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I'm Italian and live in Italy, where books on English are often odd, grammatically speaking....
For instance, in those books you can find a rule about the negative forms of "may" and "can" saying that "cannot" indicates something sure (you cannot swim = you are not able or not allowed to swim at all), while "may not" just indicates something negative as possible (you may not swim = it's not necessary you swim).

Yesterday I found another book saying the opposite, however. "Use "may not"/"must not"/"cannot" for prohibition. Examples: a) Unauthorized personnel may not enter. b) He must not forget. c) You cannot go yet".

Now, I'd understand the sentence a) as meaning that perhaps unauthorized personnel doesn't enter but may enter too....

For prohibition, I'd put: "Unauthorized personnel is not allowed/is not permitted/must not/cannot enter".

Am I wrong?
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Comments  (Page 2) 
The second reply of Mr. Pedantic has been very interesting and complete...

However, what I meant with my examples was exactly what "An Attempt" has just explained here above.

In the same line, I have another pair of sentences taken from my English grammar book.

"It cannot be that way" (meaning, if I've learnt your clarifications well, that "it's impossible for something to be in a certain way at all")
"It may not be that way" (meaning that "it's just possible (not sure...) for something not to be in a certain way".

Is that correct, please?
And what about the perfect explanation of my mind given by "An Attempt"? What could one add as a new reaction to the perspective offered by his interpretation?

My questions set apart for a while, I have to thank everyone of you for your linguistic sensitivity and insight.
I think that what Fortiter was asking about is: can we use the phrase “you may not swim in this pool” as a permission “not to swim” (if one doesn’t feel like it), i.e., a permission to refrain from swimming, and if we can, then how to distinguish such a permission from a prohibition?

Ah!

It would be a very rare occurrence. But for instance, how would we distinguish between these two signs?

1. You may not/ walk on the grass.
– a prohibition in a park.

2. You may/ not walk on the grass.
– a permission in a strange park (you are not obliged to walk on the grass).

I'm inclined to think we could only know by the context, and by our experience of 'things that are sometimes prohibited'.

In conversation, we would have to surround 'permissive may not' with other signs and phrases: a humorous facial expression, perhaps; or 'you may/ not walk on the grass – if you don't want to walk on the grass'.

On the whole, I think we'd rephrase it: 'you're allowed not to swim in the pool, you know, if you don't want to!'

MrP
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1) how could I just express uncertainty (not a prohibition) in such a sentence as: "You may not swim in my swimming pool"?

In other words, how can I render the same mood, same meaning same nuance of such a sentence as "he MAY NOT arrive on time" in the following sentence:
- You MAY NOT swim in my swimming pool
- She said I MIGHT NOT swim in her pool?

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I believe the distinction that Nona was trying to make, Fortiter, was that we don't generally use a negative to express low levels of doubt about things that we would know about.

1. You MAY NOT swim in my swimming pool.

The reason that this sounds most like permission rather than possibility is that generally, "I", the pool owner, would know about the chances of "you" swimming in 'my' pool, since I make those decisions.

So if we wanted to express this in the neutral fashion that expressed the certainty level of that you desire, you'd likely hear something like,

2. You may not get the chance to swim in my pool. [= outside factors that I'm not completely sure about cause me to say this]

The addition of "get the chance to" moves this away from permission [modal politeness] into possibility [modal chance].

The reason that we don't normally use the negative, as Nona related, is that we would switch to a negative , which relates the equal level of certainty that a positive does.

You probably won't [get the chance to] swim in my SP.

"He may go = He probably won't go" when we equate the actual chance of him going.

Positive and negative modal & do not say the same things, though they both express the same level of certainty.

Two people: A: It may rain. versus B: It may not rain.

They both allow that the chance of rain is small but they are expressing different feelings, emotions.

These, what could we call them, ... say, "personal modal meanings" differ from

3. He may not arrive on time. ,

because, from context, this appears to be an expression of pure level of certainty.

Another thing to consider is that talking about the chance of someone using 'my' pool involves considerations of modal politeness that aren't a consideration in sentence 3. This is another reason we tend not to use a negative . A positive,

"You may [get the chance to] swim in my pool" is much more affirming, hence more polite than,

"You may not [get the chance to] swim in my pool".

I realize that this may be a bit confusing, so if you have any questions feel free to ask.
"It cannot be that way" (meaning, if I've learnt your clarifications well, that "it's impossible for something to be in a certain way at all")

"It may not be that way" (meaning that "it's just possible (not sure...) for something not to be in a certain way".

Hello Fortiter

I think I missed these two items earlier. But I think your analysis is correct:

1. 'It cannot be that way.'
This is not a sentence I would expect to hear very often. One possible context:

Two men are putting up bookshelves. MrA holds the shelf in place, while MrB prepares to fix it to the wall. MrB looks at the shelf for a moment. He puts down his screwdriver:
'It can't be that way round. Try it the other way.'

(i.e. 'it is not possible!')

On the other hand, he could use the same phrase to express utter disbelief. In that case, he would stress 'can't':

'It can't be that way round! Try it the other way.'

Or:

'It can't possibly be that way round!...'

(I realize that this isn't a very good example, since a bookshelf has only 4 possible 'ways round'. We must assume therefore that MrA and MrB are not very bright. Also, they would be more likely to say: 'it can't go that way round!'.)

2. 'It may not be that way.'

This time MrA and MrB have gone for a walk in the country. Since, as we know, they're not very bright, they get lost quite quickly. At last they come to a crossroads. There are no signposts. MrA and MrB scratch their heads.

