Elements of philosophy the first section, concerning body / written in Latine by Thomas Hobbes of Malmesbury ; and now translated into English ; to which are added Six lessons to the professors of mathematicks of the Institution of Sr. Henry Savile, in the University of Oxford.

COMPUTATION OR LOGIQUE.

CHAP. I. Of Philosophy.

• 1▪ The Introduction.
• 2 The Definition of Philosophy explained.
• 3 Ratioci∣nation of the Mind.
• 4 Properties what they are.
• 5 How Properties are known by Generation, & contrarily.
• 6 The Scope of Philosophy.
• 7 The Utility of it.
• 8 The Subject.
• 9 The Parts of it.
• 10 The Epilogue.

PHILOSOPHY seems to me to be amongst men now, in the same manner as Corn and Wine are said to have been in the world in ancient time. For from the beginning there were Vines and Ears of Corn growing here and there in the fields; but no care was taken for the planting and sowing of them. Men lived therefore upon Akorns; or if any were so bold as to venture upon the eating of those un∣known and doubtfull fruits, they did it with danger of their health. In like manner, every man brought Philosophy, that is, Naturall Reason, into the world with him; for all men can rea∣son to some degree, and concerning some things: but where there is need of a long series of Reasons, there most men wander out of the way, and fall into Error for want of Method, as it were for want of sowing and planting, that is, of improving their Reason. And from hence it comes to passe, that they who content them∣selves with daily experience, which may be likened to feeding upon Akorns, and either reject, or not much regard Philoso∣phy,

are commonly esteemed, and are indeed, men of sounder judgement, then those, who from opinions, though not vul∣gar, yet full of uncertainty, and carelesly received, do nothing but dispute and wrangle, like men that are not well in their wits. I confesse indeed, that that part of Philo∣phy by which Magnitudes and Figures are computed, is highly improved. But because I have not observed the like advance∣ment in the other parts of it, my purpose is, as far forth as I am able, to lay open the few and first Elements of Philosophy in ge∣nerall, as so many Seeds, from which pure and true Philosophy may hereafter spring up by little and little.

I am not ignorant how hard a thing it is to weed out of mens mindes such inveterate opinions as have taken root there, and been cōfirmed in them by the authority of most eloquent Writers; especially, seeing true (that is accurate) Philosophy, professedly rejects not only the paint and false colours of Language, but even the very ornaments and graces of the same; and the first Grounds of all Science, are not only not beautifull, but poore, aride, and in appearance deformed. Neverthelesse, there being certainly some men, though but few, who are delighted with Truth and strength of Reason in all things, I thought I might do well to take this pains for the sake even of those few. I proceed therefore to the matter, and take my beginning from the very Definition of Philosophy, which is this.

2 PHILOSOPHY is such knowledge of Effects or Appearances, as we acquire by true Ratiocination from the knowledge we have first of their Causes or Generation: And again, of such Causes or Generations as may be from know∣ing first their Effects.

For the better understanding of which Definition, we must consider; first, that although Sense and Memory of things, which are common to Man and all living Creatures, be Knowledge, yet because they are given us immediately by Nature, and not got∣ten by Ratiocination, they are not Philosophy.

Secondly, Seeing Experience is nothing but Memory; and Prudence, or Prospect into the future time, nothing but Ex∣pectation of such things as we have already had experience of, Prudence also is not to be esteemed Philosophy.

By RATIOCINATION, I mean Computation. Now to com∣pute,

is either to collect the sum of many things that are added together, or to know what remains when one thing is taken out of another. Ratiocination therefore is the same with Addition and Substraction; and if any man adde Multiplication and Division, I will not be against it, seeing Multiplication is nothing but Addition of equals one to another, and Division nothing but a Substraction of e∣quals one from another, as often as is possible. So that all Ratio∣cination is comprehended in these two operations of the minde, Addition and Substraction.

3 But how by the Ratiocination of our Minde, we Adde and Sub∣stract in our silent thoughts, without the use of words, it will be necessary for me to make intelligible by an example or two. If therefore a man see something a far off and obscurely, although no appellation had yet been given to any thing, he will notwith∣standing have the same Idea of that thing, for which now by im∣posing a name on it, we call it Body. Again, when by comming neerer, he sees the same thing thus and thus, now in one place and now in another, he will have a new Idea thereof, namely that, for which we now call such a thing Animated. Thirdly, when standing neerer he perceives the figure, hears the voice, and sees other things, which are signes of a Rationall minde, he has a third Idea, though it have yet no appellation, namely, that for which we now call any thing Rationall. Lastly, when by looking fully and distinctly upon it he conceaves all that he has seen as one thing, the Idea he has now, is compounded of his former Ideas, which are put together in the Minde, in the same order, in which these three single names Body, Animated, Rationall, are in speech compounded into this one name Body-Animated-Rationall, or Man. In like manner, of the severall conceptions of four sides, equality of sides, and right angles, is compounded the conception of a Square. For the mind may conceive a figure of foure sides without any conception of their equality; & of that equality without conceiv∣ing a right angle; and may joyne together all these single con∣ceptions into one conception or one Idea of a Square. And thus we see how the Conceptions of the mind are compounded. A∣gain, whosoever sees a man standing neer him, conceives the whole Idea of that man; and if as he goes away he follow him with his eyes onely, he will lose the Idea of those things which

were signes of his being Rationall, whilest neverthelesse the Idea of a Body-Animated remaines still before his eies; so that the I∣dea of Rationall is substracted from the whole Idea of Man, that is to say of Body-Animated-Rationall, and there remaines that of Body-Animated; & a while after at a greater distance the Idea of Animated will be lost, & that of Body only will remain; so that at last, when nothing at all can be seen, the whole Idea will vanish out of sight. By which examples, I thinke it is manifest enough, what is the internall Ratiocination of the Mind, without words.

We must not therefore thinke that Computation, that is, Ratiocination, has place onely in numbers; as if man were distinguished from other living Creatures (which is said to have been the opinion of Pythagoras) by nothing but the faculty of numbring; for Magnitude, Body, Motion, Time, Degrees of Quality, Acti∣on, Conception, Proportion, Speech and Names (in which all the kinds of Philosophy consist) are capable of Addition and Substraction. Now such things as we adde or substract, that is, which we put into an account, we are said to consider, in Greek 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉; in which language also 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉 signifies to Compute, Reason or Rec∣kon.

4 But Effects and the Appearances of things to sense, are faculties or Powers of Bodies, which make us distinguish them from one another; that is to say, conceive one Body to be equall or unequall, like or unlike to another Body; as in the exam∣ple above, when by coming neer enough to any Body, we per∣ceive the Motion and Going of the same, we distinguish it there∣by from a Tree, a Column and other fixed Bodies; and so that mo∣tion, or going is the Property thereof, as being proper to living crea∣tures, and a faculty by which they make us distinguish them from other Bodies.

5 How the knowledge of any Effect may be gotten from the knowledge of the Generation thereof, may easily be understood by the example of a Circle: For if there be set before us a plain fi∣gure having as neer as may be the figure of a Circle, we cannot possibly perceive by sense whether it be a true Circle or no; then which neverthelesse nothing is more easie to be known, to him that knowes first the Generation of the propounded figure. For let it be known that the figure was made by the circumduction of

a Body whereof one end remained unmoved, and we may reason thus; a Body carried about, retaining alwayes the same length, applies it selfe first to one Radius, then to another, to a third, a fourth, and successively to all; and therefore the same length, from the same point, toucheth the circumference in every part there∣of; which is as much to say as all the Radii are equal. We know therefore that from such generation proceeds a figure, from whose one middle point all the extreame points are reached unto by equal Radii. And in like manner, by knowing first what figure is set before us, we may come by Ratiocination to some Genera∣tion of the same, though perhaps not that by which it was made, yet that by w^ch it might have been made; for he that knows that a Circle has the property above declared, will easily know whether a Body carried about, as is said, will generate a Circle or no.

6 The End or Scope of Philosophy, is, that we may make use to our benefit of effects formerly seen; or that by applicatiō of Bodies to one another; we may produce the like effects of those we con∣ceive in our minde, as far forth as matter, strength & industry will permit, for the commodity of humane life. For he inward glory and triumph of mind that a man may have, for the mastering of some difficult and doutfull matter, or for the discovery of some hidden truth, is not worth so much paines as the study of Philoso∣phy requires; nor need any man care much to teach another what he knowes himselfe, if he think that will be the onely benefit of his labour. The end of Knowledge is Power; and the use of Theo∣remes (which among Geometricians serve for the finding out of Properties) is for the construction of Problemes; and lastly, the scope of all speculation is the performing of some action, or thing to be done.

7 But what the Utility of Philosophy is, especially of Natural Philosophy and Geometry, will be best understood by reckoning up the chief commodities of which mankind is capable; and by comparing the manner of life of such as enjoy them, with that of others which want the same. Now the greatest commodities of mankind are the Arts, namely of measuring Matter and Motion; of moving ponderous Bodies; of Architecture; of Navigation; of making instruments for all uses; of calculating the Coelestiall Motions, the Aspects of the Stars, and the parts of Time; of Geo∣graphy,

&c. By which Sciences, how great benefits men receive, is more easily understood then expressed. These benefits are en∣joyed by almost all the people of Europe, by most of those of A∣sia, and by some of Africa; but the Americans, and they that live neer the Poles do totally want them. But why? Have they sharper wits then these? Have not all men one kinde of soule, and the same faculties of mind? What then makes this difference, except Philosophy? Philosophy therefore is the cause of all these benefits. But the Utility of Morall and Civil Philosophy is to be estimated not so much by the commodities we have by know∣ing these Sciences, as by the calamities we receive from not knowing them. Now all such calamities as may be avoided by humane industry arise from warre, but chiefly from Civil warre; for from this proceed Slaughter, Solitude, and the want of all things. But the cause of warre is not that men are willing to have it; for the Will has nothing for Object but Good, at least that which seemeth good. Nor is it from this, that men know not that the effects of war are evil; for who is there that thinks not poverty and losse of life to be great evils? The cause therefore of Civill warre, is that men know not the causes neither of Warre nor Peace, there being but few in the world that have learned those duties which unite and keep men in peace, that is to say, that have learned the rules of civill life sufficiently. Now the knowledge of these rules is Morall Philosophy. But why have they not learned them, unlesse for this reason that none hither∣to have taught them in a clear and exact method? For what shall we say? Could the ancient Masters of Greece, Egypt, Rome, and others perswade the unskillfull multitude to their innumerable opinions concerning the nature of their Gods, which they them∣selves knew not whether they were true or false, and which were indeed manifestly false & absurd; & could they not per∣swade the same multitude to civill duty, if they themselves had understood it? Or shall those few writings of Geometricians which are extant, be thought sufficient for the taking away of all controversy in the matters they treat of, and shall those innume∣rable and huge Volumes of Ethicks be thought unsufficient, if what they teach had been certain and well demonstrated? What then can be imagined to be the cause that the writings of

those men have increased science, and the writings of these have increased nothing but words, saving that the former were writ∣ten by men that knew, and the later by such as knew not the doctrine they taught onely for ostentation of their wit and elo∣quence? Neverthelesse, I deny not but the reading of some such books is very delightfull; for they are most eloquently written, and containe many cleer, wholsome and choice sentences; which yet are not universally true, though by them universally pro∣nounced. From whence it comes to passe, that the circumstances of times, places and persons being changed, they are no lesse frequently made use of to confirme wicked men in their purpo∣ses, then to make them understand the precepts of Civill duties. Now that which is chiefly wanting in them, is a true and cer∣taine rule of our actions, by which we might know whether that we undertake be just or unjust. For it is to no purpose to be bid∣den in every thing to do Right, before there be a certain Rule and measure of Right established; which no man hitherto hath esta∣blished. Seeing therefore from the not knowing of Civill duties, that is, from the want of Morall science proceed Civill warres, and the greatest calamities of mankind, we may very well attri∣bute to such science the production of the contrary commodities. And thus much is sufficient, to say nothing of the prayses and o∣ther contentment proceeding from Philosophy, to let you see the Utility of the same in every kinde thereof.

8 The Subject of Philosophy, or the matter it treats of, is every Body of which we can conceive any generation, and which we may by any consideration thereof compare with other Bodies; or which is capable of composition and resolution; that is to say, e∣very Body, of whose Generation or Properties we can have any knowledge.. And this may be deduced from the Definition of Philosophy, whose profession it is to search out the Properties of Bodies from their Generation, or their Generation from their Properties; and therefore where there is no Generation nor Property, there is no Philosophy. Therefore it excludes Theology, I meane the doctrine of God, Eternal, Ingenerable, Incompre∣hensible, and in whom there is nothing neither to divide nor compound, nor any Generation to be conceived.

It excludes the doctrine of Angels; and all such things as are

thought to be neither Bodies, nor properties of Bodies; there be∣ing in them no place neither for composition, nor division, nor a∣ny capacity of more and lesse; that is to say, no place for Ratioci∣nation.

It excludes History, as well Naturall as Politicall, though most usefull (nay necessary) to Philosophy; because such Knowledge is but Experience, or Authority, and not Ratiocination.

It excludes all such Knowledge as is acquired by Divine Inspi∣ration, or Revelation, as not derived to us by Reason, but by Di∣vine grace in an instant, and as it were by some sense supernatu∣rall.

It excludes, not onely all Doctrines which are false, but such also as are not well grounded; for whatsoever we know by right Ratiocination, can neither be false nor doubtfull; and therefore Astrology, as it is now held forth, and all such Divinations rather then sciences, are excluded.

Lastly, the doctrine of Gods Worship is excluded from Philosophy, as being not to be known by naturall reason, but by the authority of the Church; and as being the object of Faith, and not of Know∣ledge.

9 The principall parts of Philosophy are two. For two chief kinds of Bodies, and very different from one another, offer them∣selves to such as search after their Generation & Properties; One whereof being the worke of Nature, is called a Naturall Body; the other is called a Commonwealth, and is made by the wills and agree∣ment of men. And from these spring the two parts of Philosophy called Naturall and Civill. But seeing that for the knowledge of the Properties of a Common-wealth, it is necessary first to know the Dispositions, Affections and Manners of men, Civill Philoso∣phy is againe commonly divided into two parts; whereof one which treats of mens Dispositions and Manners is called Ethicks, and the other which takes cognisance of their Civil Duties is cal∣ed Politicks or simply Civill Philosophy. In the first place therefore (after I have set downe such Premisses as appertaine to the na∣ture of Philosophy in general) I will discourse of Bodies Naturall; in the second, of the Dispositions and Manners of men; and in the third, of the Civill Duties of Subjects.

10 To conclude, seeing there may be many who will not like

this my Definition of Philosophy, and will say that from the liberty which a man may take of so defining as seemes best to himselfe, he may conclude any thing from any thing (though I thinke it no hard matter to demonstrate, that this Definition of mine agrees with the sense of all men;) yet lest in this point there should be any cause of dispute betwixt me and them, I here un∣dertake no more then to deliver the Elements of that Science, by which the Effects of any thing may be found out from the known Generation of the same, or contrarily the Generation from the Effects; to the end that they who search after other Philosophy, may be admonished to seeke it from other Principles.

