words, the difference between a particular conclusion, and a general theorem.

The difference between the intellectual processes of the vulgar and of the philosopher, is perfectly analogous to that between the two states of the algebraical art before and after the time of Vieta: the general terms which are used in the various sciences, giving to those who can employ them with correctness and dexterity, the same sort of advantage over the uncultivated sagacity of the bulk of mankind, which the expert algebraist possesses over the arithmetical accomptant.

If the foregoing doctrine be admitted as just, it exhibits a view of the utility of language, which appears to me to be peculiarly striking and beautiful; as it shews that the same faculties which, without the use of signs, must necessarily have been limited to the consideration of individual objects and particular events, are, by means of signs, fitted to embrace, without effort, those comprehensive theorems, to the discovery of which, in detail, the united efforts of the whole human race would have been unequal. The advantage our animal strength acquires by the use of mechanical engines, exhibits but a faint image of that increase of our intellectual capacity which we owe to language. It is this increase of our natural powers or comprehension, which seems to be the principal foundation of the pleasure we receive from the discovery of general theorems. Such a dis overy gives us at once the command of an infinite variety of particular truths, and communicates to the mind a sentiment of its own power, not unlike to what we feel when we contemplate the magnitude of those physical effects, of which we have acquired the command by our mechanical contrivances.

It may perhaps appear, at first, to be a farther consequence of the principles I have been endeavouring to establish, that the difficulty of philosophical discoveries is much less than is commonly imagined; but the truth is, it only follows from them, that this difficulty is of a different nature, from what we are apt to suppose on a superficial view of the subject. To employ, with skill, the very delicate instrument which nature has made essentially subservient to general reasoning, and to guard against the errors which result from an injudicious use of it, require an uncommon capacity of patient attention, and a cautious circumspertion in conducting our various intellectual processes, which can only be acquired by habits of philosophical reflection. To assist and direct us in making this acquisition ought to form the most important branch of a rational logic; a science of far more extensive utility, and of which the principles lie much deeper in the philosophy of the human mind, than the trifling art which is commonly dignified with that name. The branch in particular to which the foregoing observations more immediately relate, must forever remain in its infancy, till a most difficult and important desideratum in the history of the mind is supplied, by an explanation of the gradual steps, by which it acquires the use of the various classes of words which compose the language of a cultivated and enlightened people. Of some of the errors in reasoning to which we are exposed by an incautious use of words, I took notice in the preceding section, and I shall have occasion afterwards to treat the same subject more in detail in a subsequent part of my work.

SECTION VI.

Of the Errors to which we are liable in Speculation, and in the Conduct of Affairs, in consequence of a rash Application of general Principles.

Ir appears sufficiently from the reasonings which I offered in the preceding Section, how important are the advantages which the philosopher acquires, by quitting the study of particulars, and directing his attention to general principles. I flatter myself it appears farther, from the same reasonings, that it is in consequence of the use of language alone, that the human mind is rendered capable of these comprehensive specula

tions.

In order, however, to proceed with safety in the use of general principles, much caution and address are neces-ary, both in establishing their truth, and in applying them to practice. Without a proper attention to the circumstances by which their application to particular cases must be modified, they will be a perpetual source of mistake, and of disappointment, in the conduct of affairs, however rigidly just they may be in themselves, and however accurately we may reason from them. If our general principles happen to be false, they will involve us in errors, not only of conduct but of speculation; and our errors will be the more numerous, the more comprehensive the principles are on which we proceed

To illustrate these observations fully, would lead to a minuteness of disquisition inconsistent with my general plan, and I shall therefore, at present, confiue myself to such remarks as appear to be of most essential importance.