'What now, MrA?'
'Well, MrB, I may¹ be wrong; but I think we should take the right-hand turn.'
'What makes you so sure?'
'Nothing. But we may² as well choose this as any other direction.'
'But it may³ not be that way!'
'It may³ not be any other way, either!'

Here,
a) 'I may¹ be wrong' means 'I am possibly wrong'.
b) 'we may² as well' expresses future possibility: the choices between the future possibilities are equal. There is an element of resignation in this phrase. All choices are equally likely to be wrong.
c) 'it may³ not be' means 'it is possibly not' (cf A).

If we substitute 'can':

a) 'I can't be wrong': 'it's not possible I'm wrong'.
b) 'We can as well' – confident assertion. All choices are equally likely to be right.
c) 'It can't be that way!' – strong disbelief that it's that way.

Does that help, Fortiter?

MrP
Well, I sometimes read psycholgical technique books (for therapeutic interviews/settings) becaus that's part of my job.

Now, in order to avoid or overcome and overtake or, so to say, jump over some psychological defenses patients can't drop to relax or change a damaging/bad behaviour of theirs it may be more effective and helpful to follow a "side path", not a direct one.
In particular, one mustn't forbid anything because a contradiction istinct or reflex may be aroused (if I repeat an anxious person he must not be that anxious he will probably become more and more uncontrolled, also if he consciously would like to obey me and fall asleep or so).

In those cases, an Italian psychologist would start his interview with the patient telling him: "Non credi che potresti pure NON seguire questa agitazione?" (="Don't you think you might / not follow (look at the slash: not "might not / follow") that excitement?" literally translating).

The aim of such a sentence is
a) not to contradict the symptom one wants to eliminate straight away (in order to avoid defences on starting to modify the attitude, as already said),
b) to be suggestive and allusive instead (making a kind of "offer" - the offer to get or accept a new behavioural pattern or at least the mere possibility to just figure out himself as following that pattern - not giving a command, obligation or prohibition),
c) to instil the (positive and ... beneficial) doubt the patient has the real opportunity to feel better, an aim to broaden the patient's perception and perspective to a more open and free horizon (=being calm) he clearly cannot consider as possible for him at the moment.

So, what would a brit psychologist say (in a way that keeps all the a), b) and c) nuances)?
I repeat the base sentence is "Don't you think you might / not follow (look at the slash: not "might not / follow") that excitement?".
Of course, you may change the words with something better. What I'm interested in is just seeing your translation for "may not" segment.

I solemnly declare I won't add up anything else after that!!!.... I don't want to exceed the politness limit.
I beg your pardon for my not good English (I never was to GB nor USA) and I appreciate your comprehension (and respectful silence...) about this point.

Thanks again
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So, what would a brit psychologist say (in a way that keeps all the a), b) and c) nuances)?
I repeat the base sentence is "Don't you think you might / not follow (look at the slash: not "might not / follow") that excitement?".
Of course, you may change the words with something better. What I'm interested in is just seeing your translation for "may not" segment.

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Fortiter,

There really aren't differences in the modal meanings between BrE and NaE[North American English], though there are some differences made in modal word choice. There are many ways in English for people to be indirect/to soften their suggestions.

I don't see any "may not" segment in your example. Could you point it out please?
Do you think you'd be able not to go with that impulse?
Do you think [it's / it would be] possible not to [go with / give in to] that feeling?
[What would happen / What's the worst that could happen] if you didn't give in to those feelings of nervousness?
How about just not paying attention to those feelings?
How about just ignoring those feelings? Is that a possibility? Would that work (for you)?
Maybe if you tried (just) not giving in to that feeling of agitation? How might that work for you?
What is something that might work for you? Maybe not paying attention to those thoughts? How does that sound? Isn't that something you could do?
Let's see if together we can find a way for you not to have to deal with those unpleasant feelings.
__________

We need to recognize that the distinctions you are asking about are often made by intonation in English. Only "cannot" and "can not" show this in the written form:

1) You cannot swim in the pool. [Permission denied.]* = You may not swim in the pool. = You [must not / mustn't] swim in the pool.
2) You can not swim in the pool. [Inaction permitted.] = You don't have to swim in the pool. = You needn't swim in the pool.

*Ignoring the reading in which the pool is empty, for example; that is, ignoring "can" of ability.

In the first, either the "can" or the "not" of "cannot" can be stressed; the rest of the sentence is said with falling intonation. The "a" of "cannot" is usually fully pronounced in this construct.
In the second, "you can" is "youk'n", the "k'n" very unstressed; after the briefest of pauses before the "not", the rest of the sentence has a somewhat rising intonation.
"can't" can be substituted in the first, NOT in the second!

To emphasize the meaning, other words are often added:

You cannot swim in the pool. It's too soon after dinner, and I don't want you getting stomach cramps.
You can swim in the pool or you can not swim in the pool; it's your choice, really.

CJ

ALSO: Modals
Just to say that "may not" segment is "... think you MIGHT / NOT follow ...", being MIGHT a form of MAY (they are the same verb, so I'd consider them, or what?).
And that I wish to thank everyone of you for your suggestions, capacity and .. kindness.
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Just to say that "may not" segment is "... think you MIGHT / NOT follow ...", being MIGHT a form of MAY (they are the same verb, so I'd consider them, or what?).

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and are not the same verb, Fortiter, any more than and are the same or and are the same. Each describes a range of certainty and none of those are the same.

'may' shows a stronger possibility than 'might', just as 'must' shows a stronger possibility than 'should'.

Here are four of the modals that express levels of certainty, in descending order, ie. from highest to lowest certainty.

must

should

may

might
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