CHA P. HAVING treated, at confiderable length, of those habits in which both mind and body are concerned, I proceed to make a few remarks on fome phenomena which are purely intellectual; and which, I think, are explicable on the fame principles with those which have been now under our review. EVERY person who has ftudied the elements of geometry, must have obferved many cafes in which the truth of a theorem ftruck him the moment he heard the enunciation. I do not allude to those theorems the truth of which is obvious almost to fenfe; fuch as, that any two fides of a triangle are greater than the third fide; or that one circle cannot cut another circle in more than two points; but to fome propofitions with respect to quantity, confidered abftractly, (to fome, for example, in the fifth book of Euclid,) which almoft every ftudent would be ready to admit without a demonstration. These These propofitions, however, do by no means belong to the clafs of axioms; for their evidence does not ftrike every perfon equally, but requires a certain degree of quickness to perceive it. At the fame time, it frequently happens, that, although we are convinced the propofition is true, we cannot ftate immediately to others upon what our conviction is founded. In fuch cafes, I think it highly probable, that before we give our afsent to the theorem, a procefs of thought has paffed through the mind, but has paffed through it fo quickly, that we cannot, without difficulty, arreft our ideas in their rapid fucceffion, and ftate * Of the nature of thefe proceffes of thought, I fhall treat fully in another part of my work, under the article of Reafoning. I have expreffed myfelf concerning them in this chapter, in as general terms as podible. them II. them to others in their proper and logical order. It is fome CHAP. confirmation of this theory, that there are no propofitions of which it is more difficult to give a legitimate proof from first principles, than of those which are only removed a few steps from the clafs of axioms; and that thofe men who are the most remarkable for their quick perception of mathematical truth, are feldom clear and methodical in communicating their knowledge to others.-A man of a moderate degree of quickness, the very first time he is made acquainted with the fundamental principles of the method of fluxions, or of the method of prime and ultimate ratios, is almost inftantaneously satisfied of their truth; yet how difficult is it to demonftrate these principles rigorously! WHAT I have now faid with refpect to mathematics, may be applied in a great measure to the other branches of knowledge. How many questions daily occur to us, in morals, in politics, and in common life; in confidering which, we almost inftantaneously see where the truth lies, although we are not in a condition, all at once, to explain the grounds of our conviction! Indeed, I apprehend, there are few, even among those who have devoted themselves to ftudy, but who have not been habituated to communicate their knowledge to others, who are able to exhibit, in their natural order, the different steps of any investigation by which they have been led to form a particular conclufion. The common obfervation, therefore, that an obscure elocution always indicates an imperfect knowledge of the fubject; although it may perhaps be true with respect to men who have cultivated the art of speaking, is by no II. CHA P. means to be relied on as a general rule, in judging of the talents of those whofe fpeculations have been carried on with a view merely to their own private fatisfaction. IN the course of my own experience, I have heard of more than one instance, of men who, without any mathematical education, were able, on a little reflexion, to give a folution of any fimple algebraical problem; and who, at the fame time, were perfectly incapable of explaining by what steps they obtained the refult. In these cafes, we have a direct proof of the poffibility of investigating even truths which are pretty remote, by an intellectual procefs, which, as foon as it is finished, vanishes almost entirely from the memory.-It is probable, that fomething of the fame kind takes place much more frequently in the other branches of knowledge, in which our reafonings confift commonly but of a few fteps. Indeed, I am inclined to think, that it is in this way that by far the greater part of our fpeculative conclufions are formed. THERE is no talent, I apprehend, fo effential to a public fpeaker, as to be able to ftate clearly every different ftep of thofe trains of thought by which he himself was led to the conclufions he wishes to establish. Much may be here done by ftudy and experience. Even in those cases in which the truth of a propofition feems to ftrike us inftantaneously, although we may not be able, at firft, to discover the media of proof, we feldom fail in the difcovery by perfeverance.-Nothing contributes fo much to form this talent as the ftudy of metaphyfics; not the abfurd metaphyfics of the schools, but that II. that study which has the operations of the mind for its object. CHA P. By habituating us to reflect on the fubjects of our confcioufnefs, it enables us to retard, in a confiderable degree, the current of thought; to arreft many of those ideas, which would otherwise escape our notice; and to render the arguments which we employ for the conviction of others, an exact transcript of those trains of inquiry and reasoning, which originally led us to form our opinions. THESE observations lead me to take notice of an important diftinction between the intellectual habits of men of speculation and of action. The latter, who are under a neceffity of thinking and deciding on the fpur of the occafion, are led to cultivate, as much as poffible, a quickness in their mental operations; and fometimes acquire it in fo great a degree, that their judgments feem to be almoft intuitive. To thofe, on the other hand, who have not merely to form opinions for themfelves, but to communicate them to others, it is neceffary to retard the train of thought as it paffes in the mind, fo as to be able afterwards to recollect every different step of the process; a habit, which, in fome cafes, has fuch an influence on the intellectual powers, that there are men, who, even in their private fpeculations, not only make use of words as an inftrument of thought, but form thefe words into regular fen tences. Ir may perhaps appear, at firft, a paradoxical obfervation, that one great employment of philofophers, in a refined age, II. CHAP. is to bring to light, and arrange, thofe rapid and confused trains of thought, which appear from the ftructure of languages, and from the monuments of ancient laws and governments, to have paffed through the minds of men in the moft remote and unenlightened periods. In proof, however, of this, it is fufficient to mention, the fyftematical analogy which we find, to a certain degree, running through the ftructure of the most imperfect tongues, (for example, in the formation of the different parts of the verbs,) and thofe general principles, which the philofophical lawyer traces amidst an apparent chaos of precédents and ftatutes. In the language, too, of the rudest tribe, we find words transferred from one fubject to another, which indicate, in the mind of the individual who firft made the transference, fome perception of refemblance or of analogy. Such transferences can hardly be afcribed to accident, but may be confidered as proofs that the analogies which the philosopher afterwards points out between the objects which are diftinguished by the fame name, had been perceived by the inventors of language, although it is more than probable that they never expreffed them in words, nor could even have explained them if they had been queftioned on the fubject. NOR will this appear a bold or incredible fuppofition, if we reflect on the fagacity and ingenuity which favages, and even peasants, discover, in overcoming the difficulties which occur in their fituation. They do not, indeed, engage in long proceffes of abftract reasoning, for which they have no inclination, and |