Frames /sing


Descartes’ 8th Rule: A Spinoza Touchstone

Rules For the Direction of the Mind, gives clue to Spinoza’s concept of the instrumentation of knowledge

I post here Descartes’ 8th Rule from his Regulae, as a marker to important influences upon both Spinoza’s philosophy in general – it contains the seeds of his argument for Three Knowledges, for instance – and his approach to technology, as it possesses the analogy that knowledge production is like the development of blacksmithing. This is not to mention the inclusion of possible paths to the discovery of the importance of the anaclastic, significant for the subject of Spinoza’s objection to Descartes’s claim for the importance of the hyperbolic lens. I highlight the relevant places of correspondence:

Full Text of the 8th Rule with Annotations and Highlights

Rule 8: If in the series of things to be examined we come across something which our intellect is unable to intuit sufficiently well, we must stop at that point, and refrain from the superfluous task of examining the remaining items.

The three preceding Rules prescribe and explain the order to be followed; the present Rule shows when order is absolutely necessary, and when it is merely useful. It is necessary that we examine whatever constitutes an integral step in the series through which we must pass when we proceed from relative terms to something absolute or vice versa, before considering all that follows in a series. Of course if many things belong to a given step, as is often the case, it is always useful to survey all of them in due order. But we are not forced to follow the order strictly and rigidly; generally we may proceed further, even although we do not have clear knowledge of all the terms of the series, but only of a few or just one of them.

This Rule is a necessary consequence of the reasons I gave in support of Rule Two. But it should not be thought that this Rule contributes nothing new to the advancement of learning, even though it seems merely to deter us from discussing certain things and to bring no truth to light. Indeed, all it teaches beginners is that they should not waste their efforts, and it does so in practically the same manner as Rule Two. But it shows those who have perfectly mastered the preceding seven Rules how they can achieve for themselves, in any science whatever, results so satisfactory that there is nothing further they will desire to achieve. If anyone observes the above Rules exactly when trying to solve some problem or other, but is instructed by the present Rule to stop at a certain point, he will know for sure that no amount of application will enable him to find the knowledge [scientia] he is seeking; and that not because of the defect of his intelligence, but because of the obstacle which the nature of the problem itself or the human condition presents. His recognition of this point is just as much knowledge [scientia] as that which reveals the nature of the thing itself; and it would, I think, be quite irrational if he were to stretch his curiousity any further.

[ The Example of the Anaclastic

Let us illustrate these points with one or two examples. If, say, someone whose studies are confined to mathematics tries to find the line called the “anaclastic” in optics – the line from which parallel rays are so refracted that they intersect at a single point – he will easily see, by following Rules Five and Six, that the determination of this line depends on the ratio of the angles of refraction to the angles of incidence. But he will not be able to find out what this ratio is, since it has to do with physics rather than with mathematics. So he will be compelled to stop short right at the outset. If he proposes to learn it from philosophers or derive it from experience, he will achieve nothing, for that would be to violate Rule Three. Besides, the problem before him is composite and relative; and it is possible to have experiential knowledge which is certain only of things which are entirely simple and absolute, as I shall show in the appropriate place. Again, it is no use his assuming some particular ratio between the angles in question, one he conjectures to be most likely the real one; for in that case what he was seeking to determine would no longer be the anaclastic – it would merely be the line which was the logical consequence of his supposition.

Now take someone whose studies are not confined to mathematics and who, following Rule One, eagerly seeks the truthon any question that arises: if he is faced with the same problem, he will discover when he goes into it that the ratio between the angles of incidence and the angles of refraction depends upon the changes in these angles brought about by differences in the media. He will see that these changes depend on the manner in which a ray passes through the entire transparent body [totum diaphanum], and that knowledge of this process presupposes also a knowledge of the nature of the action of light. Lastly, he will see that to understand the latter process he must know what a natural power in general is – this last being the most absolute term in the whole series. Once he has clearly ascertained this through mental intution, he will, in accordance withRule Five, retrace his course through the same steps. If, at the second step, he is unable to discern at once what the nature of light’s action is, in accordance with Rule Seven he will make an enumeration of all the other natural powers, in the hope that a knowledge of some other natural power will help him to understand this one, if only by way of analogy – but more about this latter. Having done that, he will investigate the way in which the ray passes through the whole transparent body. Thus he will follow up the remaining points in due order, until he arrives at the anaclastic itself. Even though the anaclastic has been the object of much fruitless research in the past, I can see nothing to prevent anyone who uses our method exactly from gaining a clear knowledge of it.

