For those SEP members who prefer symbolic representation, what follows is the same content from above, but set out in symbolic form.
Symbolic Deduction- Symbolic representation of Creative Unity from "Aeternitas"
"Such being the relations existing within the creative unity of
Deus sive Natura, let me next attempt to indicate symbolically the
place and significance of the lower types of unity among the subordinate parts of Natura, and their relation to the eternal whole.
I begin from the constitution of Natura naturata. This must be
represented as an infinite whole composed of infinitely many parts
ranging from highest to lowest, each in its special degree reflecting
the whole.
Let these parts be P 1, P 2, P 3, . . . . P ”, .... P°°.
No one of these will completely reflect Natura naturata, but each
will do so in some degree. They will vary, therefore, in activity
from a maximum to a minimum, and hence in passivity from a
minimum to a maximum. In other words, there will be not only
reflection of the whole by each, but also that failure to reflect the
whole which implies interaction or transiency as between the parts.
The most perfect of these immediate parts of Natura naturata will
suffer least from transiency; the least perfect will suffer it most.
Thus each part will be constituted on a general plan which may
thus be symbolized:
(i) P n includes P np1, P ”p2, P npz, . . . . P npn, . . . . P np <x,
where P ”p2 is that part of P n which is due to the immanency of
P 2 in P ” .
This series represents the activity of P n, or its adequate reflection of the whole.
But the passivity corresponding to the interaction of all the other
parts of Natura naturata may also be symbolized; for these other
parts are inadequately reflected in the imperfect nature of P n. It
is important to remember that the imperfection of any part is its
partialitas, and is therefore essential to it, and mediately essential
to the whole.
Thus: (2) P n includes Pnb1, P nb2, P nbz, .... P nbn, .... P n600,
where P nb1 is that part of P n which is due to the transiency of P 2
on P ”.
This series represents the passivity of P n, or its inadequate
reflection of the whole.
Combining the two sets of parts we have:
Pn = Pn (pi, b1), Pn (p\ b% Pn (p\ bz),
__ P n{pn,b n ),___ P ” (p“ ,6°°).
Similar expressions may be used to symbolize the constitution of
all the infinite immediate parts of Natura naturata.
I may notice here that if it were assumed that all the immediate
parts of Natura naturata exactly reflected the whole, the single
general expression for such parts would be:
Pn = Pn p i, Pn pa, pn p 3}__ p npn, ___P« P°°,
1 T he term ‘reflect’ is now used in preference to ‘reproduce’ (which has elsewhere been employed, and is in many ways a more suitable term, especially
where transiency is involved), in order to avoid confusion between real production (i.e. expression or creation), and its mere reflection in finite existence.
AETERNITAS
M O D E S OF U N I T Y 211
which is the arrangement supposed by McTaggart under a system
of ‘determining correspondence’.1 The objection to such a system
is its tacit assumption that all the parts can equally reproduce
or reflect the whole, and yet maintain their partialitas. Now
Spinoza saw quite clearly that such an arrangement is impossible.
If the whole is to have parts, those parts must be distinguishable.
Their distinctness and their partialitas are one and the same.
Further, the whole must have parts if it is to possess content, and
thus be a whole.1 2 His conclusion therefore is, as I have indicated,
that there are infinite parts of all degrees of perfection ‘from
highest to lowest’, each in its degree reflecting the whole, and each
in proportion to its partialitas being subject to the transiency of
all the other parts. From this arises, as I have contended, the distinction and confusion of eternity and duration.
According to the analysis set forth, each immediate part of
Natura naturata is partly an adequate reflection of the whole
through the immanency of the whole in the part, and partly an
inadequate reflection of it. That inadequacy is the obverse of the
transiency of the other parts in so far as they are not fully reflected,
for the spirit of the whole urges to that full and infinite expression
of which it must distributively deprive itself in order to maintain
its fullness of content. Failing to achieve full expression in the part
while maintaining its perfection in the whole, there is of necessity
that pressing-in upon the part by all the other parts in so far as they
have failed to find adequate expression in it. Thus the eternal
Kevcaais gives birth to time, and imperfection to transiency; and
thus also for each part the whole is partly transparent and partly
opaque; it is partly understood and partly imagined; it is partly
eternal and partly durational, i.e. sempiternal. So the stability of
the eternal whole is maintained, and its unity is expressed in, and
constituted by, its infinite multiplicity.
I have argued that Deus sive Natura is an eternal creative unity;
that Natura naturata conceived per se is a unity which, since each
part in its measure reflects the whole but cannot wholly reproduce
it, may be called, in that restricted sense, a self-reflecting unity."
Thus the parts of the part P ” (pn, bn) will be:
[P 0 ", ”)] \Pn (l>\ b1), ^ (p\ &1)],
[P» (pn, bn)\ \pn ( f , IP), i (p\ IP)), ....
[Pn (pn, bn)) [pn (pn, bn), Jn (pn, bn)),
....{Pn(pn, bn)) \pn (p«>, i ” ), 6»(p“ , »)],
of which the part [Pn (p», bn)) [pn (pn, bn), bn (pn, b»)) is the reflection in itself of P n (pn, bn).
