tematical division and subdivision of all the things which may be expressed by language; and, instead of the ancient division into ten categories, has made forty categories, or summagenera. But whether this division, though made by a very comprehensive mind, will always suit the various systems that may be introduced, and all the real improvements that may be made in human knowledge, may be doubted. The difficulty is still greater in the subdivisions; so that it is to be feared, that this noble attempt of a great genius will prove abortive, until philosophers have the same opinions and the same systems in the various branches of human knowledge.

There is more reason to hope that the languages used by philosophers may be gradually improved in copiousness and indistinctness; and that improvements in knowledge and in language may go hand in hand, and facilitate each other. But I fear the imperfections of language can never be perfectly remedied while our knowledge is imperfect.

However this may be, it is evident that the imperfections of language, and much more the abuse of it, are the occasion of many errors; and that in many disputes which have engaged learned men, the difference has been partly, and in some wholly, about the meaning of words.

Mr. Locke found it necessary to employ a fourth part of his Essay on Human Understanding about words; their various kinds; their imperfection and abuse, and the remedies of both; and has made many observations upon these subjects well worthy of attentive perusal.

The fourth class of prejudices are the idola theatri, by which are meant prejudices arising from the systems or sects, in which we have been trained, or which we have adopted.

A false system once fixed in the mind, becomes, as it were, the medium through which we see objects: they receive a tincture from it, and appear of another colour than when seen by a pure light.

Upon the same subject, a Platonist, a Peripatetic, and an Epicurean, will think differently, not only in matters connected with his peculiar tenets, but even in things remote from them.

A judicious history of the different sects of philosophers, and the different methods of philosophising, which have obtained among mankind, would be of no small use to direct men in the search of truth. In such a history, what would be of the greatest moment is not so much a minute detail of the dogmata of each sect, as a just delineation of the spirit of the sect, and of that point of view in which things appeared to its founder. This was perfectly understood, and, as far as concerns the theories of morals, is executed with great judgment and candour by Dr. Smith in his Theory of Moral Sentiments.

As there are certain temperaments of the body that dispose a man more to one class of diseases than to another; and, on the other hand, diseases of that kind, when they happen by accident, are apt to induce the temperament that is suited to them; there is something analogous to this in the diseases of the understanding.

A certain complexion of understanding may dispose a man to one system of opinions more than to another; and, on the other hand, a system of opinions, fixed in the mind by education or otherwise, gives that complexion to the understanding which is suited to them.

It were to be wished, that the different systems that have prevailed could be classed according to their spirit, as well as named from their founders. Lord Bacon has distinguished false philosophy into the sophistical, the empirical, and superstitious, and has made judicious observations upon each of these kinds. But I apprehend this subject deserves to be treated more fully by such a hand, if such a hand can be found.

ESSAY VII.

OF REASONING.

CHAPTER I.

OF REASONING IN GENERAL, AND OF DEMONSTRATION.

THE power of reasoning is very nearly allied to that of judging; and it is of little consequence in the common affairs of life to distinguish them nicely. On this account, the same name is often given to both. We include both under the name of reason. The assent we give to a proposition is called judgment, whether the proposition be self-evident or derive its evidence by reasoning from other propositions.

Yet there is a distinction between reasoning and judging. Reasoning is the process by which we pass from one judgment to another which is the consequence of it. Accordingly 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.

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 it is inferred, the premises.

But

Reasoning may consist of many steps; the first conclusion being a premise to a second, that 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. when there is only a single step to the conclusion, the distinction is less obvious, and the process is sometimes called judgment, sometimes reasoning. It is not strange that, in common discourse, judgment and reasoning should not be very nicely distinguished, since they are in some cases confounded even by logicians. We are taught in logic, that judgment is expressed by one proposition, but that reasoning requires two or three. But so various are the modes of speech, that what in one mode is expressed by two or three propositions, may in another mode be expressed by one. I may say, God is good; therefore good men shall be happy. This is reasoning of that kind which logicians call an enthymeme, consisting 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 is what they call a causal proposition, and therefore expresses judgment; yet the enthymeme, which is reasoning,

expresses no more.

Thus

Reasoning, as well as judgment, must be true or false; both are grounded upon evidence which may be probable or demonstrative, and both are accompanied with assent or belief.

The power of reasoning is justly accounted one of the prerogatives of

human nature; because by it many important truths have been and may be discovered, which without it would be beyond our reach; yet it seems to be only a kind of crutch to a limited understanding. We can conceive an understanding, superior to human, to which that truth appears intuitively, which we can only discover by reasoning. For this cause, though we must ascribe judgment to the Almighty, we do not ascribe reasoning to him, because it implies some defect or limitation of understanding. Even among men, to use reasoning in things that are self-evident, is trifling; like a man going upon crutches when he can walk upon his legs.

What reasoning is, can be understood only by a man who has reasoned, and who is capable of reflecting upon this operation of his own mind. We can define it only by synonymous words or phrases, such as inferring, drawing a conclusion, and the like. The very notion of reasoning, therefore, 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 conclusion, of a syllogism, and all its constituent parts, of an enthymeme, sorites, demonstration, paralogism, and many others, have the same origin.

It is nature undoubtedly that gives us the capacity of reasoning. When this is wanting, no art nor education can supply it. But this capacity may be dormant through life, like the seed of a plant, which, for want of heat and moisture, never vegetates. This is probably the case of some savages.

