Spinoza's conception of the infinite
Forbes, Daniel Alan
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In this dissertation I focus on a difficult problem in Spinoza’s metaphysics: how modes, which exist dependently, “follow” from substance (or God), which exists absolutely independently. In Chapter One I argue that Spinoza’s conception of infinity is key to resolving this problem. Infinitely many modes “follow” from infinite substance because substance consists of infinite attributes. However, the infinity of substance is unique and indivisible whereas the infinity of modes is manifold and divisible. The infinity of the attributes must somehow mediate between substance and modes. In Chapter Two I explore Spinoza’s conception of infinite substance. The absolute infinity of substance is absolutely positive, the “absolute affirmation” of its essence. This absolute affirmation consists in the expression of substance in infinite attributes; in Chapter Three I argue (following Gilles Deleuze) that the attributes are infinitely many yet nondenumerable; hence substance is infinitely yet indivisibly plural. However, though each attribute has equal power to express substance, the attribute of thought involves ideas of modes of all attributes and seems to express substance most comprehensively. In Chapter Four I develop a solution to this problem, “the thesis of radical mutual containment”: each attribute must contain and be contained by every attribute. This unique expressive relationship between the attributes constitutes the absolute infinity of substance. In Chapter Five I explain how infinite modes “follow” from substance: each attribute insofar as it “contains” all attributes is conceived as an “immediate infinite mode,” and insofar as it is “contained” by an attribute it is conceived as a “mediate infinite mode.” In Chapter Six I explain how finite modes may “follow” from substance: they contain infinity insofar as their infinite divisibility metaphysically presupposes the absolutely indivisible infinity of substance (as is argued by Martial Gueroult), and they are contained within infinity insofar as each finite mode is one of infinitely many expressions of a “thing as it is in itself.” In Chapter Seven I explore some consequences of this reading for metaphysical reductionism and the union of the mind and body.