Below is my draft translation of the preface to Christoph Wittich’s Anti-Spinoza, entitled ‘On the Method of Demonstration’. Wittich criticises Spinoza’s use of the synthetic method, and this ends up being the basis of his criticism of the Ethics in general. Later I’ll write a post about a specific application. I’ve translated more of the book, but I’m not ready to share it yet. Corrections are of course welcome. You can get the original here.
Before we undertake this Examination of Spinoza’s Ethics, which he describes as ‘demonstrated in geometrical order’, it will serve us to attach a preface on the method Spinoza chooses to use. This is the synthetic method, proceeding from definitions, axioms, and postulates, to propositions and their demonstrations. To these latter, corollaries and scholia are often attached.
But there are two types of demonstration received from mathematicians. Some proceed by analysis, others by synthesis.
Analysis reveals the true way in which things are discovered methodically and as it were a priori, so that if the reader follows and attends carefully to everything, he understands no less than if he himself had made the discoveries without being led by anyone else. But this method does not draw assent from those less attentive or hostile. Hence someone less attentive than those who make the propositions can easily refuse assent to whatever slips past him.
The synthetic method works the opposite way: the mode of discovery is hidden from the reader and another, more severe, way is shown. If the reader follows this, however hostile or resistant he is to what is demonstrated, in order to reject it he would have to deny the things demonstrated earlier, which he has already admitted. But this does not satisfy the mind, nor does it thus suit the minds of students as much as the other method, since it hides the means by which the things were discovered.
The analytic method assumes nothing that is in any way obscure, but advances from what is clear in itself to what is obscure, and thus elucidates it [what is obscure] from clear notions, rendering it no less clear than what was evident in itself. But, given this, the greatest attention is required so that the mind can assent to nothing besides what is clear in itself. And so whoever follows this method proceeds at a pace as slow and halting as his own nature dictates. Therefore [this method] does not gather together known notions at the same time as sending forth unknown ones. It offers the matter of inquiry to be freely examined in itself, using what is known. Nor are any clear and evident axioms (which all other propositions presuppose) brought before the mind besides those directly applying to the matter at hand.
The synthetic method aims more at convincing the mind of the truth than at clearly and distinctly explaining the nature of things. As it aims to convince, it gathers known notions and natural truths ahead of its demonstrations: definitions and evident axioms to which assent is given. If a conclusion subsequently arrived at is not in itself such as to command assent, the mind is forced to it by the definitions and axioms known in advance and already admitted.
Thus the analytic method does not consider those clear and evident things from which nobody dissents in themselves but rather the feeling by which they affect the mind while it attends to them accurately. Whence it does not prove the matter, if it is graspable in itself by clear attention of the mind, to those who contradict it; rather, it commands those contradicting it to apply all the power of their souls to considering it, ridding themselves of all prejudices and affects. The method’s purpose in use against another is that it forces a thing to be explained and removes the cause of its obscurity in the other’s mind.
But the synthetic method, while it establishes a proof for all those who contradict the matter, often greatly upsets the order of nature and treats immediately of things that it would only treat much later if it were following the order of nature. And this is the reason that analytic method does not use demonstrationes ab absurdum, which are frequently found in synthetic method: they can convince some minds of certain things, but no clarity flows from them. So the mind acquires a certain assent to the thing, but so long as it is ignorant of why it assents it is deprived of full satisfaction.
Although synthetic method does not leave out species of those genera of things it discusses, nevertheless it does not use divisions, nor does it observe that this or that genus has so many species or prove that the general notion of a genus can receive only these differences. Rather, it collects species into a certain order and explains their definitions. But analytic method, being very careful that nothing is omitted that will be used in what follows, begins from the most general and simple things, and, when it has explained them all (as people can generally speak of genera before saying anything of species, or of wholes before discussing parts), it divides the genus into as many species as it can admit differences and the whole into its parts and, however difficult this is, sets it forth in all its parts.
Thus truly the synthetic method often deviates greatly from the order of nature, supposing it to be unnecessary to order propositions and demonstrations in the way it would have to if it followed that order. And therefore things are often demonstrated in difficult ways and not naturally discovered, but rather greatly far-fetched, forced, and only artificially prepared and constructed. Of this, many examples can be found in Euclid.
Contrary to this, the analytic method accurately observes the order of nature, proving nothing except by the true causes and true principle of things, leading the mind by the straightest, shortest, and therefore easiest path, towards which the mind is grateful and accepting — wishing and loving to be led until a full and perfect knowledge of those things inquired into is achieved.
