Undefined Primitive Terms in Spinoza's Ethica

A geometrical definition in Spinoza’s time did not require that all the terms in the definiens be defined. Euclid’s definition of “point” uses the undefined term “part” and his definition of “line” and “surface” use the undefined term “length.” A logical sequence of reasoning, however, does require that we define each term we use as closely as we can. Systems of purely formal deduction, for example, give rise to a great deal of concern over the meaning of terms like “proposition” or “name” or even “definition.”

For that reason the presence of several undefined primitive terms in the Ethics is a fault. In a wider sense the nature of the terms that are undefined is symptomatic of deeply rooted and perhaps intractable problems facing a philosophy that operates at the level of abstraction of the Ethics. One cannot resist quoting Bacon here: "Plainly words do violence to the understanding, and confuse everything; and betray men into countless empty disputes and fictions. (p. 42)"

Spinoza uses the following terms without defining them. Unfortunately many of them are used in the definitions of some of his most basic concepts:











Spinoza uses the following undefined terms in the First Part and then later defines them in the Second Part:





Clearly these are not idle words. They are critical in building Spinoza’s definitions and establishing his propositions. Nor are they clear and distinct without further explanation. In many cases they are used to define terms that Spinoza believes require explanation.

Universe: This is a red herring. It is a mistranslation of “rerum natura” by Elwes/Boyle/Parkinson. This mistranslation is both enlightening and misleading. It is enlightening because it implies that when Spinoza spoke of “the nature of things” he really meant the group of extended bodies in empty space that Galileo and Descartes showed us how to grasp conceptually and measure mathematically. And certainly Spinoza wished to include this universe and its objects as part of that substance he called “God” and which traditional religion states is created by a transcendent God. For the post-Goethe generation “universe” could also imply some sort of dynamic, earth mother infused version of bodies in space. The translation is misleading because it implies that the Cartesian universe of bodies extended is space is all that Spinoza means by “the nature of things.”  Spinoza’s argument is a logical argument. That is part of what he meant by saying that it is supposed to be “clear and distinct.” His propositions about rerum natura are supposed to be logically valid no matter what is included in the universe, including fairy sprites and Platonic abstractions. Spinoza doesn’t endorse the inclusion of fairy sprites and Platonic abstractions in the universe of things. However, he does not need to assume or endorse the kind of reductivism that states what is and is not part of the universe. For that reductivism adds nothing to the logical validity of Spinoza’s deductions and, on grounds that are irrelevant to Spinoza’s argument, may even be wrong.

Rerum natura translated by Elwes/Boyle/Parkinson as “universe” appears in I Prop. V, I Prop. VI, I  Prop. VIII, I Prop. X, I Prop. I XIV, I Prop. XXIX, I Prop. XXXIII. In the Appendix to the First Part “universe” is sometimes used as a straight translation for “natura.”

Natura: It is not clear in the First Part of the Ethics from the text itself that “natura” has some sort of basis in meaning in the Cartesian extended universe. And since philosophers like Anselm used “nature” interchangeably with “essence” and “substance,” it could be argued that “nature” in that Section is a sort of logical equivalent to “essence” as in “the nature of a thing.”  After a bit of dithering in I Props. I-VI where "nature" and "attribute" seem to mean the same thing, I Prop. VII explicitly uses “nature” as a stand in for “essence.” If it were not for the Fourth Part, where “natura” takes on the meaning of the extended nature of natural science, and the Appendix to the First Part where Spinoza makes abundantly clear that he has no truck with a transcendent God, “nature” would remain no more than a rough equivalent to “essence.”

Essentia: This term seems to mean something like “defining property” as in “essentia involvit existentiam” but a thing’s essence can clearly have a somewhat open definition. For example essence not only “involves” existence, it also is “constituted” by one or more attributes. We cannot know for sure, however, since Spinoza does not define the term.

Ens, individuum, res singularis: These terms seem to be used interchangeably and without definition. They form a silent background to sexier terms like “substance.” By way of aside, Anselm’s use of “aliquid” or “aliqua res” is much to be preferred since unlike Spinoza’s terms it functions as a grammatical or logical placeholder and not a name. The only place in the Proslogion where Anselm uses “ens” is in the phrase “summe ens” which is clearly a name.

It is a significant fault that these terms are used without definition since they form part of the definition of all of Spinoza’s critical terms, particularly “substance” and “God.”  “Thing” is also sprinkled liberally through I Props. II-V. Unless we know what a thing or an entity is we cannot know what a substance or God is. These terms can be interpreted as logical functions and not as names somewhat on the order of “Whatever…” or “For all…” but that raises the problem of interpreting a logic that uses such terms. Indeed the problem is deeper than that. Logical functions need to be qualified. There must be an answer to the question “For all what” when we begin a correctly formed proposition with the function “For all…” And Spinoza clearly intends to use “entity” and “thing” without qualification. Otherwise his propositions would not be ‘clear and distinct,” i.e. they would not have universal validity. But not to qualify “entity” and ‘thing” in some way means that those terms are meaningless, which in turn means that Spinoza’s definitions of “substance” and “God’ are meaningless and his Propositions are meaningless.