[ Descartes’ Three Modes of Knowing ]

But let us take the finest example of all. If someone sets himself the problem of investigating every truth for the knowledge of which human reason is adequate – and this, I think, is something everyone who earnestly strives after good sense should do once in his life – he will indeed discover by means of the Rules we have proposed that nothing can be known prior to the intellect, since knowledge of everything else depends on the intellect, and not vice versa. Once he has surveyed everything that follows immediately upon knowledge of the pure intellect, among these what remains he will enumerate whatever instruments of knowledge we possess in addition to the intellect; and there are only two of these namely imagination and sense-perception. He will therefore all his energies to distinguishing and examining these three modes of knowing. He will see that there can be not truthor falsity in the strict sense except in the intellect alone, although truth and falsity often originatefrom the other two modes of knowing; and he will pay careful heed to everything that might deceive him, in order to guard against it. He will make a precise enumeration of all the paths to truthwhich are open to men, so that he may follow one which is reliable. There are not so many of these that he cannot easily discover them all by means of a sufficient enumeration; this will seem surprising and incredible to the inexperienced. And as soon as he has distinguished, with respect to each individual object, between those items of knowledge which merely fill and adorn the memory and those which really entitle one to be called more learned – an easy task to accomplish… [lacuna in the texts] he will take the view that any lack of further knowledge on his part is not at all due to any lack of intelligence or method, and that whatever anyone else can know, he too often be faced with many questions which this Rule prohibits him from taking up; yet, because he sees clearly that these questions are wholly beyond the reach of the human mind, he will not regard himself as being more ignorant on that account. One the contrary, his very knowing that the matter in question is beyond the bounds of human knowledge will, if he is reasonable, abundantly satisfy his curiosity.

[ The Techne of Knowledge By Analogy: Blacksmithing ]

Now, to prevent our being in a state of permanent uncertainty about the powers of the mind, and to prevent our mental labours being misguided and haphazard, we ought once in our life carefully to inquire as to what sort of knowledge human reason is capable of attaining, before we set about aquiring knowledge of things in particular. In order to do this the better, we should, where the objects of inquiry are equally simple, always begin our investigation with those which are more useful.

Our method in fact resembles the procedures in the mechanical crafts, which have no need of methods other than their own, and which supply their own instructions for making their own tools. If, for example, someone wanted to practise one of these crafts – to become a blacksmith, say – but did not possess any of the tools, he would be forced at first to use a hard stone (or a rough lump of iron) as an anvil, to make a rock do as a hammer, to make a pair of tongs out of wood, and to put together other such tools as the need arose. Thus prepared, he would not immediately attempt to forge swords, helmets, or other iron implements for others to use; rather he would first of all make hammers, an anvil, tongs and other tools for his own use. What this example shows is that, since in these preliminary inquiries we have managed to discover only some rough precepts which appear to be innate in our minds rather than the product of any skill, we should not immediately try to use these precepts to settle philosophical disputes or to solve mathematical problems. Rather, we should use these precepts in the first instance to seek out with extreme care everything else which is more essential in the investigation of truth, especially since there is no reason why such things should be thought more difficult to discover than any of the solutions to the problems commonly set in geometry, in physics, or in other disciplines.