And, in the first place, it is evidently impossible to establish solid general principles, without the previous study of particulars; in other words, it is necessary to begin with the examination of individual objects, and individual events, in order to lay a ground-work of ac urate classification, and for a just investigation of the laws of nature. It is in this way only that we can expect to arrive at general principles, which may be safely relied on, as guides to the knowledge of particular truths: and unless our principles admit of such a practical application, however beautiful they may appear to be in theory, they are of far less value than the limited acquisitions of the vulgar. The truth of these remarks is now so universally admitted, and is indeed so obvious in itself, that it would be superfluous to multiply words in supporting them; and I should scarcely have thought of stating them in this Chapter, if some of the most celebrated philosophers of antiquity had not been led to dispute them, in consequence of the mistaken opinions which they entertained concerning the nature of universals. Forgetting that genera and species are mere arbitrary creations which the human mind forms, by withdrawing the attention from the distinguishing qualities of objects, and giving a common name to their resembling qualities, they conceived universals to be real existences, or (as they expressed it) to be the essences of individuals; and flattered themselves with the belief, that by directing their attention to these essences in the first instance, they might be enabled to penetrate the secrets of the universe, without submitting to the study of nature in detail. These errors, which were

common to the Platonists and the Peripatetics, and which both of them seem to have adopted from the Pythagorean school, contributed, perhaps, more than any thing else, to retard the progress of the ancients in physical knowledge. The late learned Mr. Harris is almost the only author of the present age who has ventured to defend this plan of philosophizing, in opposition to that which has been so successfully followed by the disciples of lord Bacon.

"The Platonists," says he, " considering science as something ascer"tained, definite, and steady, would admit nothing to be its object which 66 was vague, indefinite, and passing. For this reason they excluded all "individuals or objects of sense, and (as Ammonius expresses it) raised "themselves in their contemplations from beings particular to beings "universal, and which, from their own nature, were eternal and defi"nite."-"Consonant to this was the advice of Plato, with respect to "the progress of our speculations and inquiries, to descend from those "higher genera, which include many subordinate species down to the "lowest rank of species, those which include only individuals. But here "it was his opinion, that our inquiries should stop, and, as to individu"als, let them wholly alene; because of these there could not possibly "be any science."*

"Such," continues this author, "was the method of ancient philosophy. The fashion, at present, appears to be somewhat altered, and "the business of philosophers to be little else than the collecting from every quarter, into voluminous records, an infinite number of sensible, 66 particular, and unconnected facts, the chief effect of which is to excite our admiration."-In another part of his works the same author observes, that "the mind, truly wise, quitting the study of particulars, as knowing their multitude to be infinite and incomprehensible, turns its "intellectual eye to what is general and comprehensive, and through "generals learns to see, and recognize whatever exists."+

66

If we abstract from these obvious errors of the ancient philosophers, with respect to the proper order to be observed in our inquiries, and only suppose them to end where the Platonists said that they should begin, the magnificent encomiums they bestowed on the utility of those comprehensive truths which form the object of science (making allowance for the obscure and mysterious terms in which they expressed them) can scarcely be regarded as extravagant. It is probable that from a few accidental instances of successful investigation, they had been struck with the wonderful effect of general principles in increasing the intellectual power of the human mind ; and, misled by that impatience in study of particulars which is so often connected with the consciousness of superior ability, they laboured to persuade themselves, that, by a life devoted to abstract meditation, such principles might be rendered as immediate objects of intellectual perception, as the individuals which compose the material world are of our external senses. By connecting this opinion with their other doctrines concerning universals, they were unfortunately enabled to exhibit it in so mysterious a form, as not only to impose on themselves, but to perplex the understandings of all the learned in Europe, for a long succession of ages.

* HARRIS's Three Treatises, pages 341, 342.

+Ibid. p. 227.

The conclusion to which we are led by the foregoing observations, is, that the foundation of all human knowledge must be laid in the examination of particular objects and particular facts; and that it is only as far as our general principles are resolvable into these primary elements, that they possess either truth or utility. It must not, however, be understood to be implied in this conclusion, that all our knowledge must ultimately rest on our own proper experience. If this were the case, the progress of science, and the progress of human improvement, must have been wonderfully retarded; for, if it had been necessary for each individual to form a classification of objects, in consequence of observations and abstractions of his own, and to infer from the actual examination of particular facts, the general truths on which his conduct proceeds, human affairs would at this day remain nearly in the same state to which they were brought by the experience of the first generation. In fact, this is very nearly the situation of the species in all those parts of the world, in which the existence of the race depends on the separate efforts which each individual makes, in procuring for himself the necessaries of life; and in which, of consequence, the habits and acquirements of each individual must be the result of his own personal experience. In cultivated society, one of the first acquisitions which children make, is the use of language; by which means they are familiarized, from their earliest years, to the consideration of classes of objects, and of general truths, and before that time of life at which the savage is possessed of the knowledge necessary for his own preservation, are enabled to appropriate to themselves the accumulated discoveries of ages.