CHAP. II. Of Names.

• 1 The necessity of sensible Moniments or Marks for the help of Memory, A Marke defined.
• 2 The necessity of Marks for the signification of the conceptions of the Mind.
• 3 Names supply both those necessities.
• 4 The Definition of a Name.
• 5 Names are Signes not of Things, but of our Cogi∣tations.
• 6 What it is we give Names to.
• 7 Names Positive and Negative.
• 8 Contradictory Names.
• 9 A Common Name.
• 10 Names of the first and second Intention.
• 11 Universall, Particular, Individuall, and Inde∣finite Names.
• 12 Names Univocall and Equivocal.
• 13 Absolute and Relative Names.
• 14 Simple and Compounded Names.
• 15 A Praedica∣ment described.
• 16 Some things to be noted concerning Praedicaments.

1 HOw unconstant and fading mens thoughts are, and how much the reco∣very of them depends upon chance, there is none but knows by infallible experience in himself. For no man is able to remember Quantities without sensible and present Measures, nor Colours without sensible and present Patterns, nor Number without the Names of Numbers disposed in order and learned by heart. So that whatsoever a man has put together in his mind by ratiocination without such helps, will presently slip from him, and not be revocable but by beginning his ratioci∣nation anew. From which it followes, that for the acquiring of Philosophy some sensible Moniments are necessary, by which our past thoughts may be not onely reduced, but also registred every one in its own order. These Moniments I call MARKS, namely, sensible things taken at pleasure, that by the sense of them such thoughts may be recalled to our mind, as are like those thoughts for which we [took them.]

2 Again, though some one man, of how excellent a wit soever, should spend all his time, partly in reasoning and partly in in∣venting Marks for the help of his memory, and advancing him∣self in learning; who sees not, that the benefit he reapes to him∣selfe will not be much, and to others none at all? For unlesse he communicate his notes with others, his science will perish with him. But if the same notes be made common to many, and so one mans inventions be taught to others, sciences will thereby be encreased to the generall good of mankind. It is therefore neces∣sary for the acquiring of Philosophy that there be certain Signes, by which what one man finds out may be manifested and made known to others. Now those things we call SIGNES, are the Ante∣cedents of their Consequents, and the Consequents of their Antecedents, as often as we observe them to go before or follow after in the same manner. For example, a thick Cloud is a Signe of Rain to follow; and Rain a Signe, that a Cloud has gone before, for this reason onely, that we seldom see Clouds without the Consequence of Rain, nor Rain at any time but when a Cloud has gone before. And of Signs some are Naturall, whereof I have already given an example; others are Arbitrary, namely, those we make choice of at our own pleasure; as a bush hung up, signifies that Wine is to be sold there; a stone set in the ground, signifies the bound of a field; and words so and so con∣nected, signifie the Cogitations and Motions of our Minde. The difference therefore betwixt Markes and Signes is this, that we make those for our own use, but these for the use of others.

3 Words so connected, as that they become signes of our Thoughts, are called SPEECH, of which every part is a Name. But seeing (as is said) both Markes and Signes are necessary for the acquiring of Philosophy, (Marks by which we may remember our own thoughts, and Signes by which we may make our thoughts known to others,) Names do both these offices; but they serve for Marks before they be used as Signes. For though a man were alone in the world, they would be usefull to him in helping him to remember; but to teach others, (unlesse there were some others to be taught,) of no use at all. Again, Names▪ though standing singly by themselves, are Marks, because they serve to recall our own thoughts to mind; but they cannot be Signes, otherwise then by being disposed and ordered in Speech,

as parts of the same. For example, a man may begin with a word, whereby the hearer may frame an Idea of some∣thing in his mind, which neverthelesse he cannot conceive to be the Idea which was in the mind of him that spake, but that he would say something which began with that word, though per∣haps not as by it selfe, but as part of another word. So that the nature of a name consists principally in this, that it is a Mark ta ken for Memories sake; but it serves also by accident, to signifie and make known to others what we remember our selves; and therefore I will define it thus:

4 A NAME is a Word taken at pleasure to serve for a Mark, which may raise in our Mind a thought like to some thought we had before, and which be∣ing pronounced to others, may be to them a Sign of what thought the speaker had or had not before in his mind. And it is for brevities sake that I suppose the Originall of Names to be Arbitrary, judging it a thing that maybe assumed as unquestionable. For cōsidering that new Names are daily made, and old ones laid aside; that diverse Nations use different Names, and how impossible it is either to observe simi∣litude, or make any comparison betwixt a Name and a Thing, how can any man imagine that the Names of Things were imposed from their natures? For though some Names of living creatures and other things, which our first Parents used, were taught by God himselfe; yet they were by him arbitrarily imposed, and af∣terwards both at the Tower of Babel, and since in processe of time, growing every where out of use, are quite forgotten, and in their roomes have succeeded others, invented and received by men at pleasure. Moreover, whatsoever the common use of words be, yet Philosophers, who were to teach their knowledge to o∣thers, had alwayes the liberty, and sometimes they both had and will have a necessity, of taking to themselves such Names as they please for the signifying of their meaning, if they would have it understood. Nor had Mathematicians need to aske leave of any but themselves to name the figures they invented Parabolas, Hyper∣boles, Cissoeides, Quadratrices, &c. or to call one Magnitude A, ano∣ther B.

5 But seeing Names ordered in speech (as is defined) are signes of our Conceptions, it is manifest they are not signes of the Things themselves; for that the sound of this word Stone should be the

signe of a Stone, cannot be understood in any sense but this, that he that heares it, collects that he that pronouunces it thinkes of a Stone. And therefore that disputation, whether Names signifie the Matter or Form, or something compounded of both, and o∣ther like subtleties of the Metaphysicks, is kept up by erring men, and such as understand not the words they dispute about.

6 Nor indeed is it at all necessary that every Name should be the Name of some Thing. For as these, a Man, a Tree, a Stone, are the Names of the Things themselves; so the Images of a Man, of a Tree and of a stone, which are represented to men sleeping, have their Names also, though they be not Things, but onely fictions and Phantasmes of things. For we can remember these; and therefore it is no lesse necessary that they have Names to mark and signifie them, then the Things themselves. Also this word Future is a Name, but no future thing has yet any being, nor do we know whether that which we call Future, shall ever have a being or no. Never∣thelesse, seeing we use in our mind to knit together things Past with those that are Present, the Name Future serves to signifie such knitting together. Moreover, that which neither is, nor has been, nor ever shall or ever can be, has a name, namely, That which nei∣ther is, nor has been, &c. Or more briefly this, Impossible. To con∣clude, this word Nothing, is a name, which yet cannot be the name of any thing. For when (for example) we substract 2 and 3 from 5, and so nothing remaining we would call that substraction to mind, this speech Nothing remains, and in it the word Nothing is not unusefull. And for the same reason we say truly Lesse then Nothing remaines, when we substract More from Lesse; for the minde feigns such remaines as these for Doctrines sake, and desires as often as is necessary, to call the same to memory. But seeing every name has some relation to that which is named, though that which we name be not alwaies a thing that has a being in Nature, yet it is lawfull for Doctrines sake to apply the word Thing, to whasoever we name; as if it were all one whether that thing be truly existent or be onely feigned.

7 The first distinction of Names, is that some are Positive, or Affirmative; others Negative, which are also called Privative and Indefinite▪ Positive are such as we impose for the likenesse, Equa∣lity

or Identity of the things we consider; Negative for the diver∣sity, Unliknesse, or Inequality of the same. Examples of the for∣mer are a Man, a Philosopher; for a Man denotes any one of a mul∣titude of men, and a Philosopher any one of many Philosophers by reason of their similitude; Also Socrates is a Positive name, because it signifies alwayes one and the same man. Examples of Negatives are such Positives as have the Negative particle Not added to them, as Not-Man, Not-Philosopher. But Positives were before Ne∣gatives; for otherwise there could have been no use at all of these. For when the name of White was imposed upon certain things, and afterwards upon other things the names of Black, Blew, Transparent, &c. the infinite dissimilitudes of these with White could not be comprehended in any one Name, save that which had in it the Negation of White, that is to say, the Name Not-White, or some o∣ther equivalent to it, in which the word White is repeated, such as Unlike to white, &c. And by these Negative▪names, we take notice our selves, and signifie to others what we have not thought of.

8 Positive and Negative names are Contradictory to one another, so that they cannot both be the name of the same thing. Besides, of Contradictory names, one is the name of any thing whatsoever; for whatsoever is, is either Man or Not-man, White or Not∣white, and so of the rest. And this is so manifest, that it needs no further proofe or explication; for they that say the same thing cannot both be, and not be, speak obscurely; but they that say, Whatsoever is, either is, or is not, speake also absurdly and ridiculously. The cer∣tainty of this Axiome, viz. Of two Contradictory Names, one is the Name of any thing whatsoever, the other not, is the originall and foundation of all Ratiocination, that is, of all Philosophy; and therefore it ought to be so exactly propounded, that it may be of it selfe cleare and perspicuous to all men; as indeed it is, saving to such, as reading the long discourses made upon this subject by the Writers of Meta∣physicks (which they beleeve to be some egregious learning) thinke they understand not, when they do.

9 Secondly, of Names, some are Common to many things, as a Man, a Tree; others Proper to one thing, as he that writ the Iliad, Homer, this man, that man. And a Common name, being the name of many things severally taken, but not collectively of all together (as Man

is not the name of all mankind, but of every one, as of Peter, Iohn, and the rest severally) is therefore called an Universall name; and therefore this word Universall is never the name of any thing exi∣stent in nature, nor of any Idea or Phantasme formed in the mind, but alwayes the name of some word or name; so that when a Li∣ving creature, a Stone, a Spirit, or any other thing is said to be Universal, it is not to be understood, that any Man, Stone, &c. ever was or can be Universall, but onely that these words, Living creature, Stone, &c. are Universall names, that is, Names common to many things; and the Conceptions answering them in our minde, are the Images and Phantasmes of severall Living Creatures, or other things. And therfore for the understanding of the extent of an Universal name, we need no other faculty but that of our imagination, by which we remember that such names bring sometimes one thing, some∣times another into our minde. Also of Common Names some are more, some lesse Common. More Common, is that which is the name of more things; Lesse Common, the name of fewer things. As Living-Creature is more Common then Man, or Horse or Lion, because it comprehends them all; and therefore a more Common name, in respect of a lesse Common, is called the Genus or a Generall name; and this in respect of that, the Species, or a Speciall Name.

10 And from hence proceeds the third distinction of Names, which is, that some are called names of the First, others of the Se∣cond Intention. Of the first Intention are the names of Things, a Man, Stone, &c. of the second are the names of names and speeches, as U∣niversall, Particular, Genus, Species, Syllogisme, and the like. But it is hard to say why those are called names of the First, and these of the Second Intention, unlesse perhaps it was first intended by us to give names to those things which are of daily use in this life, and after∣wards to such things as appertaine to science, that is, that our Se∣cond Intention was to give names to Names. But whatsoever the cause hereof may be, yet this is manifest, that Genus, Species, Defi∣nition, &c. are names of Words and Names onely; and therefore to put Genus and Species for Things, and Definition for the nature of any thing, as the Writers of Metaphysicks have done, is not right, seeing they be only significations of what we thinke of the nature of Things.

11 Fourthly, some Names are of certaine▪ and determined, others

of uncertaine and undetermined signification. Of determined and certain signification is, first, that name which is giuen to any one thing by it self, and is called an Individuall Name; as Homer, this tree, that living Creature, &c. Secondly that which has any of these words All, Eve∣ry, Both, Either, or the like added to it; and it is therefore called an Universall Name, because it signifies every one of those things to which it is Common; and of certaine signification for this reason, that he which heares, conceives in his minde the same thing that he which speakes would have him conceive. Of Indefinite signifi∣cation is, first, that Name which has the word some, or the like added to it, and is called a Particular name; Secondly a Common Name set by it selfe without any note either of Universality or Particularity, as Man, Stone, and is called an Indefinite Name; but both Particular and Indefinite names are of uncertaine signification, because the Hearer knowes not what thing it is the Speaker would have him conceive; and therefore in Speech, Particular and Inde∣finite names are to be esteemed equivalent to one another. But these words, All, Every, Some, &c. which denote Universality and Par∣ticularity, are not Names, but parts onely of Names; So that Every Man, and That Man which the Hearer conceives in his mind, are all one; and Some Man, and That Man which the Speaker thought of signifie the same. From whence it is evident, that the use of signes of this kind, is not for a mans own sake, or for his getting of know∣ledge by his own private meditation (for every man has his own, Thoughts sufficiently determined without such helpes as these) but for the sake of others; that is, for the teaching and signifying of our Conceptions to others; nor were they invented onely to make us remember, but to make us able to discourse with others.

12 Fifthly, Names are usually distinguished into Univocall, and Equivocall. Univocall are those which in the same train of Dis∣course signifie alwayes the same thing; but Equivocall those which meane sometimes one thing, and sometimes another. Thus, the Name Triangle is said to be Univocall, because it is alwayes taken in the same sense; and Parabola to be Equivocall, for the significati∣on it has sometimes of Allegory or Similitude, and sometimes of a certaine Geometricall figure. Also every Metaphor is by profes∣sion Equivocall. But this distinction belongs not so much to Names, as to those that use Names; for some use them properly and accu∣rately

for the finding out of truth; others draw them from their proper sense, for Ornament, or Deceipt.

13 Sixtly, of Names, some are Absolute, others Relative. Relative are such as are imposed for some Comparison, as Father, Sonne, Cause, Effect, Like, Unlike, Equal, Unequal, Master, Servant, &c. And those that signifie no Comparison at all are Absolute Names. But as it was noted above, that Universality is to be attributed to Words & Names onely, and not to Things; so the same is to be said of other distinctions of Names; for no Things are either Univocall or Equivo∣call, or Relative or Absolute. There is also another distinction of Names into Concrete and Abstract; but because Abstract Names proceed from Proposition, and can have no place where there is no Affirmation, I shall speake of them hereafter.

