A chicken with two feet can also be an abstract concept, paralleling with the concept of chicken's foot in the subjective world. Concepts at all different levels of abstraction can coexist in the subjective world, but the results of thought games such as adding and subtracting them do not necessarily make sense.

4. Concept is not Objective Idea

In the process of producing concept, a certain kind of things are abstracted and some attributes are ignored. The simulation of a specific bird, such as a sparrow, also ignores some attributes. Because the simulation of concrete sparrow has objective counterpart, so Plato believed that abstract concepts also have objective counterparts. Plato believed that ideas were real things in the objective world, not artificial logical constructs.

Plato's Idealism has been heavily criticized. It is now accepted that ideas do not exist in the objective world, it is just like the God doesn't exist in the objective world, but concepts do exist. The so called "do exist" is existence as logical constructs in the subjective world. The fact that concepts and ideas do not exist in the objective world does not mean that concepts are not important. On the contrary, concepts are very important and are the basis of all science and philosophy. The richness and development of concepts often represent the level of development of science and philosophy. Since idea is the same as concept in the subjective world, Plato's Objective Idealism is of great value to the development of philosophy.

Frege's concept is just Plato's idea. “And we are driven to the conclusion that number is neither spatial and physical, like Mill's piles of pebbles and gingersnaps, nor yet subjective like ideas, but non-sensible and objective." Frege said. "Now objectivity cannot, of course, be based on any sense-impression, which as an affection of our mind is entirely subjective, but only, so far as I can see, on the reason. "[6]

Frege argued that concepts had nothing to do with psychology. He said, "We suppose, it would seem, that concepts sprout in the individual mind like leaves on a tree, and we think to discover their nature by studying their birth: we seek to define them psychologically, in terms of the nature of the human mind. But this account makes everything subjective, and if we follow it through to the end, does away with truth."[7] Frege's bias was completely wrong, his error was the same as Plato's essentially.