APPENDIX II. Examination of Propositions I. - VI. in Spinoza's Ethics.

THE pantheistic system of Spinoza, embodied in his Ethics, is worked out with so much simulation of mathematical exactness, that to some authors, particularly to the German philosopher, Frederick H. Jacobi, it appeared to be theoretically irrefutable. We have already argued the absurdity of the two fundamental dogmas of Spinoza's monism.^{1} Moreover, we have set forth the ambiguity of two of his most important definitions, and pointed out the paralogism introduced by their use in the very first step of his reasoning.^{2} This, however, we could not do without referring to the connection between the first six propositions of the Ethics. In order now to enable our reader to see this connection, and to judge for himself as to the safety of the road cut by Spinoza to his famous Proposition VI., "One substance cannot be produced by another substance," we will examine thoroughly into the first six propositions of his Ethics.

Let us begin by singling out of the eight definitions and seven axioms with which the Ethics open, those which form the groundwork of the propositions we are concerned about. They are Definitions III., IV., V., and Axioms I., IV., V. Our comment on these fundamental principles will show that all of them are more or less ambiguous, and may therefore be applied in a true or in a false sense.

As regards Definitions III. and V. in particular, we shall sum up here what we have said on them at greater length in Bk. I. c. v. sect. 6.

Definition III. "By substance I mean that which is in itself and is conceived by itself." (Per substantiam intelligo id quod in se est, et per se concipitur.)

Comment. This definition may signify either (1) A substance is a natural whole, a complete individual being, in opposition to parts, properties, or modifications of such a being; or (2) a substance is a self-existing being.

In the first sense the definition is true, in the second arbitrary and false. (§ 79.)

Definition IV. "By attribute I understand that which the understanding apprehends in substance as constituting its essence." (Per attributum intelligo id quod intellectus de substantia percipit tanquam ejus essentiam constituens.)

Comment. The definition does not cover all attributes, but only the attributes of God, the one self-existing Being. Of course the Divine attributes are identical with the simple Divine essence. Each of them may therefore be said to constitute that essence, although self-existence is said to do so with most propriety.^{3} Of the attributes of creatures we cannot say this. Some of them complete one another to constitute an essence (e.g., animality and rationality in man); others are conceived as flowing from the essence of a being (e.g., understanding and free-will); others again are accidental modifications added to substance (e.g., learning in man).

We have then to choose between two alternalives. Either we must pronounce Spinoza's definition of "substance" to be taken in the second, false sense explained above, or we must reject his definition of attribute as altogether inadequate.

Definition V. "By mode I mean the affections of a substance, or that which is in something else, by which also it is apprehended." (Per modum intelligo substantiae affectiones, sive id quod in alio est, per quod etiam concipitur.)

Comment. This definition allows of three interpretations: (1) A mode is that which gives to anything its specific character (e.g., the principle of life to a dog). (2) A mode is a property accompanying a being, so to speak, by its acts (e.g., understanding, moral freedom). (3) A mode is an accidental modilication (e.g., skill).

Only in its second or third interpretation does Spinoza's definition of "mode" harmonize sufficiently with common parlance; perfectly in the third alone.

And now as to the three axioms:

Axiom I. is thus worded: "All that is, is either in itself or in something else." (Omnia, quae sunt, vel in se, vel in alio sunt.)

Comment. According to the different meanings that may be attached to the phrase, "in itself," this axiom signifies either, (1) everything is either a subject or a determination of a subject, which determination may be substantial or accidental (a substantial or accidental form); or (2) everything is either self-existent or inherent in self-existence.

In the first sense the axiom is true, in the second intrinsically contradictory, because in self-existence there can be no inherent determinations really distinct from it. (Th. VIII. and Th. XXII.)

Axiom IV. "Knowledge of an effect depends on knowledge of a cause, and involves the same." (Effectus cognitio a cognitione causae dependet, et eandem involvit.)

Comment. This means either (1) an effect as an effect cannot be known without the conception of a cause; or (2) a thing which is an effect cannot be known, unless it be conceived together with its cause.

In the first sense the axiom expresses a self-evident truism; in the second it is manifestly false. A child knows his home, his parents and relations, his toys, &c., before he in any way reflects upon the causes of these things. And accurate self-introspection will convince any one that his first conception of things is an apprehension of their existence and of some of their attributes (extension, colour, &c.), involving no notion of cause.

Axiom V. "Things that have nothing in common one with another cannot be understood through one another, or the conception of one does not involve the conception of the other." (Quae nihil commune cum se invicem habent, etiam per se invicem intelligi non possunt, sive conceptus unius alterius conceptum non involvit.)

Comment. This axiom may be explained in two ways: (1) Things really diverse cannot be explained by means of one another, unless under some aspect they are conceivable by a common idea. (2) Things really diverse can under no aspect be conceived by a common idea, because they have really nothing in common.

