Within Cognitive Psychology, there is much debate about theories of categorization. Models such as Prototype Theory (popularized by Eleanor Rosch) and Exemplar Theory (popularized by Robert Nosofsky) are probably the most popular, and are both different from Aristotelian Categories.
With respect to the basic model of cognition, categories are defined both in terms of concrete unions and abstract intersections. So, the category of fruits may be defined as either a concrete category (in which case it is a combination of experiences of individual fruits), an abstract category (in which case it consists of those properties common to the categories which participate in its definition), or some combination of both.
In Professor Rosch’s later work, she felt that many experimental paradigms were not sufficient to distinguish between prototype and exemplar theory. Similarly, I am not sure how a theory that incorporates both aspects of categorization can be effectively tested.
If anyone has a proposal for how a theory such as the basic model of cognition proposed in the whole part can be tested, please add to the comments below; I am not very familiar with the associated experimental paradigms.