14 Lastly there are Simple and Compounded Names. But here it is to be noted, that a name is not taken in Philosophy, as in Grammar, for one single word, but for any number of words put together to signifie one Thing; for among Philosophers Sentient Animated Body, passes but for one Name, being the Name of every living Crea∣ture; which yet, among Grāmarians is accounted three Names. Al∣so a Simple Name is not here distinguished from a Compounded Name by a Preposition, as in Grammar. But I call a Simple Name, that which in every kind is the most Common or most Universall; and that a Compounded Name, which by the joyning of another Name to it is made lesse Universall, and signifies that more conceptions then one were in the mind, for which that later Name was added. For example, in the conception of Man (as is shewn in the former Chap.) First, he is conceived to be something that has Extension, which is marked by the word Body. Body therefore is a Simple Name, being put for that first single Conception; Afterwards, upon the sight of such and such motion, another Conception arises for which he is called an Animated Body; and this I here call a Com∣pounded Name, as I doe also the name Animal, which is equivalent to an Animated Body. And in the same manner an Animated Rational Body, as also a Man, which is equivalent to it, is a more Compoun∣ded Name. And by this we see how the Composition of Concep∣tions in the mind is answerable to the Composition of Names; for as in the minde one Idea or Phantasme succeeds to another, and to this a third; so to one Name is added another and another succes∣sively,

and of them all is made one Compounded Name. Neverthe∣lesse we must not thinke Bodies, which are without the Minde, are compounded in the same manner, namely that there is in Nature a Body, or any other imaginable Thing existent, which at the first has no Magnitude, and then by the addition of Magnitude, comes to have Quantity, and by more or lesse Quantity to have Density or Rarity, and again by the addition of Figure to be Figurate, and af∣ter this by the injection of Light or Colour, to become Lucid or Coloured; though such has been the Philosophy of many.

15 The Writers of Logique have endeavoured to digest the Names of all the kinds of Things into certaine Scales or Degrees, by the continual subordination of Names lesse Common, to Names more Common. In the Scale of Bodies they put in the first and highest place Body simply, and in the next place under it lesse Com∣mon Names, by which it may be more limited and determined, namely Animated and Inanimated, and so on till they come to Indi∣vidualls. In like manner in the Scale of Quantities they assign the first place to Quantity, and the next to Line, Superficies, and Solid, which are Names of lesse latitude; and these Orders or Scales of Names they usually call Praedicaments and Categories; And of this Ordination not onely Positive but Negative Names also are capable; which may be exemplified by such Formes of the Praedicaments as follow.

The Form of the Praedicament of Body.

• Not-Body; or Accident
• Body
  • Not animated
  • Animated
    • Not Living-Creature
    • Living-Creature
      • Not Man
      • Man
        • Not Peter
        • Peter
• Both Accident and Body are considered
  • Absolutely as,
    • Quantity, or so much
    • Quality, or such
  • or Comparatively, which is called their Relation

The Forme of the Praedicament of Quantity.

• Quātity
  • Not Continual, as Number,
  • Continuall
    • Of it selfe, as
      • Line
      • Superficies
      • Solid
    • By Accident, as—
      • Time, by Line
      • Motion, by Line and Time
      • Force, by Motion and Solid

Where it is to be noted, that Line, Superficies and Solid may be said to be of such and such Quantity, that is, to be originally and of their own nature capable of Equality and Inequality; But we cannot say there is either Majority or Minority, or Equality, or indeed any Quantity at all, in Time, without the help of Line and Motion; nor in Motion, without Line and Time; nor in Force, other∣wise then by Motion and Solid.

The Forme of the Praedicament of Quality.

• Quality
  • Perceptiō by Sense
    • Primary
      • Seeing
      • Hearing
      • Smelling
      • Tasting
      • Touching
    • Secondary
      • Imagination
      • Affection—
        • Pleasant
        • Unpleasant
  • Sensible Quality
    • By Seeing, as Light and Colour
    • By Hearing, as Sound
    • By Smelling, as Odors
    • By Tasting, as Savours
    • By Touching, as Hardnesse, Heat, Cold, &c.

The forme of the Praedicament of Relation.

• Relation of
  • Magnitudes, as Equality and Inequality
  • Qualities, as Likenesse and Unlikenesse
  • Order
    • Together
      • In Place
      • In Time
    • Not toge∣ther
      • In Place
        • Former
        • Later
      • In Time
        • Former
        • Later

16 Concerning which Praedicaments it is to be noted in the first place, That as the division is made in the first Praedicament into Contradictory Names, so it might have been done in the rest. For as there, Body is divided into Animated and Not-Animated, so in the second Praedicament Continuall Quantity may be divi∣ded into Line and Not-line, and again, Not-line into Superficies and Not-Superficies, and so in the rest; but it was not necessary.

Secondly, it is to be observed, that of Positive Names the former comprehends the later; but of Negatives the former is compre∣hended by the later. For example Living-Creature is the Name of every Man, and therefore it comprehends the Name Man; but on the contrary Not-Man is the Name of every Thing which is Not-Living-Creature, and therefore the Name Not-Living-Crea∣ture which is put first, is comprehended by the later Name Not-Man.

Thirdly, we must take heed we do not thinke, that as Names, so the diversities of Things themselves may be searched out and determined by such Distinctions as these; or that arguments may be taken from hence (as some have done ridiculously) to prove that the kinds of Things are not infinite.

Fourthly, I would not have any man thinke I deliver the Forms above for a true and exact Ordination of Names; for this cannot be performed as long as Philosophy remains imperfect; Nor that by placing (for example) Light in the Praedicament of Quali∣ties, while another places the same in the Praedicament of Bo∣dies, I pretend that either of us ought for this to be drawn

from his opinion; for this is to be done onely by Arguments and Ratiocination, and not by disposing of words into Classes.

Lastly, I confesse I have not yet seen any great use of the Praedicaments in Philosophy. I beleeve Aristotle when he saw he could not digest the Things themselves into such Orders, might neverthelesse desire out of his owne Authority to reduce Words to such Formes, as I have done; but I doe it onely for this end, that it may be understood what this Ordination of Words is, and not to have it received or true, till it be de∣monstrated by good reason to be so.

CHAP. III. Of Proposition.

• 1 Divers Kinds of Speech.
• 2 Proposition defined.
• 3 Subject, Praedicate and Copula what they are, and Abstract and Concrete what. The Use and Abuse of Names Abstract.
• 5 Proposition Universal and Particular.
• 6 Affir∣mative and Negative.
• 7 True and False.
• 8 True and False belongs to Speech, and not to Things.
• 9 Proposition Primary, not Primary, Defini∣on, Axiome, Petition.
• 10 Proposition Necessary and Contingent.
• 11 Ca∣tegoricall and Hypotheticall.
• 12 The same Proposition diversly pronoun∣ced.
• 13 Propositions that may be reduced to the same Categoricall Propo∣sition, are Equipollent.
• 14 Universal Propositions converted by Contradi∣ctory Names, are Equipollent.
• 15 Negative Propositions are the same, whether the Negation be before or after the Copula.
• 16 Particular Pro∣positions simply converted, are Equipollent.
• 17 What are Subaltern, Contrary, Subcontrary and Contradictory Propositions.
• 18 Consequence what it is.
• 19 Falsity cannot follow from Truth.
• 20 How one Proposition is the Cause of another.

1FRom the Connection or Contexture of Names arise diverse kinds of Speech, whereof some signifie the Desires and Affections of Men; such are first Interroga∣tions, which denote the desire of Knowing; as Who is a good Man? In which speech there is one Name expressed, & another desired and expected from him of whom we aske the same. Then Prayers, which signifie the desire of having something; Promises, Threats, Wishes, Commands, Complaints, and other significations of other Affecti∣ons. Speech may also be Absurd and Insignificant; as when there is a succession of Words, to which there can be no succession of Thoughts in the mind to answer them; and this happens often to such, as understanding nothing in some subtil matter, doe never∣thelesse, to make others beleeve they understand, speake of the same

incoherently; For the connection of incoherent Words, though it want the end of Speech (which is Signification) yet it is Speech; and is used by the Writers of Metaphysicks almost as frequently as Speech significative. In Philosophy there is but one kinde of Speech usefull, which some call in Latine Dictum, others Enuntiatum & Pronunciatum; but most men call it Proposition, and is the speech of those that Affirm or Deny, and expresseth Truth or Falsity.

2 A PROPOSITION is a Speech consisting of two Names copulated by which he that speaketh signifies he conceives the later Name to be the Name of the same thing whereof the former is the Name; or (which is all one) that the for∣mer Name is comprehended by the later. For example, this speech Man is a Living Creature, in which two Names are copulated by the verb Is, is a Proposition, for this reason, that he that speakes it conceives both Living Creature and Man to be Names of the same thing, or that the former Name Man is comprehended by the later Name Living Creature. Now the former Name is commonly called the Subject, or Antecedent, or the Contained Name, and the later the Prae∣dicat, Consequent or Containing Name. The signe of Connection a∣mongst most Nations is either some word, as the word is in the Proposition Man is a living Creature, or some Case or Termination of a word, as in this Proposition, Man walketh (which is equiva∣lent to this, Man is walking) the Termination by which it is said he walketh, rather then he is walking, signifieth that those two are understood to be copulated, or to be Names of the same Thing.

But there are, or certainly may be some Nations that have no word which answers to our Verbe Is, who neverthelesse forme Propositions by the position onely of one Name after another, as if instead of Man is a Living Creature, it should be said Man a Living Creature; for the very order of the Names may sufficiently shew their connection; and they are as apt and usefull in Philosophy, as if they were copulated by the Verbe Is.

3 Wherefore in every Proposition three things are to be con∣sidered, viz. the two Names, which are the Subject and the Prae∣dicate, and their Copulation; both which Names raise in our Minde the Thought of one and the same Thing; but the Copulation makes us thinke of the Cause for which those Names were im∣posed on that Thing. As for example, when we say a Body is mo∣veable, though we conceive the same thing to be designed by both

those Names, yet our Minde rests not there, but searches fur∣ther what it is to be a Body, or to be Moveable, that is, wherein con∣sists the difference betwixt these and other Things, for which these are so called, others are not so called. They therefore that seeke what it is to be any thing, as to be Moveable, to be Hot, &c. seek in Things the causes of their Names.

And from hence arises that distinction of Names (touched in the last Chap.) into Concrete and Abstract. For Concrete is the Name of any thing which we suppose to have a being, and is therefore called the Subject, in Latine Suppositum, and in Greek 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉; as Body, Moveable, Moved, Figurate, a Cubit high, Hot, Cold, Like, Equal, Appius, Lentulus and the like; and Abstract is that which in any Subject denotes the Cause of the Concrete Name, as to be a Body, to be Moveable, to be Moved, to be Figurate, to be of such Quantity, to be Hot, to be Cold, to be Like, to be Equall, to be Appius, to be Lentulus, &c. Or Names equivalent to these, which are most commonly called Abstract Names, as Corporeity, Mobility, Motion, Figure, Quantity, Heat, Cold, Likenesse, Equality, and (as Cicero has it) Appiety and Lentulity. Of the same kind also are Infinitives; for to Live and to Move are the same with Life and Motion, or to be Living, and to be Moved. But Abstract Names denote onely the Causes of Concrete Names, and not the Things themselves. For example when we see any thing, or conceive in our Minde any Visible thing, that Thing appears to us, or is conceived by us, not in one Point, but as having Parts distant from one another, that is, as being extended and filling some space. Seeing therefore we call the Thing so conceived Body, the cause of that name is, that that Thing is extended, or the Extension or Corporeity of it. So when we see a Thing appeare sometimes here, sometimes there, and call it Moved or Removed, the Cause of that Name is that it is Moved or the Motion of the same.

And these Causes of Names; are the same with the Causes of our Conceptions, namely some Power or Action, or Affection of the Thing conceived, which some call the Manner by which any thing workes upon our senses, but by most men they are called Accidents; I say Accidents, not in that sense in which Acci∣dent is opposed to Necessary; but so, as being neither the Things themselves, nor parts thereof, do neverthelesse accompany the

Things in such manner, that (saving Extension) they may all perish and 〈◊〉〈◊〉 destroyed, but can never be abstracted.

4 There is also this difference betwixt Concrete and Abstract Names, that those were invented before Propositions, but these after; for these could have no being till there were Propositi∣ons, from whose Copula they proceed. Now in all matters that concerne this life, but chiefly in Philosophy, there is both great Use and great Abuse of Abstract Names; and the use consists in this, that without them we cannot for the most part either Rea∣son, or compute the Properties of Bodies; for when we would multiply, divide, adde or substract Heat, Light, or Motion, if we should double or adde them together by Concrete Names, saying (for example) Hot is double to Hot, Light double to Light, or Moved double to Moved, we should not double the Properties, but the Bodies themselves that are Hot, Light, Moved, &c. which we would not doe. But the Abuse proceeds from this, that some men seeing they can consider, that is (as I said before) bring into account the Increasings and Decreasings of Quantity, Heat and other Accidents, without considering their Bodies or Subjects (which they call Abstracting, or making to exist apart by themselves,) they speake of Accidents, as if they might be sepa∣rated from all Bodies. And from hence proceed the grosse errors of writers of Metaphysicks; for, because they can consider Thought without the consideration of Body, they inferre there is no need of a ••••inking-Body; and because Quantity may be considered without considering Body, they thinke also that Quantity may be without Body, and Body without Quantity; and that a Bo∣dy ••as Quantity by the addition of Quantity to it. From the same fountaine spring those insignificant words, Abstract Substance, Separated Essence and the like; as also that confusion of words deri∣ved from the Latine Verb Est, as Essence, Essentiality, Entity, Entitative; besides Reality, Aliquiddity, Quiddity, &c. which could never have been heard of among such Nations as do not Copulate their Names by the Verbe Is, but by Adjective Verbs, as Runneth, Rea∣deth, &c. or by the mere placing of one Name after another; and yet seeing such Nations Compute and Reason, it is evident that Philosophy has no need of those words Essence, Entity and other the like barbarous Termes.

There are many Distinctions of Propositions, whereof the first is, that some are Universall, others Particular, others Indefinite, and others Singular; and this is commonly called the distinction of Quantity. An Universall Proposition is that whose subject is affected with the sign of an Universall Name, as Every man is a Living Crea∣ture. Particular, that whose subject is affected with the sign of a Particular Name, as Some Man is learned. An Indefinite Proposition has for its Subject a Common Name, and put without any sing; as Man is a Living Creature, Man is Learned. And a Singular Propositi∣on is that whose Subject is a singular Name, as Socrates is a Philoso∣pher, This man is black.

6 The Second Distinction is into Affirmative and Negative, and is called the Distinction of Quality. An Affirmative Proposition is that whose Praedicate is a Positive Name, as Man is a Living Creature. Negative, that whose Praedicate is a Negative Name, as Man is Not-a-stone.

7 The third Distinction is, that one is True, another False. A True Proposition is that, whose Praedicate containes, or compre∣hends its Subject, or whose Praedicate is the Name of every thing, of which the Subject is the Name; as Man is a Living Crea∣ture is therefore a True Proposition, because whatsoever is called Man, the same is also called Living Creature; and Some Man is sick, is True, because sick is the Name of Some Man. That which is not True, or that whose Praedicate does not containe its Subject, is called a False Proposition, as Man is a Stone.

