happens in nature, Judgment informs us, that there must be a cause of this change, which had power to produce it; and thus we get the notions of cause and effect, and of the relation between them. (See Art. 13. Illus. 1, 2, 3.) When we attend to body, we perceive that it cannot exist without space; hence we get the notion of space, which is neither an object of sense nor of consciousness, and of the relation which bodies have to a certain portion of unlimited space, as their place. (See Art. 244. Illus. 3 and 4.)

Corol. All our notions, therefore, of relations, may more properly be ascribed to Judgment, as their source, and origin, than to any other power of the mind. For, we must first perceive relations by our Judgment, before we can conceive them without judging of them; as we must first perceive colours by sight, before we can conceive them without seeing them.

Illus. 4. The relations of unity and number are so abstract, that it is impossible they should enter into the mind until it has some degree of Judgment. We see with what difficulty, and how slowly, children learn to use, with understanding, the names even of small numbers, and how they exult in this acquisition whenever they have attained it. Every number is conceived by the relation which it bears to unity, or to known combinations of units; and, upon that account, as well as on account of its abstract nature, all distinct notions of it require some degree of Judgment.

Corol. In Chapter IX. of this Book, it was clearly shewn how much Judgment enters, as an ingredient, into all determinations of Taste; and in Chapter XII. we shall have occasion to shew, that, in all moral determinations, and in many of our passions and affections, Judgment is a necessary concomitant; so that this faculty, after we come to those years in which reason exercises its powers, mingles with most of the operations of our minds, and, in analysing them, cannot be overlooked without confusion and error.

CHAPTER XI.

OF REASON.

I. Definition and Analysis of this Faculty. 293. REASON is the faculty by which we are made acquainted with abstract or necessary truth; and enabled to discover the essential relations of things.

Obs. The power of Reasoning is very nearly allied to that of judging; and, in the common affairs of life, the same term is applied to both. We include both under the name of Reason.

Ilus. The distinction that has been made between Judgment and Reasoning, is not perhaps founded so much in any natural diversity of the nature or the objects of the faculties, as in the various manner in which the same faculty is occasionally applied. This, then,

seems to be the foundation of the distinction. When the truth which is asserted, or the falsity which is denied, is perfectly obvious, and requires little or no examination, the faculty is then commonly called Judgment (Art. 278. Illus. 1.); but, when the truth which is asserted, or the falsity which is denied, is more remote from common apprehension, and requires a careful examination, the faculty has then been dignified with the name of Reasoning.

Corol. 1. Reasoning being then the process by which we pass from one judgment to another, which is a consequence of the preceding; our judgments are distinguished into INTUITIVE, which are not grounded upon any preceding judgment, and DISCURSIVE, which are deduced from some preceding judgment by Reasoning.

2. In all Reasoning, therefore, there must be a proposition inferred, and one or more from which it is inferred. And this power of inferring, or drawing a conclusion, is only another name for Reasoning; the proposition inferred, being called the conclusion, and the proposition, or propositions, from which that conclusion has been inferred, being called the premises.

294. Reasoning may consist of many steps; the first conclusion being a premise to the second, the second to a third, and so on, till we come to the last conclusion. A process, consisting of many steps of this kind, is so easily distinguished from judgment, that it is never called' by that name: But when there is only a single step to the conclusion, the distinction is less obvious, and the process is, as we have shewn above, sometimes called Judgment, sometimes Reasoning.

Obs. The Logicians themselves, as well as the illiterate, sometimes confound Judgment with Reasoning, though their definition of both be, in general terms, what we have now (Art. 294.) expressed. So various indeed are the modes of speech, that what in one mode is expressed by two or three propositions, may, in another, be expressed by one.

Example. Thus I may say, God is good; therefore all good men shall be happy. This species of Reasoning the Logicians call an Enthymeme, as it consists of an antecedent proposition, and a conclusion drawn from it. But this reasoning may be expressed by one proposition, thus: Because God is good, good men shall be happy. This other species of Reasoning they call a casual proposition, which therefore expresses judgment; yet the Enthymeme, which is Reasoning, expresses no more.

295. Reasoning, as well as Judgment, must be true or false, (Art. 45.); both are founded upon evidence, which may be PROBABLE OF DEMONSTRATIVE (Art. 302.), and both are accompanied with ASSENT OF BELIEF. (Illus. Art. 48.)

Obs. What Reasoning is, can be understood only by a man who has reasoned, and who is capable of reflecting upon the operations

of his own mind. We can define it only by synonymous words, or phrases, such as inferring, drawing a conclusion, and such like.

Corol. The very notion, therefore, of Reasoning, can enter into the mind by no other channel than that of reflecting upon the operation of Reasoning in our own minds, and the notions of Premises and Conclusions, of a Syllogism, and all its constituent parts, of an Enthymeme, of Sorites, Demonstration, Paralogism, and many other technical terms of logic, have the same origin.

296. The faculty of Reasoning is undoubtedly the gift of Nature; and in vain shall we attempt to supply the want of this gift where it is not, by art or education. In different individuals this faculty will be found in different degrees; yet the power of Reasoning seems to be acquired by habit, as much as the power of walking, running, or swimming.

Illus. We are not able to recollect its first exertions in ourselves, nor clearly to discern them in others; because they are then feeble, and need to be led by example, and supported by authority. But, by degrees, the faculty acquires strength, chiefly by means of imitation and exercise.

297. The exercise of Reasoning on various subjects, not only strengthens the faculty, but furnishes the mind with stores of materials.

Illus. 1. Every train of Reasoning which is familiar, becomes a beaten track, or pathway of many others. It removes many obstacles which lie in our way, and smooths many roads which we may have occasion to travel in future disquisitions.

