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Full Idea
The nearest I can get to a quick definition is to say that a concept is a way of thinking of some thing or kind of things, whether or not a really existent thing or kind of things.
Gist of Idea
A concept is a way of thinking of things or kinds, whether or not they exist
Source
E.J. Lowe (What is the Source of Knowledge of Modal Truths? [2013], 2)
Book Ref
-: 'Mind' [-], p.6
A Reaction
The focus on 'things' seems rather narrow. Are relations things? He makes concepts sound adverbial, so that there is thinking going on, and then we add 'ways' of doing it. Thinking depends on concepts, not concepts on thinking.