Now these words True, Truth, and True Proposition are equiva∣lent to one another; For Truth consists in Speech, and not in the Things spoken of; and though True be sometimes opposed to to Apparent or Feigned, yet it is alwayes to be referred to the Truth of Proposition; for the Image of a Man in a Glasse, or a Ghost, is therefore denyed to be a very Man, because this Pro∣position, A Ghost is a man, is not True; for it cannot be denied but that a Ghost is a very Ghost. And therefore Truth or Verity is not any Affection of the Thing, but of the Proposition concern∣ing it. As for that which the Writers of Metaphysicks say, that A thing, One thing, and a Very thing, are equivalent to one a∣nother, it is but trifling and childish; for who does not know, that A Man, One Man, and a Very Man, signifie the same.

8 And from hence it is evident, that Truth and Falsity have no place but amongst such Living Creatures as use Speech. For though some brute Creatures, looking upon the Image of a Man in a Glasse, may be affected with it as if it were the Man him∣selfe, and for this reason feare it or fawne upon it in vain; Yet they doe not apprehend it as True or False, but onely as Like; and in this they are not deceived. Wherefore, as men owe all their True Ratiocination to the right understanding of Speech; So also they owe their Errors to the misunderstanding of the same; and as all the Ornaments of Philosophy proceed onely from Man, so from Man also is derived the ugly absurdity of False opinions. For Speech has something in it like to a Spiders Web (as it was said of old of Solons laws;) for by contexture of words tender and delicate Wits are insnared and stopt; but strong Wits breake easily through them.

From hence also this may be deduced, that the first Truths were arbitrarily made by those that first of all imposed Names upon Things, or received them from the imposition of others. For it is true (for example) that Man is a Living Creature; but it is for this reason, that it pleased men to impose both those Names on the same thing.

9 Fourthly, Propositions are distinguished into Primary and not Primary. Primary is that wherein the Subject is explicated by a Praedicate of many Names, as Man, is a Body Animated Rationall; for that which is comprehended in the Name Man is more largely expressed in the Names Body, Animated, and Rationall joyned toge∣ther; and it is called Primary, because it is first in Ratiocination; for nothing can be proved, without understanding first the name of the Thing in question. Now Primary Propositions are nothing but Definitions, or parts of Definitions, and these onely are the prin∣ciples of Demonstration, being Truths constituted arbitrarily by the Inventors of Speech, and therefore not to be demonstrated. To these Propositions, some have added others, which they call Primary and Principles; namely Axiomes and Common Notions; which (though they be so evident that they need no proofe, yet) because they may be proved, are not truly Principles; & the lesse to be re∣ceived for such, in regard Propositions not intelligible, and some∣times manifestly false, are thrust on us under the Name of Principles

by the clamour of Men, who obtrude for evident to others all that they themselves thinke True. Also certaine Petitions are common∣ly received into the number of Principles; as for example, That a streight line may be drawne between two points, and other Petitions of the Writers of Geometry; and these are indeed the Principles of Art or Construction, but not of Science and Demonstration.

10 Fiftly, Propositions are distinguished into Necessary, that is, necessarily True; and True, but not necessarily, which they call Contingent. A Necessary Proposition is when nothing can at any time be conceived or feigned, whereof the Subject is the Name, but the Praedicate also is the Name of the same thing; as Man is a Living-Creature is a necessary Proposition, because at what time soever we suppose the name Man agrees with any thing, at that time the name Living-Creature also agrees with the same. But a Contin∣gent Proposition is that which at one time may be true, at another time false; as Every Crow is Black; which may perhaps be true now, but false hereafter. Again, in every Necessary Proposition, the Praedicate is either equivalent to the Subject, as in this, Man is a Rational Living-Creature; or part of an equivalent Name, as in this, Man is a Living-Creature, for the Name Rational Living-Creature, or Man, is compounded of these two, Rational and Living-Creature. But in a Contingent Proposition this cannot be; for though this were true, Every Man is a Lyar, yet because the word Lyar is no part of a Compounded name equivalent to the Name Man, that Proposi∣tion is not to be called Necessary, but Contingent, though it should happen to be true alwayes. And therefore those Propositions on∣ly are Necessary, which are of Sempiternal Truth, that is, true at all times. From hence also it is manifest, that Truth adheres not to Things, but to Speech onely; for some Truths are eternal; for it will be eternally true, if Man, then Living-Creature; but that any Man, or Living-Creature should exist eternally, is not necessary.

11 A sixth Distinction of Propositions is into Categorical and Hy∣potheticall. A Categoricall Proposition is that which is simply or abso∣lutely pronounced, as Every Man is a Living Creature, No Man is a Tree; and Hypotheticall is that which is pronounced conditionally, as, If any thing be a Man the same is also a Living Creature, If any thing be a Man the same is also Not-a-stone.

A Categoricall Proposition, and an Hypothetical answering it, doe

both signifie the same, if the Propositions be Necessary; but not if they be Contingent. For example, if this, Every Man is a Living-Creature, be true, this also will be true, If any thing be a Man, the same is also a Living-Creature; but in Contingent Propositions, though this be true, Every Crow is Black; yet this, If any thing be a Crow the same is Black, is false. But an Hypotheticall Proposition is then rightly said to be true, when the Consequence is true; as Every Man is a Living-Creature is rightly said to be a true Proposition, because of whatsoever it is truly said That is a Man, it cannot but be truly said also The same is a Living-Creature. And therefore whensoever an Hy∣potheticall Proposition is true, the Categoricall answering it is not only true, but also necessary; which I thought worth the noting, as an argument, that Philosophers may in most things reason more so∣lidly by Hypotheticall then Categoricall Propositions.

12 But seeing every Proposition may be & uses to be pronounced and written in many formes, and we are obliged to speake in the same manner as most men speake; yet they that learne Philoso∣phy from Masters, had need to take heed they be not deceived by the Variety of expressions. And therefore whensoever they meet with any obscure Proposition, they ought to reduce it to its most Simple and Categoricall forme; in which the Copulative word Is must be expressed by it selfe, and not mingled in any manner either with the Subject or Praedicate, both which must be separa∣ted and cleerly distinguished one from another. For example, if this Proposition Man can not sinne, be compared with this, Man can∣not sinne, their difference will easily appeare if they be reduced to these, Man is able not to sinne, and Man is not able to sinne, where the Praedicates are manifestly different. But they ought to doe this si∣lently by themselves, or betwixt them and their Masters onely; for it will be thought both ridiculous and absurd, for a man to use such language publiquely. Being therefore to speake of Equipollent Propositions, I put in the first place all those for Equipollent, that may be reduced p••rely to one and the same Categoricall Proposition.

13 Secondly, that which is Categoricall and Necessary, is E∣quipollent to its Hypotheticall Proposition; as this Categorical, A Right-lined Triangle has its three Angles equal to two Right angles, to this Hypotheticall, If any Figure be a Right-lined Triangle, the three Angles of it are equal to two Right Angles.

14 Also, any two Universall Propositions, of which the Termes of the one (that is, the Subject and Praedicate) are Con∣tradictory to the Termes of the other, and their Order inverted, as these, Every man is a Living Creature, and Every thing that is not a Living Creature, is not a Man, are Equipollent. For seeing Every Man is a Living Creature is a true Proposition, the Name Living Creature containes the Name Man; but they are both Positive Names; and therefore (by the last Article of the praecedent Chapter) the Negative Name Not Living Creature containes the Negative Name Not Man; Wherefore Everything that is not a Living Creature is not a Man is a true Proposition. Likewise these, No Man is a Tree, No Tree is a Man, are Equipollent. For if it be true that Tree is not the Name of any Man, then no one thing can be signified by the two Names Man and Tree, wherefore No Tree is a Man is a true Proposition. Also to this, Whatsoever is not a Living Creature is not a Man, where both the Termes are Negative, this other Proposi∣tion is Equipollent, Onely a Living Creature is a Man.

15 Fourthly, Negative Propositions, whether the particle of Negation be set after the Copula as some Nations doe, or before it, as it is in Latine and Greeke, if the Termes be the same, are equipollent; as for example, Man is not-a-Tree and Man is not-a-Tree, are equipollent, though Aristotle deny it. Also these, Every Man is not a Tree, and No Man is a Tree are equipollent, and that so mani∣festly, as it needs not be demonstrated.

16 Lastly, all Particular Propositions that have their Termes inverted, as these, Some Man is Blind, Some Blind thing is a Man, are equipollent; for either of the two Names, is the Name of some one and the same Man; and therefore in which soever of the two Or∣ders they be connected, they signifie the same Truth.

17 Of Propositions that have the same Termes, and are pla∣ced in the same Order, but varied either by Quantity or Quali∣ty, some are called Subaltern, others Contrary, others Subcontrary, and others Contradictory.

Subaltern, are Universal and Particular Propositions of the same Quality; as, Every Man is a Living Creature, Some Man is a Living Creature; or, No Man is Wise, Some Man is not Wise. Of these i•• the Universal be true, the Particular will be true also.

Contrary, are Universal Propositions of different Quality; as

Every Man is happy, No Man is happy. And of these if one be true the other is false; also they may both be false, as in the example given.

Subcontrary, are Particular Propositions of different Quality; as Some Man is learned, Some Man is not learned; which cannot be both false, but they may be both true.

Contradictory are those that differ both in Quantity and Quality; as Every Man is a Living Creature, Some Man is not a Living Creature; which can neither be both true, nor both false.

18 A Proposition is said to follow from two other Propositions, when these being granted to be true, it cannot be denyed but the other is true also. For example, let these two Propositions, Every Man is a Living Creature, and Every Living Creature is a Body, be sup∣posed true, that is, that Body is the Name of Every Living Crea∣ture, and Living Creature, the Name of Every Man. Seeing therefore, if these be understood to be true, it cannot be understood that Body is not the name of Every man, that is, that Every Man is a Body, is false, this Proposition will be said to follow from those two, or to be necessarily inferred from them.

19 That a true Proposition may follow from false Propositions, may happen sometimes; but false from true, never. For if these, Every Man is a Stone, and Every Stone is a Living Creature, (which are both false) be granted to be true, it is granted also that Living Crea∣ture is the name of Every Stone, and Stone of Every Man, that is, that Living Creature is the Name of Every Man; that is to say, this Pro∣position Every Man is a Living Creature, is true, as it is indeed true. Wherefore a true Proposition may sometimes follow from false. But if any two Propositions be true, a false one can never follow from them. For if true follow from false, for this reason onely, that the false are granted to be true, then truth from two truths granted will follow in the same manner.

20 Now seeing none but a true Proposition will follow from true, and that the understanding of two Propositions to be true, is the cause of understanding that also to be true which is deduced from them; the two Antecedent Propositions are commonly called the Causes of the inferred Proposition, or Conclusion. And from hence it is that Logicians say, the Premisses are Causes of the Con∣clusion; which may passe, though it be not properly spoken; for

though Understanding be the cause of Understanding, yet Speech is not the cause of Speech. But when they say, the Cause of the Properties of any thing, is the Thing it self, they speake absurd∣ly. Eor example, if a Figure be propounded which is Triangu∣lar; Seeing every Triangle has all its angles together equal to two right angles, from whence it follows that all the angles of that Figure are equal to two right angles, they say for this reason, that that Figure is the Cause of that Equality. But seeing the Fi∣gure does not it self make its angles, and therefore cannot be said to be the Efficient-Cause, they call it the Formall-Cause; whereas in deed it is no Cause at all; nor does the Property of any Figure fol∣low the Figure, but has its Being at the same time with it; only the Knowledge of the Figure goes before the Knowledge of the Properties; and one Knowledge is truly the Cause of another Knowledge, namely the Efficient-Cause.

And thus much concerning Proposition; which in the Progress of Philosophy is the first Step, like the moving towards of one Foot. By the due addition of another Step I shall proceed to Syllo∣gisme, and make a compleat Pace. Of which in the next Chapter.

CHAP. IV. Of Syllogisme.

• 1 The Definition of Syllogisme.
• 2 In a Syllogisme there are but three Termes.
• 3 Major, Minor and Middle Term; also Major and Mi∣nor Proposition, what they are.
• 4 The Middle Terme in every Syllogisme ought to be determined in both the Propositions to one and the same thing.
• 5 From two Particular Propositions nothing can be concluded.
• 6 A Syllo∣gisme is the Collection of two Propositions into one Summe.
• 7 The Figure of a Syllogisme what it is.
• 8 What is in the mind answering to a Syllogisme.
• 9 The first Indirect Figure how it is made.
• 10 The second Indirect Fi∣gure how made.
• 11 How the third Indirect Figure is made
• 12 There are many Moods in every Figure, but most of them Uselesse in Philosophy.
• 13 An Hypotheticall Syllogisme when equipollent to a Categoricall.

1. A Speech consisting of three Propositions, from two of which the third followes, is called a SYLLOGISME; and that which followes is called the Conclusion; the other two Premisses. For example this Speech, Every man is a Li∣ving Creature, Every Living Creature is a Body, therefore, Every Man is a Body, is a Syllogisme, because the third Proposition follows from the two first; that is, if those be granted to be true, this must also be granted to be true.

2 From two Propositions which have not one Terme common, no Conclusion can follow; and therefore no Syllogisme can be made of them. For let any two Premisses, A man is a Living Creature, A Tree is a Plant, be both of them true, yet because it cannot be col∣lected from them that Plant is the Name of a Man, or Man the Name of a Plant, it is not necessary that this Conclusion, A Man is a Plant should be true. Corollary, Therefore in the Premisses of a Syllogisme there can be but three Termes.

Besides there can be no Terme in the Conclusion, which was not in the Premisses. For let any two Premisses be, A Man is a Living Creature, A Living Creature is a Body, yet if any other Terme be put

in the Conclusion, as Man is two footed; though it be true, it cannot follow from the Premisses, because from them it cannot be col∣lected, that the Name Two footed belongs to a Man; and therefore againe, In every Syllogisme there can be but three Termes.

3 Of these Termes, that which is the Predicate in the Conclu∣sion, is commonly called the Major; that which is the Subject in the Conclusion, the Minor, and the other is the Middle Term; as in this Syllogisme, A Man is a Living Creature, A Living Creature is a Body, therefore, A Man is a Body, Body is the Major, Man the Minor and Living Creature the Middle Term. Also of the Premisses, that in which the Major Terme is found, is called the Major Proposition, and that which has the Minor Term the Minor Proposition.

4 If the Middle Terme be not in both the Premisses determi∣ned to one and the same singular thing, no Conclusion will follow, nor Syllogisme be made. For let the Minor Terme be Man, the Mid∣dle Terme Living Creature, and the Major Term Lyon; and let the Pre∣misses be Man is a Living Creature, Some Living Creature is a Lyon, yet it will not follow that, Every or Any Man is a Lyon. By which it is manifest, that in every Syllogisme, that Proposition which has the Middle Terme for its Subject, ought to be either Universal or Singular, but not Particular nor Indefinite. For example, this Syllogism, E∣very man is a Living Creature, some Living Creature is four-footed, there∣fore some Man is four-footed, is therefore faulty, because the Middle Term, Living Creature, is in the first of the Premisses determined onely to Man, for there the Name of Living Creature is given to Man onely, but in the later Premisse it may be understood of some other Living Creature besides Man. But if the later Premisse had been Universall, as here, Every Man is a Living Creature, Every Living Creature is a Body, therefore Every Man is a Body, the Syllogisme had been true; for it would have followed that Body had been the Name of Every Living Creature, that is of Man, that is to say, the Conclusion Every Man is a Body had been true. Like∣wise when the Middle Term is a Singular Name, a Syllogisme may be made, I say a true Syllogisme, though uselesse in Philosophy, as this, Some Man is Socrates, Socrates is a Philosopher, therefore Some Man is a Philosopher; for the Premisses being granted, the Conclu∣sion cannot be denyed.

