If you put possibly or conceivably after could / might / may, you are indicating that it is possible, but fairly unlikely, that something will happen or be the case.

These conditions could possibly be accepted.

can / could (not may) are used to talk about specific possibilities in wh-questions or with adverbs such as only or hardly.

Who can / could that be at this time of night?

NOTE	might is used in more tentative (less) direct questions: Might the losses be due to currency fluctuations?

could have / might have can be used for a specific past possibility to say that there was a possibility of something happening in the past, although it did not in fact happen.

John could have posted the letter. (= I’m not sure whether he did or not.)

She might have done it; she had the motive. (= Perhaps she did it.)

NOTE	might have expresses a past opportunity which we know was not taken. I might have gone to drama school, but my parent wouldn’t let me.

could expresses doubtful possibility or possibility / ability in unreal conditions:

He could be at home.

If we had money, we could buy a car.

can is never used to express a current possibility / probability.

– Where’s Julia? – She could be in the garden. (She can be in the garden.)

can / can’t have are used to express possibility in the conditional sentences and implied conditionals to refer to ability or capability that was not used owning to personal failure or lack of opportunity.

To express negative possibility couldn’t have is used to say that it is impossible that something happened or was the case.

It couldn’t have been wrong.

The money was not, and never could have been the property of the Workers’ Party.

NOTE

Degrees of certainty can be expressed as: He is at home. (it’s a certain fact) He could be at home. (doubtful possibility) He should be at home. (doubtful possibility) He ought to be at home. (doubtful possibility) He may be at home. (it’s possible, but uncertain) He might be at home. (less certain than may) He isn’t at home. (it’s a certain fact) He can’t be at home. (it’s nearly certain) He couldn’t be at home. (more tentative than can’t) He may not be at home. (possible, but uncertain) He might not be at home. (less certain than may not)

3. Impossibility. In this function can’t / couldn’t are used:

• for things which we know are impossible;

You can’t get blood out of a stone.

• to make negative deductions;

He can’t be a doctor, he is not wearing a white coat.

• to say that something is impossible because we are unwilling to do it;

I couldn’t pick up a spider; they terrify me.

NOTE	When we think that something is possibly not the case we use might not or may not. The shops may not / might not be open today; it’s a bank holiday. (= Perhaps they are not open.)

can’t is used to express a logical impossibility.

– Where’s Julia? – She could be in the kitchen. – No, she can’t be there. I’ve just come from the kitchen.

If we are certain that something will be possible or impossible in the future will / won’t be able to can be used.

We’ll be able to travel to the moon one day.

4. Incredulity, doubt, astonishment. To express incredulity and doubt can is used with all the forms of the infinitive in interrogative and negative sentences. The Russian equivalent is ‘неужели не ..., разве не ...’. Astonishment is expressed only in the interrogative sentences. The simple infinitive is found with stative verbs. The continuous infinitive is used with dynamic verbs.

– Can she be waiting for us? – It cannot be true! It’s incredible.

can + perfect infinitive refers the action to the past.

Can he have told a lie?

can + perfect continuous infinitive is used to express actions begun in the past and continued up to the present.

Can she have been waiting for us so long?

could with reference to the present used in this way implies more uncertainty.

Could it be true? Could he have told a lie?

Could she be waiting for us? Could she have been waiting for us so long?

Strong incredulity or doubt is expressed by can followed by the corresponding form of the verb to fail + indefinite infinitive.

Can he fail to do it?  Can he have failed to do it?

NOTE

You can render Russian ‘неужели не’ using the verb to fail + infinitive, negative prefixes, negative pronouns, antonyms, synonyms. Can you have failed to find him? (Неужели ты его не нашел?) Can he have been out? (Неужели его не было дома?) Can he be unaware of it? (Неужели он не знает этого?) could implies more uncertainty: Could he be short? (Неужели он не высок ростом?) Could he have found nobody there? (Неужели он там никого не застал?) Could he have failed to find anybody there?

5. Disbelief / improbability (only in negative sentences). Emotionally coloured can ‘не может быть, что ...; вряд ли ...; не может / мог + инфинитив’ is used with different forms of the infinitive. could makes the statement less categorical.

It can’t be true.  It couldn’t be true.

She can’t be reading now.  She couldn’t be reading now

She can’t have read this book.  She couldn’t have read this book

She can’t have been reading his book all the time.  She couldn’t have been reading his book all the time.

can’t / couldn’t have is used to express surprise or disbelief.

She couldn’t have done it; she is such a nice woman.

could is often used to express surprise, anger, etc. in the present.

I could eat my hat!

6. Giving and asking permission. can ‘можно, могу ли я ...; иметь право’ is used to say that someone is allowed to do something. can and could (indicative and subjunctive) are followed only by the non-perfect infinitive with reference to the present or future.

She can go with you.

If you want to ask permission to do something, you can use Can I ...? or Could I ...? (more polite). can is less formal. May I ...? sounds very polite and formal. Might I ...? sounds even more formal. You can also make your request very polite by adding perhaps or possibly about Could / May I ...?

Could I perhaps bring a friend with me?

You can ask permission in a stronger way by using can’t / couldn’t if you think you may not be given the permission you want.

Can’t I come?

be allowed to is used to express permission, to say what the rule is.

He was allowed to cross the border.

Compare the questions with may and be allowed to used in them.

May I take a photo of you? (= Will you allow it?)

Are we allowed to take photos? (What is the rule?)

NOTE	Verbs and verb phrases related in meaning ‘permission / prohibition’ to can / could / may / might are the following:
	 (not) be allowed to:  (not) be permitted to:  be forbidden to:  be prohibited:  be not to:  negative imperative:	You’re (not) allowed to stay out late. You’re (not) permitted to stay out late. You’re forbidden to stay out late. Smoking is (strictly) prohibited. You’re not to smoke. Don’t smoke!

could can be used when there is an idea of condition.

Why don’t you ring him? You can / could use my phone.

could is used to express present or future permission.

Could I smoke in here?

could / couldn’t can also express general permission in the past. When a particular action was permitted and performed was / were allowed to is used instead of could.

On Sundays we could (= were allowed to) stay up late.

I had a visa so I was allowed to cross the frontier.

In the 1950s British children could leave school at the age of 14.

But to talk about permission on a specific occasion in the past and for perfect and continuous tenses and passives be allowed to must be used.

I could leave early yesterday.  I was allowed to leave early yesterday.

As a child he had been allowed to do exactly what he liked.

These are words and expressions of giving someone permission.

– Can I go with you? – OK. (informal)

– Can I go with you? – Sure. (informal)

– Can I go with you? – Yeah. (informal)

– Can I go with you? – All right. (informal)

– Can I go with you? – No problem. (informal)

– Can I go with you? – Of course. (more formal and emphatic)

– Can I go with you? – Yes, do. (more formal and emphatic)

– Can I go with you? – By all means. (more formal and emphatic)

– Can I go with you? – I don’t see why not. (if uncertain / enthusiastic about giving permission)

You can give someone permission to do something what they have not asked for it by saying you can ... .