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Full Idea
Identity supposes an uninterrupted continuance of existence….Otherwise we must suppose a being to exist after it has ceased to exist, and to have existed before it was produced, which are manifest contradictions.
Gist of Idea
Continuity is needed for existence, otherwise we would say a thing existed after it ceased to exist
Source
Thomas Reid (Essays on Intellectual Powers 3: Memory [1785], III.Ch 4)
Book Ref
'Personal Identity', ed/tr. Perry,John [University of California 1975], p.108
A Reaction
I take the point to be that if something is supposed to survive a gap in its existence, that must imply that it somehow exists during the gap. If a light flashes on and off, is it really a new entity each time?