Spinoza's Method 1.
by
Halbert Hains Britan
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§ 3. The geometrical method in Spinoza's Ethics has long been to students of that work both a stumbling-block and foolishness. To the modern mind ingrained with scientific principles and prejudices the method of geometry seems utterly inapt and unfitted for the presentation of philosophical truth. It can but be of the greatest importance, therefore, if we can learn from this early work,2. our only precedent in Spinoza's writings for the method used in the Ethics, just why Spinoza used the geometrical method in the Principles. And this is our sole chance for learning why he employed this method; there is little help to be gained by even the most careful study of the Ethics alone. When he wrote that work, Spinoza's opinions and habits of thought had so far become crystalized that he did not introduce any comment that would serve to make this point clear. Our answer to this question, therefore, must be found in the work below or it will not be found at all.
When we turn, now, to the Principles to consider the method in which it is presented we are soon forced to the conclusion that this geometrical method was not employed because Spinoza thought he could thus present an irrefragable body of truth. He did not use this method because of the apodeictic character of its proof. This is conclusively shown by the fact that he used the method alike to present propositions in which he believed and those to which as he said he held the exactly opposite opinion.3. In the latter cases the proof is no less rigid, the argument no less logical than when he has given propositions which held his hearty assent. Let us then get this idea firmly fixed in our minds, that Spinoza did not regard the geometrical method, either in the work translated below or in the Ethics, as an apodeictic demonstration of the opinions he thus expresses. Such an opinion is flatly contradicted in his first use of this method, and we have no reason for believing that it was in any way different in the case of its later use. Whatever his purpose may have been, it was not to present by its use a philosophical system that would not win, but compel assent. Not a little of the difficulty in understanding the Ethics arises from the failure to properly comprehend the purpose of the method in which it is presented. So long as we think of it as a presentation of truth as indubitable as geometry, and yet as general as philosophical principles must needs be, so long will we become entangled in the meshes and fail to see the true significance of the matter contained in these unyielding forms.
But if it is true as we have said that Spinoza did not employ the geometrical method for the sake of its unassailable cogency, wherein was its virtue? If it could be used, as was indisputably the case, to prove error as well as truth, propositions which were directly opposed to his belief, as well as propositions in which he firmly believed, why was it used at all? And why did Spinoza's friends see such virtue in it that they requested the immediate publication of every fragment of Descartes' philosophy which Spinoza had put in this form? The answer to these questions which apply primarily to the Principles will throw a flood of light upon the Ethics.
To state it briefly, Spinoza's purpose in employing the geometrical method was pedagogical not philosophical. That is, he put the Principles of Descartes in this close form of Proposition and Demonstration not to establish the truth of the conclusions but that the pupil whom he was instructing in that system might more readily and more clearly comprehend what Descartes was endeavoring to establish. Truth and error did not enter into his consideration at all, for he used the same form and the same kind of proof to express what he disbelieved as well as what he regarded as true. The circumstances under which the Principles of Descartes' Philosophy was written absolutely preclude any other conclusion. When Spinoza began this work he apparently had no idea of publication, but it was done solely for the benefit of his pupil to whom he was teaching the Cartesian philosophy. So far as there was any justification for a new presentation of the truth which Descartes had already so well expressed it was in the method alone. What advantage could it be to repeat the same conclusions, relying always upon the same argument if it was not to present in a clearer way what were not otherwise so easily comprehended? Spinoza put Descartes' Principles in geometrical form because he believed that was the form best adapted to the requirements of his pupil's mind. His purpose was to present the conclusions of Descartes in their most logical form so that they might be easiest learned and most thoroughly understood. This method, therefore, was not employed as a method of proof, for Spinoza, at that time, was not interested in that, but in order that he might be in his presentation strictly logical and consistently pedagogical. Considered in this way the difficulty in reconciling the discrepancy between the method Spinoza employed, and his position upon some of the propositions given, disappears. The method is true and sound but the premises upon which the conclusions are grounded were not well taken. This fact, however, does not destroy the value of this method in presenting logically and pedagogically a conclusion be it never so weak when judged upon the grounds of belief and well reasoned judgment. There is a clear and a forceful way to present a seeming truth as well as that which is indubitable. Hence, we affirm that the only possible virtue in the geometrical method was its conformity to the demands of the thinking mind. It was pedagogically a superior method of presenting conclusions logically to the mind. That this same purpose was the chief one that led Spinoza to employ this method in the Ethics is the logical inference. Although his other works had not been written under this form, when he comes to write what he regarded as his last and master work he returns to this method. This time he is to express only what he firmly believed, but can we think that he was dogmatic enough to think that his conclusions must forever remain indisputable? Such a conclusion is not in harmony with his catholic sympathies and even temper. But here as in the former case the most satisfactory conclusion is, that this was the most direct method of expressing his opinions, and above all it was in accord with the great principles of Mediæval Logic.
