All of the Sciences without exception have been developed into their present position in just this manner; and they fall easily into three great classes, namely, the Exact, the Physical, and the Moral Sciences. The ground of this triple classification is partly the distinct subject-matter in the three classes of Sciences, and partly the distinctive prominence of one or more of the logical processes of construction in each.
Thus, the class of the Exact Sciences consists only of the formal Logic, and pure Mathematics. These two are distinct from all other sciences, because their logical method of procedure is wholly Deductive. Deduction is the process of the mind, by which we pass from a _general_ truth to a _particular_ case under it, that is to say, from _more_ to _less_ inclusive propositions. Stuart Mill argues at much length in his book on Logic, that even the axioms of pure Mathematics are originally gained by Induction, while others claim that the truth of these axioms is perceived _intuitively_, but no matter how this point is decided, the construction process of the Pure Mathematics is from the General to the Particular. So it is also with the Aristotelian logic, whose Major Premise, whether only _supposed_ to be true or intuitively _perceived_ or inductively _proved_ is always General in its terms. This is the form of Aristotle's Syllogism:--All sinners deserve to be punished; John is a sinner; and therefore, John deserves punishment.
Physical Sciences are those concerned with the classifications and laws of action belonging to material substances. There are a great circle of these, of which Astronomy, Botany, and Chemistry, may serve as examples. They have been mostly developed since the time, and in accordance with the methods, of Lord Bacon; who, in strong reaction against the Deductive logic of Aristotle, exalted Induction or the mode of generalizing from _particulars_, as the true way of building up Sciences; and, as the subject-matter of each of the physical sciences is well open to observation and experiment, to Induction and Deduction, and to corrective verifications, both inductive and deductive, the new method proved remarkably pregnant and successful. Each of these sciences has a distinct _Class_ of objects or phenomena to which its attention is directed; the class is circumscribed by the scientific Conception and Definition; its devotees as a rule are skilled in using the Baconian tools; and consequently, its conclusions receive the confidence and control the action of men. All of the Physical Sciences are constantly enlarging "the body of exact definitions and sound principles" connected with their several classes "of facts or phenomena."