The first sense is true, the second false, involving, as it does, the absurd position of nominalism, that there are no universal ideas based upon the objective similarity of diverse essences.

Now let us see how Spinoza proves his first six propositions by the help of the ambiguous principles just explained. We give a translation both of his propositions and of his demonstrations, omitting nothing; and add our respective comments to each.

Proposition I. "Substance is prior in nature to its affections." (Substantia prior est natura suis affectibus.)

Demonstration. "This is comprised in Definitions III. and IV."

Comment. We have already fully commented on this first step of Spinoza's reasonings. (Bk. I. c. v. sect. 6.) Therefore it will suffice to remark here shortly that Proposition I. is true, if you take Definition III. in the first, and Definition V. in the second or third sense explained above. In other words, if you suppose that substance signifies any natural whole, and mode either a natural property or an accidental modification of such a whole, Proposition I. cannot be denied. If you, however, take Definition III. in the second and false sense to mean a self-existing being, and Definition V. in any of the three meanings compatible with its ambiguity, Spinoza's Proposition I. means that "a self-existent being is prior in nature either to its specific determination or to its natural properties or to its accidental modifications," an assertion which involves the absurdity that self-existence is a changeable subject. (Cf. Th. XXII.) In Spinoza's system there is no room for Proposition I. but in its second false sense, as will appear from the following:

Proposition II. "Two substances having different attributes have nothing in common with one another." (Duae substantiae diversa attributa habentes, nihil inter se commune habent.)

Demonstration. "This too appears from Definition III.; for each must be comprised in itself and conceived by itself; or, the conception of the one does not involve the conception of the other."

Comment. If to signify any being complete in itself as a natural whole Definition III. is taken in its first (true) meaning, Proposition II. is false, because diverse natural wholes, of however different attributes, may nevertheless, under one or other aspect, resemble one another, and on account of this similarity have the same attribute in common, inasmuch as its import is realized in each of them. Thus, for instance, a man and his dog have the same attribute, "animality," in common. Of either of them I say, with perfect truth, "This substance is an animal." And I say also rightly, "The substance which is really identical with the animal dog is other than that which is really identical with the animal man." If, however, Spinoza's Definition III. is taken in its second (false) meaning, so as to make substance identical with self-existence, there is no raison d'être for Proposition II.; because self-existence can only be one substance. (Th. VII.)

Proposition III. "Of things that have nothing in common, one cannot be the cause of another." (Quae res nihil commune inter se habent, earum una alterius causa esse non potest.)

Demonstration. "If the things have nothing in common, neither can they (by Axiom V.) be understood one from the other, and so (by Axiom IV.> they cannot be causes of one another: q.e.d"

Comment. If the phrase, "to have something in common," is applied in a sense quite usual, so as to mean, "to have the same predicate," Proposition III. is based on a false supposition, because there are no things which would not have at least the predicate "being" in common.

If, however, the phrase, "to have nothing in common," shall mean "to exist as diverse realities," Proposition III. is false, and the proof given by Spinoza does not really support it, unless each of the two ambiguous Axioms V. and IV. be taken in its second false meaning, pointed out above. Indeed, Spinoza's conclusion would only follow if it be supposed that Axiom V., "Things that have nothing in common one with another cannot be understood through one another," is true if you take it to mean, "Diverse things under no aspect can be conceived by a common idea;" and that the truth enunciated by Axiom IV., "Knowledge of an effect depends on knowledge of a cause, and involves the same," is no other but this manifest falsehood, "The idea of an effect, however the latter may be viewed, involves necessarily the idea of its cause."

Proposition IV. "Two or more different things are distinguished from each other either by diversity of the attributes of substances, or by diversity in the affections of these same substances." (Duae aut plures res distinctae vel inter se distinguuntur ex diversitate attributorum substantiarum, vel ex diversitate earundem affectionum.)

Demonstration. "All that is, is either in itself or in something else (by Axiom I.), that is to say, there is nothing out of or beyond the understanding except substances and their affections (by Definitions III. and V.). There is consequently nothing out of the understanding by which individual things can be distinguished from each other except substances, or -- and this comes to the same thing -- their attributes and affections (by Definition IV.)"

Comment. Different things are in the first place distinguished from one another by their different substantial being, and secondarily by their attributes and affections. In commenting upon Definition IV. we have given reasons to show that there is a difference between the substantial being of created things, or what we may call their physical essence, and the attributes of that essence. Moreover, while the essential attribute remains the same, the affections of an individual thing may vary indefinitely. The same man of whom I have to predicate constantly moral responsibility may attach his heart now to money, now to pleasure, now to virtue, &c.

