Chapter 6

1454. The idea of being would not be in us prior to all experience if we could form it for ourselves through abstraction. If we could form it in this way, there would be no a priori reasoning, the forces proper to which we are describing [. . .]. It will be useful, therefore, to reinforce the truth we are demonstrating and those following it, that is, that the idea of being cannot come to us through abstraction. The analysis just carried out on this idea offers us a new opportunity of doing this.

Let us examine the nature of abstraction to see what its capacities are. `To abstract’ means simply to separate a part or element of a thing and consider it as though the other part from which it is separated did not exist. When I analyse an idea, therefore, I discover only what that idea contains. I do not impose any law on the idea; I simply adapt myself to it. I do not say first: `Such and such must be found in this idea, such and such must not be found there.’ I cannot establish any rule of this kind with pure abstraction, but only acknowledge that which is, without defining that which should be.

Nevertheless, the formation of abstracts is subject to certain unchangeable laws. For example, by power of abstraction I can consider extension in a straight line separately from a surface or solid extension. But the abstract that I have formed of the straight line is subject to the following law: `It cannot reasonably be considered by me as a true being, subsisting of itself and divided from the other two dimensions.’ On the other hand, if I consider the upper half of a column and abstract from the lower half, I find that this kind of abstraction is subject to a different law: `The upper half can be considered by me as a being that really subsists, divided and detached from the lower half of the column.’

Again, I abstract the weight from a body. I can consider the body abstractly without weight for as long as I please, but subject to this law: `If I consider it deprived of weight, I cannot at the same time consider it as heavy.’ Either of these contraries is thinkable by me, but not the two together.

Abstraction has its limits and laws, therefore, which must be maintained. All of them can be reduced to three: abstraction cannot 1. make two contradictory things non-contradictory; 2. make it conceivable that an accident subsist without a substance; 3. make an effect conceivable without a cause. These three primary laws of abstraction are not produced by abstraction, but by the efficacy of these three principles of contradiction, substance and cause. The efficacy of the three principles cannot arise from abstraction, therefore. Abstraction is a faculty subject to these principles which it follows and obeys; it does not produce them.

But these principles, which impose limits and laws on abstraction itself, and on the other operations of the human understanding,(326) are simply the idea of being considered in its applications.
The idea of being directs abstraction through its own intimate force, therefore, and imposes laws upon it. Consequently it cannot be produced and originated by abstraction (cf. NS, 243).

1455. When in the course of this work I call the idea of being in general most abstract, I do not mean, therefore, that it has been produced by the operation called abstraction, but simply that of its own nature it is set apart and separate from all subsistent beings. It is true that in the order of formed abstractions it could be said that there is something more abstract than even the idea of being; the idea of unity, of possibility, and so on, are ideas that suppose an abstraction carried out on being itself, although they cannot be thought by the mind unless it continues to have being present to itself, and refers these ideas to being.

Notes

(326) Some thinkers reduce all the operations of human understanding to analysis and synthesis. Let me simply observe that two kinds of synthesis have to be very carefully distinguished. They are very different from one another, and in one of them the understanding exercises a special efficacy which is not so marked in the other. The usual general definition of synthesis is `a conjunction of ideas', but this cannot be considered valid because it indicates only one kind of synthesis. The kind it does not indicate requires greater attention because by it the spirit not only joins ideas already possessed, but produces new ideas for itself. It does this in two ways, the first of which is that of primitive synthesis. Here the spirit, by joining a feeling to the idea of being, produces perceptions and ideas of things (cf. NS, 118–132). The second appertains to the integrating faculty of the understanding through which we rise immediately from the idea of an effect to form that of a cause, or carry out some similar movement (cf. OT, 623 ss.). Negative ideas are produced with the second kind of synthesis, positive ideas with the first.