5 And therefore of two Premisses, in both which the Middle

Terme is Particular, a Syllogisme cannot be made; for whether the Middle Terme be the Subject in both the Premisses, or the Predicate in both, or the Subject in one and the Predicate in the other, it will not be necessarily determined to the same thing. For let the Pre∣misses be,

• Some Man is blind
• Some Man is learned

In both which the Middle Term is the Subject,

It will not follow, that Blind is the Name of any learned Man, or Learned the Name of any Blind Man, seeing the Name Learned does not containe the Name Blind, nor this that; and therefore it is not necessary that both should be Names of the same Man. So from these Premisses.

• Every Man is a Living Creature
• Every Horse is a Living Creature

In both which the Middle Terme is the Predicate,

Nothing will follow. For seeing Living Creature is in both of them Indefinite, which is equivalent to Particular, and that Man may be one kind of Living Creature, and Horse another kind, it is not neces∣sary that Man should the be Name of Horse, or Horse of Man. Or if the Premisses be,

• Every Man is a Living Creature
• Some Living Creature is four-footed

In one of which the Middle Terme is the Subject, and in the other the Predicate,

The Conclusion will follow, because the Name Living Creature be∣ing not determined, it may in one of them be understood of Man in the other of Not-Man.

6 Now it is manifest from what has been said, that a Syllo∣gisme is nothing but a Collection of the summe of two Propositi∣ons, joyned together by a common Term, which is called the Middle Terme. And as Proposition is the Addition of two Names, so Syllogisme is the adding together of three.

7 Syllogismes are usually distinguished according to their di∣versity of Figures, that is, by the diverse position of the Middle Term. And againe in Figure there is a distinction of certain

Moods, which consist of the differences of Propositions in Quantity & Quality. The first Figure is that, in which the Terms are placed one after another according to their latitude of Signification; in which order the Minor Term is first, the Middle Term next, and the Major last; as if the Minor Term be Man, the Middle Term Living Creature and the Major Term Body, then, Man is a Living Crea∣ture, is a Body, will be a Syllogisme in the first Figure; in which, Man is a Living Creature, is the Minor Proposition; the Major, Li∣ving Creature is a Body, and the Conclusion or sum of both Man is a Body. Now this Figure is called Direct, because the Termes stand in direct Order; and it is varied by Quantity and Quality into four Moods; of which the first is that wherein all the Terms are Posi∣tive, and the Minor Term Universal, as Every Man is a Living Crea∣ture, Every Living Creature is a Body; in which all the Propositions are Affirmative and Universall. But if the Major Term be a Negative Name, and the Minor an Universall Name, the Figure will be in the second Mood, as, Every Man is a Living Creature, Every Living Creature is not a Tree, in which the Major Proposition and Conclu∣sion are both Universall and Negative. To these two are commonly addded two more, by making the Minor Term Particular. Also it may happen that both the Major and Middle Termes are Nega∣tive Terms, and then there arises another Mood, in which all the Propositions are Negative, and yet the Syllogisme will be good; as, if the Minor Term be Man, the Middle Term Not a Stone, and the Major Terme, Not a Flint, this Syllogisme, No Man is a Stone, Whatsoever is not a Stone is not a Flint, therefore No Man is a Flint, is true, though it consist of three Negatives. But in Philosophy, the Profession whereof is to establish Universall Rules concern∣ing the Properties of Things, seeing the difference betwixt Ne∣gatives and Affirmatives is onely this, that in the former the Sub∣ject is affirmed by a Negative Name, and by a Positive in the later, it is superfluous to consider any other Mood in direct Fi∣gure, besides that, in which all the Propositions are both Uni∣versal and Affirmative.

8. The Thoughts in the mind answering to a Direct Syllogism, proceed in this manner; First, there is conceived a Phantasme of the thing named, with that Accident or Quality thereof for which it is in the Minor Proposition called by that name which

is the Subject; next, the Mind has a Phantasme of the same thing with that Accident or Quality for which it hath the name that in the same Proposition is the Predicate; Thirdly, the Thought returns of the same thing as having that Accident in it, for which it is called by the Name that is in the Predicate of the Major Propo∣sition; and lastly, remembring that all those are the Accidents of one and the same thing, it concludes that those three Names are also Names of one and the same thing; that is to say, the Conclusion is true. For example, when this Syllogisme is made, Man is a Living Creature, A Living Creature is a Body, therefore Man is a Body, the Mind conceives first an image of a Man speaking or discoursing, and remembers that that which so appears, is called Man; then it has the image of the same Man moving, and remem∣bers that that which appeares so is called Living Creature; thirdly, it conceives an image of the same Man as filling some place or space, and remembers that what appeares so is called Body; and lastly, when it remembers, that that thing which was extended, and moved and spake, was one and the same thing, it concludes that the three Names Man, Living Creature, and Body, are Names of the same thing, and that therefore Man is a Living Creature is a true Proposition. From whence it is manifest, that Living Crea∣tures that have not the use of Speech, have no Conception or Thought in the Mind, answering to a Syllogisme made of Univer∣sall Propositions; seeing it is necessary to Thinke not only of the Thing, but also by turnes to remember the diverse Names, which for diverse considerations thereof are applied to the same.

9 The rest of the Figures arise either from the Inflexion, or Inversion of the first or direct Figure; which is done by changing the Major, or Minor, or both the Propositions into converted Pro∣positions aequipollent to them.

From whence follow three other Figures; of which, two are In∣flected, and the third Inverted. The first of these three is made by the Conversion of the Major Proposition. For let the Minor, Mid∣dle and Major Terms stand in direct order, thus, Man is a Living Creature, Is not a Stone, which is the first or direct Figure; the Infle∣xion will be by converting the Major Proposition in this manner,

Man is a Living Creature,

A stone is not a Living Creature; And this is the second

Figure, or the first of the Indirect Figures; in which the Con∣clusion will be, Man is not a stone. For (having shewn in the last Chap. 14 Article, that Universall Propositions converted by con∣tradiction of the Termes are aequipollent,) both those Syllo∣gismes conclude alike; so that if the Major be read (like Hebrew) backwards, thus, A Living Creature is not a Stone, it will be direct again, as it was before. In like manner this Direct Syllogisme, Man is not a Tree, is not a Pear-tree, will be made Indirect by convert∣ing the Major Proposition (by contradiction of the Termes) into another aequipollent to it, thus,

Man is not a Tree,

A Pear-tree is a Tree; for the same Conclusion will follow, Man is not a Pear-tree.

But for the Conversion of the Direct Figure into the first Indi∣rect Figure, the Major Terme in the Direct Figure ought to be Negative. For though this Direct, Man is a Living Creature, is a Bo∣dy be made Indirect, by converting the Major Proposition, thus,

Man is a Living Creature.

Not a Body is not a Living Creature, Therefore

Every Man is a Body; yet this Conversion appeares so obscure, that this Mood is of no use at all. By the Conversion of the Ma∣jor Proposition, it is manifest, that in this Figure, the Mi dle Terme is alwayes the Predicate in both the Premisses.

10 The second Indirect Figure is made by converting the Minor Proposition, so as that the Middle Term is the Subject in both. But this never concludes Uniuersally, and therefore is of no use in Philosophy. Neverthelesse I will set down an example of it; by which this Direct.

Every Man is a Living Creature,

Every Living Creature is a Body, by Conversion of the Minor Proposition will stand thus,

Some Living Creature is a Man,

Every Living Creature is a Body, Therefore

Some Man is a Body.

For Every Man is a Living Creature, cannot be converted into this, Every Living Creature is a Man; and therefore if this Syllo∣gisme

be restored to its Direct forme, the Minor Proposition will be Some Man is a Living Creature, and consequently the Conclusi∣on will be Some Man is a Body, seeing the Minor Terme Man, which is the Subject in the Conclusion, is a Particular Name.

11 The third Indirect or Inverted Figure, is made by the Conversion of both rhe Premisses. For Example, this Direct Syl∣logisme,

Every Man is a Living Creature,

Every Living Creature is not a Stone, Therefore

Every Man is not a Stone; being Inverted will stand thus,

Every Stone is not a Living Creature

Whatsoever is not a Living Creature, is not a Man, Therefore

Every Stone is not a Man. Which Conclusion is the Con∣verse of the Direct Conclusion, and aequipollent to the same. The Figures therefore of Syllogisms, if they be numbred by the diverse scituation of the Middle Terme onely, are but three; in the first whereof the Middle Term has the Middle place; in the second, the last; and in the third, the first place. But if they be numbred according to the scituation of the Termes simply, they are four; for the first may be distinguished againe into two, namely into Direct and Inverted. From whence it is evident, that the controversie among Logicians concerning the fourth Fi∣gure, is a meer 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉, or contention about the Name thereof; for as for the thing it selfe, it is plain, that the scituation of the Termes (not considering the Quantity or Quality by which the Moods are distinguished) makes four differences of Syllogismes, which may be called Figures, or have any other Name at plea∣sure.

12 In every one of these Figures there are many Moods, which are made by varying the Premisses according to all the differen∣ces they are capable of, by Quantity and Quality; as namely, in the Direct Figure there are six Moods; in the first Indirect Fi∣gure, four; in the second, fourteen; and in the third, eighteen. But because from the Direct Figure I rejected as superfluous all Moods besides that which consists of Universal Propositions, and whose Minor Proposition is Affirmative, I doe together with it reject the Moods of the rest of the Figures which are made by Conversion of the Premisses in the Direct Figure.

13 As it was shewed before, that in Necessary Propositions a Categoricall and Hypotheticall Proposition are aequipollent; so likewise it is manifest that a Categoricall and Hypotheticall Syl∣logisme are aequivalent. For every Categoricall Syllogisme, as this,

Every Man is a Living Creature,

Every Living Creature is a Body, Therefore

Every Man is a Body, is of equall force with this Hypotheti∣call Syllogisme.

If any thing be a Man, the same is also a Living Creature,

If any thing be a Living Creature, the same is a Body, Therefore

If any thing be a Man, the same is a Body. In like manner, this Categorical Syllogisme in an Indirect Figure

No Stone is a Living Creature,

Every Man is a Living Creature, Therefore

No Man is a Stone, or

No Stone is a Man, is aequivalent to this Hypotheticall Syllogisme.

If any thing be a Man, the same is a Living Creature,

If any thing be a a Stone, the same is not a Living Creature, Therefore

If any thing be a Stone, the same is not a Man, or

If any thing be a Man, the same is not a Stone.

And thus much seemes sufficient for the nature of Syllogismes; (for the doctrine of Moods and Figures is cleerely delivered by others that have written largely and profitably of the same.) Nor are Precepts so necessary as Practice for the attaining of true Ratiocination; and they that study the Demonstrations of Ma∣thematicians, will sooner learn true Logick, then they that spend time in reading the Rules of Syllogi••ing which Logicians have made; no otherwise then little Children learn to goe, not by Pre∣cepts, but by exercising their feet. This therefore may serve for the first Pace in the way to Philosophy.

In the next place I shall speak of the Faults and Errors, into which men that reason unwarily, are apt to fall; and of their Kinds and Causes.

CHAP. V. Of Erring, Falsity and Captions.

• 1. Erring and Falsity how they differ. Error of the Mind by it selfe without the use of Words, how it happens.
• 2 A sevenfold Incoherency of Names, every one of which makes allwayes a false Proposition.
• 3. Examples of the first manner of Incoherency.
• 4 Of the second.
• 5 Of the third.
• 6 Of the fourth.
• 7 Of the fifth.
• 8 Of the sixth.
• 9 Of the seventh.
• 10 Falsity of Propositions detected by resolving the Terms with Definitions continued till they ••ome to Simple Names, or Names that are the most Generall of their kind.
• 11 Of the fault of a Syllogisme consisting in the Implication of the Termes which the Copula
• 12 Of the fault which consists in Equivocati∣on.
• 13 Sophisticall Captions are oftner faulty in the matter then in the forme of Syllogismes.

1 MEn are subject to Erre not onely in Affim∣ing and Denying; but also in Perception, and in silent Cogitation. In Affirming and Denying, when they call any thing by a Name, which is not the Name thereof; as if from seeing the Sun first by reflection in Water, and after∣wards again directly in the Firma∣ment, we should to both those appear∣ances give the Name of Sunne, and say there are two Sunnes; which none but men can d••e; for no other Living Creatures have the use of Names. This kind of Error onely deserves the name of Falsity, as arising, not from sense, nor from the Things themselves but from pronouncing rashly; for Names have their constitution, not from the Species of Things, but from the Will and Consent of Men. And hence it comes to passe, that men pronounce Falsely by their own negligence, in departing from such appellations of things as are agreed upon, and are not deceived neither by the Things, nor by the Sense; for they do not perceive that the thing they see is called Sunne, but they give it that Name from their owne will and agreement. Tacite Errors, or the Errors of

Sense and Cogitation, are made, by passing from one Imaginati∣tion to the Imagination of another different thing; or by feign∣ing that to be Past, or Future, which never was, nor ever shall be; as when by seeing the Image of the Sunne in Water, we ima∣gine the Sunne it selfe to be there; or by seeing swords, that there has been or shall be fighting, because it uses to be so for the most part; or when from Promises we feigne the mind of the Promiser to be such and such; or lastly, when from any Signe we vainly imagine something to be signified, which is not. And Er∣rors of this sort are common to all things that have sense; and yet the Deception proceeds neither from our senses, nor from the Things we perceive; but from our selves, while we feigne such things as are but meer Images, to be something more then Ima∣ges. But neither Things, nor Imaginations of Things can be said to be False, seeing they are truly what they are; nor doe they as Signes promise any thing which they do not performe; for they indeed do not promise at all, but we from them; nor doe the Clouds, but we from seeing the Clouds, say it shall rain. The best way therefore to free our selves from such Errors as arise from naturall Signes, is first of all, before we begin to reason con∣cerning such conjecturall things, to suppose our selves ignorant, and then to make use of our Ratiocination; for these Errors pro∣ceed from the want of Ratiocination; whereas Errors which con∣sist in Affirmation and Negation, (that is, the Falsity of Proposi∣tions) proceed only from Reasoning amisse. Of these therefore, as repugnant to Philosophy, I will speake principally.

2 Errors which happen in Reasoning, that is, in Syllogizing, consist either in the Falsity of the Premisses, or of the Inference. In the first of these cases, a Syllogisme is said to be faulty in the Matter of it; and in the second case, in the Forme. I will first consider the Matter, namely how many wayes a Proposition may be false; and next the Forme, and how it comes to pass, that when the Premises are True, the Inference is notwith∣standing False.

