Spinoza's Ethics

1. A APPROACHES TO PPROACHES SPINOZA PINOZA

One of the most remarkable features of the Ethics is its axiomatic form. Spinoza sets out at the start a small

number of definitions and axioms that are assuredly true, and proceeds to deduce from these the rest of his

philosophy. In this respect, the work is an attempt to use a theory of philosophy that is modelled upon Euclid's

Elements. Historically, the axiomatic form had a long tradition; direct influence upon Spinoza has been

attributed amongst others to Descarte, Hobbes and Geulincx [7, p. 169]. But the Ethics is significant in that it is

"the only major philosophical work of the 17th century rationalists which undertakes, and at least in form

achieves, the frequently expressed goal of extending the mathematical Ð''method' in this direction." [9, p. 16]

What should we make of the use of axiomatic form? In 1834, Heine wrote:

Dann finden wir bei Spinoza, wie bei Descartes, die der Mathematic abgeborgte BeweisfÐ"јhring. Dieses ist in groÐ"ÑŸes

Gebrechen. Die mathematishe Form gibt dem Spinoza ein herbes Ð"„uÐ"ÑŸere. Aber dieses ist wie die herbe Schale der Mandel;

der Kern ist um so erfreulicher.

(Then we find in Spinza's work, as in Descartes, proofs backed up by mathematics. This is a great crime. Mathematical form

gives Spinoza a bitter/unpalatable surface. But this is like the bitter shell of an almond. The kernel itself is all the more

pleasurable for it.)

The notion that the axiomatic form makes Spinoza difficult to approach is a common one; so too is the notion

that there is the Ð''real philosophy of Spinoza' hidden inside, struggling to get out (see, eg. [13, p. xi]). This view

reaches its most extreme form in Wolfson [6], who describes the axiomatic method as a purely literary mode of

presentation which has little to do with the actual philosophy. As a mode of presentation it might have several

ends: a greater clarity (although the bafflement with which it is often met suggests a lack of success in this

respect); authority and prestige through association with Greek mathematics [10, p. 270]; the guarantee of

correctness through the use of deduction; or the ability to compel readers [7, p. 144].

An alternative view is that the axiomatic form is a necessary part of Spinoza's Ethics: that the work would

be inexpressible in any other form; or that its layout was chosen to reflect the mathematical order of nature in

that causes always precede effects [10, p. 266]; or that, since Spinoza had concluded that reason (ratio) and

intuition (scientia intuitiva)Ð'--these being the second and third kinds of knowledgeÐ'--were the routes to true

knowledge [II, prop. 41], and since intution could not be conveyed in a book [7, p. 164], it would be absurd

for him to use any form other than reason. (And this ratio is by definition axiomatic: for argument-by-example,

and unordered argument, are part of the first kind of knowledge [II, note 2 to prop. 40]).

A second remarkable property of Spinoza's axiomatic form is the "fundamental disagreement among

interpreters concerning practically every aspect of this method" [12, p. 55]. Nothing written in the previous

paragraphs is uncontroversial. Is the form axiomatic, geometric or mathematical [10, p. 264]? Is it a form

(synthetic, referring to the manner in which knowledge is laid out), or a method (analytic, referring the the

manner in which knowledge is gained) [7, p. 153]? Are Spinoza's definitions and axioms assuredly true [10,

p. 273]? Is there a fluid boundary between axioms and propositions [13, p. 157]? The extent of disagreement

between interpretations, says Jarrett, "inclines one to suspect that no interpreter can cast off the biases of his own

outlook, in order to give a relatively objective interpretation of Spinoza" [9, p. 16]

In this essay we present the results of computer-based quantitative analysis of the structure of the whole

of Spinoza's Ethics. This is done with two ends. First, we use quantitative techniques as an aid to textual

investigation: the computer can point out particular interesting features of propositions that might otherwise go

unnoticed. Second, a statistical analysis of the entire structure will provide objective data about overal structural

and thematic patterns. This may provide a little additional evidence for some of the aforementioned

controversies.

2. M METHOD AND NOTATION

ETHOD The source used in this study was the Latin text in the 1977 edition of Ethique [4], arranged by the French

Spinoza Committee.

Most proofs make explicit reference to the earlier theorems upon which they depend: for instance,

consider the proof for p5.4:

2

QuÐ"¦ omnubus communia sunt, non possunt concipi nisi adÐ"¦quate (per Prop. 38 p. II); adeoque (per Prop. 12 et Lemma 2, quod

havetur post Schol. Prop. 13 p. II) nulla est Corporis affectio, cujus aliquem clarum et distinctum non possumus formare

conceptum. Q.E.D.

(That