Please help me with finding a formal definition of what an object is and how to compare two objects. To illustrate, if one is asked to compare, for example, two balls given to him or her, the comparison will be between the balls properties (size, weight, color, material they are made of, etc.). It is impossible to compare just objects without comparing their properties. We know it from day-to-day life, although I need references to formal definitions of ?object? and ?object comparison?. I dag tons of materials available on-line, mainly related to philosophy art, but didn?t find clear definitions neither for an object nor for objects comparison. All explanations of what an object is and how the objects are compared are quite extensive and only lead to the awareness of these concepts but to their clear definition. I am asking you for a reference to clear and short statements of what an object is and how to compare objects. Particularly, I would be more than happy if someone could provide a reference just stating something like ?Objects are compared by comparing their properties?. It would be enough, but I need a reference to only a monograph with the author(s) known in the scientific world, or an encyclopedia, or a university textbook, or an article in a scientific publication or something similar, but not to a Wikipedia or the like?