The state, condition, or act of being an alien or foreigner; the legal status of not belonging to a particular place.
From 'alien' (from Latin 'alienus' meaning foreign) combined with the suffix '-ship' (Old English 'scipe' meaning state or condition). This creates a noun describing the quality or status of being alien to a place.
The suffix '-ship' is magical for creating status words—think friendship, citizenship, leadership. Alienship captures the feeling of being perpetually 'other,' which explains why it appears in immigration law and philosophy discussing belonging.
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