LECTURE VII.

Of METHOD in Argumentative difcourfes; of AN ALYSIS and SYNTHESIS; and of GEOMETRICAL DEMONSTRATION.

THE greatest difficulty, in point of method, is

found in properly arranging the parts of an argument, fo as to give them the moft 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 discourses, the analytic and the Synthetic; and the diftribution is complete and accurate. For, in all science, we either proceed from particular observations to more general conclufions, which is analyfis; or, beginning with more general and comprehenfive propofitions, we defcend to the particular propofitions which are contained in them, which is fynthefis.

In the former method we are obliged to proceed in our investigation of truth: for it is only by comparing a number of particular observations which are felf-evident, that we perceive any analogy in effects, which leads us to apprehend an uniformity in their cause, 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, thofe truths which were the refult of our own inquiry, may be made as intelligible to others as thofe by which we arrived at the knowledge of them; and it is easier to show how one general principle comprehends the particulars comprised 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 difcoveries are generally the refult of fuch 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 feveral keys that will open one or two of them only, at last to produce that which will open them all?

Notwithstanding this, in theories not perfectly afcertained, or with regard to fentiments not generally admitted, it may be adviseable to inform others in the method of analyfis; because then, beginning with no principles or positions 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 hypothe fis, find that none would anfwer except that which

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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 enquiry, 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 stricteft demonftration) hath been delivered at first by the investigators of it in this method of analyfis; 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 fchools, 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 analyfis in every thing they learn. Analytical difcourfes are, therefore, more properly addreffed to those persons who have gone through their preparatory studies, and who have leisure 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 synthetic, is adopted, as best suits the taste of the writer.

A method the most properly analytic is purfued 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 written in the analytic method, as beft fuited to the infant ftate of the science. The fcience of theology hath been, perhaps, too precipitately handled in the method of fynthesis, or fyftematically; and feveral 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 fynthesis and analysis, and of proper ufe of both, I proceed to confider them feparately and more particularly.

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Since the fubject of every fynthetic difcourfe is fome propofition or theorem, which is to be proved, and the bulk of the discourse a kind of demonftra

tion, it may be of confiderable service to a compofer to have in view the methods of demonftration ufed by mathematicians.

Truth, whether geometrical, metaphysical, moral, or theological, is of the fame nature, and the evidence of it is perceived in a fimilar manner by the fame human minds. Now it is univerfally allowed that the form in which evidence is prefented by Euclid, and other geometricians of reputation, is that in which it gains the readiest and most irrefiftible admiffion into the mind; and their method of conducting a demonstration, and disposing of every thing preceding it, and fubfequent to it, hath been fo generally approved, that it is established and invariable. Such a fuccefsful 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 fynthetic demonftration, 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 moralists.

Every propofition is, by geometricians, demonftrated either from axioms, that is, felf-evident truths; or fuch as have been elsewhere demonftrated from thofe which are felf-evident.

In like manner, whatever we propofe to demonftrate, the last appeal lies to self-evident truths; in moral