Seeing therefore that Proposition onely is True, (Chap. 3. Art. 7.) in which are copulated two Names of one and the same thing; and that alwayes False, in which Names of different things are copulated; look how many wayes Names of different things

may be copulated, and so many wayes a False Proposition may be made.

Now all things to which we give Names, may be reduced to these four kinds, namely, Bodies, Accidents, Phantasmes, and Names themselves; and therefore in every true Proposition it is necessa∣ry that the Names copulated, be both of them Names of Bodies, or both Names of Accidents, or both Names of Phantasmes, or both Names of Names. For Names otherwise copulated are incohe∣rent, and constitute a False Proposition. It may happen also that the Name of a Body, of an Accident, or of a Phantasme may be copulated with the Name of a Speech. So that copulated Names may be Incoherent seven manner of wayes.

• 1 If the Name of a Body be copulated with the Name of an Accident.
• 2 If the Name of a Body be copulated with the Name of a Phantasme.
• 3 If the Name of a Body be copulated with the Name of a Name.
• 4 If the Name of an Accident be copulated with the Name of a Phantasme.
• 5 If the Name of an Accident be copulated with the Name of a Name.
• 6 If the Name of a Phantasme be copulated with the Name of a Name.
• 7 If the Name of a Body, of an Accident or of a Phan∣tasme be copulated with the Name of a Speech.

Of all which I will give some examples.

3 After the first of these wayes Propositions are false, when Abstract Names are copulated with Concrete Names; as (in Latine and Greek) Esse est Ens, Essenti•• est Ens, 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉 (i.) Quidditas est Ens, and many the like which are found in Aristotles Metaphysicks. Also, the Understanding worketh, the Understanding un∣derstandeth, the Sight seeth, A Body is Magnitude, A Body is Quantity, A Body is Extension, To Be a Man is a Man, Whitenesse is a White thing, &c. which is as if one should say The Runner is the Running, or the Walke Walketh. Moreover, Essence is separated, Substance is Abstracted; and others like these, or derived from these (with which com∣mon Philosophy abounds). For seeing no Subject of an Accident, (that is, No Body) is an Accident; no Name of an Accident ought to be given to a Body, nor of a Body to an Accident.

4 False in the second Manner are such Propositions as these,

A Ghost is a Body, or a Spirit, that is, a thinne Body; Sensible Species fly up and down in the Air, or are moved hither and thither, which is pro∣per to Bodies; also, A Shadow is Moved, or is a Body; Light is Moved, or is a Body; Colour is the Ob••ect of Sight, Sound of Hearing; Space or Place is Extended; and innumerable others of this kind. For see∣ing Ghosts, sensible Species, a Shadow, Light, Colour, Sound, Space, &c. appeare to us no lesse sleeping then waking, they cannot be things without us, but onely Phantasmes of the mind that imagins them; and therefore the Names of these, copulated with the Names of Bodies, cannot constitute a true Proposition.

5 False Propositions of the third kind, are such as these; Genus est Ens, Universale est Ens, Ens de Ente Praedicatur. For Genus, and Universale, and Praedicare are Names of Names, and not of Things. Also Number is Infinite, is a false Proposition; for no number can be Infinite, but onely the word Number is then called an Indefi∣nite Name when there is no determined Number answering to it in the Mind.

6 To the fourth kind belong such false Propositions as these, ▪An Object is of such Magnitude or Figure as appeares to the Beholders; Co∣lour, Light, Sound, are in the Object; and the like. For the same Ob∣ject appeares sometimes greater, sometimes lesser, sometimes square, sometimes round according to the diversity of the Distance and Medium; but the true Magnitude and Figure of the thing seen is allwayes one and the same; so that the magnitude and figure which appeares, is not the true magnitude and figure of the Object, nor any thing but Phantasme; and therefore in such Propositions as these, the Names of Accidents are copulated with the Names of Phantasmes.

7 Propositions are false in the fifth manner, when it is said that The Definition is the Essence of a thing; Whitenesse, or some other Acci∣dent is the Genus, or Universal. For Definition is not the Essence of any thing, but a speech signifying what we conceive of the Essence thereof; and so also not Whitenesse it selfe, but the word White∣nesse, is a Genus, or an Universall Name.

8 In the sixth manner they Erre, that say the Idea of any thing is U∣niversal; as if there could be in the Mind an Image of a Man which were not the Image of some one Man, but of Man simply, which is impossible; for every Idea is one, and of onething; but they are

deceived in this, that they put the Name of the thing for the Idea thereof.

9 They erre in the seventh manner, that make this distincti∣on between things that have being, that some of them exist by themselves, others by Accident; Namely, because Socrates is a Man is a Necessary Proposition, and Socrates is a Musician a Contingent Proposition, therefore they say some things exist necessarily or by themselves, others contingently or by Accident; whereby, seeing Necessa∣ry, Contingent, By it selfe, By Accident, are not Names of Things, but of Propositions, they that say any thing that has being, exists by Accident, copulate the Name of a Proposition with the Name of a Thing. In the same manner also they Erre, which place some Ideas in the Understanding, others in the Fancy; as if from the Understand∣ing of this Proposition Man is a Living Creature, we had one Idea or Image of a Man derived from sense to the Memory, and another to the Understanding; wherein that which deceives them is this, that they think one Idea should be answerable to a Name, another to a Proposition; which is false; for Pr••position signifies onely the or∣der of those things one after another, which we observe in the same Idea of Man; so that this Proposition Man is a Living Creature, raises but one Idea in us, though in that Idea we consider that first, for which he is called Man, and next that for which he is called Living Creature. The Falsities of Propositions in all these several manners, is to be discovered by the Definitions of the Copulated Names.

10 But when Names of Bodies are copulated with Names of Bodies, Names of Accidents with Names of Accidents, Names of Names with Names of Names, and Names of Phantasmes with Names of Phantasmes, if we neverthelesse remaine still doubtfull whether such Propositions are true; we ought then in the first place to find out the Definition of both those Names, and againe the Definitions of such Names as are in the former Definition, and so proceed by a continuall Resolution till we come to a simple Name, that is, to the most Generall or most Universall Name of that kind; and if after all this the Truth or Falsity thereof be not evident, we must search it out by Philosophy, and Ratiocination, beginning from Definitions. For every Proposition Universally true, is either a Definition, or part of a Definition, or the evidence of it depends upon Definitions.

11 That fault of a Syllogisme which lyes bid in the Forme thereof, will allwayes be found either in the implication of the Copula with one of the Termes, or in the Aequivocation of some word; and in either of these wayes there will be four Terms, which (as I have shewne) cannot stand in a true Syllogisme. Now the implication of the Copula with either Terme, is easily detected by reducing the Propositions to plain and cleere Praedication; as (for example) if any man should argue thus,

The Hand toucheth the Pen,

The Pen toucheth the Paper, Therefore

The Hand toucheth the Paper; the Fallacy will easily appear by reducing it, thus,

The Hand, is, touching the Pen,

The Pen, is, touching the Paper, Therefore

The Hand, is, touching the Paper; where there are manifestly these four Termes, The Hand, Touching the Pen, The Pen, and Touch∣ing the Paper. But the danger of being deceived by Sophismes of this kind, does not seem to be so great, as that I need insist long∣er upon them.

12 And though there may be Fallacy in Aequivocal Terms, yet in those that be manifestly such there is none at all; nor in Metaphors; for they professe the transferring of Names from one thing to another. Neverthelesse sometimes Aequivocalls (and those not very obscure) may deceive; as in this argumentation, It belongs to Metaphysicks, to treat of Principles; But the first Principles of all, is, that the same thing cannot both exist and not exist at the same time; and therefore it belongs to Metaphysicks to treat whether the same thing may both exist and not exist at the same time; where the Fallacy lies in the Aequivocation of the word Principle; for whereas Aristotle in the be∣ginning of his Metaphysicks sayes, that the treating of Principles be∣longs to primary science, he understands by Principles, Causes of things, and certaine Existences which he calls Primary; but where he sayes a Primary Proposition is a Principle, by Principle there he means the be∣ginning and cause of Knowledge, that is the understanding of words, which if any man want, he is incapable of learning.

13 But the Captions of Sophists and Scepticks, by which they were wont of old to deride and oppose Truth, were faulty for

the most part, not in the Forme, but in the Matter of Syllogisme; and they deceived not others oftner then they were themselves deceived. For the force of that famous argument of Zeno against Motion, consisted in this Proposition, Whatsoever may be divided into parts infinite in number, the same is infinite; which he without doubt thought to be true, yet neverthelesse is false. For to be divided into infinite parts, is nothing else but to be divided ••••••o as many parts as any man will. But it is not necessary that a Line should have parts infinite in number, or be infinite, because I can divide and subdi∣vide it as often as I please; for how many parts soever I make, yet their number is finite; but because he that sayes Parts, simply, without adding how many, does not limit any number, but leaves it to the determination of the Hearer, therefore we say commonly a line may be divided infinitely; which cannot be true in any o∣ther sense.

And thus much may suffice concerning Syllogisme, which is as it were the first Pace towards Philosophy; in which I have said as much as is necessary, to teach any man from whence all true ar∣gumentation has its force. And to enlarge this Treatise with all that may be heaped together, would be as superfluous, as if one should (as I said before) give a young child Precepts for the tea∣ching of him to goe; for the Art of Reasoning is not so well learn∣ed by Precepts as by Practice, and by the reading of those books in which the Conclusions are all made by severe Demonstration. And so I pass on to the way of Philosophy, that is, to the Method of Study.

CHAP. VI. Of Method▪

• 1 Method and Science defined.
• 2 It is more easily known concerning Singu∣lar then Universall things, That they are; and contrarily, it i•• more easily knowne concerning Universall then Singular things, Why they are, or what are their Causes.
• 3 What it is Philosophers seek to know.
• 4 The first Part, by which Principles are found out is purely Analyticall.
• 5 The highest Causes, and most Universall in every kind, are knowne by them∣selves.
• 6 Method from Principles fonnd out, tending to Science simp∣ly, what it is.
• 7 That Method of Civill and Naturall Science which proceeds from Sense to Principles, is Analytical; and againe that which begins at Principles, is Syntheticall.
• 8 The Method of searching out, whether any thing propounded, be Matter or Accident.
• 9 The Method of seeking whether any Accident be in this, or in that Subject.
• 10 The Method of searching after the Cause of any Effect propounded.
• 11 Words serve to Invention, as Markes; to Demonstration, as Signes.
• 12 The Method of Demonstration is Syntheticall.
• 13 Definitions onely are Pri∣mary and Universal Propositions.
• 14 The Nature and Definition of a Definition.
• 15 The Properties of a Definition.
• 16 The Nature of a Demonstration.
• 17 The Properties of a Demonstration, and Order of things to be demonstrated.
• 18 The Faults of a Demonstration.
• 19 Why the Ana∣lyticall Method of Ge••metricians cannot be treated of in this place.

1 FOr the understanding of Method, it will be necessary for me to repeat the de∣finition of Philosophy, delivered a∣bove (Chap. 1. Art. 2.) in this manner, Philosophy is the knowledge we acquire by true Ratiocination, of Ap∣pearances, or apparent Effects, from the knowledge we have of some possible Pro∣duction or Generation of the same; and of such Production as has been or may be, from the knowledge we have of the Effects. METHOD therefore in the Study of Philosophy, is the shortest way of finding out Effects by their

known Causes, or of Causes by their known Effects. But we are then said to know any Effect, when we know, that there be Causes of the same, and in what Subiect those Causes are, and in what Subiect they produce that Effect, and in what Manner they work the same. And this is the Science of Causes, or as they call it of the 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉. All other Sci∣ence, which is called the 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉, is either Perception by Sense, or the Imagination, or Memory remaining after such Perception.

The first Beginnings therefore of Knowledge, are the Phan∣tasmes of Sense and Imagination; and that there be such Phan∣tasmes we know well enough by Nature; but to know why they be, or from what Causes they proceed, is the work of Ratioci∣nation; which consists (as is said above, in the 1. Chap. 2. Art.) in Composition, and Division or Resolution. There is therefore no Method, by which we find out the Causes of things, but is either Compositive, or Resolutive, or partly Compositive, and partly Resolutive. And the Resolutive is commonly called Analyticall Method, as the Compositive is called Syntheticall.

2 It is common to all sorts of Method, to proceed from known things to unknown; and this is manifest from the cited Definition of Philosophy. But in Knowledge by Sense, the whole object is more known, then any part thereof; as when we see a Man, the Conception or whole Idea of that Man is first or more known, then the particular Ideas of his being figurate, animate, and rationall; that is, we first see the whole Man, and take notice of his Being, before we observe in him those other Particulars. And therefore in any knowledge of the 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉, or that any thing is, the beginning of our search is from the whole Idea; and contrarily, in our knowledge of the 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉, or of the Causes of any thing, that is, in the Sciences, we have more knowledge of the Causes of the Parts, then of the Whole. For the Cause of the Whole is compounded of the Causes of the Parts; but it is necessary that we know the things that are to be compounded, before we can know the whole Com∣pound. Now by Parts, I do not here mean Parts of the thing it self, but Parts of its Nature; as, by the Parts of Man I do not understand his Head, his Shoulders, his Arms, &c. but his Figure, Quan∣tity, Motion, Sense, Reason, and the like; which Accidents be∣ing compounded or put together, constitute the whole Nature of Man, but not the man himselfe. And this is the meaning of that

common saying, namely, that some things are more knowne to us, others more known to Nature; for I do not thinke that they which so distinguish, mean, that something is known to Nature, which is known to no man; and therefore, by those things that are more known to Us, we are to understand, things we take no∣tice of by our Senses, and by more known to Nature, those we acquire the knowledge of by Reason; for in this sense it is, that the Whole, that is, those things that have Universal Names, (which for brevities sake I call Universall) are more knowne to us then the Parts, that is, such things as have Names lesse Universal, (which I therefore call Singular;) and the Causes of the Parts, are more known to Nature then the Cause of the Whole; that is, Universalls then Singulars.

3 In the Study of Philosophy men search after Science either Simply, or Indefinitely; that is, to know as much as they can, without propounding to themselves any limited question; or they enquire into the Cause of some determined Appearance, or endeavour to find out the certainty of something in question; as what is the cause of Light, of Heat, of Gravity, of a Figure pro∣pounded, and the like; or in what Subiect any propounded Acci∣dent is inhaerent; or what may conduce most to the generation of some propounded Effect from many Accidents; or in what manner particular Causes ought to be compounded for the production of some certaine Effect. Now according to this variety of things in question, sometimes the Analyticall Method is to be used, and sometimes the Syntheticall.

