ob res turpissimum, est, quod discere non potest, qui sibi jam se scire persuasit, et per se ipsa temeritas non bene affecti Animi signum est; For the word Opinari, in the purity of the Latin Tongue, signifies a disposition of Mind, that consents too lightly to uncertain things, and so believes that he knows what he does not understand, and therefore all the Philosophers maintained, Sapientem nihil Opinari; and Cicero blaming himself for that defect, says that he was Magnus Opinator.

CHAP. IV.

Of the Composition and Simplicity of IDEAS, and of the manner of knowing by Abstraction or Precision.

WE have affirmed by the bye, in the second Chapter; that we may apprehend the Mode or Form without considering distinctly the Substance of which it is the Mode, from whence we take an occasion to explain, what is Abstraction of the Intellect.

The narrow Limits to which our Souls are confined are the reason that we cannot perfectly apprehend things, if a little compounded, without considering them in Parts, and according to the several shapes that they may receive. Which is that, which we generally call knowing by Abstraction.

But in regard that things are variously compounded, some of Parts really distinct, which we call Integral, as the Body of Man, Number, &c. It is easy thence to understand, that the Mind may consider one Part and not another, because these Parts are really distinguished: But this is not that which we call Abstraction.

Now it will be more advantagous to consider these Parts separately, to a distinct knowledge of which we can never else attain. For example the Body of Man can be no otherwise known, than by dividing it into all its Parts; as well similar as dissimilar, and by setting several names upon every one. Arithmetic also stands upon this foundation. For we have no need of Art to measure or compt little Numbers, for the Mind is able to receive them entire. So that the whole Art consists in numbering separately those Parts of Number, which being whole we cannot reckon. For as Capacious as the Mind is, it is impossible for it to multiply two Numbers consisting of eight or nine Figures, without a separate Multiplication of each Figure by itself.

Secondly, we know by Parts, when we apply ourselves to one manner not considering the Substance; or to two separately, which are not however inherent in one and the same subject. This is done by the Geometricians who make a Body extended in Length,

Breadth, and Profundity, the Object of Geometry. But for the more accurate knowledge of this they first apply themselves to the Consideration of one only Dimension. Then they consider two dimensions, Length and Breadth, which they call a Superficies; aud lastly all the three dimensions together, which they call solid Bodies.

Hence it appears how vain and ridiculous the Subtleties of the Sceptics are, who endeavour to call in question the certainty of Geometry, because it supposes Lines and Superficies that never were; for it does not suppose Lines without Latitude, nor Superficies without Profundity; but it supposes that Longitude may be considered without the consideration of Latitude; which is a thing beyond all Controversy, for in measuring the distance between City and City, we only measure the length of the way, not troubling ourselves about the Breadth.

Now by how many the more Manners we divide things, so much the more capable we become of accurately understanding them. Thus we see in motion, when the determination to what place is not rightly distinguished as well from the motion, as the parts of the determination, so long nothing can clearly be concluded concerning the causes of Reflection and Distinction, which is done by the help of this Distinction, as may be seen in the Second Chapter of Des Cartes's Optics.

Thirdly, we know by Abstraction, when the thing has several Attributes, but we only consider one, setting all the rest aside. For Example, I consider, That I think and by Consequence that I am he who thinks. Now in this Idea of myself thinking, I can only consider the Thing-Thinking, not considering that I am the Thing-Thinking, though in Me, Myself, and the Thing-Thinking are one and the same, and so the Idea which I have conceived of the Person-Thinking will not only represent me myself but all other Persons that think. In the same manner, if I consider an Equilateral Triangle, as it is described in such a Paper, with all its other determining Circumstances; that Idea will only represent this Triangle to me. But if I call off my thoughts from the consideration of these particular accidents, and apply myself to the consideration of this Figure, as consisting of three Lines; the Idea thus formed will hence more clearly explain the Equality of the Lines, and thence I become more apt and Skilful to make a representation of all other Triangles of the same Nature. If I am to go farther, and not to stop at the Contemplation of the Equality of Lines, but am to consider it as a figure consisting of three right Lines, this Idea will express all the sorts of Triangles. Lastly, if

omitting the number of the Lines, I only conceive a superficies bounded with Right-Lines, I shall form an Idea of Figures consisting of Right-Lines; and thus by degrees I may ascend to extension itself. For in these Abstractions, the inferior degree contains the superior, together with some conjoined determination. Thus I think contains the Thing Thinking: thus an equilateral Triangle contains a Triangle, and thus a Triangle comprehends á Right-lined Figure, and the upper degree represents many things so much the more clearly, by how much the less it is determined.

Lastly, it is manifest, that by the benefit of Extraction, Common Ideas are produced out of Singular, and out of Common ones still more Common. By which we are admonished to proceed to what is to be said concerning the Universality and Particularities of Ideas.

CHAP. V.

