INFINITE.—Letter XII
to Meyer distinguishes three infinites:
1.That which is unlimited by nature
(either infinite in its kind as is each attribute, or absolutely infinite
as is substance). This infinite forms part of the properties of a
Being involving necessary existence, together with eternity, simplicity,
and indivisibility: "For, if the nature of this being were limited,
and conceived as limited, that nature would beyond the said limits
be conceived as nonexistent" (Letter XXXV);
2. That which is unlimited by
virtue of its cause. Here Spinoza is referring to the immediate infinite
modes in which the attributes are expressed absolutely. And doubtless
these modes are indivisible; yet they have an actual infinity of parts,
all of which agree with and are indissociable from one another: thus
the modal essences contained in the attribute (each essence is an
intensive part or a degree). It is for this reason that, if we consider
one of these essences abstractly, apart from the others and from the
substance that produces them, we apprehend it as limited, external
to the others. Moreover, since the essence does not determine the
existence and duration of the mode, we apprehend duration as something
which may be more or less, and existence as being composed of more
or fewer parts; we apprehend them abstractly as divisible quantities;
3. That which
cannot be equal to any number, although it is more or less large and
comprises a maximum and a minimum (the example of the sum of inequalities
of distance between two nonconcentric circles, in the letter to Meyer).
This infinite refers to the finite existing modes and to the mediate
infinite modes which they compose under certain relations. Indeed,
each modal essence as a degree of power comprises a maximum and a
minimum; and insofar as the mode exists, an infinity of extensive
parts {corpora simplicissima) pertain to it under the relation that
corresponds to its essence. This infinite is not defined by the number
of its parts, since the latter always exist as an infinity that exceeds
any number; and it can be more or less large, since to an essence
whose degree of power is double that of another there corresponds
an infinity of extensive parts two times greater. This variable infinite
is that of the existing modes, and the infinite set of all these sets,
together with the characteristic relations, constitutes the mediate
infinite mode. But when we conceive the essence of a mode abstractly,
we also conceive its existence abstractly, measuring it, counting
it, and making it depend on an arbitrarily determined number of parts
(cf. #2).
Hence there is no indefinite that
is not abstractly conceived. Every infinite is actual.
INTELLECT
(INFINITE INTELLECT, IDEA OF GOD)
The intellect, whether infinite
or finite, is only a mode of the attribute of thought {Ethics,
I, 31). In this sense, it does not constitute the essence of God
any more than does will. Those who ascribe intellect and will to God's
essence conceive God according to anthropological or even anthropomorphic
predicates. As a result, they can save the distinction between essences
only by invoking a divine intellect that surpasses our own, has a
pre-eminent status compared to ours, and is related to ours through
simple analogy. In this way, one falls into all the confusions of
an equivocal language (as with the word dog which designates
both a heavenly constellation and a barking animal, I, 17, schol.).
The Ethics conducts a twofold
critique of a divine intellect which would be that of a legislator,
containing models or possibilities according to which God would rule
creation, and of a divine will which would be that of a prince or
tyrant, creating ex nihilo (I, 17, schol.; 33, schol. 2). These
are the two great misunderstandings that distort both the notion
of necessity and the notion of freedom.
The true status of the infinite
intellect is captured in the following three propositions; 1. God
produces with the same necessity by which he understands himself.
2. God understands all that he produces. 3. God produces the form
in which he understands himself and understands all things. These
three propositions show, each in its own way, that the possible does
not exist, that all that is possible is necessary (God does not conceive
contingencies in his intellect, but 1. merely understands everything
that
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Gilles Deleuze
follows from his nature or his
own essence; 2. necessarily understands everything that follows from
his essence; 3. necessarily produces this understanding of himself
and of things). It should be pointed out, however, that the necessity
invoked by these three propositions is not the same in each case,
and that the status of the intellect seems to vary.
According to the first, God produces
as he understands himself and as he exists (II, 3, schol.).
The necessity for God to understand himself appears to be not just
based on the necessity of existing but equal to it. Hence the idea
of God comprehends substance and the attributes, and produces an infinity
of ideas just as substance produces an infinity of things in the attributes
(II, 4). And there corresponds to the idea of God a power of thinking
equal to that of existing and acting (II, 7). How does one reconcile
these characteristics with the purely modal being of the infinite
intellect? The answer is in the condition that the power of the idea
of God must be understood objectively: "Whatever follows
formally from God's infinite nature follows objectively in God from
his idea in the same order and with the same connection" (idem,
II, 7, cor.). So to the extent
that it represents the attributes and the modes, the idea of God has
a power equal to that which it represents. But this "objective"
power would remain virtual, would not be actualized, contrary to
all the requirements of Spinozism, if the idea of God and all the other ideas
that follow from it were not themselves formed—that is, if
they did not have their own formal being. Now, this formal being
of the idea can only be a mode of the attribute of thought. Indeed,
this is how the idea of God and the infinite intellect are distinguished
terminologically from one another;
the idea of God is the idea in its objective being, and the infinite
intellect is the same idea considered in its formal being. The two
aspects are inseparable; one cannot dissociate the first aspect from
the second except by making the power of comprehending an unac-tualized
power.
