Superphysics
Section 7

# Abstract Ideas

## Abstract or General Ideas are Specific Ideas Which are Given a Name

Are abstract or general ideas conceived by the mind in a general or particular way?

George Berkeley was a great philosopher. He has asserted that all general ideas are merely specific ideas annexed to a certain term, which:

• gives them a more extensive meaning, and
• makes them recall other individuals similar to them.

For me, this is one of the greatest and most valuable discoveries recently made in the republic of letters.

I shall confirm it by some arguments to put it beyond all doubt.

When we create most of our general ideas, we abstract away from it every quantity and quality.

An object continues to be regarded as part of its kind despite small changes in its space, time, and other properties. This is a dilemma that answers the nature of those abstract ideas. The abstract idea of a man represents men of all sizes and all qualities.

This can only be done by representing: All possible sizes and all possible qualities at once, or

This is absurd as it would imply an infinite capacity in the mind. No particular one at all. This is the common representation for our abstract ideas. It represents no specific degree of quantity or quality. But this is wrong. I shall show this error: by proving that it is impossible to conceive any quantity or quality without creating a precise notion of its degrees, and by showing that even if the mind’s capacity is not infinite, we can at once create a notion of all possible quantities and qualities for the purposes of reflection and conversation, however imperfect. Proposition 1: The mind cannot create any notion of quantity or quality without creating a precise notion of degrees of each.

We may prove this by three arguments: Argument 1: Objects that are different are distinguishable.

Objects that are distinguishable are separable by the thought and imagination. These propositions are equally true in the inverse: Objects that are separable are also distinguishable. Objects that are distinguishable are also different. How else can we separate what is not distinguishable or distinguish what is not different? To know whether abstraction implies a separation, we only need to: consider it in this view, and examine whether all the simple ideas which we abstract out of our general ideas is different from the ideas which we retain as essential in those general ideas. The precise degree of any quality is not different from that quality. For example, a physical line’s precise length is not different from the physical line itself. Therefore, these two ideas are not separated in the mind. The general idea of a physical line appears in the mind with a precise degree of quantity and quality, despite all our abstractions and refinements. However, it may be made to represent other lines which have different degrees of quantity and quality. Argument 2: An object or impression must enter the mind with a quantity and quality.

This confusion arises because impressions are faint and unsteady. It does not come from the mind’s inability to receive impressions that have no clear quantity and quality. An impression without a quality or quantity would be a contradiction. It would imply that it is possible for the same thing to be and not to be. Since all ideas are derived from impressions and are nothing but copies and representations of impressions, whatever is true of the one must be true for the other. Impressions and ideas differ only in their strength and vivacity. The connection between impressions and ideas is not based on their vivacity. Therefore, the connection cannot be affected by any variation in their vivacity. An idea is a weaker impression. A strong impression must necessarily have a quantity and quality. Therefore, its copy or representative must also have a quantity and quality.

## Argument 3: A general principle in philosophy is that everything in nature is individual.

It is absurd to suppose that a triangle can have no precise sides and angles and yet exist.

If this is absurd in reality, it must also be absurd in idea, since no clear and distinct idea which we can form is absurd and impossible.

But forming the idea of an object and forming an idea is simply the same thing.

The reference of the idea to an object is an extraneous denomination.

It bears no mark or character in itself. It is impossible to form an idea of an object that has quantity and quality but has no precise degree of either. It follows that there is an equal impossibility of forming an idea that is unlimited in quantity and quality. Abstract ideas are therefore in themselves individual, however they may become general in their representation. The image in the mind is only that of a specific object even if the application of it in our reasoning is the same, as if it were universal.

Abstract Ideas and Generalizations Arise from the Tendency of Mind to Connect Ideas Readily

Proposition 2: The creation of ideas beyond their nature comes from our collecting all their possible qualities and quantities in such an imperfect manner for the purposes of life.

When we find a resemblance [Footnote 2] among several objects that often occur to us, we apply the same name to all of them, whatever:

• differences we may observe in their quantity and quality, and
• other differences may appear among them.

After we have acquired this habit, the hearing of that name:

• revives the idea of one of these objects, and
• makes the imagination conceive it with all its particular circumstances and proportions.

### Footnote 2

Even different simple ideas may be similar to each other. It does not matter that they are more similar than they are different. Blue and green are different simple ideas. But they are more similar than blue and red, even if they cannot be separated in their perfectly simple form as colors. It is the same case with particular sounds, tastes, and smells. These admit of infinite resemblances when compared generally. This is certain even from the very abstract term ‘simple idea’. ‘Simple idea’ comprehends all simple ideas. These simple ideas resemble each other in their simplicity. Yet from their very nature, this simplicity is not separable from the other simple ideas. It is the same case with all the degrees in any quality. They are all similar. Yet the quality in any individual, is not distinct from the degree. But the same word is also frequently applied to other individuals that are different from that idea immediately present to the mind.

That word is unable to revive the idea of all these individuals, but only touches the soul and revives that acquired habit. They are only present in power to the mind, and not in fact nor in reality. We do not draw them all out distinctly in the imagination. Instead, we keep ourselves ready to survey any of them, depending on our need. That word raises up an individual idea, along with a certain habit. That habit produces any other individual habit that we need. But the production of all the ideas, to which the name may be applied, is impossible in most cases. We shorten that task by a more partial consideration. We then find only a few inconveniences in our reasoning from that abridgment.

This is one of the most extraordinary circumstances: after the mind has produced an individual idea, a habit is revived by the general or abstract name of that idea.

This habit readily suggests any other individual idea if by chance we do not agree with first individual idea. For example, if we mention ’triangle’, we often create the idea of an equilateral triangle. We then assert that its three angles are equal to each other. However, this thinking of angles makes us realize that not all triangles are equilateral. We then think about scalene and isosceles triangles and make us perceive the falsehood of our first idea. Hasty Generalizations Lead to False Reasoning and Sophistry Some imperfection in the mind’s faculties prevent the mind from suggesting those subsequent ideas.

This imperfection is often the source of false reasoning and sophistry. This is principally the case with abstruse and compounded ideas. On other occasions: the habit is more entire, and we seldom run into such errors.

The custom is so entire that the very same idea may be:

• annexed to different words, and
• employed in different reasonings without any danger of mistake.

For example, the idea of an equilateral triangle with a perpendicular inch serves us in talking about:

• a shape,
• a rectilinear shape,
• a regular shape
• a triangle, and
• an equilateral triangle.

In this case, all these terms are attended with the same idea.

But as these terms are applied to an awareness of ideas, they:

• excite their particular habits, and
• keep the mind watchful that no contrary idea is created.

Before those habits have become perfect, the mind might not be content with creating only one individual idea.

It may run over several ideas in order to make itself understand:

• its own meaning, and
• our awareness of that collection of ideas, which it intends to express by the general term.