4 But to those that search after Science indefinitely, which consists in the knowledge of the Causes of all things, as far forth as it may be attained, and the Causes of Singular things are com∣pounded of the Causes of Universall or Simple things, it is ne∣cessary that they know the Causes of Universall things, or of such Accidents as are common to all Bodies, that is, to all Matter, before they can know the Causes of Singular things, that is, of those Accidents by which one thing is distinguished from ano∣ther. And againe they must know what those Universall things are, before they can know their Causes. Moreover, seeing Uni∣versall things are contained in the Nature of Singular things, the knowledge of them is to be acquired by Reason, that is, by Re∣solution.

▪For example, if there be propounded a Conception or Idea of some Singular thing, as of a Square, this Square is to be resolved into a Plain, terminated with a certaine number of equall and straight lines and right angles. For by this Resolution we have these things Universall or agreeable to all Matter, namely, Line, Plain, (which containes Superficies,) Terminated, Angle, Straightness, Rectitude and Equality; and if we can find out the Causes of these, we may compound them all together into the Cause of a Square. Againe, if any man propound to himselfe the Conception of Gold, he may by Resolving come to the Ideas of Solid, Visible, Heavy, (that is, tending to the Center of the Earth, or down∣wards,) and many other more Universall then Gold it selfe; and these he may Resolve againe, till he come to such things as are most Universall. And in this manner by Resolving continu∣ally, we may come to know what those things are, whose Cau∣ses being first known severally, and afterwards compounded, bring us to the Knowledge of Singular things. I conclude there∣fore, that the Method of attaining to the Universall Knowledge of Things, is purely Analyticall.

5 But the Causes of Universall things (of those at least that have any Cause) are manifest of themselues, or (as they say com∣monly) known to Nature; so that they need no Method at all; for they have all but one Universall Cause, which is Motion. For the variety of all Figures arises out of the variety of those Mo∣tions by which they are made; and Motion cannot be understood to have any other Cause besides Motion; nor has the Variety of those things we perceive by Sense, as of Colours, Sounds, Savours, &c. any other Cause then Motion, residing partly in the Objects that work upon our Senses, and partly in our selves, in such man∣ner, as that it is manifestly some kind of Motion, though we can∣not without Ratiocination come to know what kind. For though many cannot understand till it be in some sort demonstrated to them, that all Mutation consists in Motion; yet this happens not from any obscurity in the thing it selfe, (for it is not intelligible that any thing can depart either from Rest, or from the Motion it has, except by Motion;) but either by having their Naturall Discourse corrupted with former Opinions received from their Masters, or else for this, that they do not at all bend their mind to the enquiring out of Truth,

6 By the Knowledge therefore of Universalls, and of their Causes (which are the first Principles by which we know the 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉 of things,) we have in the first place their Definitions, (which are nothing but the explication of our Simple Concepti∣ons.) For example, he that has a true Conception of Place, can∣not be ignorant of this Definition, Place is that space which is posses∣sed or filled adaequately by some Body; and so, he that conceives Motion aright, cannot but know, that Motion is the privation of one Place, and the acquisition of another. In the next place, we have their Ge∣nerations or Descriptions; as, (for example,) that a Line is made by the Motion of a Point, Superficies by the Motion of a Line, and one Mo∣tion by another Motion, &c. It remains, that we enquire, what Mo∣tion begets such and such Effects; as, what Motion makes a Straight line, and what a Circular; what Motion thrusts, what drawes, and by what way; what makes a thing which is seen or heard, to be seen or heard sometimes in one manner, sometimes in another. Now the Method of this kind of Enquiry, is Composi∣tive. For first we are to observe what Effect a Body moved pro∣duceth, when we consider nothing in it besides its Motion; and we see presently that this makes a Line, or length; next, what the Motion of a long Body produces, which we find to be Superficies; and so forwards, till we see what the Effects of Simple Motion are; and then in like manner, we are to observe what proceeds from the Addition, Multiplication, Substraction and Division of these Motions, and what Effects, what Figures, and what Pro∣perties they produce; from which kind of Contemplation sprung that part of Philosophy which is called Geometry.

From this consideration of what is produced by Simple Motion, we are to passe to the consideration of what Effects one Body mo∣ved worketh upon another; and because there may be Motion in all the severall parts of a Body, yet so as that the whole Body re∣main still in the same place, we must enquire, first, what Motion causeth such and such Motion in the whole, that is, when one Bo∣dy invades another Body which is either at Rest, or in Motion, what way, and with what swiftnesse the invaded Body shall move; and again, what Motion this second Body will generate in a third, and so forwards. From which Contemplation shall be drawn that part of Philosophy which treats of Motion.

In the Third place we must proceed to the Enquiry of such Ef∣fects, as are made by the Motion of the Parts of any Body, as, how it comes to passe, that things when they are the same, yet seeme not to be the same, but changed. And here the things we search after are sensible Qualities, such as Light, Colour, Transpa∣rency, Opacity, Sound, Odour, Savour, Heat, Cold and the like; which because they cannot be known till we know the Causes of Sense it selfe, therefore the consideration of the Causes of Seeing, Hearing, Smelling, Tasting and Touching belongs to this third place; and all those qualities and Changes above mentioned are to be re∣ferred to the fourth place; which two considerations compre∣hend that part of Philosophy which is called Physiques. And in these four parts is contained whatsoever in Naturall Philosophy may be explicated by Demonstration properly so called. For if a Cause were to be rendred of Natural Appearances in special, as, what are the Motions and Influences of the heavenly Bodies, and of their parts, the reason hereof must either be drawn from the parts of the Sciences above mentioned, or no reason at all will be given, but all left to uncertaine conjecture.

After Physiques we must come to Morall Philosophy; in which we are to consider the Motions of the Mind, namely Appetite, Aver∣sion, Love, Benevolence, Hope, Fear, Anger, Emulation, Envy, &c. what Causes they have, and of what they be Causes. And the reason why these are to be considered after Physiques, is, that they have their Causes in Sense and Imagination, which are the Sub∣ject of Physicall Contemplation. Also the reason why all these Things are to be searched after in the order abovesaid, is, that Physiques cannot be understood, except we know first what Mo∣tions are in the smallest parts of Bodies; nor such Motion of Parts, till we know what it is that makes another Body move; nor this, till we know what Simple Motion will effect. And because all Ap∣pearance of things to sense is determined, and made to be of such and such Quality and Quantity by Compounded Motions, every one of which has a certaine degree of Velocity, and a certaine and determined way; therefore in the first place we are to search out the wayes of Motion simply, (in which Geometry consists;) next the wayes of such generated Motions as are manifest; and lastly the wayes of internal and invisible Motions, (which is the

Enquiry of Naturall Philosophers.) And therefore they that stu∣dy Naturall Philosophy, study in vaine, except they begin at Geometry; and such Writers or Disputers thereof, as are ig∣norant of Geometry, do but make their Readers and Hearers lose their time.

7 Civill and Morall Philosophy doe not so adhere to one another, but that they may be severed. For the Causes of the Motions of the Mind are known not onely by Ratiocination, but also by the Experience of every man that takes the paines to observe those Motions within himselfe. And therefore not only they that have attained the knowledge of the Passions and Perturbations of the Mind, by the Syntheticall Method and from the very first Principles of Philosophy, may by proceeding in the same way come to the Causes and Necessity of constituting Common-wealths, and to get the Knowledge of what is Naturall Right, and what are Ci∣vill Duties; and in every kind of Government, what are the Rights of the Commonwealth, and all other Knowledge apper∣taining to Civill Philosophy, for this reason, that the Principles of the Politiques consist in the Knowledge of the Motions of the Mind, and the Knowledge of these Motions from the knowledge of Sense and Imagination; but even they also that have not learn∣ed the first part of Philosophy, namely Geometry and Physiques, may notwithstanding attain the Principles of Civill Philosophy, by the Analyticall Method. For if a Question be propounded, as Whe∣ther such an Action be Just or Uniust; if that Uniust be resolved into Fact against Law, and that notion of Law into the Command of him or them that have Coercive Power; and that Power be derived from the Wills of Men that constitute such Power to the end they may live in Peace, they may at last come to this, that the Appetites of Men and the Passions of their Minds are such, that unlesse they be restrained by some Power, they will alwayes be making warre upon one another; which may be known to be so by any mans ex∣perience, that will but examine his owne Mind. And therefore from hence he may proceed by Compounding, to the determi∣nation of the Justice or Injustice of any propounded Action. So that it is manifest by what has been said, that the Method of Phi∣losophy to such as seek Science simply, without propounding to themselves the Solution of any Particular question, is partly Ana∣lyticall,

and partly Syntheticall; namely, that which proceeds from Sense to the invention of Principles, Analyticall; and the rest Syn∣theticall.

8 To those that seek the Cause of some certaine and pro pounded Appearance or Effect, it happens sometimes, that they know not whether the thing whose Cause is sought after, be Matter or Body, or some Accident of a Body. For though in Geometry, when the Cause is sought of Magnitude, or Proportion, or Figure, it be certainly known that these things, namely Mag∣nitude, Proportion and Figure are Accidents; yet in Naturall Philosophy, where all questions are concerning the Causes of the Phantasmes of sensible things, it is not so easie to discern between the things themselves from which those Phantasmes proceed, and the Appearances of those things to the sense; which have deceived many, especially when the Phantasmes have been made by Light. For Example, a Man that looks upon the Sunne, has a certaine shining Idea of ••••e Magnitude of about a fo••t over; and this he calls the Sunne, thoug•…•…e know the Sunne to be truly a great deale bigger and in like 〈…〉〈…〉, the Phantasme of the same thing appears sometimes ••••und▪ by being 〈…〉〈…〉 a ••arre off, and sometimes square, by being neerer. Whereupon ••t may well be doubted whether that Phantasme be Ma•…•…▪ or some Body Naturall, or onely some Accident of a Body; in the examina∣tion of which doubt we may use this Method. The Properties of Matter and Accidents already found out by Us by the Syntheti∣call Method from their Definitions, are to be compared with the Idea we have before us; and if it agree with the Properties of Matter or Body, then it is a Body; otherwise it is an Accident. Seeing therefore Matter cannot by any endeavour of ours be ei∣ther Made or Destroyed, or Encreased, or Diminished, or Mo∣ved out of its place, whereas that Idea Appeares, Vanishes, is En∣creased, and Diminished, and Moved hither and thither at plea∣sure; we may certainly conclude that it is not a Body, but an Accident onely. And this Method is Syntheticall.

9 But if there be a doubt made concerning the Subject of any known Accident, (for this may be doubted sometimes, as in the praecedent example doubt may be made in what Subject that Splendor and apparent Magnitude of the Sunne is) then our en∣quiry

must proceed in this manner. First, Matter in Generall must be divided into parts, as into Object, Medium, and the Sen∣tient it selfe, or such other parts as seem most conformable to the thing propounded. Next, these parts are severally to be exami∣ned how they agree with the Definition of the Subject; and such of them as are not capable of that Accident are to be rejected. For example, If by any true Ratiocination the Sunne be found to be greater then its apparent Magnitude, then that Magnitude is not in the Sunne; If the Sunne be in one determined straight line, and one determined distance, and the Magnitude and Splendor be seen in more lines and distances then one, as it is in Reflecti∣on or Refraction, then neither that Splendor nor apparent Mag∣nitude are in the Sun it self, and therefore the Body of the Sun cannot be the Subject of that Splendor and Magnitude. And for the same reasons the Aire and other parts will be reje∣cted, till at last nothing remain which can be the Subject of that Splendor and Magnitude but the Sentient it selfe. And this Method, in regard the Subject is divided into parts is Analitycall; and in regard the Properties both of the Subject and Accident are compared with the Accident concerning whose Subject the en∣quiry is made, it is Syntheticall.

10 But when we seek after the Cause of any propounded Ef∣fect; we must in the first place get into our Mind an exact Notion or Idea of that which we call Cause, namely, that A Cause is the Summe or Aggregate of all such Accidents both in the Agents and the Pa∣tient, as concurre to the producing of the Effect propounded; all which ex∣isting together, it cannot be understood but that the Effect existeth with them; or that it cannot possibly exist if any one of them be absent. This being known, in the next place we must examine singly every Accident that accompanies or praecedes the Effect, as farre forth as it seemes to conduce in any manner to the production of the same, and see whether the propounded Effect may be conceived to exist, without the existence of any of those Accidents; and by this meanes separate such Accidents as do not concurre, from such as concurre to produce the said Effect; which being done, we are to put together the concurring Accidents, and consider whether we can possibly conceive that when these are all present, the Effect propounded will not follow; and if it be evident that

the Effect will follow, then that Aggregate of Accidents is the entire Cause, otherwise not; but we must still search out and put together other Accidents. For example, if the Cause of Light be propounded to be sought out; first, we examine things without us, and find that whensoever Light appeares, there is some prin∣cipall Object, as it were the fountaine of Light, without which we cannot have any perception of Light; and therefore the con∣currence of that Object is necessary to the generation of Light. Next we consider the Medium, and find that unlesse it be dispo∣sed in a certaine manner, namely, that it be transparent, though the Object remain the same, yet the Effect will not follow; and therefore the concurrence of Transparency is also necessary to the generation of Light. Thirdly, we observe our own Body, and find that by the indisposition of the Eyes, the Brain, the Nerves, and the Heart, that is, by Obstructions, Stupidity and Debility we are de∣prived of Light, so that a fitting disposition of the Organs to re∣ceive impressions from without is likewise a necessary part of the Cause of Light. Again, of all the Accidents inhaerent in the Ob∣ject, there is none that can conduce to the effecting of Light, but onely Action, (or a certain Motion,) which cannot be conceived to be wanting, whensoever the Effect is present; for, that any thing may shine, it is not requisite that it be of such or such ••ag∣nitude or Figure, or that the whole Body of it be moved out of the place it is in, (unlesse it may perhaps be said, that in the Sun or other Body, that which causeth Light is the light it hath in it selfe; which yet is but a trifling exception, seeing nothing is meant thereby but the Cause of Light; as if any man should say that the Cause of Light is that in the Sunne which produceth it;) it remaines therefore that the Action by which Light is genera∣ted, is Motion only in the parts of the Object. Which being understood, we may easily conceive what it is the Medium con∣tributes, namely, the continuation of that Motion to the Eye; and lastly what the Eye and the rest of the Organs of the Senti∣ent contribute, namely, the continuation of the same Motion to the last Organ of Sense, the Heart. And in this manner the Cause of Light may be made up of Motion continued from the Original of the same Motion, to the Original of Vitall Motion, Light being nothing but the alteration of Vitall Motion, made by the impression upon it of Motion continued from the Ob∣ject.

But I give this onely for an example, for I shall speak more at large of Light, and the generation of it in its proper place. In the mean time it is manifest, that in the searching out of Cau∣ses, there is need partly of the Analyticall, and partly of the Syn∣theticall Method; of the Analyticall, to conceive how circumstances conduce severally to the production of Effects; and of the Syn∣theticall, for the adding together and compounding of what they can effect singly by themselves. And thus much may serve for the Method of Invention. It remaines that I speake of the Method of Teaching, that is, of Demonstration, and of the Meanes by which we demonstrate.

