First Part of Spinoza’s Ethica: Concerning God

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II. Only One Substance Exists:

The one substance argument is such a striking element of Spinoza’s philosophy that it can blind even the careful reader to the other propositions in the First Part of the Ethics. To read some Spinoza commentators, this is the unique and distinguishing character of what they call Spinoza’s metaphysics. By this they appear to mean that the one substance argument contains some sort of universalizing speculative claim about the nature of the universe somewhat on the order of Plato's Theory of Forms. Needless to say there is nothing in Spinoza's actual text that even hints at any type of Coleridgean Naturtheologie. (Although there would be an interesting culture historical comparison of Spinoza's view that the universe can be studied as a comprehensively organized whole using a minimum set of basic concepts such as "substance" and the vision of his contemporaries, the Dutch landscape painters, whose art simply instills in the viewer a feeling of nature as a seamless whole held together by the invisible forces of the sky and the atmosphere.)

The one substance argument, however, is not meant to stand on its own as a view of how the universe is organized. It is not comparable to Descartes' theory of vortices or even Aristotle's theory of substance and accident. The one substance argument in Spinoza is a step leading to the final conclusion of the First Part of the Ethics that the universe has no external cause or creator.

Like the first argument that substance exists necessarily, the one substance argument is marred by basic logical flaws. Still, as we shall see, the logical fallacies of these arguments do not vitiate Spinoza's ultimate conclusions nor do they impugn the considerable originality and indeed rigor by which one may draw these conclusions.

Spinoza's Argument:

  1. Substance exists and exists necessarily (From the preceding – I Prop VII)
  2. At least one substance exists and exists necessarily (From (1) and the logical law that if some things are x then at least one thing is x (where "x" can stand for any arbitrarily chosen attribute. Spinoza did not articulate this step explicitly. Again we ignore the overarching issue of whether existence is predicable or not. We are concerned with the form of the logical reasoning independently of the meaning of the terms used.)
  3. There cannot be more than one substance each having the same attribute. (I Prop. V)
  4. There is only one substance.

A subordinate step in the argument between 2 and 3 is never explicitly stated although it is assumed in I Prop. II:

       2a. One substance is distinguished from another by a difference in attribute.


As long as we accept (2a) as axiomatic and as long as substance is conceived as possessing only one attribute, then  (3) and (4) follow logically from (2) and (2a). At this stage of the argument the attribute that differentiates substance is existence. However, later extension and mind will be introduced as additional attributes of substance. At that point the logical necessity of the argument fails because the concept of one substance having the attribute existence/extension and the concept of another substance having the attribute existence/mind are logically compatible with (2) and (2a).

Spinoza argues in I Prop. VIII that there cannot be more than one substance because each substance would not then be infinite. Fine. He may have proved that there are no infinite substances. In any event this is not a proof that there is only one (infinite) substance.

Spinoza proposes a different argument for the uniqueness of substance in Note II of I Prop. VIII:

  1. Each distinct individual of a kind must have a distinct cause of its existence. (Spinoza actually says that from definition alone existence of a certain number of individuals does not follow. There must be a distinct cause outside the definition itself of the existence of each individual.)
  2. Substance has only one cause of its existence, namely itself. (Spinoza actually says that the existence of substance is contained in its definition.)
  3. Since there is only one cause for the existence of any substance, there must only be one substance.

Error: Spinoza uses “cause” in two different senses in this argument. In (1) “cause” appears to mean physical causality. The cause of each individual man’s existence is the impregnation of a distinct human egg by a distinct human sperm. In (2) “cause” means logical dependence. Since these are in fact two different concepts with two different meanings one does not exclude the other. If “cause” is understand as physical causality and assuming that “a causes a” has any meaning at all in that case, then there is no logical reason why there cannot be two separate substances each causing itself. If “cause” is understood as logical dependence then the propositions “a exists” and “b exists” where it is not the case that a=b  can consistently be logically dependent on two distinct propositions as follows:

(a) If a exists and a is x (where "x" stands for any arbitrarily chosen attribute), then a exists.

(b) If b exists and b is y (where "y" stands for an arbitrarily chosen attribute and it is not the case that x=y), then b exists.

In other words there is nothing logically inconsistent in the notion that there may be two distinct substances such that each physically causes itself or such that the concept of the existence of each is logically dependent on itself as long as the concept of each distinct substance differs from the concept of the other. Spinoza himself provides that potentially distinct content in the attributes of extension and mind. We are assuming of course for the sake of argument that there is some meaning to the notion that the existence of a thing can be logically dependent on that thing’s concept

Prop. X contains what appears to be a separate argument for the uniqueness of substance. Spinoza reasons that two different attributes may be attributes of the same substance, i.e. they need not be attributes of two different substances. But he moves from "may" to "must" by concluding that those attributes must be attributes of a single substance. Nothing in Prop. X validates Spinoza's stronger conclusion.

Conclusion: Two substances differently conceived can have one thing in common, namely that they both exist, and nothing else in common. This contradicts Prop. II but is consistent with Def. III. For the conception of one such substance is not dependent on the conception of the other. Therefore, even if we take Spinoza's definitions at face value, there can be more than one substance.

Note 1: The correct translation of Prop. V is: “There cannot be given in the nature of things multiple substances of the same nature or attribute.” This clearly shows the difficulties Spinoza experiences in stating his argument. First, “to be given” (dare) is used without definition as a primitive term. Second, “natura” is used twice in the same sentence with what appears to be two different meanings.

Note 2: Latin, as we know, lacks articles, definite and indefinite, and this can lead to a great deal of confusion in translating into the modern European languages and also from Greek which does have articles. On a first reading Spinoza appears to trade on this confusion, speaking of substance sometimes to mean “a substance” and sometimes to mean “substance.” However, this particular confusion does not appear to vitiate Spinoza’s argument. He does not use substance as a mass term (as Hume mistakenly believed when he equated Spinoza’s “substance” with “substrate”). And he does freely use the plural term “substantiae.” He uses “substantia” more like “deus” which can mean either “God” or “a god.” As a side note, one wonders how many philosophical confusions have been produced by inaccurate translations from Greek to Latin involving articles. There’s a thesis subject for you! [Next ]

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