In the first place, this complex
status of the idea of God as infinite intellect is what explains
that the idea of God has as much unity or substance as God himself,
but is capable of imparting this unity to the modes themselves—hence
the central role of II, 4. Secondly, this complex status accounts
for the attribute of thought, as we will see when we consider the
relations of the mind and the body.
Furthermore, our intellect is
explained as an integral part of the divine intellect (II, 11, cor.;
43 schol.). Indeed, the fact that the infinite intellect
is a mode explains the adequation of our intellect to the infinite
intellect. Of course we do not know everything pertaining to God;
we only know the attributes that are involved in our being. But all
that we know of God is absolutely adequate, and an adequate idea is
in us as it is in God. The idea that we have of God himself—that is,
what we know of him—is therefore the idea that God has of himself
(V, 36). So the absolutely adequate character of our knowledge is
not just based in a negative way on the "devalorization"
of the infinite intellect, reduced to the condition of a mode; the
positive basis is in the uni-vocity of the attributes which have only
one form in the substance whose essence they constitute and in the
modes that imply them, so that our intellect and the infinite intellect
may be modes, but they nonetheless objectively comprehend the corresponding
attributes as they are formally. This is why the idea of God will
play a fundamental role in adequate knowledge, being considered first
according to a use that we make of it, in connection with the common
notions (second kind of knowledge), then according to its own being
insofar as we are a part of it (third kind).
Negation
The
Spinozist theory of negation (its radical elimination, its status
of abstraction and its fiction) rests on the difference between distinction,
always positive, and negative determination. Every determination is
negation. (Letter L, to Jelles)
1.
Attributes are in reality distinct, that is to say the nature of each
must be concieved without anything that relates itself to another.
Each is infinite in its own genre or nature, it can not be determined
or limited by anything of the same nature. This is not to say the
same that attributes define themselves by opposition of one with others:
the logic of the real distinction defines each nature by itself, by
its positive independent essence. All nature is positive, therefore
unlimited and undetermined within its genre, in the manner that it
necessarily exists (letter XXXVI, to Hudde). To positivity as infinite
essence (cor)responds affirmation as necessary existence (Ethics,
I, 7 and 8). This is because all the really distinct attributes,
precisely in virtue of their distinction without opposition, affirm
themselves in the form of one and the same substance where they express
esssence and existence. The attributes are at once the positive forms
of the essence of substance and the affimative forms of its existence.
The logic of the real distinction is a logic of co-essential positivities
and co-existent affirmations.
2.
On the other hand, the finite is well limited and determined - limited
in its nature, by other things of the same nature-; determined in
its existence, by something that denies existance in a certain place
or a certain moment.
The
Spinozist expression 'modo certo et determinato' means; within a limited
and determined mode. The existing finite mode is limited within its
essence as much as it is determined in its existence. The limitation
concerns the essence, and the determination, the existence: the two
figures of the negative. All the above is true only in the abstract,
that is to say, when considering the mode in itself, seperated from
the cause that makes it be in essence and in existence.
For
the essence of the mode is a degree of power potential (puissance).
This degree in itself does not signify a limit or a boundary, an opposition
with the other degrees, but an instrinsic positive distinction such
that all the essences or degrees come together and form an infinite
assembly in virute of their common cause.
As
for the 'existant' mode, it is true that it is determined to exist
and act, that it opposes itself to other modes, and that it passes
to perfections more or less great. But 1) says that it is determined
to exist, saying that an infinity of parties are determined from outside
and enter under the relations that characterise their essence; these
extrinsic parties belong then to their essence but do not constitute
it, they miss nothing of this essence when the mode does no still
exist or when it does not exist more (IV, end of the preface). And
all that exists, affirms its existence across all the parties: its
existence is therefore a new type of distinction, extrinsic distinction
by which the essence affirms itself in its duration (III,7); 2) The
existing mode opposes itself to the other modes that threaten to destroy
these parties, it is affected by other modes, dangerous or useful.
And following these affections of the parties, it increases its power
to act or passes to a greater perfection (joy and sadness).
