The Infinite Divisibility of Our Ideas of Space and Time

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

The mind’s capacity is limited and can never fully conceive infinity.

Obviously:

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.

We can divide this idea into parts which are perfectly simple and indivisible.

I reject the mind’s infinite capacity.

Instead, I believe that the mind can reach the final division of its ideas.*

Superphysics Note

This is now Planck length and Planck time which are not derived experimentally, but from derivation from known constants

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 divisible into those parts.

But the idea of a grain of sand* is not divisible into an infinite number of different ideas.

Superphysics Note

Here, Hume is mixed up between the idea of a grain of sand and a physical grain of sand. A grain of sand is divisible into atoms. So clearly, he means the metaphysical idea of a grain of sand.

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.
Walk away until you lose sight of it.

The moment before it vanished, the spot was perfectly indivisible.

The smallest parts of distant bodies do not convey any sensible impression because their impressions are already the smallest and cannot be further reduced.

It is not because of the lack of light striking our eyes.

A telescope gives parts to the spot, which to the naked eye appeared as one.

This shows 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, the smallest are:

some ideas in our imagination
some images that we see

Our senses:

gives us disproportional images of things
show a thing as small and single when it is really large and has 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 think that there are other objects vastly more minute.

We 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.

Superphysics Note

Here, Hume misunderstands Descartes’ animal spirits and is why we assume that this section attacks Descartes.

Instead, we should rather conclude that the difficulty is 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 of all their parts.

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.

The Infinite Divisibility of Our Ideas of Space and Time

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

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