The Ethics are set out in geometrical form, an arrangement intended to parallel the canonical example of a rigorous structure of argument producing unquestionable results: the example being the geometry of Euclid. The structure is synthetic rather than analytic; Spinoza begins with definitions and axioms and then derives the consequences. Both definitions and axioms are intended to carry high levels of certainty. The axioms are supposed to be indubitably true, to reflect ‘common notions’. The definitions could in principle be regarded as less certain; they could be regarded as stipulated, with the remainder of the results being of the form that if the definitions are true, then the results are true. While this is possible, we can take it that Spinoza believes his definitions are also in fact truly reflective of reality.
However, there are immediate difficulties. We open with “by cause of itself, I understand that whose essence involves existence” . We must be careful here because it already involves a variant of the ontological argument. Essence is generally defined as a property without which something cannot exist. So the definition refers to something that cannot exist without existing, which in fact has either no referents or encompasses the whole universe and thus has no explanatory power. Spinoza will later employ this ontological argument, and so if we accept it here, we must accept his subsequent position.
The axioms also display varying levels of certainty. Axiom 1 has the form (A v ~A): “Each thing that exists exists either in itself or in something else” . This of course is certain as it stands, though we must take note of the dichotomy introduced and its subsequent use, which may be less certain. On the other hand, axiom 4 seems more questionable: “Knowledge of an effect depends on the knowledge of the cause” . This seems to confuse ontology and epistemology. Hume would argue that we never observe cause or effect, merely constant conjunction. Even when setting that aside, there are manifold examples of situations wherein we claim to have knowledge of an effect without knowing anything of its cause. A child can observe a ship sinking without knowing anything about metal fatigue. The same objection applies to definition 4. Spinoza’s rigid determinism is expressed in axiom 3: “From a given determinate cause there necessarily follows an effect”
Spinoza’s three major concepts are substance, attribute and mode. A substance is any self-sufficient entity that can be conceived solely through itself. An attribute is an essential property of a substance. A mode, or affection, is the opposite of a substance in that it can only exist as a way of being of something else, i.e. it cannot be understood through itself solely. Spinoza espouses monism in the physical realm at least, and in p5, he brings these concepts together to argue that there is only one substance: “There cannot exist in the universe two or more substances of the same […] attribute” .
The argument proceeds via the claim that substances could only be distinguished either by having different attributes or different modes. If the former is the case, Spinoza has made his point; if the latter, then Spinoza claims that a difference merely in mode is insufficient to make a distinction.
Bennett holds that Spinoza commits the modal fallacy in this p5: the claim is that Spinoza has invalidly argued from (Fx and possibly Fy) to possibly (Fx and Fy). The inference is indeed logically invalid from the following substitution: x = the first student in the room, y = the second student in the room, F = the property of being the oldest student in the room. Spinoza is supposed to have done this in the move from ‘two substances x and y differ only modally’ to ‘two substances x and y could become the same and thus really be one substance’. However, a more charitable interpretation here would allow that Spinoza is guilty not of an error but of a suppressed assumption, viz. that a substance can be in any mode and may move freely among them irrespective of whether any other putative substance is already ‘occupying’ that mode. While this should have been spelt out, it does not seem a fatal error.
In p7, Spinoza introduces his version of the ontological argument: “It belongs to the nature of substance to exist” . Spinoza must be using his own definition of ‘substance’. In the tradition, the term is often associated with Aristotle, who would not have understood the idea of a single substance. “That Aristotle accepted it as a consequence of the identity of a substance with its essence that an individual substance like Socrates or Callias was identical with his essence may be disputed.”
While we do find support here for Spinoza’s line that a substance and its essence are identical, Aristotle clearly holds that there are multiple substances, as does Descartes. This would be a problem for Spinoza at this point, because then his version of the ontological argument would be open to the standard ‘floodgates’ objection, whereby if we can define a perfect dog or perfect island, then these must exist. It could be a neat inversion of the problem for Spinoza to claim that since he has used the ontological argument and this objection can be made when there are multiple substances, then there can be only one substance. There will also turn out to be a theological argument, because there cannot be more than one perfect being: the existence of one would impair the putative perfection of the other. Since Spinoza will later argue for the identity of the one substance, the universe and a perfect being, this line carries weight from his perspective.
Nevertheless, p5 and p7 are incompatible with a traditional definition of ‘substance’. Charlton considers various solutions to this, including Russell’s view that a substance is something self-causing – note the consistency of this with definition 1 and the fittingness that Spinoza should open his treatise with a reference, albeit disguised, to a perfect being. Also mentioned is Curley’s view that a substance is anything that is independent of everything else.
It is held in p8 that “every substance is necessarily infinite” . Spinoza needs this because following his identification of the one substance with a perfect being, he will be open to a concern of Descartes that finitude is “unworthy of the divine nature” in Spinoza’s own later comment on the problem. The solution is that nothing external can act on the perfect being or limit it if it is infinite.
Spinoza aims to support his argument in p7 in p8s: “If anyone were to say, therefore, that he has a clear and distinct, that is true idea of substance and yet doubts whether such a substance exists, then that would be the same as if he were to say, if you please, that he has a true idea and yet is inclined to think that it may be false”.
Spinoza has adopted Descartes’ clear and distinct perception test of truth. The form of the argument is a reductio, because the consequent that someone could simultaneously consider a proposition to be false and true at the same time is clearly unappealing. But whether the antecedent entails the consequent seems open to question. It appears that Spinoza subscribes to a correspondence theory of truth, in that if a proposition is true then there is, following Aquinas, an adaequatio intellectus et rei, meaning that what is in the mind corresponds well or adequately to a real entity. Spinoza often speaks of adequate ideas later in his work.
So the current argument viewed in this light seems to say that if someone considers that they have a clear and distinct idea of substance, then that idea is true, which means it is adequate, which means that it must correspond to something existing in the world. Objections to this would include the point that the clarity and distinctness test may not actually be a valid guide to truth, and in fact Descartes needs the existence of a perfect being as a guarantor of that. This is fine for Descartes, but Spinoza does not have a perfect being who is personal; his perfect being is one infinite substance comprising all that there is, and taking no interest in humanity: such an entity would not seem likely to confer guarantees. Further, to what extent is it reasonable to claim that we can have a clear and distinct perception of infinity? Also a variant of the argument from illusion may be relevant here, in that we often have clear and distinct perceptions of false propositions that we must correct by reason.
Later in this same section, Spinoza gives an interesting further demonstration by considering a universe comprising 20 men. Since he is determinist, each man must have a cause. But “the true definition of man does not involve the number 20” as may be appreciated from the fact that a different number could have been chosen. So the cause must be external, and “everything of whose nature several individuals can exist must necessarily have an external cause” . This is neat, because it reinforces Spinoza’s line on substance as being single and self-caused, and is a good example of his style of argument.
Spinoza, Ethics, Ed. and Tr. G H R Parkinson, Oxford University Press, 2000 (henceforward Ethics), p. 75, def. 1
Ethics, p. 77
J Bennett, A Study of Spinoza’s Ethics, Hackett Publishing Company, 1984
Ethics, p. 78
M. J. Woods, ‘Substance and Essence in Aristotle’, Proceedings of the Aristotelian Society, New Series, Vol. 75, (1974 – 1975), pp. 167-180
William Charlton, ‘Spinoza’s Monism’, The Philosophical Review, Vol. 90, No. 4 (Oct., 1981), pp. 503-529