But, before all things, a means must be devised for improving the understanding and purifying it, as far as may be at teh outset, so that it may apprehend things without error, and in the best way possible.
p5.
Reflection shows that all modes of perception or knowledge may be reduced to four:
I. Perception arising from hearsay or from some sign which everyone may name as he pleases
II. Perception arising from mere experience--that is, from experience not yet classified by the intellect, and only so called because the given envent has happened to take place, and we have no contradictory fact to set against it, so that it therefore remains unassailed in our mind.
III. Perception arising when the essence of on thing is inferred from another thing, but not adequately; this comes when from some effect we gather its cause, or when it is inferred from some general proposition that some property is always present.
IV. Lastly, there is the perception arising when a thing is perceived solely through its essence, or through the knowledge of its proximate cause.
p6.
The intellect, by its native strength, makes for itself intellectual instruments, whereby it acquires strength for performing other intellectual operations, and from these operations gets again frest instrumetns, or the power of pushing its investigations further, and thus gradually proceeds till it reaches the summit of wisdom.
p10.
In order to know that I know, I must first know... the idea of an object has its own individuality, which may become the subject for yet another idea.
p11.
In order to be free from fault, the following rules should be observed in definition.
I. If the thing in question be created, the definition must comprehend the proximate cause. (Re: the construction of a circle).
II. A conception or definition of a thing should be such that all the properties of that thing, in so far as it is considered by itself, and not in conjunction with other things, can be deduced from it.
p32.
The rules for the definition of an uncreated thing are as follows:
I. The exclusion of all idea of cause--that is, the thing must not need explanation by anything outside itself.
II. When the definition of the thing has been given, there must be no room for doubt as to whether the thing exists or not.
III. It must contain, as far as the mind is concerned, no substantives which could be put into an adjectival form; in other words, the object defined must not be explained through abstractions.
IV. Lastly, though this is not absolutely necessary, it should be possible to deduce from the definition all the properties of the thing defined.
p33.
The properties of the understanding which I have chiefly remarked, and which I clearly understand, are the following:
1. It involves certainty --- in other words, it knows that a thing exists in reality as it is reflected subjectively.
2. That it perceives certain things, or forms some ideas absolutely, some ideas from others. Thus it forms the idea of quantity absolutely, without reference to any other thoughts; but ideas of motion it only forms after taking into consideration the idea of quantity.
3. Those ideas which the understanding forms absolutely express infinity; determinate ideas are derived from other ideas. Thus in the idea of quantity, perceived by means of a cause, the quantity is determined, as when a body is perceived to be formed by the motion of a plane, a plane by the motion of a line, or, again, a line by the motion of a point. All these are perceptions which do not serve towards understanding quantity, but only towards determining it. This is proved by the fact that we conceive them as formed as it were by motion, yet this motion is not perceived unless the quantity be perceived also; we can even prolong the motion to form an infinite line, which we certainly could not do unless we had an idea of infinite quantity.
4. The understanding forms positive ideas before forming negative ideas.
5. It perceives things not so much under the condition of duration as under a certain form of eternity, and in an infinite number; or rather in perceiving things it does not consider either their number or duration, whereas, in imagining them, it perceives them in a determinate number, duration, and quantity.
6. The ideas which we form as clear and distinct, seem to follow from the sole necessity of our nature, that they appear to depend absolutely on our sole power; with confused ideas the contrary is the case. They are often formed against our will.
7. The mind can determine in many ways the ideas of things, which the understanding forms from other ideas: thus, for instance, in order to define the plane of an ellipse, it supposes a point adhering to a cord to be moved around two centers, or, again, it conceives an infinity of points, always in the same fixed relation to a given straight line, or a cone cut in an oblique plane, so that the angle of inclination is greater than the angle of the vertex of the cone, or in an infinity of other ways.
8. The more ideas express perfection of any object, the more perfect are they themselves; for we do not admire the architect who has planned a chapel so much as the architect who has planned a splendid temple.
p36-37.