In one of his monumental works, Physics, Aristotle sets out to investigate the appropriate divisions of science. According to Aristotle, a science is possible if and only if there are knowable objects. There cannot be a science of dragons, for example, because dragons do not exist and hence a ‘science’ of dragons would lack knowable objects and thus would not be a ‘science’. Furthermore, he thought the aim of scientific knowledge was the attainment of universal and necessary truths; that is, truths that apply everywhere, at all times, and of necessity must apply.
The first division of science, according to Aristotle, was theoretical science. Those who engage in theoretical science seek knowledge for its own sake. For Aristotle theoretical science in turn was divided into three sub-categories. The first sub-category studies natural objects which generate movement and growth internally; that is, 
living objects as well as the the ‘heavenly bodies’ and geological phenomena. The second sub-category of theoretical science studies objects in abstraction from their motion. In other words, it studies the quantitative aspect of objects. This second division of theoretical science is the domain of mathematics. The third and final sub-category of theoretical science is the study of objects that are not in motion, or are immovable. This is the study of “first causes”, so to speak, and is the domain of theology.
The second division of science for Aristotle was productive science. Such a science aims at the creation of a product. A science of computers, for example, aims at the production of computers. For Aristotle only human beings, who alone have rationality, are capable of engaging in productive science. A bird which builds a nest is merely acting according to its instincts, and not at all according to reason and scientific knowledge. Thus, only human beings can engage in productive science, and create a product through the utilization of theoretical knowledge.
The third and final division of science for Aristotle was practical science. Such a science aims at knowledge of action, or praxis. The science of action underlies the ability to act well, or to live the good life, which according to Aristotle was a life guided by reason.
These three divisions, according to Aristotle, encompass every conceivable object or phenomena which science can investigate. And up until today, over 2000 years after Aristotle proposed these three divisions of science, no one has been able to think of an object of science which does not fall into one of these three categories.
