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postuma； preceding his Ethics； and also in the letter quoted above； he has two circles； one of
which lies within the other； which have not； however； a common centre。
“The inequalities of the space between A B and C D exceed every number； and
yet the space which lies between is not so very great。” That is to say； if I wish
to determine them all； I must enter upon an infinite series。 This “beyond”
always； however； remains defective； is always affected with negation； and yet
this false infinite is there to hand； circumscribed； affirmative； actual and present
in that plane as a complete space between the two circles。 Or a finite line
consists of an infinite number of points； and yet the line is present here and determined； the
“beyond” of the infinite number of points； which are not complete； is in it complete and called
back into unity。 The infinite should be represented as actually present； and this comes to pass in
the Notion of the cause of itself； which is therefore the true infinity。 As soon as the cause has
something else opposed to it — the effect — finitude is present； but here this something else is at
the same time abrogated and it becomes once more the cause itself。 The affirmative is thus
negation of negation； since； according to the well…known grammatical rule； duplex negatio
affirmat。 In the same way Spinoza's earlier definitions have also the infinite already implied in
them； for instance in the case of the just mentioned cause of itself； inasmuch as he defines it as that
whose essence involves existence （supra； p。 258）。 Notion and existence are each the Beyond of
the other； but cause of itself； as thus including them； is really the carrying back of this “beyond”
into unity。 Or （supra； p。 259） “Substance is that which is in itself and is conceived from itself；”
that is the same unity of Notion and existence。 The infinite is in the same way in itself and has also
its Notion in itself； its Notion is its Being； and its Being its Notion； true infinity is therefore to be
found in Spinoza。 But he has no consciousness of this； he has not recognized this Notion as
absolute Notion； and therefore has not expressed it as a moment of true existence； for with him the
Notion falls outside of existence； into the thought of existence。
g。 Finally Spinoza says in the seventh place： “God is a Being absolutely infinite； i。e。 a substance
consisting of infinite attributes； each of which expresses an eternal and infinite essence。” Does
substance； one might here ask； possess an infinite number of attributes？ But as with Spinoza there
are only two attributes； thought and extension； with which he invests God； “infinite” is not to be
taken here in the sense of the indeterminate but positively； as a circle is perfect infinity in itself。
The whole of Spinoza's philosophy is contained in these definitions； which； however； taken as a
whole are formal； it is really a weak point in Spinoza that he begins thus with definitions。 In
mathematics this method is permitted； because at the outset we there make assumptions； such as
that of the point and line； but in Philosophy the content should be known as the absolutely true。 It
is all very well to grant the correctness of the name…definition； and acknowledge that the word
“substance” corresponds with the conception which the definition indicates； but it is quite another
question to determine whether this content is absolutely true。 Such a question is not asked in the
case of geometrical propositions； but in philosophic investigation it is the very thing to be first
considered； and this Spinoza has not done。 Instead of only explaining these simple thoughts and
representing them as concrete in the definitions which he makes； what he ought to have done was
to examine whether this content is true。 To all appearance it is only the explanation of the words
that is given； but the content of the words is held to be established。 All further content is merely
derived from that； and proved thereby； for on the first content all the rest depends； and if it is
established as a basis； the other necessarily follows。 “The attribute is that which the understanding
thinks of God。” But here the question is： How does it come that besides the Deity there now
appears the understanding； which applies to absolute substance the two forms of thought and
extension？ and whence come these two forms themselves？ Thus everything proceeds inwards；
and not outwards； the determinations are not developed from substance； it does not resolve itself
into these attributes。
2。 These definitions are followed by axioms and propositions in which Spinoza proves a great
variety of points。 He descends from the universal of substance through the particular； thought and
extension； to the individual。 He has thus all three moments of the Notion； or they are essential to
him。 But the mode； under which head falls individuality； he does not recognize as essential； or as
constituting a moment of true existence in that existence； for it disappears in existence； or it is not
raised into the Notion。
a。 The main point then is that Spinoza proves from these Notions that there is only One
Substance； God。 It is a simple chain of reasoning； a very formal proof。 “Fifth Proposition： There
cannot be two or more substances of the same nature or of the same attribute。” This is implied
already in the definitions； the proof is therefore a useless and； wearisome toil； which only serves to
render Spinoza more difficult to understand。 “If there were several” （substances of the same
attribute） “they must be distinguished from one another either by the diversity of their attributes or
by the diversity of their affections” （modes）。 “If they are distinguished by their attributes； it would
be directly conceded that there is only one substance having the same attribute。” For the
attributes are simply what the understanding grasps as the essence of the one substance； which is
determined in itself； and not through anything else。 “But if these substances were distinguished by
their affections； since substance is by nature prior to its affections it would follow that if from
substance its affections were abstracted and it were regarded in itself； i。e。； in its truth； it could
henceforth not be regarded as distinct from other substances。” “Eighth Proposition： All substance
is necessarily infinite。 Proof： For otherwise it must be limited by another substance of the same
nature； in which case there would be two substances of the same attribute； which is contrary to the
fifth proposition。” “Every attribute must be conceived for itself；” as determination reflected on
itself。 “For attribute is what the mind conceives of substance as constituting its essence； from
which it follows that it must be conceived through itself；” i。e。； substance is what is conceived
through itself （see the fourth and third definitions）。 “Therefore we may not argue from the plurality
of attributes to a plurality of substances； for each is conceived by itself； and they have all been；
always and at the same time； in subst