And just as it harms not a little the perspicuous perceptions of the mind if we try to constrain it within the form of the syllogism, since then it passes over considering those propositions whose truth is obvious in order to examine propositions that are not so clear, so the mind is restricted by definitions and axioms separated from their matter and not collected under a natural series. For then it cannot enjoy its own liberty nor be led in the way it prefers: where prior thoughts are not greatly removed from what follows but immediately connected to it, as is precisely followed in the analytic method.
Spinoza, who examines method in his Treatise on the Emendation of the Intellect, seems to commend the method per analysin. Thus on p.367 he says: ‘The true method is the way that truth itself, or the objective essences of things or the ideas (all these signify the same thing) should be sought in order’, which is general, but he attaches this: ‘But for this it is necessary to understand what a true idea is, distinguishing it from other perceptions, and to investigate its nature, so that the power of our intelligence can be known and our mind constrained by a norm’ — he means to say, ‘to the norm of a true idea’, as is clear from what follows — ‘to understand by it all things that are to be understood, in addition revealing and making certain rules, so that the mind is not uselessly fatigued.’ P.368 explains this: ‘That method will be good which explains how the mind is to be led by the norm of a given true idea.’ And also: ‘As the idea of a perfect being is more excellent than the ideas of other things, the most perfect Method will be the one that shows how the Mind is to be led by the norm of the given idea of the most perfect being.’ Then on p.386 he says: ‘The right way of discovery is to form thoughts from some given definition, so that we proceed more favourably and easily the better our definition.’
But whatever we make of this, I do not think that Spinoza in his Ethics follows it, directing everything by the norm of the given idea of the most perfect being. And I think he admits many things that oppose the synthetic method to this method, since in what follows we are given most explicit demonstrations of what nobody truly doubts.
Here then we propose to the reader what is first to be weighed, which is written in a Letter to Simon de Vries in 1663, of which we read p.461. Spinoza says there:
‘distinction is to be made between two kinds of definition — between the definition that serves to explain a thing whose very essence is to be sought and which alone is in doubt, and the definition that is proposed only to be examined. Since the first has a determinate object it should be true. But the second does not require this.
E.g., if somebody asks me for a description of the Temple of Solomon, I should produce a true description of the Temple, unless I want merely to chatter. But if I have conceived in my mind some Temple that I wish to build, from whose description I conclude that I should buy so much land, so many thousand stones, and so much other material, will any sane person tell me that I have concluded badly here because I have adhered to a false definition? Or will anyone demand that I prove my definition? This would really be nothing other than telling me that I have not conceived what I have conceived, or to demand proof that I have conceived it, which is really talking nonsense.
Whence a definition either explains a thing as it is outside the intellect (and then it should be true and not differ from a Proposition or an Axiom, except that it deals only with things or their essences and affections, whereas the latter can be extended to eternal truths), or it explains a thing insofar as we conceive of it, or could conceive of it, and then it differs from axioms and propositions in that it need not be conceived absolutely nor, like an axiom, be taken as true.’
This is the same distinction that others make between real and nominal definitions — those broadly applied as the situation arises, to which are attached definitions of second notions, which should be dealt with only afterwards if one wishes to follow the analytical method.
And given that here the question was about God, the World, Souls, Men, etc. which are really existing things, there was no call for nominal definitions or second notions; the words should have been taken in the sense in which everybody accepts and employs them, and with which men are accustomed to using them in conversation. For it is certain that the definitions Spinoza takes up from the method of geometers should be restricted to explaining things whose essence can be examined and hence can be true. This is really the way that geometers define triangles, squares, circles, and other similar things, for these have a determinate object which is sought, and they explain things as they are outside the intellect. Nor otherwise could they support propositions revealing certain of their properties. If, therefore, we can show that many definitions to which Spinoza adheres do not explain things as they are outside the intellect, and that nothing outside the intellect answers to many of them, then his propositions and the whole series of them, which rests upon this foundation, will certainly fall.
But perhaps you will say, Spinoza is not thus to be reproached for having used definitions of those terms to which no things answer, but rather that he used different words than those that people use in ordinary conversation. Thus he understood by ‘attribute’ that which others understand by ‘substance’ when he ascribed a distinct essence to each attribute, and called that a substance which embraces all of these attributes having distinct essences — so that only God, to whom infinite real attributes are assigned, is called a substance. But he cannot really be excused in this way, for the license is not granted to him to change the meanings of words as he pleases, no more than a geometer is allowed to define a circle as a square and apply this definition further. But nor is this the sole vice of which we convict him. Rather, he has proposed definitions that have no truth in any things, which yet his further propositions and demonstrations are built upon, and which therefore should have explained things outside the intellect and thus been true, and ought not then to have been different from Propositions or Axioms.