Is a GiftCulture one without property?

My suspicion is that it isn't. The concept of a gift seems to require that it belongs to someone : the giver, in order for it to be able to be given. At which point it also belongs to someone, the receiver.

In all cultures property is something which has to be conceptualized (OnProperty). And some things might be conceptualized that way, and other things not. For example, a MatriarchalSociety might have no concept of land as property (which can be owned or traded) but might allocate the products of labour on a gift basis (eg. I gather fruit and give it to anyone who seems hungry).

Nevertheless, gifting of scarce things must imply property.


Any counters to this?