the use of "can be" in passive voice

I'm not a native English speaker and I see a sort of striking contradiction in the use of the expression in the passive voice

something can/can not be + past participle

e.g

the problem can not be solved

or

I can't be killed

or

the door can be opened

I know what the English native speakers want to say with this expresion but I see it weird to attribute "can" to an object ; then "can" and the passive voice are contradictory - isn't it like saying :

the door can undergo to be opened

Can is bound to all what relates to ability,action...while the passive voice is bound to the passivity,non action...thus the expression is like

the door is active to be passive

1)"can" and "undergo" does not go together !

2)It's human that can,not objects (such as "doors") or abstract things (such as "problems")

I know ,maybe, I have not well explained my idea - but is this a legacy from an old language or just an habit that became a rule ?

Solution 1:

There is no mystery.
In a passive sentence the subject becomes the agent, which is often omitted.

• The problem can't be solved. (by anyone here) = No one here can solve the problem.
• The door can't be opened (by us) = We can't open the door.

The agent is the person or thing that performs the action and is the subject of the active sentence. In most passive sentences, the agent is not mentioned. If it is mentioned, however, it is usually preceded by the preposition by.

Grammaring

Solution 2:

"Can" is potentially ambiguous between a permission sense and a possibility sense. "This door can be opened" in the permission sense is "Someone (unspecified) has permission (for that person(s)) to open the door" but in the possibility sense means "It is possible (for someone/thing) to open the door."

In the possibility sense, there is no change of sense when the clause with "open" is passivized: "It is possible for the door to be opened (by someone/thing), which can be expressed using "can": "The door can be opened (by someone/thing)."

In the permission sense, however, passivizing makes for a difficulty. "Someone (unspecified) has permission for the door to be opened (by that person(s))" is not entirely coherent, and it cannot be simplified and rephrased with "can", "The door can be opened", because it implies that "the door" is receiving permission. Doors are not people, so they can't be given permission.