The Infinite Divisibility of Our Ideas of Space and Time

The Limitation of the Mind Limits our Cognition of the Existence of Objects

Philosophers often greedily embrace whatever is paradoxical and is contrary to the first and most unprejudiced notions of mankind.

They think that this would show the superiority of their science. Their science could discover opinions so far from ordinary conception.

On the other hand, anything proposed to us which causes surprise and admiration, satisfies the mind that it:

• indulges itself in that surprise and admiration, and
• will never be persuaded that its pleasure is entirely baseless.

From these dispositions in philosophers and their disciples, arises that mutual complaisance between them.

The philosophers furnish many strange and unaccountable opinions. Their disciples then so readily believe them.

The most obvious example of this mutual complaisance is in the doctrine of infinite divisibility.

I shall examine this with the ideas of space and time. Obviously, the capacity of the mind is limited and can never fully conceive infinity.

It is also obvious that:

• whatever can be divided to infinity, must consist of an infinite number of parts, and
• it is impossible to limit the number of parts, without limiting the division.

Our idea of any finite quality is not infinitely divisible.

By proper distinctions and separations, we can divide this idea into parts which are perfectly simple and indivisible.

We reject the mind’s infinite capacity.

Instead, we suppose that the mind can reach the final division of its ideas.

Therefore, the imagination may reach a minimum idea which it cannot further subdivide or reduce without destroying.

When you tell me of the 1/1,000th and 1/10,000th part of a grain of sand, I have a distinct idea of:

• these numbers, and
• their different proportions.

But the images that I create in my mind to represent the sand themselves, are:

• not different from each other, and
• not inferior to that image of a grain of sand itself.

What consists of parts is distinguishable into those parts. What is distinguishable is separable.

But the idea of a grain of sand is:

• not distinguishable, and
• not separable into 20, much less into 1,000, 10,000, or an infinite number of different ideas.

The same is true for the impressions of the senses and the imagination.

Put a spot of ink on paper, fix your eye on that spot, and walk away that finally you lose sight of it. The moment before it vanished, the image or impression was perfectly indivisible. The smallest parts of distant bodies do not convey any sensible impression, not because of the lack of light striking our eyes.

It is because they are removed beyond that distance, at which their impressions were:

• reduced to a minimum, and
• incapable of any further reduction.

A microscope or telescope, which renders them visible, does not produce any new rays of light.

It only spreads the rays which always flowed from them.

By that means, it:

• gives parts to impressions, which to the naked eye appear simple and uncompounded, and
• advances to a minimum, what was formerly imperceptible.

We may hence discover the error of the common opinion:

• that the mind’s capacity is limited on both sides, and
• that it is impossible for the imagination to create an adequate idea of what goes beyond a certain size.

There are ideas and images perfectly simple and indivisible.

Therefore, nothing can be smaller, than:

• some ideas which we form in the fancy, and
• some images which appear to the senses.

The only defect of our senses is that they:

• give us disproportional images of things, and
• represent as minute and uncompounded what is really great and composed of so many parts.

We are not sensible of this mistake.

We take the impressions of those minute objects to be equal to the objects. We find by reason that there are other objects vastly more minute.

We too hastily conclude that these more minute objects are inferior to any idea of our imagination or impression of our senses.

We can create ideas no greater than the smallest atom of the animal spirits of an insect 1,000 times smaller than a mite.

We should rather conclude, that the difficulty lies in enlarging our conceptions to create a just notion of a mite or an insect 1,000 times smaller than a mite.

To form a just notion of these animals, we must have a distinct idea representing every part of them.

According to the system of infinite divisibility, this idea is:

• utterly impossible, and
• extremely difficult because of the vast number and multiplicity of these parts.