§ 4. In order to appreciate Spinoza's motives in using the geometrical method, and to see its cogency we must remember that this was an age of deduction. If we are seeking the real causes that led Spinoza to believe in this method and to accept it as the best form in which to express not only mathematical but philosophical truth, we will find it in the fact that at this time the old Aristotelian Logic dominated his mind completely. The leaven which Bacon had introduced into the world of reflective thought had not leavened the whole, but Spinoza still held to Deduction as the great Organon of truth. For him the warrant for truth was rational not empirical. Explanations of phenomena were deductive not inductive. The proof of any proposition did not consist in an appeal to facts empirically obtained, but in a syllogistic deduction from premises previously, and better known. The whole tenor of thought on the continent was still deductive, and whatever did not conform to this method was illogical and untrue.
In confirming Spinoza in this belief the influence of Descartes was important. He had proven that indubitable truth does not lie in the field of objective experience but in the subjective assertion that I, a thinking being, exist. Philosophy must begin with an assertion that cannot be doubted and then proceed to build a system founded upon this truth. According to his formula Epistemology must precede Metaphysics. The next step was to establish the verity of God in order that we might be justified in our belief in the external world. Such was the position of philosophic thought when Spinoza began to reflect upon the problems of human experience. There was no serious attention paid to the Novum Organum of Bacon but Spinoza took his problem from the old scholastics and with this, their ideas of logical, methodical proof.
Instead of accepting the conclusions of Descartes as the starting point, viz., his cogito ergo sum, and his proof of God's veracity, by which empirical knowledge is made credible, and employing the method of Bacon to build upon this foundation already laid, Spinoza turns back a step and begins anew the impossible task of deducing the world in thought. Instead of following the role of an humble learner in a world whose mysteries are unfathomable he aspired to be a system maker in the most didactic way. The task he imposed upon himself was the old task of deductive thought. Individual facts of human experience were not data on which conclusions could be based, but phenomena to be explained by deducing them from some primary, and fundamental principle.4 The world was not something to be taken as it is and studied empirically, but it was regarded as a problem to be explained dialectically. Spinoza was dominated completely by this deductive ideal of truth. His idea of philosophical explanation was deductive, his logic was deductive, his proof was deductive, hence his method also was deductive. When this fact is sufficiently emphasized and consistently remembered we may still regret the method Spinoza used in the Ethics, but we must commend his strict adherence to the principles of Mediæval Logic. In this dry, stilted form of Axiom, Definition, Proposition, Demonstration, and Corollary, deductive logic reaches the height of consistency.
From the standpoint of deductive thought, therefore, and this is the point of view from which it was used, the geometrical method, we venture to affirm, was the most logical presentation of truth, mathematical or philosophical, that could be made. It was wellnigh if not perfectly in accord with the strictest demands of Deduction and seemed so at first sight to those accustomed to the logic of that time. It seems stiff and unnatural to us because we are so inured to the modern method of science that anything out of harmony with this seems artificial and unreal. With our eyes fastened upon individual facts as the starting point and general principles as the goal, to follow Spinoza we must run with our eyes behind us. What he saw ahead we see behind, and what we look forward to as the goal of philosophical explanation he had accepted as the starting point of reflection. So complete is the inversion that there is no way to harmonize his method with present ideas of proof and logical procedure. Reconciliation is impossible; either we must give up one and cling to the other, or we must reject the one in toto and rely wholly upon the other. While he accepts the most fundamental principles as true and tries to show, how the phenomena of experience result from these, we accept the facts of experience as the primary truths, and correlating and analyzing these, seek for more general conclusions. The rigidity of deductive logic, therefore, gave rise to this method and instead of being censured for his application of this method of geometry in philosophy Spinoza should be commended, for his close conformity to the principles of the thought of his time. If Deduction is the correct Organon of truth, and we must ground our belief not on observation and experiment but upon some rational principle, then the geometrical method is the most logical and consistent form in which to present philosophical truth. Mathematics, a deductive science, has not discarded this method and never will. And just as soon as we can get the deductive point of view, Spinoza's method will not seem artificial nor inapt, but perfectly logical and perfectly suited to the purposes for which it was employed. But from the modern standpoint it will always be regarded as an attempt to commensurate what is incommensurable.