But the most useful inquiry we can make at this stage is to ask: What is human knowledge and what is its scope? We are at present treating this as one single question which in our view is the first question of all that should be examined by means of the Rules described above. This is a task which everyone with the slightest love of truth ought to undertake at least once in his life, since the true instruments of knowledge and the entire method are involved in the investigation of the problem. There is, I think, nothing more foolish than presuming, as many do, to argue about the secrets of nature, the influence of the heavens on the lower regions, the prediction of future events, and so on, without ever inquiring whether human reason is adequate for discovering matters such as these. It should not be regarded as an arduous or even difficult task to define the limits of the mental powers we are conscious of possessing, since we often have no hesitation in making judgments about things which are outside of us and quite foreign to us. Nor is it an immeasurable task to seek to encompass in thought everything in the universe, with a view to learning in what way particular things may be susceptable of investigation by the human mind. For nothing can be so many-sided or diffuse that it cannot be encompassed within definite limits or arranged under a few headings by means of a method of enumeration we have been discussing. But in order to see how the above points apply to the problem before us, we shall first divide into two parts whatever is relevant to the question; for the question ought to relate either to us, who have the capacity for knowledge, or the actual things it is possible to know. We shall discuss these two parts separately.

Within ourselves we are aware that, while it is the intellect alone that is capable of knowledge, it can be helped or hindered by three other faculties, viz. imagination, sense-perception, and memory. We must therefore look to these faculties in turn, to see in what respect each of them could be a hindrance, so that we may be on our guard, and in what respect and asset, so that we may make full use of their resources. We shall discuss this part of the question by way of sufficient enumeration, as the following Rule will make clear. [Rule Nine: We must concentrate our mind’s eye totally upon the most insignificant and easiest of matters, and dwell on them long enough to acquire the habit of intuiting the truth distinctly and clearly.]

We should then turn to the things themselves; and we should deal with these only in so far as they are within the reach of the intellect. In that respect we divide them into absolute simple natures and complex or composite natures. Simple natures must all be either spiritual or corporeal, or belong to each of these categories.  As for composite natures, there are some which the intellect experiences as composite before it decides to determine anything about them: but there are others which are put together by the intellect itself. All these points will be explained at greater length in Rule Twelve, where it will be demonstrated that there can be no falsity save in composite natures which are put together by the intellect. In view of this, we divide natures into the latter sort into two further classes, viz. those that are deduced from natures which are the most simple and self-evident (which we shall deal with throughout the next book), and those that presuppose others which experience shows us to be composite in reality. We shall reserve the whole of the third book for an account of the latter.

Throughout this treatise we shall try to pursue every humanly accessible path which leads to knowledge of the truth. We shall do this very carefully, and show that paths to be very easy, so that anyone who has mastered the whole method, however mediocre his intelligence, may see that there are no paths closed to him that are open to others, and that his lack of further knowledge is not due to any want of intelligence or method. As often as he applies his mind to acquire knowledge of something, either he will be entirely successful, or at least he will realize that success depends upon some observation which it is not within his power to make – so he will not blame his intelligence, even though he is forced to come to a halt; or, finally, he will be able to demonstrate that the thing he wants to know wholly exceeds the grasp of the human mind – in which case he will not regard as more ignorant on that account, for this discovery amounts to knowledge [scientia] no less than any other.

– trans. John Cottingham

Here we have a trinity of kinds of knowledge which in rough scheme matches that offered most fully by Spinoza in the second scholium of Ethicspart II, proposition 40. Spinoza’s triad is instead of sense-perception, imagination and intellect, is: imagination, reason and intuition. What may be of interest is that when we read of the three knowledges in Tschinhaus’s summation, it is presented as the Cartesian three:

“Because knowledge is either sensual, imaginative, or intuitive. He believes a sort of Pythagorical transmigration, namely that the mind goes from body to body.” – Leibniz’s 1675 record of Tschirnhaus’ summary of Spinoza’s Theory, mentioned here: Pythagorian Spinoza? 

