Unextended molecules are the realization of the geometrical point, in all its exactness.
The arguments for or againstunextended points, for or against the infinite divisibility of matter seem equally conclusive.
The unextended is zero in the order of extension, and in order to arrive at zero by a decreasing geometrical progression it must be continued ad infinitum.
The position of bodies in general is the sum of their relations; the particular extension of each body is only the sum of the relations of its parts among themselves, until we come by an infinite division to unextended or infinitesimal points.
The unextended has no dimensions; therefore, no matter how many unextended points we may take, we can never form extension with them.
Some maintain that there are unextended points in which the division ends, and that all composite bodies are formed of these.
The first, which favors unextended points, admits the existence of the centre of gravity in all its scientific purity.
The unextendedpoint represents nothing determinate to us except the denial of extension; when, therefore, we ask if this point joined with others like it can occupy space, we ask if the unextended can be extended.
You wish to know whether extension may be produced from unextended points, and the method which you employ consists in imagining them already approached, and then trying to see if any part of space can be filled by them.
Suppose we have arrived at unextended points, how shall we reconstitute extension?
No one ever defined unity to be the negation of number, yet we always define the unextended to be that which has no extension.
I cannot conceive unextended matter, indeed, but I can easily conceive immaterial extension, an unfilled space Further, if the essence of the soul consisted in thought, it must be always thinking.
But how is the unextended soul capable of cognizing extended body?
Now let me ask you two questions: First, Whether it be agreeable to the usage either of philosophers or others to give the name Matter to an unextended active being?
This question has not escaped more recent British psychologists, including Stewart, Brown, Mill, and Bain, who seem to hold that unextendedcolour is perceivable and imaginable.
The Mind, Spirit, or Soul is that indivisible unextended thing which thinks, acts, and perceives.
The kingdom of the extended is set into the representing subjects; only the immaterial world of unextended purely spiritual monads remains as independently real.
Space, if it is to be freed from contradictions, must be regarded exclusively as spatial order, as relations between unextendedmaterial atoms.
Straight lines, planes and volumes are the spatial relations between two, three or four unextended atoms, and points are a merely convenient geometrical fiction, by which possible atoms are replaced.
Hence we obtain anunextended term for spatial relations, precisely of the kind we require.
An ultimate atom, or simple, unextended point; something ultimate and indivisible.
But for extended substances with parts to act upon unextended substances is without a parallel, and inconceivably absurd.
All unextended points have a relation to space, though they are no part of space, and do not occupy space; but an unextended substance to have no relation to space cannot be as much as a point.
A point is a located nothing, but an unextended substance is nothing, having no location.
Philosophers of ancient times imagined the existence of an immaterial substance, unextended in its nature, like nothing.
Since on which side soever he views it, either as an unextended substance or as a thinking extended matter, the difficulty to conceive either will, whilst either alone is in his thoughts, still drive him to the contrary side.
