Mathematics is of narrower scope. What it studies is no longer "real being as such," but only real being in so far as it exhibits number and geometrical form. Since Aristotle holds the view that number and figure only exist as determinations of objects given in perception (though by a convenient fiction the mathematician treats of them in abstraction from the perceived objects which they qualify), he marks the difference between Mathematics and First Philosophy by saying that "whereas the objects of First Philosophy are separate from matter and devoid of motion, those of Mathematics, though incapable of motion, have no separable existence but are inherent in matter." Physics is concerned with the study of objects which are both material and capable of motion. Thus the principle of the distinction is the presence or absence of initial restrictions of the range of the different branches of Science. First Philosophy has the widest range, since its contemplation covers the whole ground of the real and knowable; Physics the narrowest, because it is confined to a "universe of discourse" restricted by the double qualification that its members are all material and capable of displacement. Mathematics holds an intermediate position, since in it, one of these qualifications is removed, but the other still remains, for the geometer’s figures are boundaries and limits of sensible bodies, and the arithmetician’s numbers properties of collections of concrete objects. It follows also that the initial axioms or postulates of Mathematics form a less simple system than those of First Philosophy, and those of Physics than those of Mathematics. Mathematics requires as initial assumptions not only those which hold good for _all_ thought, but certain other special axioms which are only valid and significant for the realm of figure and number; Physics requires yet further axioms which are only applicable to "what is in motion." This is why, though the three disciplines are treated as distinct, they are not strictly co-ordinate, and "First Philosophy," though "first," is only _prima inter pares_. We thus get the following diagrammatic scheme of the classification of sciences:-- Science | +−−−−−−−−−−−+−−−−−−−−−−−−+ | | Theoretical Practical | +−−−+−−−−−−−−−+−−−−−−−−−−−+ | | | First Philosophy Mathe− Physics or matics Theology