Spinoza addresses this problem in Proposition 40 of the Second Part. What he says, however, is not encouraging. The Note to II Prop. XL is one of the earliest and best stated criticisms of the use of universal abstract terms, the so-called transcendentals. His technique is genetic and makes use of his theory of mind. Spinoza argues that the body has limited capacities and so cannot retain and order all the images that come to it. Accordingly all these images become confused and merge together and terms are invented to stand for the confusion. This argument has a high degree of validity. Unfortunately Spinoza cites as particularly confused terms “entity” (“ens” mistranslated by Elwes/Boyle/Parkinson as “being”), “thing” (“res”) and “something” (“aliquid”). It is almost as if he had forgotten that he used these terms in important passages in the First Part. In any event, if this criticism is valid, then it also applies to the many passages in the First Part where these terms play a critical role in the definitions and propositions.

The confusion does not end there. In the same Note (II Prop. XL) Spinoza uses the term “particular” or “particular thing” (“singularis”) which was introduced in II Prop IX without definition. It appears to be roughly equivalent to “thing” but it is used in this context (though not in II Prop IX) with a reference to quantity. Spinoza argues that we confuse together a number of particular things to come up with general terms and specifically universal terms like “thing.”  But without explanation “particular” is also an empty universal term. Spinoza uses one empty word in the course of his attack on other empty words.

There is a good reason why the terms in question may be meaningless or undefinable and it is a logical reason that is more compelling than Spinoza’s genetic analysis. That is, any attempt to define such a term at a sufficient level of generality leads to paradox.

Esse, dare: By not defining these terms Spinoza assumes the position of a kind of existential agnostic. For if Spinoza accepts a materialist definition of “existence as “having location and extension,” then the existence of a separate God becomes a matter of verification and a logical argument for God’s existence is both insufficient and unnecessary. And it cannot be argued that there is anything whose essence involves location and extension and therefore exists by definition. But a definition like Anselm’s tacit understanding of “existence” includes Platonic Forms and just about anything else you can think of. In that case, God exists because, after all, what doesn’t exist? Since he doesn’t explicitly choose either of these alternatives, Spinoza avoids their pitfalls. But by not defining “esse” and “dare” he cannot say what exactly he has proved.

Infinitus: It is too bad that “infinite” is not defined since it plays an important role in the argument that there can only be one substance. In I Prop. VIII where “infinite (infinita)” is first used Spinoza specifies that to be finite at a minimum involves being “limited by something of the same nature (mistranslated by Elwes as “kind”).” But as usual this just compounds the problem. We have already reviewed the vagueness surrounding “nature” and the several different senses it appears to have in the Ethics. Now we are faced with the concept of being limited (terminari). I am fairly sure that Spinoza does not mean or does not mean exclusively that if something is limited it has a boundary in space and time, but without a definition one can never be sure. Conceptual delimitation is a promising but probably unsuccessful candidate without further explanation. It is easy to limit a description (concept). Just write “not” in front of the word that stands for it. “Dog” is limited by “Not Dog.” So, without further explanation, “Substance” can be limited by “Not Substance.” Spinoza could say, and maybe he thinks he is saying, that the concept of substance cannot be limited by just putting a “not” in front of the word “substance.” He could say that “Not Substance” is meaningless and that is what he means by the infinity of substance. But he doesn’t say that and accordingly he doesn’t say what it means for “Not Substance” to be meaningless. “Infinite” appears so often in the Ethics in different contexts that the lack of a rigorous definition, actually the lack of any definition, is not a good thing. However, the concept of “infinite attributes” is part and parcel of Spinoza’s second argument from the First Part, the argument where he purports to demonstrate that there is only one substance. There is a striking resemblance between Spinoza's discussion of infinite attribute's and Anselm's argument that God is infinite. As far as philosophical intentions are concerned, Spinoza's use of the concept of infinite attributes fits neatly into the overall intention of the First Part of the Ethics. Spinoza is once again showing that proofs that God is infinite, whatever that may mean, do no more than prove that the universe is infinite. As we shall see in our reconstruction of a more modest version of that argument, we can reach Spinoza’s goal, or what we think is Spinoza’s goal without resorting to the concept of infinite attributes.


Note 1: There is an uncomfortable community in the Ethics between Spinoza's stinging criticism of general terms like these as meaningless and due to the simple misuse of language and Spinoza's own use of the terms in his geometrical deductions. The discomfort can be clarified a bit by taking note of the extent of Spinoza's ambition. He wanted to attack metaphysical proofs of the existence of God from two angles. On the one hand, he poured scorn on the very language as meaningless and on the other he constructed a deduction to show that, even using the questionable terminology, the inevitable conclusion is that there is no God.

Note 2: Commentators frequently sidestep the verbal morass by asserting that these terms were in common use by scholastic philosophers. The problem is scholastics like Anselm didn't define their terms either.