Of the Universality, Particularity, and Singularity of Ideas. ALTHOUGH whatever exists be Singular, nevertheless by the help of Abstractions, we may have several sorts of Ideas, of which some will express Singulars; and such is the Idea which every one has of himself; others will express many things together, as when a Man thinks a Triangle, considering nothing else but that it is a figure containing three Lines, and as many Angles; which Idea so formed, may serve for the apprehension of all other Triangles.

Ideas representing one thing, are called Singular and Individual: and their Objects are called Individuals, but they that represent several things, are called Universal, Common or General.

The names that denote the first, are Proper Names, as Socrates, Rome, Bucephalus. Those that signify the latter Common and Appellatives as a Man, a City, a Horse. And as well Universal Ideas as Common names may be called Generical Terms.

Note that there are two sorts of Generical Terms, one of those that are called Univocals, to which the universal ideas are so attached, that the same name may agree with several things according to the same sound, and the same Notion that is annexed to the Sound; of which sort are a Man, a City, a Horse.

The other is of those that are called Equivocals, the Sound of which is the same, annexed to different Ideas, so that the same sound or word may agree to several things, but not according to the same but various Ideas which custom has subjected to the word. Thus Canon signifies a great Gun, an Ecclesiastical De

cree, and a Rule of Art; for these significations belong all to different Ideas.

These Universal Equivocals are of two sorts. For various Ideas subjected to one Sound, have either no Relation one with another, as in the word Canon; or else they have some Relation; as when the name primarily signifies one Idea: others no otherwise than as they relate to the first Idea, as the Cause, Effect or Sign, and these Equivocals are called Analogous; thus Animals, the Air, and Diet are said to be Healthy.

Now the Idea first joined to the word, denotes Health, which is proper to Animals; but others are added, approaching near to the primary Idea, as being the Cause of Health; and therefore we call the Air Healthy, and Diet Healthy, because they both contribute to the preservation of Health.

Nevertheless when we hear speak only of Universal Terms, we understand Univocals only, with the Universal Ideas annexed.

But among all these Universal Ideas there are two which it highly concerns us rightly to distinguish, that is to say, Comprehension and Extension.

I call the Comprehension of an Idea all those attributes that are\ contained within it, so that none can be taken away, but the Idea must be destroyed. Thus the Comprehension of the Idea of a Triangle, includes Extension, Figure, Three Lines, Three Angles, and the equality of those Angles with two right Angles.

I call Extension the Subjects with which the Idea agrees, which are also called the Inferiors of the Universal Term, which being related to those, carries the name of Superior. Thus the Generical Idea of a Triangle extends itself to all the several Species of Triangles.

But though the Generical Idea confusedly extends itself to all the inferior Subjects, nevertheless between the Attributes which it comprehends, and the Subjects to which it is extended, the difference arises from hence, that we cannot despoil the Idea of any of its attributes without destroying it, as hath been said; whereas we may restrain the Extension of the same, by applying it to some of the Subjects, yet never injure the Idea. ノ

Now the Restriction of the Generical Idea may happen two ways. First by the addition of an Idea distinct and determined. Thus if I add to the. Generical Idea of a Triangle, that it has a right Angle, I restrain the Generical Idea of a Triangle to a certain species of a Triangle, which is therefore called a Rectangle Triangle.

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Secondly, By the addition of an Idea confused, and undetermined; as if a Man should say, some Triangle. In which case the Term is made particular, because that now it extends itself only to a part of the Subjects, which before comprehended all, and yet that part to which it is restrained is not determined.

CHAP. VI.

Of the Five Universal Ideas; Genus, Species, Difference, Proper,

and Accident.

WHAT has been said in the former Chapters opens us a way for the explanation in few words of those Universals which are Vulgarly made use of in the Schools.

For when the Generical Idea represents to us their Objects as Things, and that in Substantives and absolute Terms, it is called either Genus or Species.

Of Genus.

Genus is called an Idea as being so common that it extends itself also to other Universal Ideas. Thus a square Figure of four sides is a Genus, in respect of a Parallellogram or a Trapezium. And in like manner Substance is the same in respect of Substance extended, which is a Body, and the Thinking Substance, which is a Spirit.

Of Species.

But the common Idea which is another more Common and General, is called Species. Thus a Parallellogram and Trapezium are Species of a Square Figure: and thus Body and Spirit are

Species of Substance.

But one and the same Idea may be called a Genus, if it be referred to other Ideas to which it extends itself: but the Species, if it relates to an Idea more General, to which it is subservient. Thus Body is a Genus in respect of a Body animate or inanimate; but a Species in respect of Substance. Thus a Square is a Genus in respect of a Parallellogram, but a Species in respect of a Figure indeterminately taken.

But there is another Notion of Species which does not fall but upon those Ideas, which cannot be called Genuses, as when any Idea has only under it individuals and singulars. Thus a Circle has only under it singular Circles, which yet are all of the same Species, and these Species are called the Lower most..

There is also a Genus which cannot be a Species, which is called the Supreme of all Genuses, whether it be Ens or Substance.