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On the Improvement of the Understanding
[P91 thru P110]



   Now, in order at length to pass on to the second part of this method [see: P49], [N1] I shall first set forth the object aimed at, and next the means for its attainment. The object aimed at is the acquisition of clear and distinct ideas, such as are produced by the pure intellect, and not by chance physical motions. In order that all ideas may be reduced to unity, we shall endeavor so to associate and arrange them that our mind may, as far as possible, reflect subjectively the reality of nature, both as a whole and as parts.
[Note N1]: The chief rule of this part is, as appears from the first part, to review all the ideas coming to us through pure intellect, so as to distinguish them from such as we imagine: the distinction will be shown through the properties of each, namely, of the imagination and of the understanding.

   As for the first point, it is necessary (as we have said) for our purpose that everything should be conceived, either solely through its essence, or through its proximate cause. If the thing be self-existent, or as is commonly said, the cause of itself, it must be understood through its essence only; if it be not self-existent, but requires a cause for its existence, it must be understood through its proximate cause. For, in reality, the knowledge of an effect is nothing else than the acquisition of more perfect knowledge of its cause. [N1]   [P93] Therefore, we may never, while we are concerned with inquiries into actual things, draw any conclusions from abstractions; we shall be extremely careful not to confound that which is only in the understanding with that which is in the thing itself. The best basis for drawing a conclusion will be either some particular affirmative essence, or a true and legitimate definition. For the understanding can not descend from universal axioms by themselves to particular things, since axioms are of infinite extent, and do not determine the understanding to contemplate one particular thing more than another.   [P94] Thus the true method of discovery is to form thoughts from some given definition. This process will be the more fruitful and easy in proportion as the thing given be better defined. Wherefore, the cardinal point of all this second part of method consists in the knowledge of the conditions of good definition, and the means of finding them. I will first treat of the conditions of definition.
[Note N1]: Observe that it is hereby manifest that we cannot understand anything of nature without at the same time increasing our knowledge of the first cause, or God.

   A definition, if it is to be called perfect, must explain the inmost essence of a thing, and must take care not to substitute for this any of its properties. In order to illustrate my meaning, without taking an example which would seem to show a desire to expose other people's errors, I will choose the case of something abstract, the definition of which is of little moment. Such is a circle. If a circle be defined as a figure, such that all straight lines drawn from the center to the circumference are equal, every one can see that such a definition does not in the least explain the essence of a circle, but solely one of its properties. Though, as I have said, this is of no importance in the case of figures and other abstractions, it is of great importance in the case of physical beings and realities: for the properties of things are not understood so long as their essences are unknown. If the latter be passed over, there is necessarily a perversion of the succession of ideas which should reflect the succession of nature, and we go far astray from our object.

   In order to be free from this fault, the following rules should be observed in definition:-
I. If the thing in question be created, the definition must (as we have said) comprehend the proximate cause. For instance, a circle should, according to this rule, be defined as follows: the figure described by any line whereof one end is fixed and the other free. This definition clearly comprehends the proximate cause.
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, as may be seen in the definition given of a circle: for from that it clearly follows that all straight lines drawn from the center to the circumference are equal. That this is a necessary characteristic of a definition is so clear to any one, who reflects on the matter, that there is no need to spend time in proving it, or in showing that, owing to this second condition, every definition should be affirmative. I speak of intellectual affirmation, giving little thought to verbal affirmations which, owing to the poverty of the language, must sometimes, perhaps, be expressed negatively, though the idea contained is affirmative.

   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.
   All these rules become obvious to any one giving strict attention to the matter.

   I have also stated that the best basis for drawing a conclusion is a particular affirmative essence. The more specialized the idea is, the more is it distinct, and therefore clear. Wherefore a knowledge of particular things should be sought for as diligently as possible.


[NOTE: This area is not usually identified as the third part of method but based on the reference in P49 it seems to apply to it. - TNEFF]
   As regards the order of our perceptions, and the manner in which they should be arranged and united, it is necessary that as soon as is possible and rational, we should inquire whether there be any being (and, if so, what being) that is the cause of all things, so that its essence, represented in thought, may be the cause of all our ideas, and then our mind will to the utmost possible extent reflect nature. For it will possess, subjectively, nature's essence, order, and union. Thus we can see that it is before all things necessary for us to deduce all our ideas from physical things--that is, from real entities proceeding, as far as may be, according to the series of causes, from one real entity to another real entity, never passing to universals and abstractions, either for the purpose of deducing some real entity from them, or deducing them from some real entity. Either of these processes interrupts the true progress of the understanding.   [P100] But it must be observed that, by the series of causes and real entities, I do not here mean the series of particular and mutable things, but only the series of fixed and eternal things. It would be impossible for human infirmity to follow up the series of particular mutable things, both on account of their multitude, surpassing all calculation, and on account of the infinitely diverse circumstances surrounding one and the same thing, any one of which may be the cause for its existence or non-existence. Indeed, their existence has no connection with their essence, or (as we have said already) is not an eternal truth.   [P101] Neither is there any need that we should understand their series, for the essences of particular mutable things are not to be gathered from their series or order of existence, which would furnish us with nothing beyond their extrinsic denominations, their relations, or, at most, their circumstances, all of which are very different from their inmost essence. This inmost essence must be sought solely from fixed and eternal things, and from the laws, inscribed (so to speak) in those things as in their true codes, according to which all particular things take place and are arranged; nay, these mutable particular things depend so intimately and essentially (so to phrase it) upon the fixed things, that they cannot either be or be conceived without them.

