X.

How words

may be un

derstood.

"Hence it usually happens, that when we combine LECT. words together, to each of which apart a meaning or notion answers, we imagine we understand what we without utter, though that which is denoted by such combined mening words be impossible, and, consequently, can have no meaning; for that which is impossible is nothing at all, and of nothing there can be no idea. For instance, we have a notion of gold, as also of iron: but it is impossible that iron can, at the same time, be gold, consequently neither can we have any notion of irongold; and yet we understand what people mean when they mention iron-gold.

proved.

"In the instance alleged, it certainly strikes every Further one at first that the expression iron-gold is an empty sound; but yet there are a thousand instances in which it does not so easily strike. For example, when I say a rectilineal two-lined figure, contained under two right lines, I am equally well understood as when I say a right-lined triangle, a figure contained under three right-lines and it should seem we had a distinct notion of both figures. However, as we show in geometry that two right-lines can never contain a space, it is also impossible to form a notion of a rectilineal two-lined figure; and, consequently, that expression is an empty sound. Just so it holds with the vegetable soul of plants, supposed to be a spiritual being, whereby plants are enabled to vegetate or grow. For though those words taken apart are intelligible, yet in their combination they have no manner of meaning. Just so if I say that the Attractive Spirit, or Attractive Cord, as Linus calls it, or the Attractive Force, as some philosophers at this day, is an immaterial principle superadded to matter, whereby the attractions in nature are performed; no

X.

LECT. notion or meaning can possibly be joined with these words. To this head also belong the Natural Sympathy and Antipathy of Plants; the Band of Right or law, (vinculum juris), used in the definition of Obligation, by Civilians; the Principle of Evil of the Manicheans," &c."

a Logic or Rational Thoughts on man of Baron Wolfius, c. ii., P. 54the Powers of the Human Under- 57; London, 1770.—ED. standing. Translated from the Ger

LECTURE XI.

STOICHEIOLOGY.

SECT. I.-OF THE PRODUCTS OF THOUGHT.

I. ENNOEMATIC.

III. RECIPROCAL RELATIONS OF CONCEPTS.

A. QUANTITY OF EXTENSION-SUBORDINATION AND

CO-ORDINATION.

XI.

I Now proceed to the third and last Relation of Con- LECT. cepts, that of concepts to each other. The two former relations of notions, to their objects and to their subject,-gave their Quantity and Quality. This, the relation of notions to each other, gives what is emphatically and strictly denominated their Relation. In this rigorous signification, the Relation of Concepts may be thus defined.

¶ XXXI. The Relation proper of notions con- Par. XXXI. Reciprocal sists in those determinations or attributes which Relations of Concepts. belong to them, not viewed as apart and in themselves, but as reciprocally compared. Concepts can only be compared together with reference, either, 1°, To their Extension; or, 2°, To their Comprehension. All their relations are, therefore, dependent on the one or on the other of these quantities."

¶ XXXII. As dependent upon Extension, con- Par.XXXII. cepts stand to each other in the five mutual

a Cf. Krug, Logik, § 36.-ED.

Under Ex

LECT.
XI.

Examples of the five

mutual re

lations of Concepts.

relations, 1o, Of Exclusion; 2°, Of Coextension; 3o, Of Subordination; 4°, Of Co-ordination; and, 5o, Of Intersection.

4.

1. One concept excludes another, when no part of the one coincides with any part of the other. 2. One concept is coextensive with another when each has the same number of subordinate concepts under it. 3. One concept is subordinate to another, (which may be called the Superordinate), when the former is included within, or makes a part of, the sphere or extension of the latter. Two or more concepts are co-ordinated when each excludes the other from its sphere, but when both go immediately to make up the extension of a third concept, to which they are co-subordinate. 5. Concepts intersect each other, when the sphere of the one is partially contained in the sphere of the other."

Of Exclusion, horse, syllogism, are examples: there is no absolute exclusion.

For,

As examples of Coextension,-the concepts, living being, and organised beings, may be given. using the term life as applicable to plants as well as animals, there is nothing living which is not organised, and nothing organised which is not living. This reciprocal relation will be represented by two circles covering each other, or by two lines of equal length and in positive relation.

As examples of Subordination and Co-ordination, man, dog, horse, stand, as correlatives, in subordination to the concept animal, and, as reciprocal correlatives, in co-ordination with each other.

a Cf. Krug, Logik, § 41.-ED.

XI.

What I would call the reciprocal relation of In- LECT. tersection, takes place between concepts, when their spheres cross or cut each other, that is, fall partly within, partly without, each other. Thus, the concept black and the concept heavy mutually intersect each other, for of these some black things are heavy, some not, and some heavy things are black, some not.

CONCEPTS, THEIR RELATIONS PROPER TO WIT OF

tion and

Of these relations those of Subordination and Co- Subordinaordination are of principal importance, as on them Co-ordinaa The notation by straight lines 1848.-ED. was first employed by the Author in