It appears then that Proposition IV. is altogether false, and based upon a false application of the inadequate Definition IV. In order to be in harmony with truth, Proposition IV. must be thus worded: "Two or more different things are distinguished from each other by their different undivided substantial being; from this primary difference there follows a difference in their attributes, and in their affections, or accidental modifications, if they are capable of any such." The restriction, "if they," &c., is added with reference to the Divine substance, which is immutable.

Proposition V. "In the order of existence there cannot be two or more substances of the same nature or attribute." (In rerum natura non possunt dari duae aut plures substantiae ejusdem naturae sive attributi.)

Demonstration. "Did several distinct substances exist, they would be distinguished from each other either by diversity of attributes or by diversity of affections =modes= (as appears by the proposition immediately preceding); if by diversity of attributes only, it were then conceded that there is but one substance of the same attribute; if by diversity of affections, then inasmuch as substance is prior in nature to its affections (by Proposition I.), if we set aside its affections, and consider the substance in itself, which is to consider it truly (by Definitions III. and V.), the substance in that case could not be conceived as distinct from anything else; so that, as stated in the preceding proposition, there cannot be several substances, but one substance only."

Comment. First of all, Spinoza appeals in vain to his Proposition IV. as a firm basis of that under consideration; for we have shown above that Proposition IV. is false, and based upon false reasoning.

In development of his proof of the present proposition, Spinoza adds another piece of false information by telling us that, setting aside affections of substances, and considering them "in themselves, or truly," there is no longer any distinction of substances. This false statement he bases upon Definition III. and Definition V. Yet it does not follow from these definitions, unless we take Definition III. in its second, false sense, so as to define substance to be self-existence.

We see then that Proposition V., which has been sometimes termed the Argumentum Achilleum of Spinoza, deserves that name in that it is really vulnerable, like Achilles, if only you strike at the vulnerable spot.

The truth underlying Proposition V. amounts to this, that two different substances cannot have the same physical attribute in common. But nobody wishes to signify this, when he says that two substantial beings, say Peter and Paul, have the attnbute "rationality" in common. The meaning is that, as regards the import of this attribute, they resemble each other perfectly, and that there is consequently in their different physical substantiality a real foundation for a logical identity of attribute.

Proposition VI. "One substance cannot be produced by another substance." (Una substantia non potest produci ab alia substantia.)

Demonstration. "In the preceding proposition we have seen that there cannot in the order of existence be two substances of the same attribute, or that have anything in common (by Proposition II.); and so (by Proposition III.) one cannot be the cause of, or be produced by another: q.e.d."

To the demonstration Spinoza adds by way of corollary, "Substance cannot be produced by anything else." And in order to make this corollary, which on the hypothesis that Proposition VI. was really proved, is evident enough, still more plausible, he supports it by the reductio ad absurdum in this manner: "If substance could be produced by something else, the knowledge of substance would have to depend on a knowledge of its cause (by Axiom IV.), in which case it would not be substance (by Definition III.)."

Comment. As appears clearly from the demonstration of Proposition VI., it rests entirely on Proposition V., Proposition II., and Proposition III., all of them ambiguous, and only applicable to support Proposition VI., if they are taken in a sense manifestly false, and sophistically supposed by Spinoza as really proved.

For the demonstration of this Proposition VI. to hold, we must assume that (a) there cannot be several substances of the same logical attribute, grounded on their physical similarity (false sense of Proposition V.); (b) two substances having physically different attributes, have nothing logically in common, based upon real physical similarity (false sense of Proposition II.); (c) things that have nothing physically in common (or that are, considered in their physical existence, not one thing, but many things), cannot be cause and effect (false sense of Proposition III.).

Only, I say, by assuming all these false interpretations of ambiguously worded propositions, can any connection be made out between the premisses and the conclusion of the demonstration by which Spinoza proves Proposition VI. Consequently this proposition, which is the whole foundation of his pantheistic monism, must be pronounced to be a miserable sophism.

The same verdict must be given on the accessory proof contained in the corollary. A simple appeal to Axiom IV. and Definition III., so Spinoza thinks, is enough to show that "substance cannot be produced by anything else." Indeed, if you interpret Axiom IV. to mean that an effect under no aspect is conceivable without the conception implying the conception of its cause; and if you take Definition III. to imply that "substance" is synonymous with "self-existence," the conclusion in due course runs that no effect can be a substance, and that consequently there is only One substance effecting changes in itself. But such a process of reasoning, taken for what it is really worth, evinces no more than that from two absurd premisses there follows as usual an equally absurd conclusion.

{1} Natural Theology, Th. X. pp. 112, seq.

{2} Loc. cit. Bk. I. c. v. sect. 6, pp. 200, seq.

{3} Cf. Bk. II. c. vii.