in a descending scale; and proceeding in double or complex comparisons, by the help of a third, or middle term. To these two, which are direct, is added the analogic, which is indirect and subservient to them. Analogy compares things already known by whatever way, with those which are not known, and, from their similitude, infers the truth of the latter. This is a method of vast utility and extent, and supplemental to both the former. These three methods are essentially different, and constitute severally the whole business of logic, as an instrumental art, or rather, as the particular method of each 5.

Universal truth assumes a special form, according to the specific nature of its different means, which constitute those various substances and subjects of mind and body, from which its particular principles are supplied. According to these particular principles, and the method of reasoning adapted to them, truth separates into particular kinds, possessed of different degrees of evidence and convic

5 Sect. iv.

tion. The general rule, by which reason should conduct her operations in each, is thisto investigate its proper principles, to pursue them in the proper method, and embrace its proper truth with a just and due assent.

To apply this general rule to the different branches of science, constitutes the first part of my plan; which, by exhibiting a parallel of their principles, their reasoning, and their truths, forms a general chart of their distinct and separate provinces, and subdivisions; whilst, by placing them in juxtaposition and by their comparative survey, it furnishes a general scale, by which the proper nature and weight of the truth of each may be respectively adjusted".

Every thing which is the subject of human knowledge, belongs either to mind or body. Metaphysic is the universal science, logic the universal art; these treat more immediately of the former. Physics belong to the latter. Between these, lies a science, which relates to and partakes of both, having its subject derived from the sensible qualities of body,

but abstracted by an act of mind. These are the mathematics; comprehending quantity continuous and discrete, or magnitude and multitude, and accordingly separating into geometry and arithmetic. The evidence of the external senses, exercised on bodies in respect to quantity (from which all other attributes are abstracted with so much ease, as to supersede the necessity of induction), is the primary principle of mathematical science. These begin with general ideas, capable of clear and adequate definition, of being exhibited to the eye by diagrams and signs; being simple modes, distinct from all other ideas, absolute and unchangeable in themselves, and to be exactly measured and ascertained. These ideas being compared, form a few general propositions which are axioms or secondary principles. They compel conviction from a single act of judgment, and are, therefore, self-evident, though not intuitive. On account of these axioms, mathematical reasoning is perfectly syllogistic, reducing

Those who wish to be ocularly convinced of this assertion, may consult the Euclid of Herlinus (Argent. 1566), in which the first six books are laboriously converted into syl

general truths under more general, till they terminate in the most general. These conclusions, or demonstrated theorems, may be applied, in the same way, to the proof of others almost ad infinitum. The truths resulting from such a process are purely scientific, carrying the most absolute and irresistible conviction. In these, the Will has no concern; they belong to the Intellect.

The science of Physics, or natural philosophy, investigates the qualities of things individual and particular, the properties and operations of natural body. The evidence of the external senses forms the primary principle of physics, aided by experiment, and philosophical observation. Its method of reasoning, from a number of experiments and observations to general causes, or secondary principles, is purely and exclusively inductive, but is extended by ana

logisms. Barrow, in his Lectiones Mathematica, p. 106, has turned the first proposition into enthymemes. See also Clavius's Euclid, lib. i. prop. 1.-"It would have been difficult," observes Dugald Stewart (vol. ii. p. 260), "to devise a more effectual expedient for exposing to the meanest understanding the futility of the syllogistic theory."-Editor. 9 Part i. chap. 1.

logy. When these secondary principles, or laws of physics, have been thus established, they will account for the truth of particulars by superinduction, without any aid of syllogism; but mathematics apply, with great effect, to those physical forms, which are capable of mensuration. As experiments do not penetrate into the essence of things, but only inform the senses of apparent qualities or effects, as the induction is partial and confined, and the conclusions particular; physical truth is inferior in rank to mathematical, and is not strictly demonstrative. But though not admitting demonstration, it forms a most useful and interesting part of science 10.

After Physics, Metaphysics, or the philosophy of mind, may be most usefully and successfully cultivated. Consciousness is their primary principle, assisted by observations on the intellectual and moral faculties. Their method of reasoning, from a number of such observations accurately made, is inductive, assisted by analogy, to form their secondary or general principles. This method

10 Part i. chap. 2.