2. When men of equal parts apply their reasoning powers to any subject, the man who has reasoned much on the same, or on similar subjects, has a like advantage over him who has not, as the mechanic, who has all the tools of his art, has over him who has his tools to make, or even to invent.

298. In a train of Reasoning, the evidence of every step, where nothing is left to be supplied by the reader or the hearer, must be immediately discernible to every man of ripe understanding, who has a distinct comprehension of the premises and conclusions, and who compares them together.

Obs. To be able to comprehend, in one view, a combination of steps of this kind is more difficult, and seems to require a superior natural ability; yet, in all of us, it may be much improved by habit.

299. But the highest talent in Reasoning is the Invention of proofs; by which truths remote from the premises are brought to light.

Obs. In all works of understanding, Invention has the highest praise (Art. 26. Illus.); it requires an extensive view of what relates to the subject, and a quickness in discerning those affinities and relations which may be subservient to the purpose. (See Art. 264. Illus. 1 and 2. and Corol. 1 and 2.)

300. In all Invention there must be some end in view; and Sagacity in finding out the road that leads to that end, is, properly speaking, what we call Invention.

Obs. In this chiefly, and in clear and distinct conceptions, consist that superiority of understanding which we have called Genius. See Art. 265. Illus.)

301. In every chain of Reasoning, the evidence of the last conclusion can be no greater than that of the weakest link of the chain, whatever may be the strength of the rest. (See Art. 294. Obs. and Example.)

302. Reasonings are either PROBABLE OF DEMONSTRATIVE. (See Art. 295. Illus.)

1. In every step of demonstrative Reasoning, the inference is necessary, and we perceive it to be impossible that the conclusion should not follow from the premises.

11. In probable Reasoning, the connexion between the premises and the conclusion is not necessary, nor do we perceive it to be impossible that the first should be true while the last is false.

Corol. Hence demonstrative Reasoning has no degrees, nor can one demonstration be stronger than another, though, in relation to our faculties, one may be more easily comprehended than another. Every demonstration gives equal strength to the conclusion, and leaves no possibility of its being false.

II. Analysis of Demonstrative Reasoning.

303. DEMONSTRATIVE Reasoning can be applied only to truths that are necessary, and not to those that are contingent.

Obs. Of all created things, the existence, the attributes, and, consequently, the relations resulting from those attributes, are contingent. They depend on the power and will of him who made them. These are matters of fact, and admit not of demonstration.

Corol. The field of Demonstrative Reasoning, therefore, is the various relations of things abstract; that is to say, of things which we conceive, without regard to their existence. We have a clear and adequate comprehension of these, as they are conceived by the mind, and are nothing but what they are conceived to be. Their relations and attributes are immutable.

Obs. 1. They are the things to which the Pythagoreans and Platonists gave the name of ideas; and, if we take leave to borrow this meaning of the word idea from those ancient philosophers, we must then agree with them that, ideas are the only objects about which we can reason demonstratively.

2. There are many even of our ideas about which we can carry on no considerable train of reasoning; let them be ever so well defined, ever so perfectly comprehended, their agreements and disagreements are few, and these are discernible at once. A step or

two brings us to the conclusion, and there we are stopped. (Example 294.) There are others, about which we may, by a long train of demonstrative Reasoning, arrive at conclusions very remote and unexpected.

304. Demonstrative Reasonings are reducible to two classes:

I. They are either METAPHYSICAL,

II. Or they are MATHEMATICAL.

Illus. 1. In Metaphysical Reasoning, the process is always short. The conclusion is but a step or two, seldom more, from the first principle, or axiom, on which it is grounded, and the different conclusions depend one upon another.

2. In Mathematical Reasoning, on the contrary, the field has no limits. One proposition leads on to a second, that to a third, and so on, without end. And the reason why demonstrative Reasoning has such extensive limits in the Mathematics, is owing chiefly to the nature of quantity, which is the object of Mathematical Reasoning.

Example 1. Every quantity, as it has magnitude, and is divisible into parts without end; so, in respect of its magnitude, it has a certain ratio to every quantity of that kind. The ratios of quantities are innumerable; such as a half, a third, a fourth, a tenth, double, triple, quadruple, centuple, and so on. All the powers of number are insufficient to express the varieties of ratios. For there are innumerable ratios which cannot be expressed perfectly by numbers; such as, the ratio of the side to the diagonal of a square, of the circumference of a circle to its diameter. And, of this infinite variety of ratios, every ratio may be clearly conceived, and distinctly expressed, so that it shall not be mistaken for any other.

2. Extended quantities, such as lines, surfaces, solids, besides the variety of relations they have in respect of magnitude, have no less variety in respect of figure; and every Mathematical figure may be accurately defined, so as to be distinguished from every other figure.

Illus. 3. There is nothing of this kind in other objects of abstract Reasoning. Some of them have various degrees; but these are not capable of measure, nor can they be said to have an assignable ratio to others of the kind. They are either simple, or compounded of a few indivisible parts; and, therefore, if we may be allowed the expression, touch only in a few points. But Mathematical quantities being made up of parts without number, can touch in innumerable points, and be compared in innumerable different ways.

305. Some Demonstrations are called direct, others indirect.

Illus. 1. Every Youth acquainted with the elements of Euclid, knows that Direct Demonstration leads straight forward to the conclusion to be drawn, while the indirect arrives at the proof by a proposition contradictory to that which is to be proved. The inference drawn from Demonstration ad absurdum, is grounded on an axiom in logic, "That of two contradictory propositions, if one be false, the other must be true."