The main objective of our research is to present and discuss some of the many aspects involved in the intuitive notion of 'concept' present in the works of Plato, Aristotle, Porphyry of Tyre, Aquinas, Kant and Frege, related to the formal notion of 'concept' established by the Formal Concept Analysis (FCA). Many philosophers worked on concepts with different approaches, considering them as the intermediary between the world and the mind, or even as something that expresses the essence of a thing. Despite the differences, it is possible to see that philosophers generally agree that concepts are elements of thoughts having at least two characteristics: i) they are applicable to certain objects (i.e., its extension) and ii) they expresses the properties that all the objects satisfying them have in common (i.e., its intension). Formal Concept Analysis is a mathematical theory which deals with a formalization of the notion of concept, defined in terms of a set of objects (i.e., its extent), a set of attributes (i.e., its intent) and a binary relation between them. These concepts are determined and represented in a systematic form of data named 'formal context', in which their relations of implication and dependency are exhibited. Given that the intuitive and formal notions have some similarities, since FCA was developed upon well-established philosophical background, we present a study and comparison between these notions, through an interdisciplinary approach.