To Spinoza's associates, however, men accustomed to the deductive point of view the geometrical method used in this early work did not seem strange or inapt. On the other hand, to them this method, as soon as it appeared, appealed as a great improvement even over the sunclear method of Descartes, and they at once sought to have him put the remainder of Descartes' Principles in this form and allow it to be published. From the Preface of Dr. Meyer we might infer that they considered this an infallible method of presenting truths; but this is not essential. All that we now wish to show is that to minds whose thoughts were habitually deductive, the geometrical method applied to philosophy did not seem artificial nor inappropriate, but well devised and the best possible method of presenting any truth logically and forcibly.
We thus come to the real causes that led Spinoza to make use of the geometrical method in his philosophical system. He believed that this method was pedagogically the correct one because he believed deduction was the correct way to establish truth. It matters but little whether we say that Spinoza believed the method of geometry was the best method to present truth to the learning mind, because it conformed so perfectly to the principles of deduction, or whether we say because Deduction is the Organon of truth the geometrical method is the acme of logical consistency. The truth that we wish to make clear is that the geometrical method had its real causes in Deduction, and the immediate occasion of its use in a desire to conform strictly to the requirements of the mental processes of the student. Spinoza was correct in his reasoning, therefore, and abundantly justified in his use of this method. It was the climax, of logical purpose and failed to receive the approval of succeeding ages not from any weakness in itself nor because it was ill applied, but because the whole process of thought has been reversed. Had Deduction retained its hold upon the minds of the thinking few, Spinoza's innovation would have been praised as it has since been censured.
Reference to this early work of Spinoza, then, offers a very considerable aid in understanding the method of the Ethics. We have found the purpose, I believe, he had in view when he employed it both in his earliest and in his latest works. As we have seen he certainly did not regard this method in the nature of a proof of the positions taken in the Principles, and we find no reason for believing that he did in the Ethics. Besides, in this last work his purpose was practical rather than speculative or theoretical. He did not give his life to meditation like Descartes, primarily for the sake of truth, but ultimately that he might point out to man the way of blessedness and peace. His purpose was, as the title of the work indicates, ethical not metaphysical. He uses demonstration in his work and yet not for the sake of the demonstration but that he might convince. With his logical mind, so little influenced by prejudice of any kind, conviction followed demonstration, and he thought that it was always so. However, Spinoza did not depend upon this method to produce conviction in his readers but upon the truth in the premises from which he started. The geometrical method would enable others to see clearly what he had learned through years of reflection. If once we understand why it was used, that it rested upon an implicit faith in scholastic logic, and that it was the crowning attempt of a logical mind to conform absolutely to the strictest demand of this iron-clad reason, there need be but little difficulty in following his argument and to some degree at least in appreciating his presentation. But to do this the essential thing is to get rid just as far as we can of our scientific prejudices, and grasp the problem as it was envisaged by Spinoza, with its mediæval atmosphere. Otherwise the method will remain, as it seems at first, an incomprehensible application of geometrical method to subject matter which has no relation at all to the form into which it is put. But remembering that that was a deductive age, even philosophical truth, we see, was thought to be not dissimilar to the mathematical truth which geometry adequately demonstrates. Back of Spinoza's attempt to apply the geometrical method to philosophy was the more fundamental attempt to make philosophy as truly deductive as geometry. This method, therefore, was the logical method, the method best adapted to the thought of the age, or as we have expressed it above, it was used because of its pedagogical correctness.
§ 5. Spinoza's complete reliance upon Deduction as the true order of all methodical thought and of proof, calls attention to another thought of fundamental importance in understanding his philosophy. Instead of building upon the great conclusion of Descartes according to the method of the Novum Organum he turns back to the long tried logic of the Scholastics and seeks by a more perfect adherence to the principles of their logic to deduce a system and explain experience, and, Pantheism is the result. To be true to Deduction, and it was Spinoza's purpose to be perfectly so, the starting point for reflective thought must be a concept which includes all that is to be deduced. The logical starting point of Spinoza's system, therefore, is with the concept of God. Since the attempt is to be made to follow in thought the plan of creation the first step will be to learn everything possible of the Creator. So in the Ethics we find Spinoza, true to the demands of deductive thought, dividing his work exactly the reverse of what modern philosophical treatment demands. In Part I. he treats of God, in Part II. of the Origin and then the nature of mind and then in Part III. of its affects, etc. Before we study the mind we must study God, before we study its nature we must study its origin. In every way the order is just the reverse of that followed today in attempts to solve the mysteries of Reality or to understand Experience.
