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Whether a writer difcourfe of the mechanic, or the liberal arts, fuch as grammar, oratory, &c. the nature of the thing will direct him, in general, to divide the fubject into its proper diftinct parts, and to give an account of what is most essential in the first place, and what is only ornamental afterwards.
Of METHOD in Argumentative difcourfes; of ANALYSIS and SYNTHESIS; and of GEOMETRICAL DEMONSTRATION.
HE greateft difficulty, in point of method, is found in perly arranging the parts of an argument, fo as to give them the most weight, and encrease the degree of evidence refulting from the whole, by the aptness of their order and connexion.
Logicians fpeak of two kinds of method in argumentative dis-courses, the analytic and the fynthetic; and the diftribution is complete and accurate. For, in all science, we either proceed from particular obfervations to more general conclufions, which is analyfis; or, beginning with more general and comprehenfive propofitions, we descend to the particular propofitions which are contained in them, which is fynthefis.
In the former method we are obliged to proceed in our inveftigation of truth: for it is only by comparing a number of particular obfervations which are felf-evident, that we perceive any analogy in effects, which leads us to apprehend an uniformity in their caufe, in the knowledge of which all science confifts. In the latter method it is generally more convenient to explain a fyftem of science to others. For, in general, those truths which
were the refult of our own inquiry, may be made as intelligible to others as those by which we arrived at the knowledge of them; and it is eafier to fhow how one general principle comprehends the particulars comprized under it, than to trace all those particulars to one that comprehends them all.
On the other hand, the analytic method is properly to communicate truth to others in the very manner in which it was difcovered; and first discoveries are generally the result of such a laborious and minute examination, as is, in its own nature, a flow and tedious procedure. Is it not much readier to take the right key at first, and open a number of locks, than begin with examining the locks, and after trying several keys that will open one or two of them only, at last to produce that which will open
Notwithstanding this, in theories not perfectly ascertained, or with regard to sentiments not generally admitted, it may be advifeable to inform others in the method of analysis; because then, beginning with no principles or pofitions but what are common, and univerfally allowed, we may lead others infenfibly, and without shocking their prejudices, to the right conclufion. It is as if the perfons we are inftructing did themselves make all the observations, and, after trying every hypothefis, find that none would answer except that which we point out to them. This method is more tedious, but perhaps more fure. Before we admit any hypothefis, we naturally confider whether it will agree with every obfervation previously made, and every propofition previously admitted; and therefore in a method of communication borrowed from that cautious method of inquiry, we are of course led diftinctly to confider, and very particularly to obviate all kinds of objections.
In fact, almost every branch of science (except fome parts of pure mathematics, capable of the ftricteft demonftration) hath been delivered at first by the investigators of it in this method of analysis; and it hath not been till after fome time that the patrons of it have digested it into a synthetic, or fyftematic form.
This latter method, however, is abfolutely neceffary when any branch of science is introduced into Schools, where there is occafion for the most concife and compendious methods of inftruction. It is only the elements of science that can be learned in schools, and it would take up too much of the little time that youth can give to their studies, to lead them through all the flow proceffes of analysis in every thing they learn. Analytical discourses are, therefore, more properly addreffed to those persons who have gone. through their preparatory ftudies, and who have leifure for new Speculations.
These two methods are feldom ufed abfolutely unmixed in any work of confiderable length, except by mathematicians; and for: the greater variety, in long difcourfes, a method fometimes partaking more of the analytic, and fometimes leaning more to the fynthetic, is adopted, as beft fuits the taste of the writer.
A method the most properly analytic. is pursued by mathematicians in all kinds of algebraic investigations, in approximations, and in experimental philofophy: whereas the geometric method. of propofition and demonstration is of the fynthetic kind.
A great variety of modern treatises upon moral fubjects, in which mankind are far from being agreed, have lately been writ ten in the analytic method, as best suited to the infant state of the science. The science of theology hath been, perhaps, too precipitately handled in the method of synthesis, or systematically;,
and several ingenious perfons, being aware of it, have gone back, and have begun again in the more cautious method of analytical inquiry.
Having thus given a general idea of the nature of the methods of synthesis and analysis, and of the proper use of both, I proceed to confider them separately and more particularly.
Since the subject of every fynthetic discourse is some propofition, or theorem, which is to be proved, and the bulk of the discourse a kind of demonftration, it may be of confiderable service to a composer to have in view the methods of demonstration used by
Truth, whether geometrical, metaphyfical, moral, or theological, is of the fame nature, and the evidence of it is perceived in a similar manner by the fame human minds. Now it is univerfally allowed that the form in which evidence is presented by Euclid, and other geometricians of reputation, is that in which it gains the readiest and most irresistible admiffion into the mind; and their method of conducting a demonstration, and difpofing of every thing preceding it, and fubfequent to it, hath been fo generally approved, that it is established and invariable. Such a fuccessful method of procedure with respect to mathematical truth, certainly deferves the attention and imitation of all who are defirous to promote the interefts of any kind of truth..
In order, therefore, to give the most perfect rules of synthetic demonstration, I fhall explain the method of geometricians, and endeavour to show how far it may be adopted, or imitated with advantage, by writers in general, and particularly by divines and. moralifts..