Part I of Spinoza’s Ethica ordine geometrico demonstrata is often read as if it merely reiterates the same doctrinal claims in slightly varied forms. This impression arises from treating Part I as a linear sequence of propositional contents. Yet such a reading fundamentally misconstrues its architecture. Part I is not organized around repetition of theses but around a rigorously differentiated chain of functions. Once this functional differentiation is overlooked, the frequent use of reductio arguments and the repeated affirmation of substance’s uniqueness appear redundant, and the geometrical method itself seems opaque.
To grasp the structure of Part I, one must first clarify the role of the definitions. The definitions are not introduced in order to explain the contents of concepts such as substance, attribute, or God. Their function is rather to determine in advance which distinctions are permissible and which conceptual operations are excluded. Definitions do not derive conclusions; they establish the scope within which subsequent operations can meaningfully occur. In this sense, the definitions delineate the entire conceptual space of Part I in advance.
Against this background emerge the propositions that function as blocks on possibility. The first decisive instance is Proposition 5 (E1P5). Although E1P5 states that no two or more substances can share the same attribute, the issue at stake is not the empirical number of substances. What is at issue is whether the conceptual operation of distinguishing multiple substances under the same attribute is coherent at all. The reductio argument employed here does not merely refute a provisional hypothesis. Rather, it exposes an inconsistency between the definitions themselves and thereby establishes that such a mode of thinking is impossible. E1P5 functions to close off the very possibility-space of plural substances.
This closure is reinforced by Proposition 8 (E1P8), which asserts that every substance is necessarily infinite and thereby excludes the conceptual construction of a finite substance. Whereas E1P5 blocks multiplicity, E1P8 blocks finitude. These are not independent claims but coordinated operations that delimit the mobility of the substance concept from two directions. At this point, it becomes conceptually fixed that substance can be neither multiple nor finite.
Yet even at this stage, the ontological status of substance is not fully determined. This task is carried out by Proposition 11 (E1P11). Often interpreted as a proof of God’s existence, E1P11 is more accurately understood in functional terms as an ontological junction. For the first time, the concept of God as defined in Definition 6, the concept of substance, and the necessity of existence are connected within a single proposition. Only here does God become an object that can be treated ontologically within the system.
On the basis of this connection, Proposition 14 (E1P14) can be introduced. When E1P14 states that no substance other than God can exist or be conceived, it does not introduce a new exclusion of possibilities. The multiplicity and finitude of substance have already been ruled out by E1P5 and E1P8, and E1P11 has already established God as an existing substance. The function of E1P14 is to determine, within an already closed space of possibilities, the only remaining coherent configuration. It is here—and only here—that the identification of substance with God is completed within the system.
The functional chain of Part I does not end there. Proposition 15 (E1P15), which asserts that everything that exists is in God and cannot be conceived without God, serves a different purpose. It does not add a new ontological claim. Rather, it functions as a permission for systematic expansion. By establishing the immanence of all things in God, E1P15 authorizes the subsequent discussions of attributes, modes, and finite things in Parts II and beyond.
Seen in this light, Part I of the Ethics is structured as a chain of clearly differentiated functions: the setting of conceptual scope by definitions, the blocking of illegitimate possibilities, the ontological connection of key concepts, the systematic identification of substance and God, and finally the authorization of further development. Within this chain, reductio arguments are not rhetorical embellishments but standard instruments assigned to the task of blocking possibilities. Substance monism is not asserted by any single proposition. It emerges as a structural consequence of a sequence of functions, each of which must be fulfilled in turn.