It will be admitted (and we shall see it perhaps more clearly when we again have occasion to revert to this subject) that demonstrative reasoning implies a constant reference to such axioms; that its advancement through the successive series of propositions is by means of their aid. But it is too evident to require remark, that these axioms are nothing more than particular instances of the relative suggestion of identity and diversity, expressed in words. It is the perceptions of agreement and disagreement, actually arising in the mind, and not the mere verbal expression of them, which form the true cement and bond of the successive links, and impart consistency and strength to the whole chain.

§ 206. (II.) Relations of degree, and names expressive of them. Another class of those intellectual perceptions, which are to be ascribed to the Judgment, or what we term more explicitly the power of RELATIVE SUGGESTION, may properly enough be named perceptions of relations of Degree. Such perceptions of relation are found to exist in respect to all such objects as are capable of being considered as composed of parts, and as susceptible, in some respects, of different degrees.We look, for instance, at two men; they are both tall; but we at once perceive and assert that one is taller than the other. We taste two apples; they are both sweet; but we say that one is sweeter than another. That is to say, we discover, in addition to the mere perception of the man and the apple, a relation, a difference in the objects in certain respects.

There are terms in all languages employed in the expression of such relations. In English, a reference to the particular relation is often combined in the same term which expresses the quality. All the words of the comparative and superlative degrees, formed by merely altering the termination of the positive, are of this description, as whiter, sweeter, wiser, larger, smaller, nobler, kinder, truest, falsest, holicst, and a multitude of others. In other cases

(and probably the greater number), the epithet expressive of the quality is combined with the adverbs more and most, less and least. But certainly we should not use such terms if we were not possessed of the power of relative suggestion. We should ever be unable to say of one apple that it is sweeter than another, or of one man that he is taller than another, without considering them in certain definite respects, and without perceiving certain relations. So that, if we had no knowledge of any other than relations of Degree, we should abundantly see the importance of the mental susceptibility under review, considered as a source of words, and of grammatical forms in language.

It will be noticed, as we proceed from one part of the mind to another, that we are able to indicate not only cognitive results, but results in language also, as well as in knowledge. New terms and words, constituting the elements of language, are the necessary results of new thoughts and feelings; and it will be found further, that their relations to each other are the basis, in whole or in part, of grammatical forms; so that, in certain important respects, the philosophy of language may be regarded as having its foundation in the philosophy of mind.

§ 207. Relations of degree in adjectives of the positive form. Although relations of degree are discoverable more frequently in comparative and superlative adjectives than anywhere else, they may sometimes be detected also in abstract terms which have the appearance of being entirely positive, and not unfrequently in adjectives of the positive form.-Let it be considered, as one instance among many others, what we mean when we say of a person, He is an AGED man. though the epithet has the positive form, we always tacitly compare the age of the subject of it with that of others, of people in general, and place the particular number of years to which he may have attained by the side of that period which we are in the habit

Al

of regarding as the ordinary term of man's pilgrimage.--It is the same when we say of any person that he is YOUNG. He is then, by a tacit mental reference, considered as falling far short of an assumed period, an approximation to which gives to another person the reputation of age.

Buffier, whose remarks are generally entitled to great weight, illustrates this subject as follows.*"If we should, for example, never have seen or heard of any hill or mountain of greater height than a quarter of a mile, as might happen to some of the inhabitants of the Low Countries, a mountain a mile high would appear a considerable one to such people; but this mountain would be looked upon as inconsiderable and trifling to the people of the Alps, who are accustomed to see mountains of much greater height." And again he says, "What has been here said of greatness is manifestly applicable to all the other qualities of long, broad, happy, unhappy, convenient, inconvenient, easy, difficult, rich, poor, good, bad, excellent, and many others of a similar nature, that have no determinate sense, but by a relation founded on an arbitrary and accidental idea formed within our own minds. A man thought himself miserable in having a slight headache: being afterward seized with a giddiness and violent swimming in the head, the first reflection that occurred to him was, how happy he was when he had only his first headache. We here see that the arbitrary idea on which the comparison and relation are founded changes the signification, and, in a manner, the nature of the qualities of happy and miserable."

§ 208. (III.) Of relations of proportion.

Among other relations which are discovered to us by the power of judgment or relative suggestion are those of PROPORTION; a class of relations which are peculiar in this, that they are felt only on the presence of three or more objects of thought. They are *First Truths of Pere Buffier, part ii., chap. xxviii.

discoverable particularly in the comparison of numbers, as no one proceeds far in numerical combinations without a knowledge of them. On examining the numbers two, three, four, twenty, twenty-seven, thirty-two, nine, five, eight, and sixteen, we feel certain relations existing among them; they assume a new aspect, a new power in the mental view. We perceive (and we can assert, in reference to that perception) that three is to nine as nine to twenty-seven; that two is to eight as eight to thirty-two; that four is to five as sixteen to twenty.

And when we have once felt or perceived such relation actually existing between any one number and others, we ever afterward regard it as a property inseparable from that number, although the property had remained unknown to us until we had compared it with others. We attach to numbers, under such circumstances, a new attribute, a new power; the same as we do, under similar circumstances, to all the other subjects of our knowledge. There are many properties, for instance, of external bodies which were not known to us at first, but, as soon as they are discovered, they are, of course, embraced in the general notion which we form of such bodies, and are considered as making a part of it. And pursuing the same course in respect to numbers, if, on comparing them with each other, we perceive certain relations never discovered before, the circumstance of their sustaining those relations ever afterward enters into our conception of them.

§ 209. (IV.) Of relations of place or position.

Other feelings or perceptions of relation arise when we contemplate the place or position of objects. Our minds are so constituted, that such perceptions are the necessary results of our contemplations of the outward objects by which we are surrounded. Perhaps we are asked, What we mean by position or place? "Without professing to give a confident answer, since it is undoubtedly difficult, by any mere form of words, fully

to explain it, we have good grounds for saying that we cannot conceive of any body as having place without comparing it with some other bodies. If, therefore, having two bodies fixed, or which maintain the same relative position, we can compare a third body with them, the third body can then be said to have place or position.

This may be illustrated by the chessmen placed on the chessboard. We say the men are in the same place, although the board may have been removed from one room to another. We use this language, because we consider the men only in relation to each other and the parts of the board, and not in relation to the room or parts of the room.-Again, a portrait is suspended in the cabin of a ship; the captain points to it, and says to a by-stander that it has been precisely in the same place this seven years. Whereas, in point of fact, it has passed from Europe to Africa, from Africa to America, and perhaps round the whole world. Still the speaker uttered no falsehood, because he spoke of the portrait (and was so understood to speak of it) in relation to the ship, and particularly the cabin, and not in relation to the parts of the world which the ship had visited. Such instances show that place is relative.

Hence we may clearly have an idea of the place or position of all the different parts of the universe, considered separately, because they may be compared with other parts, although we are unable to form any idea of the place or position of the universe considered as a whole, because we have then no other body with which we can compare it. If it were possible for us to know all worlds and things at once, to comprehend the universe with a glance, we could not assert, with all our knowledge of it, that it is here, or there, or yonder, or tell where it would be.

But if place express a relative notion, then it follows that all words which involve or imply the place or position of an object are of a similar character. Such are the words high and low, superior and infe