Rule: Like allows an infinitive object only if it expresses a repeatable state or event.
Example of error:
(1) Do you like to live in Hamburg?
Like can take either infinitive or -ing participle objects, and in most cases there is no difference in meaning:
I like washing/to wash the dishes.
There are contexts, however, such as (1), where the -ing participle seems definitely preferable--likewise in the following sentence:
Do you like living/*to live alone, now that your husband has moved out?
Legenhausen (1975:65; cf. also Kiparsky and Kiparsky 1970) describes the preference for the -ing complement in such sentences as follows:
Mit der Wahl der -ing-Komplementierpartikel wird der durch das Verb des eingebetteten Satzes ausgedrückten Handlung faktische Realitdt zugeordnet.
In other words, since the speaker knows it to be a fact that the person spoken to already does live alone, the -ing form is preferable, since the infinitive would leave room for doubt, which in this case does not exist. The same analysis holds for (1). The speaker knows the addressee lives in Hamburg, so the infinitive form-which would leave this as an open question--is inappropriate. Nevertheless, even if I know for a fact that you always wash the dishes, I can ask you:
Do you really like to wash/washing the dishes?
Wash the dishes, like live in Hamburg in (1), is a factitive complement (since I know it is true), so why is the infinitive permissible here and not in (1)? The difference seems to have more to do with repeatability than with factivity. In all the cases where the infinitive complement is not acceptable, the complement expresses a predication (normally a state) that is true at the moment of utterance, but is not considered something that is repeatable. Washing the dishes is repeatable, but living in Hamburg is not. Compare:
He likes being/to be the center of attention (repeatable)
He likes being/*to be a policeman (not repeatable)
I don't like knowing/to know too much about other people's business (repeatable)
I like having/*to have a brother (not repeatable)
I don't like having/to have colds (repeatable)
Do you think he likes dying/*to die? (not repeatable)
Having colds, being the center of attention, and knowing about people's business are all considered repeatable states or conditions, whereas having a brother, being a policeman, and dying are not repeatable. This restriction seems to apply to some other emotive verbs as well (e.g. love, hate), though not to all, e.g.:
He loves/hates being/to be a policeman.
but
He prefers being/to be a policeman.