That's exactly opposite of what we are trying to achieve through getters and setters.
Actually, it is not. The reason for declaring getters and setters is to hide the fields. This is done to avoid unwanted coupling; i.e. clients of an API depending on the implementation details of the API. (That coupling can be problematic for a number of reasons.)
The reason for making the getters and setters private is to make the corresponding part of the object's abstract state private. That's largely independent of the decision to use getters and setters or not.
While the case for using getters and setters is not as strong for private state, there are still tangible benefits. For instance:
The getter/setter methods provide a place for adding extra behavior or error checking code.
They can provide a place for logging state changes or access to the fields.
They can provide a place for adding your debug code while testing. (Probably not the best way of debugging.)
Getters and setters can be overridden. You can't do that with fields (private or not).
