Definition of Shape

To define the word ‘shape’, we may:

• create in our mind the ideas of circles, squares, triangles of different sizes and proportions, and
• not rest on one image or idea.

We form the idea of individuals whenever we use any general term.

We seldom or never can exhaust these individuals.

Those which remain are only represented by means of that habit, by which we recall them whenever needed. This then is the nature of our abstract ideas and general terms. In this way, we account for the foregoing paradox, that some ideas are specfic in their nature, but general in their representation.

A specific idea becomes general by being annexed to a general term.

This general term:

• has a relation to many other particular ideas, from a customary conjunction, and
• readily recalls those ideas in the imagination.

The only difficulty is the habit which so readily:

• recalls every particular idea we may have occasion for, and
• is excited by any word or sound we commonly annex to it.

I think the most proper method of explaining this act of the mind is by producing:

• other instances analogous to it, and
• other principles which facilitate its operation.

It is impossible to explain the ultimate causes of our mental actions.

But it is enough to give any satisfactory account of them from experience and analogy.

Reflection 1: When we mention any big number, such as 1,000, the mind generally has no adequate idea of it.

It can only produce such an idea through its idea of decimals, under which the number is comprehended. However, this imperfection in our ideas is never felt in our reasonings. It seems to be an instance parallel to the present reasoning of universal ideas.

Reflection 2: We have several instances of habits, which may be revived by a single word.

A person who has memorized a discourse can remember it through that single word. Reflection 3: We do not annex distinct and complete ideas to every term we use.

When we talk of ‘government’, ’negotiation’, and ‘conquest’, we seldom go through all the simple ideas that make up these complex ideas. Despite this imperfection, we can avoid talking nonsense on these subjects. We can perceive contradictions among these ideas, even if we were not experts in government, negotiation, and conquest. For example, instead of saying Argument 1 that ’the weaker party in a war always can seek negotiation’, we might say Argument 2 that ’the weaker always have recourse to conquest’. Our habit of attributing certain relations to ideas: still follows the words, and makes us immediately perceive the absurdity of Argument 2 because of the difference between ‘weaker’ and ‘conquest’.

Reflection 4: The individuals are collected together and placed under a general term which resembles each other.

This relation must:

• facilitate their entrance in the imagination, and
• make them be suggested more readily.

We shall be satisfied if we consider the thought’s common progress in reflection or conversation.

The imagination’s readiness is most admirable.

This readiness:

• suggests its ideas, and
• presents those ideas the moment they become necessary or useful.

The fancy runs from one end of the universe to the other in collecting those ideas belonging to any subject.

One would think that:

• the whole intellectual world of ideas was at once presented to us, and
• we only pick out the ideas most proper for our purpose.

However, only the ideas collected by a kind of magical faculty in the soul may be present.

This faculty is called ‘genius’ as it is most perfect in the greatest geniuses.

But it cannot be explained by the utmost efforts of human understanding.

These four reflections help remove difficulties in my hypothesis on abstract ideas.

My hypothesis is so contrary to the prevailing hypothesis in philosophy. Honestly, I place my chief confidence in my proposition on the impossibility of general ideas, according to the common method of explaining them.

We must seek some new system for this. Currently, no system exists other than what I have proposed. If ideas are specific in their nature and finite in their number at the same time, only by habit can they: become general in their representation, and contain an infinite number of other ideas under them. I shall use the same principles to explain that distinction of reason which is so much talked of, but so little understood in the schools.

Of this kind is the distinction between:

• shape and the body shaped, and
• motion and the body moved.

The difficulty of explaining this distinction arises from the above principle, that all different ideas are separable.

It follows that if the shape is different from the body, their ideas must be separable and distinguishable.

If they are not different, their ideas cannot be separable nor distinguishable.

What then is meant by a ‘distinction of reason’, since it implies neither a difference nor separation?

To remove this difficulty, we must go back to the foregoing explanation of abstract ideas.

The mind would never distinguish a shape from the body shaped, as being indistinguishable, different, nor separable, if it did not observe that there might be many different resemblances and relations, even in this simplicity.

When a sphere of white marble is presented, we receive only the impression of a white colour in a sphere-shape.

We are unable to separate the colour from that shape.

But if we observe a black marble sphere and a white marble cube afterwards and compare them with the white marble sphere, we find two separate resemblances in what before seemed, and really is, perfectly inseparable.

After a little more practice of this kind, we begin to distinguish the shape from the colour by a ‘distinction of reason’.

We consider the shape and colour together, since they are in effect the same and undistinguishable.

But we still view them in different aspects, depending on their differences with other objects. When we see a white marble sphere, we create an idea of its shape and colour.

But when we see a black marble sphere next, we tacitly consider only the shape of the white marble sphere because of its resemblance.

In the same way, we consider its white colour only when we see its resemblance with the white marble cube. Through this, we accompany our ideas with a kind of reflection which habit makes us insensible of. A person who wants us to consider a white marble sphere without thinking of its colour, wants an impossibility.

His meaning is that we should consider the shape and colour together, but still keep the resemblance to:

• the black marble sphere, or
• any other sphere of whatever colour or substance.