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   Whence these fixed and eternal things, though they are themselves particular, will nevertheless, owing to their presence and power everywhere, be to us as universals, or genera of definitions of particular mutable things, and as the proximate causes of all things.

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   But, though this be so, there seems to be no small difficulty in arriving at the knowledge of these particular things, for to conceive them all at once would far surpass the powers of the human understanding. The arrangement whereby one thing is understood before another, as we have stated, should not be sought from their series of existence, nor from eternal things. For the latter are all by nature simultaneous. Other aids are therefore needed besides those employed for understanding eternal things and their laws; however, this is not the place to recount such aids, nor is there any need to do so, until we have acquired a sufficient knowledge of eternal things and their infallible laws, and until the nature of our senses has become plain to us.

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   Before betaking ourselves to seek knowledge of particular things, it will be seasonable to speak of such aids, as all tend to teach us the mode of employing our senses, and to make certain experiments under fixed rules and arrangement which may suffice to determine the object of our inquiry, so that we may therefrom infer what laws of eternal things it has been produced under, and may gain an insight into its inmost nature, as I will duly show. Here, to return to my purpose, I will only endeavor to set forth what seems necessary for enabling us to attain to knowledge of eternal things, and to define them under the conditions laid down above.

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   With this end, we must bear in mind what has already been stated, namely, that when the mind devotes itself to any thought, so as to examine it and to deduce therefrom in due order all the legitimate conclusions possible, any falsehood which may lurk in the thought will be detected; but if the thought be true, the mind will readily proceed without interruption to deduce truths from it. This, I say, is necessary for our purpose, for our thoughts may be brought to a close by the absence of a foundation.   [P105] If, therefore, we wish to investigate the first thing of all, it will be necessary to supply some foundation which may direct our thoughts thither. Further, since method is reflective knowledge, the foundation which must direct our thoughts can be nothing else than the knowledge of that which constitutes the reality of truth, and the knowledge of the understanding, its properties, and powers. When this has been acquired we shall possess a foundation wherefrom we can deduce our thoughts, and a path whereby the intellect, according to its capacity, may attain the knowledge of eternal things, allowance being made for the extent of the intellectual powers.

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   If, as I stated in the first part, it belongs to the nature of thought to form true ideas, we must here inquire what is meant by the faculties and power of the understanding. The chief part of our method is to understand as well as possible the powers of the intellect, and its nature; we are, therefore, compelled (by the considerations advanced in the second part of the method) necessarily to draw these conclusions from the definition itself of thought and understanding.   [P107] But, so far, we have not got any rules for finding definitions, and, as we cannot set forth such rules without a previous knowledge of nature, that is without a definition of the understanding and its power, it follows either that the definition of the understanding must be clear in itself, or that we can understand nothing. Nevertheless this definition is not absolutely clear in itself; however, since its properties, like all things that we possess through the- understanding, cannot be known clearly and distinctly, unless its nature be known previously, the definition of the understanding makes itself manifest, if we pay attention to its properties, which we know clearly and distinctly. Let us, then, enumerate here the properties of the understanding, let us examine them, and begin by discussing the instruments for research which we find innate in us.

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   The properties of the understanding which I have chiefly remarked, and which I clearly understand, are the following:--
I. It involves certainty --in other words, it knows that a thing exists in reality as it is reflected subjectively.
II. 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.
III. 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 toward understanding quantity, but only toward 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 so as to form an infinite line, which we certainly could not do unless we had an idea of infinite quantity.
IV. The understanding forms positive ideas before forming negative ideas.
V. 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.
VI. The ideas which we form as clear and distinct, seem so 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.
VII. 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 round two centres, 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.
VIII. 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.

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   I do not stop to consider the rest of what is referred to thought, such as love, joy, etc. They are nothing to our present purpose, and cannot even be conceived unless the understanding be perceived previously. When perception is removed, all these go with it.

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   False and fictitious ideas have nothing positive about them (as we have abundantly shown) which causes them to be called false or fictitious; they are only considered as such through the defectiveness of knowledge. Therefore, false and fictitious ideas as such can teach us nothing concerning the essence of thought; this must be sought from the positive properties just enumerated; in other words, we must lay down some common basis from which these properties necessarily follow, so that when this is given, the properties are necessarily given also, and when it is removed, they too vanish with it.

[The rest of the treatise is wanting.]

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