Cause Principle Unity

Cause, principle and unity
gather countless species under determined genera, which Archytas first
declared to be ten in number; they gather the determined genera into one
being, a single thing: but this thing, this being, is understood by them as a
name, a term, as a logical concept, and finally a vain thing. For then, when
they treat of the physical, they no longer recognize a single principle of
reality and of being for all that is, as they have recognized a common concept
and name for all that which is expressible and intelligible. All this is
due to their intellectual weakness.
Thirdly, you must know that substance and being are distinct from and
independent of quantity, so that number and measure are not substance,
but relative to substance; not being, but relative to being. We must define
substance, therefore, as essentially without number and without measure
and, consequently, as one and undivided in all particular things – which,
themselves, owe their particularity to number, that is, to things relative to
substance. Thus, whoever apprehends Poliinnio as Poliinnio does not
apprehend a particular substance, but apprehends substance in the particular
and in the differences which characterize it and which, by these
differences, comes to place this man under a species in number and multiplicity.
7 And here, just as certain accidents of man cause the multiplication
of what we call human individuals, so certain accidents of animals multiply
the species of animality. Similarly, certain accidents of what is vital cause
the multiplication of what is animated and alive. It is no different for
certain corporeal accidents which cause the multiplication of corporeality,
in the same way certain accidents of the substantial multiply the substance.
And finally, in the same way, certain accidents of being cause the multiplication
of entity, truth, unity, being, the true, the one.
Fourthly, if you consider the signs and the proofs thanks to which
we wish to demonstrate the coincidence of contraries, it will not be difficult
to infer that all things are one in the end. All number, be it odd or even,
finite or infinite, is reduced to a unity which, repeated in a finite series,
posits number, and by an infinite repetition, negates number. You will
adopt signs from mathematics and proofs from other moral and speculative
sciences. Let us look at signs first: tell me what is more unlike a straight
line than the circle? Is there anything more opposite to a straight line than
a curve? And yet, they coincide in the principle and the minimum, since
7 The one substance of Bruno’s world is manifest in Poliinnio, and since he belongs to a number of
different species, such as man, philosopher, tall, etc., the number and multiplicity which are associated
with Poliinnio result from his belonging to various species rather than from the unity of substance
which is manifested in him.
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