The Fourth Part of Logick

    of Method, or an orderly disposition of our thoughts.

    Cap. 1. of the general method of knowing.

    Althô perhaps there may be some men of so sagacious a witt, that without difficulty they may peirce into difficult things, and know how to solve abstruse questions, yet will none ever obtain certain knowledge, unless they first know how their mind is to be directed, and what order it ought to observe: and therefore method is necessary, or some doctrine whereby the mind may be helped in searching for truth; and may free it self from error, confusion and obscurity.

    This method may be defined, such a series or disposition of things to be handled as may be most accomodated to the capacity of the Learner.

    That our minds may be sufficiently helped here, & so knowledge obtained 3 things are requisites

    1. 1. that the thing proposed be clearly and distincly perceived.
    2. 2. that we pass a right Judgment on the things thus rightly perceived. &c
    3. 3. that we lay up in our memories truths thus discovered, or those things which we have rightly perceived and Judged of. by the due observance of these 3 precepts we may help all the infirmities of our minds. for since the ostacles of knowledge are either, 1—Too great præcipitance of mind, A clear & distinct perception takes away that; 2—Error or doubt: they are removed by this right Judgment, or, 3—oblivion and forgetfulnesse: that likewise will be prevented by this memory or Remembrance.

    A clear and distinct perception will be much furthered, if removeing all precipitance, we attend heedfully to the thing proposed, and view it as it were with internal eyes; to which it will conduce much if we consider of but one thing at once, for plenty of objects does certainly breed confusion.

    That we may duely observe the 2d precept, is requisite evermore that knowledge preceed Judg: and that simple terms be placed before such as are complex and if at any time it happens, that we are brought into doubt concerning any thing, we shall readily escape error, if we suspend Judgment, affirming or denying nothing til more light is brought, and all obscurities therefore removed.

    Yet we are not to think that all things which are true do carry the same certainty with them; for some things are only contingently true, i.e. they might be false, thus, if I Judge that a man is pious because he frequents the church, lives in the practice of prayer &c which things ordinarily are sufficient for me to Judge a man pious by, and yet it is possible that this man may be void of all true piety notwithstanding these his actings, somethings are altogether certain and true; as propositions of eternal verity, bis quatore sunt octo, Ternarius est numerus &c:103

    But because it availes little or nothing to know the nature of things, unless we withall Remember them, we are therefore to Learn how things understood by us may be committed to memory, and so to be Imprinted on it as to be hardly lost or removed thence: and this will readily be attained if we follow the order of our method, i.e. if we commit nothing to memory but what has been found out and rightly Judged of by us: for we dayly find that things clearly perceived are most strongly fastened on our mind, and that such things as are proposed in order are more easily retained, then such as are confused.

    How ever we shall yet further promote and help memory, if we get a tranquill and even spirit, and suffer not our understanding to be distracted about too many objects: and we shall the better retain things in memory if we oft go over them in our minds, diligently reflecting on them, and attending to them as we speak them.

    Cap. 2. of Special method and first of Analysis.

    The word Method is here to be taken somewhat more strictly then it was in the preceeding article: for our design there was only to teach Novists what order they ought to keep in the obtaining of knowledge: Whereas here we are not only to treat of the forming conceptions, but also enquiry is to be made how we may regularly dispose our conceptions when framed. and therefore

    Method is 2 fold; for it either finds out the truth and so is called Analysis, or method of Resolution (which likewise may be termed method of invention) or it teaches the truth when found out, and is termed Synthesis, or method of composition, which likewise may be called the method of handling a doctrine.

    Of Analysis

    The whole body of any science is seldom Analysed or delivered Analytically; Analysis being only in use to solve questions. Every question is either concerning a name, or a thing.

    By the question of a name here we understand not that which hunts for names whereby things may by signified, but that which searches for things signfied by names, of this kind are such as tend to the solving of (Ænigma’s or) Riddles; and such as do explain the obscure sense of A criptical Reader.

    The question of A thing is 4 fold.

    1. 1. when we search for a cause from effects: Thus when we consider the Attractive power in a Load Stone and enquire into the cause of it.
    2. 2. the 2d kind is; when from causes we find out effects as when we consider of the wind’s blowing and the water’s flowing, and enquire into the benefit of the one or other; how they might prove useful and advantagious to us.
    3. 3. the third kind is; when from parts we are lead to a knowledge of an whole: thus many numbers being given, enquiry is made what the summe of all would be, they being added together.
    4. 4. the 4th and last kind is; when an whole being given and one part, enquiry is made what another part is. thus when a numberd is given, and part of it is taken away, we ask, what is the remainder.

    Here we are to note that as in Analysis so in synthesis, we are evermore to proceed from A thing more known to a that which is less known, this rule is common to all method, neither is any method to be accounted good which at all deviates from this principle: yet in this, Analysis or method of Resolution differs from that which is called method of composition, that Analysis proceeds from lesse generalls to more generalls, whereas synthesis begins at a more general and goes to a less general: for thus if we enquire whether man’s soul is Immortal its evident that we do not go from universal axioms after this manner, nulla substantia propriè dess{}itur, destructio nihil aliud est, quam partium dissollutio, and thence quod partibus caret destrui nequit;104 but on the other hand we gradually arise to those general notions: so that those 2 methods [Analysis and Synthesis] do not differ among themselves any other way than the ascent & descent of the same mountain: or the way whereby we go from a valley to the top of a mountain and that very way whereby we go from the top of the mountain to the valley which lies at the foot of it.105

    Cap. 3. Of the Method of Composition.

