we are going to study the case of some examples of functions: Ability to do something: can speak French (in the present) / I could speak French (in the past)" Both can and could here refer to the ability to speak French Permission to do something: "Can I watch TV? / May I watch TV? / I could watch TV (polite permission)" To ask the permission to do something, we can use the verbs can or may if we know the person whom we are asking and could for a polite way to ask for presenting respect to the person whom we are asking. Request: "Can you give me this, please? / Could you give me this, please? (Polite request) / Will you please open the window? [...]

[...] Whereas may refers a weak possibility that the speaker expresses." Now we had a brief explication about differences between can and may, we are able to discuss and compare their uses in our examples. Example "Whatever appeal "eye-for-an-eye" revenge may have in the ordinary course of criminal behavior" / may be objectively hurt by my consent and I may subjectively regret it." In this first example, the meaning of the modal verb (may) is a weak possibility from a personal point of view and not a known fact. That is why the writer chose may instead of can. [...]

[...] / Would you please open the window? (Polite request)" It is the same way to request for something; there are modals for requesting in normal way (such as: can and will) and others for a polite request (could and would). Possibility: "It can get very cold in Russia / It could get very cold in Russia / It may snow tomorrow / It might snow tomorrow (less possible) / she must be hungry" Generally, it is more difficult to choose between modals to express possibility. [...]

[...] English grammar - Modal forms and use of `can' and `may' Modal forms Is it possible to describe and understand the function(s) of modal forms independently of their context of use? In English grammar, there are several modal verbs (can, could, may, might, will, would, should to, must and shall). These modals are generally used to express functions like permission, ability, obligation, lack of necessity, advice, possibility or probability. Each one of modal verbs expresses multiple functions: Can: ability, permission, possibility, request, offer and suggestion. [...]

[...] "Indeed, religious law can present significant choice of law and conflicting law issues" As we have "indeed" here, so the speaker is talking about a general truth or a real fact, that is why he used the modal can. Example "Older adults can experience problems" In this sentence, an ability is expressed, so the right choice was to use the verb can instead of may. "Various aspects of age-related cognitive decline may be attributable to PFC degradation" I think that it is a suggestion here, and since it is not a discussion between peers, the polite suggestion form was used by using may. [...]