Tertium Organum

I see it, therefore it is. 
This assertion is the main source of all illusions. The right way to put it 
would be: 
I see it, therefore it is not! 
Or at any rate: 
I see it, therefore it is not 
so! 
We can say the latter, but animals cannot. For them whatever they see - is. 
They have to believe what they see. 
How does the world appear to animals? 
For animals the world is a series of complex moving surfaces. Animals live 
in a 
two-dimensional
world; their universe has the appearance and properties 
of a 
surface.
And on this surface there take place a vast number of movements 
of the most varied and fantastic character. 
Why should the world appear as a surface to animals? 
First of all, because it appears as a surface 
to us. 
But we 
know 
that the world is not a surface, whereas animals cannot know 
it. They accept everything as it appears. They cannot correct what the eye 
sees, or cannot do so to the same degree as we can. 
We can measure in three directions; the quality of our mind enables us to 
do so. Animals can measure simultaneously only in two directions; they can 
never measure in three directions at once. This is due to the fact that, having 
no concepts, they are incapable of keeping in mind the measurements of the 
first direction while measuring the second and third. 
I will explain this more clearly. 
Let us imagine ourselves measuring a 
cube.
In measuring a cube in three 
directions, we must, while measuring in one direction, keep in mind, 
remember,
the two others. But things can only be kept in mind as concepts, 
i.e. we can remember them only by connecting them with various concepts, 
by labelling them in one or another way. 

---

Thus, having labelled the first two directions -
length
and 
breadth,
it is 
possible to measure the 
height. 
Otherwise it could not be done. As 
representations 
the first two measurements of a cube are absolutely identical 
and are bound to merge in our mind into one. An animal has no concepts, so 
it cannot label the first two measurements of the cube as length and breadth. 
Therefore, at the moment when it begins to measure the height of the cube, 
the first two measurements will merge into one. An animal measuring a cube 
and possessing no concepts but only representations, will resemble a cat I 
once observed. She dragged her kittens - there were five or six of them - into 
different rooms and could not collect them together again. She would get 
hold of one, carry it over to another and put them side by side. Then she 
would start looking for the third, bring it along and place it with the other 
two. Then immediately she would seize the first, carry it to another room and 
put it there beside the fourth; then she would again run to the first room, 
catch hold of the second and drag it somewhere else to the fifth, and so on. 
For a whole hour the cat struggled with her kittens, genuinely harassed, but 
could do nothing. Clearly she had no concepts to help her remember how 
many kittens there were in all. 
It is extremely important to explain to oneself an animal's relationship to 
the measurement of solids. 
The whole point is that animals see nothing but surfaces. (This we can say
with the utmost conviction, since we ourselves see nothing but surfaces.)
Seeing only surfaces, animals can represent to themselves only two 
dimensions. The third dimension, side by side with the first two, can only be
thought, 
i.e. this dimension must be a concept. But animals have no concepts; 
the third dimension appears also as a representation. Consequently, at the 
moment of its appearance, the first two representations invariably merge into 
one. Animals see the difference between two dimensions, but cannot see the 
difference between