Whether this is Tschinhaus’s mistake, Leibniz’s mistake, or something that tells us how to read the substantive nature of Spinoza’s second knowledge (i.e., is reason and order finding still an imaginary process?, addressed here Spinoza’s Two Concepts of Order ), cannot be decided. (Of course within his three knowledges, despite a conceptual link, there is Spinoza’s radical break with Descartes over the issue of falsity.)

But what is more interesting for its bearing upon how to read Spinoza’s view of technology and craft, is that Spinoza appropriates whole Decartes analogy of the the techne of knowledge, and he does so in the earliest of his texts, Treatise on the Emendation of the Intellect:

To this end the first point to consider is that this is not a case of an enquiry extending to infinity. That is, to find the best method of seeking the truth, there is not need of another method for seeking the method of seeking the truth, and there is no need of a third method to seek the second method, and so on to infinity. For in that way we should never arrive at knowledge of the truth, or indeed at any knowledge. The case is analogous to that of material tools, where the same kind of argument could be employed. To work iron, a hammer is needed, and to have a hammer, it must be made. For this purpose there is need of another hammer and other tools, and again to get these there is need of other tools, and so on to infinity. In this way one might try to prove, in vain, that men have no power to work iron.

But the fact is that at first, with the tools they were born with, men succeeded, however laboriously and imperfectly, in making some very simple things; and when these were made they made other more complex things with less labour and greater perfection; and thus advancing gradually from the simplest works to the making of tools, and from tools to other works and other tools, they have reached a point where they can make very many complex things with little labour. In just this same way the Intellect by its inborn power makes intellectual tools for itself by which it acquires other powers for other intellectual works, and from these works still other tools – or capacity for further investigation – and thus makes steady progress until it reaches the summit of wisdom (30-31).

– trans. Samuel Shirley

There are other significant correspondences, some of which may bear upon Spinoza’s approach to technology and optics. For instance, in Rule 8 Descartes takes up the careful path to possibly discover the anaclastic line for hyperbolic lenses, one which involves the close measurement of angles of incidence and refraction. Does this help us understand Spinoza’s critique of Descartes over enthused embrace of the hyperbolic lens for telescopes, in his letter 39 to Jelles:

Descartes writes: “…he will easily see, by following Rules Five and Six, that the determination of this line depends on the ratio of the angles of refraction to the angles of incidence.”

And Spinoza suggests: “…and so he does not consider the size of the angle which the rays make when they cross one another at the surface of the eye…he seems deliberately to have passed over it in silence, because, I imagine, he knew of no other means of gathering rays proceeding in parallel from different points onto as many other points, and therefore he could not determine this angle mathematically…Perhaps he was silent so as not to give any preference to the circle above other figures which he introduced”

Somehow Spinoza feels that he had located in Descartes’ treatment of the production of the size of images on the retina a lacuna, the absence of an angle of incidence factor, one that is both essential to telescope construction, and that Spinoza sees as revealing the superiority of spherical lenses. Could it be that Spinoza has in mind in Descartes’ Rule 8 and the method that precedes it?

And lastly, between, the condition that all knowledge should be considered in view of human powers of cognition (again and again repeated by Descartes in terms of an accepted limit to human knowledge), is directly stated by Spinoza in his Four Rules for Best Perceiving, in the Emendation:

1. To have an exact knowledge of our nature which we wish to perfect, and at the same time to know as much of the nature of things as necessary.

2. Therefore to infer correctly the differences, agreements and oppositions of things.

3. To conceive aright the extent to which things can, and cannot, be acted upon.

4. To compare this result with the nature and power of man.

In short, Descartes’ Rule 8 provides a foundation text for many of the considerations we have for assessing how Spinoza conceived of knowledge. From it we have the capacity to trace out the correspondences and then the strong deviations. Not having enough time to do this here, I will return to this later. Already Spinoza is providing a more comprehensive, totalizing view of constructed knowledge, contextualizing tool use within a more complete knowledge is power equation one which will make the more measurement of man a necessary component in any measurement of technical means of knowing.


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