11 In the Method of Invention the use of words consists in this, that they may serve for Marks, by which, whatsoever we have found out may be recalled to memory; for without this all our Inventions perish, nor will it be possible for us to go on from Principles beyond a Syllogisme or two, by reason of the weak∣nesse of Memory. For example, if any man by considering a Triangle set before him, should find that all its angles together taken are equall to two right angles, and that by thinking of the same tacitely, without any use of words either understood or expressed; and it should happen afterwards that another Tri∣angle unlike the former, or the same in different scituation should be offered to his consideration, he would not know readi∣ly whether the same property were in this last or no; but would be forced as often as a different Triangle were brought before him (and the difference of Triangles is infinite) to begin his contem∣plation anew; which he would have no need to do if he had the use of Names; for every Universal Name denotes the conceptions we have of infinite Singular things.. Neverthelesse as I said a∣bove, they serve as Markes for the helpe of our Memory, whereby we register to our selves our own Inventions; but not as Signes by which we declare the same to others; so that a man may be a Philosopher alone by himselfe without any Master; Adam had this capacity; But to Teach, that is to Demonstrate, supposes two at the least, and Syllogisticall Speech.

12 And seeing Teaching is nothing but leading the Mind of him we teach, to the knowledge of our Inventions, in that Track by which we attained the same with our own Mind; therefore

the same Method that served for our Invention, will serve also for Demonstration to others, saving that we omit the first part of Method which proceeded from the Sense of Things to Universal Principles; which because they are Principles, cannot be demon∣strated; and seeing they are known by Nature (as was said above in the 5th. Article) they need no Demonstration, though they need Explication. The whole Method therefore of Demonstra∣tion is Syntheticall, consisting of that order of Speech, which be∣gins from Primary or most Universall Propositions, which are manifest of themselves, and proceeds by a perpetuall composi∣tion of Propositions into Syllogismes, till at last the Learner un∣derstand the truth of the Conclusion sought after.

13 Now such Principles are nothing but Definitions; where∣of there are two sorts; one, of Names that signifie such things as have some conceiveable Cause, and another of such Names as signifie things of which we can conceive no Cause at all. Names of the former kind are, Body or Matter, Quantity or Extension, Mo∣tion, and whatsoever is common to all Matter. Of the second kind are, such a Body, such and so great Motion, so great Magnitude, such Figure, and whatsoever we can distinguish one Body from another by. And Names of the former kind are well enough de∣fined, when by Speech as short as may be, we raise in the Mind of the Hearer perfect and cleer Ideas or Conceptions of the Things named, as when we Define Motion to be the leaving of one place, and the acquiring of another continually; for though no Thing Moved, nor any Cause of Motion be in that Definition, yet at the hearing of that Speech, there will come into the Mind of the Hearer an Idea of Motion cl••er enough. But Definitions of things which may be understood to have some Cause, must consist of such Names as expresse the Cause or Manner of their Gene∣ration, as when we Define a Circle to be a Figure made by the circumduction of a straight line in a plaine, &c. Besides Defini∣tions, there is no other Proposition that ought to be called Pri∣mary, or (according to severe truth) be received into the number of Principles. For those Axiomes of Euclide, seeing they may be demonstrated are no Principles of Demonstration, though they have by the consent of all Men gotten the authority of Principles, because they need not be Demonstrated. Also those Petitious or Postulata (as they call them) though they be Principles

yet they are not Principles of Demonstration, but of Constru∣ction onely; that is, not of Science, but of Power; or (which is all one) not of Theoremes, which are Speculations, but of Pro∣blemes, which belong to Practice, or the doing of something. But as for those common received Opinions, Nature abhorres Va∣nity, Nature doth nothing in Vaine, and the like, which are nei∣ther evident in themselves, nor at all to be demonstrated, and which are oftner false then true, they are much lesse to be ackow∣ledged for Principles.

To returne therefore to Definitions, The reason why I say that the Cause and Generation of such things as have any Cause or Generation, ought to enter into their Definitions, is this. The End of Science, is the Demonstration of the Causes and Gene∣rations of Things; which if they be not in the Definitions, they cannot be found in the Conclusion of the first Syllogisme that is made from those Definitions; and if they be not in the first Conclusion, they will not be found in any further Conclusion deduced from that; and therefore by proceeding in this manner we shall never come to Science; which is against the scope and intention of Demonstration.

14 Now seeing Definitions (as I have said) are Principles or Primary Propositions, they are therefore Speeches; and seeing they are used for the raising of an Idea of some Thing in the mind of the Learner, whensoever that Thing has a Name, the Definition of it can be nothing but the Explication of that Name by Speech; and if that Name be given it for some com∣pounded Conception, the Definition is nothing but a Resolution of that Name into its most Universall parts. As when we define Man, saying, Man is a Body Animated, Sentient, Rationall, those Names Body Animated, &c. are parts of that whole Name Man; so that Definitions of this kind alwayes consist of Genus and Diffe∣rence; the former Names being all till the last, Generall; and the last of all, Difference. But if any Name be the most Universall in its kind, then the Definition of it cannot consist of Genus and Difference, but is to be made by such circumlocution as best expli∣cateth the force of that Name. Again, it is possible, and happens often that the Genus and Difference are put together, and yet make no Definition; as these Words a Straight Line containe

both the Genus and Difference; but are not a Definition, unlesse we should thinke a Straight Line may be thus defined, A Straight Line is a Straight Line; and yet if there were added another Name consisting of different Words, but signifying the same thing which these signifie, then these might be the Definition of that Name. From what has been said it may be understood how a Definition ought to be defined, namely, That it is a Proposition, whose Praedicate Resolves the Subiect, when it may, and when it may not, it exemplifies the same.

15 The Properties of a Definition are,

First, that it takes away Aequivocation, as also all that mul∣titude of Distinctions, which are used by such as think they may learn Philosophy by Disputation. For the Nature of a Definiti∣on is to define, that is, to determine the signification of the de∣fined Name, and to pare from it all other Signification besides what is contained in the Definition it selfe; and therefore one Definition does as much, as all the Distinctions (how many soe∣ver) that can be used about the Name defined.

Secondly, That it gives an Universall Notion of the thing defined, representing a certaine Universall Picture thereof, not to the Eye, but to the Mind. For as when one paints a Man, he paints the image of some Man; so he that defines the Name Man, makes a Representation of some Man to the mind.

Thirdly, That it is not necessary to dispute whether Definitions are to be admitted or no. For when a Master is instructing his Scholar, if the Scholar understand all the parts of the thing de∣fined, which are Resolved in the Definition, and yet will not admit of the Definition, there needs no further Controversie be∣twixt them, it being all one as if he refused to be taught. But if he understand nothing, then certainely the Definition is faulty; for the nature of a Definition consists in this, that it exhibit a cleare Idea of the thing defined; and Principles are either known by themselves, or else they are not Principles.

Fourthly, That in Philosophy, Definitions are before de∣fined Names. For in teaching Philosophy, the first beginning is from Definitions, and all progression in the same till we come to the Knowledge of the thing compounded, is Compositive. Seeing therefore Definition is the explication of a Compounded Name

by Resolution, and the progression is from the parts to the com∣pound, Definitions must be understood before Compounded Names; nay when the Names of the parts of any Speech be ex∣plicated, is it not necessary that the Definition should be a Name Compounded of them. For example, when these Names, Aequilaterall, Quadrilaterall, Right-angled, are sufficiently under∣stood, it is not necessary in Geometry that there should be at all such a Name as Square; for defined Names are received in Phi∣losophy for brevities sake onely.

Fiftly, That Compounded Names which are defined one way in some one part of Philosophy, may in another part of the same be otherwise defined; as a Parabola and an Hyperbole have one Definition in Geometry, and another in Rhetorique; for Definitions are instituted and serve for the understanding of the Doctrine which is treated of. And therefore as in one part of Philosophy, a Definition may have in it some one fit Name for the more briefe explanation of some proposition in Geome∣try; so it may have the same liberty in other parts of Philoso∣phy; for the use of Names is particular (even where many a∣gree to the setling of them) and arbitrary.

Sixtly, That no Name can be defined by any one Word; be∣cause no one Word is sufficient for the Resolving of one or more words.

Seventhly, That a defined Name ought not to be repeated in the Definition. For a defined Name, is the whole Compound, and a Definition is the Resolution of that Compound into parts; but no Totall can be part of it selfe.

16 Any two Definitions that may be compounded into a Syllo∣gisme, produce a Conclusion; which because it is derived from Principles, that is, from Definitions, is said to be Demonstrated; and the Derivation or Composition it selfe is called a Demonstra∣tion. In like manner, if a Syllogisme be made of two Propositi∣ons, whereof one is a Definition, the other a Demonstrated Conclusion, or neither of them is a Definition, but both former∣ly demonstrated, that Syllogisme is also called a Demonstration, and so successively. The Definition therefore of a Demonstrati∣on is this, A DEMONSTRATION is a Syllogism or Series of Syllogisms derived and continued from the Definitions of Names, to the last Conclusion.

And from hence it may be understood, that all true Ratiocinati∣on, which taketh its beginning from true Principles, produceth Science, and is true Demonstration. For as for the Originall of the Name, although that which the Greeks called 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉, and the Latines Demonstratio was understood by them for that sort onely of Ratiocination, in which by the describing of certaine Lines and Figures, they placed the thing they were to prove, as it were before mens Eyes, which is properly 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉, or to shew by the Figure; yet they seem to have done it for this reason, that unlesse it were in Geometry (in which only there is place for such Figures) there was no Ratiocination certaine, and ending in Sci∣ence, their Doctrines concerning all other things being nothing but Controversie and Clamour; which neverthelesse hapned not because the Truth to which they pretended could not be made e∣vident without Figures, but because they wanted true Principles, from which they might derive their Ratiocination; and therefore there is no reason but that if true Definitions were praemised in all sorts of Doctrines, the Demonstrations also would be true.

17 It is proper to Methodical Demonstration,

First, That there be a true Succession of one Reason to another, according to the Rules of Syllogizing delivered above.

Secondly, That the Praemisses of all Syllogismes be demon∣strated from the first Definitions.

Thirdly, That after Definitions, he that Teaches or Demon∣strates any thing, proceed in the same Method by which he found it out; namely, that in the first place those things be de∣monstrated which immediately succeed to Universal Definitions (in which is contained that part of Philosophy which is called Philosophia Prima.) Next, those things which may be demonstra∣ted by Simple Motion (in which Geometry consists.) After Geome try, such things as may be taught or shewed by manifest Action, that is, by Thrusting from, or Pulling towards. And after these, the Motion or Mutation of the invisible parts of Things, and the Do∣ctrine of Sense & Imagination & of the internal Passions, especi∣ally those of Men, in which are comprehended the Grounds of Ci∣vil Duties, or Civil Philosophy; which takes up the last place. And that this Method ought to be kept in all sorts of Philosophy, is e∣vident from hence, that such things as I have said are to be taught

last cannot be demonstrated, till such as are propounded to be first treated of, be fully understood. Of which Method no other Example can be given, but that Treatise of the Elements of Philosophy, which I shall begin in the next Chapter, and con∣tinue to the end of the worke.

18 Besides those Paralogismes, whose fault lies either in the Falsity of the Praemisses, or the want of true Composition, of which I have spoken in the praecedent Chapter, there are two more which are frequent in Demonstration; one whereof is com∣monly called Petitio Principii; the other is the supposing of a False Cause; and these do not onely deceive Unskilfull Learners but sometimes Masters themselves, by making them take that for well demonstrated which is not demonstrated at all. Petitio Principii, is when the Conclusion to be proved, is disguised in other Words, and put for the Definition or Principle from whence it is to be demonstrated; and thus by putting for the Cause of the Thing sought, either the Thing it selfe or some Effect of it, they make a Circle in their Demonstration. As for example, He that would Demonstrate that the Earth stands still in the Center of the World, and should suppose the Earths Gravity to be the Cause thereof, and define Gravity to be a quality by which eve∣ry heavy Body tends towards the Center of the World, would lose his labour; for the question is, What is the Cause of that quality in the Earth; and therefore he that supposes Gravity to be the Cause, puts the Thing it selfe for its own Cause.

Of a False Cause I find this example in a certaine Treatise where the thing to be demonstrated is the Motion of the Earth. He begins therefore with this, that seeing the Earth and the Sun are not alwayes in the same scituation, it must needs be that one of them be locally moved; which is true; next he affirms that the Vapours which the Sun raises from the Earth and Sea are by reason of this Motion necessarily moved; which also is true; from whence he infers the Winds are made, and this may passe for granted; and by these Winds he sayes the Waters of the Sea are moved, and by their Motion the bottome of the Sea, as if it were beaten forwards, moves round; and let this also be granted; wherefore he concludes, the Earth is moved; which is neverthelesse is a Paralogisme. For if that wind were

the Cause why the Earth was from the beginning moved round, and the Motion either of the Sunne or the Earth were the Cause of that Wind, then the Motion of the Sunne or the Earth was before the Wind it self; and if the Earth were Moved be∣fore the Wind was made, then the Wind could not be the cause of the Earths revolution; but if the Sunne were Moved, and the Earth stand still, then it is manifest the Earth might remain Unmoved notwithstanding that Wind; and therefore that moti∣on was not made by the Cause which he alledgeth. But Paral∣logismes of this kind are very frequent among the Writers of Physiques, though none can be more elaborate then this in the Example given.

19 It may to some men seem pertinent to treat in this place of that Art of the Geometricians, which they call Logistica, that is, the Art, by which, from supposing the thing in question to be true, they proceed by Ratiocination, till either they come to something knowne, by which they may demonstrate the truth of the thing sought for; or to something which is impossible, from whence they collect that to be false which they supposed true. But this Art cannot be explicated here, for this reason, that the Method of it can neither be practised, nor understood unlesse by such as are well versed in Geometry; and among Geometricians themselves, they that have most Theoremes in readiness, are the most ready in the use of this Logistica; so that in∣deed it is not a distinct thing from Geometry it selfe; for there are in the Method of it three parts; the first whereof consists in the finding out of Equality betwixt known and unknown things, which they call Equation; and this Equation cannot be found out but by such as know perfectly the Nature, Properties and Transpositions of Proportion, as also the Addition, Substracti∣on, Multiplication, and Division of Lines and Superficies, and the Extraction of Roots; which are the parts of no meane Geo∣metrician. The Second is, when an Equation is found, to be able to judge whether the Truth or Falsity of the Question may be deduced from it or no; which yet requires greater Know∣ledge. And the third is, when such an Equation is found, as is fit for the solution of the Question, to know how to Resolve the same in such manner, that the Truth or Falsity may there∣by

manifestly appeare, which in hard questions cannot be done without the Knowledge of the Nature of Crooked-lined Fi∣gures; but he that understands readily the Nature and Proper∣ties of these, is a Compleat Geometrician. It happens besides, that for the finding out of Equations there is no certaine Me∣thod, but he is best able to do it, that has the best Naturall Wit.