And yet from his point of view his order is the only logical one. Attention has been called to these facts to show the supreme logical importance of this concept of God, in Spinoza's philosophical system. His thought so hinges upon this idea for the reasons we have just mentioned, that its mastery is the prerequisite for an intelligent comprehension of the main tenets of his Pantheism. If we wish to understand why Spinoza's reflection led him from a Deistic conception of God to Pantheism rather than to Theism, or if we wish to adequately appreciate the truth in Pantheism we must preface our study with the closest investigation possible of the idea of God. The key that has not yet been used for such study is the historical development of that idea. We cannot appreciate Spinoza's definition of God, for example, unless we are acquainted with some of the prior conceptions of substance and with the various attempts to explain Descartes' Dualism. Nor can we - and this is the region in which our inquiry lies - appreciate or rightly comprehend the attributes of Spinoza's God unless we see how his ideas on this subject developed from the more orthodox theology of a previous period.
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1. This is an excerpt
from Halbert Hains Britan’s "Introduction" to his translation of
Spinoza’s Principles of Descartes’ Philosophy (The Open Court Publishing
Co., 1905).
This e-text and its footnotes were created by Carl Mickelsen. Permission is granted for
electronic copying, distribution in print form for educational purposes and personal use.
No permission is granted for commercial use of this material.
Carl Mickelsen - carlmick@moscow.com
2. Spinoza’s, The Principles of Descartes’ Philosophy. Published in 1663, this is the earliest of Spinoza’s writing and the only one to which he subscribed his name.
3. In support of this proposition, the author had earlier introduced Spinoza’s following letter to Oldenburg:
Distinguished Sir:
I have at length received your long wished for letter, and am at liberty to answer it. But before I do, I will briefly tell you what has prevented my replying before. When I removed my household goods here in April, I set out for Amsterdam. While there certain friends asked me to impart to them a treatise containing, in brief, the second part of the principles of Descartes treated geometrically, together with some of the chief points treated in metaphysics, which I had formerly dictated to a youth, to whom I did not wish to teach my own opinions openly. They further requested me, at the first opportunity, to compose a similar treatise on the first part. Wishing to oblige my friends I at once set myself to the task, which I accomplished in a fortnight, and handed over to them. They then asked leave to print it, which I readily granted on the condition that one of them should, under my supervision, clothe it in more elegant phraseology, and add a little preface warning readers that I do not acknowledge all the opinions there set forth as my own, in as much as I hold the exact contrary to much that is there written, illustrating the fact by one or two examples. All this the friend who took charge of the treatise promised to do, and this is the cause for my prolonged stay in Amsterdam. Since I returned to this village I have hardly been able to call my time my own, because of the friends who have been kind enough to visit me. At last, my dear friend, a moment has come when I can relate these occurrences to you, and inform you why I allow this treatise to see the light. It may be that on this occasion some of those who hold the foremost positions in my country will be found desirous of seeing the rest of my writings, which I acknowledge to be my own, they will thus take care that I am enabled to publish them without any danger of infringing the laws of the land. If this be as I think, I shall doubtless publish at once; if things fall out otherwise, I would rather be silent than obtrude my opinions on men, in defiance of my country, and thus render them hostile to me. I therefore hope, my friend, that you will not chafe at having to wait a short time longer; you shall then receive from me the treatise printed, or the summary of it you ask for. If meanwhile you would like to have one or two copies of the work now in the press I will satisfy your wish as soon as I know of it and of means to send the book conveniently.
Letter XIII, The Chief Works of Spinoza (R.H.M. Elwes trans., 1883)
4. Frederick Coplestone makes somewhat similar points: "It is, indeed, obvious that Spinoza did not attach primary importance to the external trappings of this method, such as the formulas of exposition, the use of the letters like Q.E.D. [quod erat demonstrandum - therefore it is demonstrated] and words like corollary. The true philosophy could be presented without the use of these geometrical adornments and forms. Conversely, a false philosophy could be presented in a geometrical dress. It is, therefore, true to say that Spinoza did not regard the method as infallible if one is thinking simply of externals. But if by method one means not so much the external geometrical trappings as the logical deduction of propositions from definitions expressing clear and distinct ideas and from self-evident axioms, it seems to me that the method was certainly in Spinoza's eyes an infallible means of developing the true philosophy. . . . And if the intellect operates with clear and distinct ideas and deduces their logical implications it cannot err; for it is operating according to its own nature, the nature of reason itself." A History of Philosophy, Vol. IV.
