By Gillian Howie (auth.)
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Extra info for Deleuze and Spinoza: Aura of Expressionism
The ﬁrst concerns the relationship between the attributes. We have already suggested that 22 Deleuze and Spinoza in some sense the attribute can be described as a reason or cause of substance and also that substance is self-caused. It would seem that the logical implication is that substance, or God, must be causa sui under each attribute. If an attribute is an essential property of something then F(a) such that a is F in all possible worlds. Now there are two possibilities. If there are two essential properties (F, G) and if each is strictly identiﬁed with substance then there must be more than one substance such that (F(a) and G(b)).
Deleuze claims that the extension for each term is unlimited, is inﬁnite. Immediately we can see that this requires quantiﬁcation. It is just not the case that everything is extended – only extended things are extended. Also, though, Deleuze does not wish to identify the term with the class of things falling under it – the attribute of extension is not a class of extended things. Indeed he insists that an attribute is inﬁnite because it has no parts (30). The argument for this is that substance is convertible with attributes and not modes, that the inﬁnite cannot be deﬁned in terms of an inﬁnity of parts, otherwise there would be two different types of things and the inﬁnite would not be inﬁnite.
Deleuze presents us with something a little more convoluted. The capacity to exist (possible existence corresponding to the essence of a thing), is a power.