    Synthesis, or method of composition consists cheifly in this, that it proceeds from more general things to lesse generals and from more simple to more compounded things: and by this mode of proceeding all repetitions are avoided which ever more breed either confusion or tediousness.

    That this method may be in all respects taught clearly, and first to obtain it’s designed end, Viz a clear and distinct knowledge of the truth, many things are heedfully to be observed: but since generall precepts separated from all matter are very difficult to be understood; we shall consider the synthesis of Geometricians which is always thought most efficacious to demonstrate truth and persuade: we shall therefore show what is commendable in their Method, & then propose what their defects and failings were.

    Since then Geometricians design’d to assert nothing but was most evident and certain, they Imagined that this their design might be attained if so be that they did heedfully observe these 3 rules.

    1. 1. that they left nothing ambiguous in the terms proposed.
    2. 2. that they deduced reasoning only from certain and evident principles; such principles as could be doubted of by no man that had his witts about him.
    3. 3. that they demonstratively proved every conclusion: demonstratively. i.e. by the help of premised definitions, evident and granted axiomes, or propositions which no sooner are demonstrated but obtain the title of principles

    To these 3 heads the whole of what Geometricians observe may be reduced, and so far they kept to a good rule and fam’d themselves, in that hereby they banished all disputations and controversies out of their schooles.

    Nevertheless it cannot be denied, but that they have fallen into some errors or defects, which althô (possibly) they have not carried them from their proposed end, have led them thrô many by-wayes and occasioned much roughness, of which their method or way might have been void, and wholly destitute.

    Their defects then were

    1. 1. That they laboured more about certainty then evidence; more about convincing the understanding then enlightning it. that is they laboured not so much to show the way how these and those truths came to be so, as to demonstrate that they are truths.
    2. 2. that they oftentimes prove those things which need no proof, i.e. althô they acknowledge that such things as are clear of themselves need no truth, yet they often attempt the proof of such truths.
    3. 3. that they demonstrate by something impossible, i.e. by some absurdity or Impossibility that would arise from that which is contrary to their Position:
    4. 4. that they demonstrate by things aliene & remote. This is an Imperfect way of demonstrating, being contrary to the ordinary course of nature which takes but one step at once.
    5. 5. that they do not observe the natural order of things i.e. by going from simples to compounds, and from generals to particulars: this fault, as also the 4th and some others are too often to be found in Euclids Elements.
    6. 6. that they do not sufficiently use divisions and partitions.

    That which is censured and found fault with here as to the method of Geometricians is not, that they omitt any species of a genus which they design at any time to handle, but this viz—that they do not at first say of the genus that it has so many species and cannot have more because the general Idea of the genus cannot receive more differences and so proceed to the species: to make this more plain let us take this example.

    Euclid in his first book has definitions of all the species of a triangle without premising the distribution of triangle in general; now who can but see that it would be much more clear if the matter were thus proposed.

    A Triangle may be divided either according to it’s sides or according to it’s angles,

    Thus have we at Large shown what is good & what is bad in the method of Geometricians and hence: we may be abundantly informed as to method in general, or in other sciences when we are called to make use of it therein.

    Cap. 4. of the 8 principle Rules relating to Method.

    From what has been said in the foregoing chapter it may be Justly concluded that we shall attain to a method indeed more perfect and absolute than that which is in use among Geometricians themselves, if so be that we do carefully attend unto 8 rules which we shall here propose, whereof the 2 first do belong to Idea’s and so respect the first part of Logick; the next do belong to axiomes and consequently the 2d part: the 5 and 6th do respect argumentation and are related to the 3d part: and the 2 last rules are about order and so more Immediately belong to the fourth and last part of Logick.

    The 2 Rules of definitions.

    1. 1. That we Leave nothing obscure, ambiguous or equivocal in the terms, but define the same most plainly.
    2. 2. That in all definitions we evermore use terms either perfectly known in themselves, or such as were before sufficiently explained.

    The 2 Rules of axiomes

    1. 3. That we lay down no axiome (or nothing for an axiome) which is not amost clear and evident truth.
    2. 4. That we take that only for evident, which by a moderate attention is known to be a truth.

    The 2 Rules of demonstration.

    1. 5. That we prove all obscure propositions, by the help of premised definitions being granted axiomes or demonstrated propositions.
    2. 6. That we never abuse the ambiguity of terms.

    The 2 Rules of Method

    1. 7. That we handle things, as much as we can, according to natural order, by beginning at the more generals and the more simple, and by explaining whatever belongs to the nature of a genus before we descend to particular species.
    2. 8. That we divide as far as we can every genus into it’s species, every totum into all it’s parts and every difficulty into all it’s cases.

    In those 2 last rules are inserted those words (as far as we can) for it somtimes happens that they cannot be rigorously observed, whether by reason of the limits of mans mind, or those bounds which we are forced to assign every science.

    And thus we have proposed these 8 rules, which if we attend heedfully to, will be of great use to us in delivering any science, as the neglect and non-observance thereof will prove prejudicial unto knowledge and with these rules doth our fourth and last part of Logick conclude.

    Upon the prickly bush of Logick grows

    of other Sciences the fragrant rose.106