Notwithstanding, however, the stationary condition in which the race must of necessity continue, prior to the separation of arts and professions, the natural disposition of the mind to ascend from particular truths to general conclusions, could not fail to lead individuals, even in the rudest state of society, collect the results of their experience, for their own instruction and that of others. But, without the use of general terms, the only possible way of communicating such conclusions would be by means of some particular example, of which the general application was striking and obvious. In other words, the wisdom of such ages will necessarily be expressed in the form of fables or parables, or in the still simpler form of proverbial instances, and not in the scientific form of general maxims. In this way, undoubtedly, much useful instruction, both of a prudential and moral kind, might be conveyed: at the same time, it is obvious, that, while general truths continued to be expressed merely by particular exemplifications, they would afford little or no opportunity to one generation to improve on the speculations of another; as no effort of the understanding could combine them together, or employ them as premises. in order to obtain other conclusions more remote and comprehensive. For this purpose, it is abɛolutely necessary that the scope or moral of the fable should be separated entirely from its accessary circumstances, and stated in the form of a general proposition.

From what has now been said, it appears, how much the progress of human reason, which necessarily accompanies the progress of society, is owing to the introduction of general terms, and to the use of general

propositions. In consequence of the gradual improvements which take place in language as an instrument of thought, the classifications both of things and facts with which the infant faculties of each successive race are conversant, are more just and more comprehensive than those of their predecessors: the discoveries which, in one age were confined to the studious and enlightened few, becoming, in the next, the esta blished creed of the learned, and in the third, forming part of the elementary principles of education. Indeed, among those who enjoy the advantages of early instruction, some of the most remote and wonderful conclusions of the human intellet are, even in infancy, as completely familiarized to the mind as the most obvious phenomena which the material world exhibits to their senses

If these remarks be just, they open an unbounded prospect of intellectual improvement to future ages; as they point out a provision made by nature to facilitate and abridge, more and more. the process of study, in proportion as the truths to be acquired increase in number. Nor is this prospect derived from theory alone. It is encouraged by the past history of all the sciences; in a more particular manner, by that of mathematics and physics, in which the state of discovery, and the prevailing methods of instruction may, at all times, be easily compared together. In this last observation I have been anticipated by a late eminent mathematician, whose eloquent and philosophical statement of the argument cannot fail to carry conviction to those who are qualified to judge of the facts on which his conclusion is founded:

"To such of my readers, as may be slow in admitting the possibility of this progressive improvement in the human race, allow me to state, as an example, the history of that science in which the advances of discovery are the most certain, and in which they may be measured with the greatest precision Those elementary truths of geometry and "of astronomy which, in India and Egypt, formed an occult science, "upon which an ambitious priesthood founded its influence, were become, in the times of Archimedes and Hipparchus, the subjects of "common education in the public schools of Greece. In the last cen"tury, a few years of study were sufficient for comprehending all that "Archimedes and Hipparchus knew; and, at present, two years em"ployed under an able teacher, carry the student beyond those con❝clusions, which limited the inquiries of “Leibnitz and of Newton."Let any person reflect on these facts; let him follow the immense "chain which connects the inquiries of Euler with those of a Priest of "Memphis; let him observe, at each epoch, how genius outstrips the "present age, and how it is overtaken by mediocrity in the next; he "will perceive, that nature has furnished us with the means of abridg"ing and facilitating our intellectual labour, and that there is no reason "for apprehending that such simplifications can ever have an end.— "He will perceive, that at the moment when a multitude of particular "solutions, and of insulated facts, begin to distract the attention, and "to overcharge the memory, the former gradually lose themselves in "one general method, and the latter unite in one general law; and that "these generalizations continually succeeding one to another like the suc"cessive multiplications of a number by itself, have no other limit, than that infinity which the human faculties are unable to comprehend."

*See Note (M.)