Although the capacity be purely the gift of nature, and probably given in very different degrees to different persons; yet the power of reasoning seems to be got by habit, as much as the power of walking or running. Its first exertions we are not able to recollect in ourselves, or clearly to discern in others. They are very feeble, and need to be led by example, and supported by authority. By degrees it acquires strength, chiefly by means of imitation and exercise.

The exercise of reasoning on various subjects not only strengthens the faculty, but furnishes the mind with a store of materials. Every train of reasoning, which is familiar, becomes a beaten track in the way to many others. It removes many obstacles which lay in our way, and smooths many roads which we may have occasion to travel in future disquisitions. When men of equal natural parts apply their reasoning power 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 store of tools for his work, has of him who has his tools to make, or even to invent.

In a train of reasoning, the evidence of every step, where nothing is left to be supplied by the reader or hearer, must be immediately discernible to every man of ripe understanding who has a distinct comprehension of the premises and conclusion, and who compares them together. 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. In all, it may be much improved by habit.

But the highest talent in reasoning is the invention of proofs; by which truths remote from the premises are brought to light. In all works of understanding, invention has the highest praise; 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.

In all invention there must be some end in view: and sagacity in finding road that leads to this end, is, I think, what we call invention. In

this chiefly, as I apprehend, and in clear and distinct conceptions, consist that superiority of understanding which we call genius.

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.

The most remarkable distinction of reasonings is, that some are probable, others demonstrative.

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. 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.

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.

It was, I think, the opinion of all the ancients, that demonstrative reasoning can be applied only to truths that are necessary, and not to those that are contingent. In this, I believe they judged right. Of all created things, the existence, the attributes, and consequently the relations resulting from those attributes, are contingent. They depend upon the will and power of him who made them. These are matters of fact, and admit not of demonstration.

The field of demonstrative reasoning, therefore, is the various relations of things abstract, that is, of things which we conceive, without regard to their existence. Of these, as they are conceived by the mind, and are nothing but what they are conceived to be, we may have a clear and adequate comprehension. Their relations and attributes are necessary and immutable. They are the things to which the Pythagoreans and Platonists gave the name of ideas. I would beg leave to borrow this meaning of the word idea from those ancient philosophers, and then I must agree with them, that ideas are the only objects about which we can reason demonstratively.

There are many even of our ideas about which we can carry on no considerable train of reasoning. Though they be ever so well defined, and perfectly comprehended, yet their agreements and disagreements are few, and these are discerned at once. We may go a step or two in forming a conclusion with regard to such objects, but can go no farther. There are others, about which we may, by a long train of demonstrative reasoning, arrive at conclusions very remote and unexpected.

The reasonings I have met with that can be called strictly demonstrative, may, I think, be reduced to two classes. They are either metaphysical, or they are mathematical.

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 not upon one

another.

It is otherwise in mathematical reasoning. Here the field has no limits. One proposition leads on to another, that to a third, and so on without end. If it should be asked why demonstrative reasoning has so wide a field in mathematics, while, in other abstract subjects, it is confined within very narrow limits? I conceive this is chiefly owing to the nature of quantity, the object of mathematics.

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 the kind. The ratios of quantities are innumerable, such as, a half, a third, a tenth, double, triple. All the powers of number are insufficient to express the variety of ratios. For there are innumerable ratios which cannot be perfectly expressed by numbers, such as, the ratio of the side to the diagonal of a square, of the circumference of a circle to the diameter. Of this infinite variety of ratios, every one may be clearly conceived, and distinctly expressed, so as to be in no danger of being mistaken for any other. 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 distinguish it from all others.

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 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, can touch only in few points. But mathematical quantities being made up of parts without number, can touch in innumerable points, and be compared in innumerable different

ways.

There have been attempts made to measure the merit of actions by the ratios of the affections and principles of action from which they proceed. This may perhaps, in the way of analogy, serve to illustrate what was before known; but I do not think any truth can be discovered in this way. There are no doubt degrees of benevolence, self-love, and other affections; but, when we apply ratios to them, I apprehend we have no distinct meaning.

Some demonstrations are called direct, others indirect. The first kind leads directly to the conclusion to be proved. Of the indirect some are called demonstrations ad absurdum. In these the proposition contradictory to that which is to be proved is demonstrated to be false, or to lead to an absurdity; whence it follows, that its contradictory, that is, the proposition to be proved, is true. This inference is grounded upon an axiom in logic, That of two contradictory propositions, if one be false, the other must be true.

Another kind of indirect demonstration proceeds by enumerating all the suppositions that can possibly be made concerning the proposition to be proved, and then demonstrating, that all of them excepting that which is to be proved, are false; whence it follows, that the excepted supposition is true. Thus one line is proved to be equal to another, by proving first that it cannot be greater, and then that it cannot be less: for it must be either greater, or less, or equal; and two of these suppositions being demonstrated to be false, the third must be true.

All these kinds of demonstration are used in mathematics, and perhaps some others. They have all equal strength. The direct demonstration is preferred where it can be had, for this reason only, as I apprehend, because it is the shortest road to the conclusion. The nature of the evidence and its strength is the same in all: only we are conducted to it by different roads.