Règles pour la direction de l’esprit

The Rules for the Direction of the Mind were written in 1628 but had to wait over seventy years (fifty years after Descartes’ death) for their publication in 1701. This book is certainly regarded as a critical element of the Cartesian canon but it has not received quite the play of the Meditations and its much celebrated Cogito. That is a shame because the Rules deal with scientific method and avoid the theological speculations of the Meditations. Consequently the Rules relate to both real and current issues in a way the Meditations do not. Three items are introduced in the Rules, which, each in its own way, aids in establishing the scientific and philosophical revolution associated with the author. These are:

1) The creation of new tools for scientific reasoning to supplement and replace the classification-syllogism format of Aristotelian and mediaeval science.

2) The replacement of the substance-accident model of physical objects with a model based on extension, figure and motion.

3) A theory of faculties to explain how the mind operates, particularly with respect to knowledge and error.

Let’s review these items in detail:

(1) The Rules propose a reform in method, a reform motivated by a dissatisfaction with the intellectual tools of the time such as were available for accumulating knowledge and using what was known to discover new truths. Specifically Descartes sets about to replace syllogistic logic (“les machines de guerre des syllogismes probables de la scolastique,” p. 40) with a better approach. His objection to syllogistic logic is interesting (Règles, Pléiade pp. 71 ff). Despite a few rhetorical flourishes Descartes does not attack the validity of well-formed syllogistic inference. That would be a sort of radical skepticism. There is nothing invalid in the relationship between the conclusion and the premises of a well-formed syllogism. “… la raison, qui s’y confie…peut…par la vertu de la forme, aboutir à une conclusion certaine.” (Cf. also p. 90) Rather, the form of the syllogism does not produce a truth that is not already contained in the meaning of the premises. “…les dialecticians ne peuvent former aucun syllogisme en règle qui aboutisse à une conclusion vraie, s’ils n’en ont pas eu d’abord la matière, c’est-à-dire s’ils n’ont pas auparavant connu la vérité même qu’ils déduisent dans leur syllogisme.” From a practical point of view, anyone who needs a syllogism to conclude that Socrates is mortal from the famous premises must be very slow indeed. While the conclusion of a well-formed syllogism might indeed follow from its premises, the real problem in the search for truth is discovering and establishing truths that may be contained in the premises. In order to discover such truths Descartes outlines a method that incorporates direct observations and logical deduction. Descartes' new method requires him to to transform arithmetic and geometry in such a way that they are fit to produce deductive chains of reasoning. As applied to arithmetic, his technique is to abstract from individual operations of adding, multiplying etc. in such a way as to arrive at abstract formulas where variable letters act as placeholders for any (whole) numbers whatsoever. The new method is mathesis universalis. It is a content-free method for reasoning about quantities that applies with equal facility to arithmetic and geometry. Symbols are introduced for economy of expression and to help the mathematician retain in his memory intermediate steps from long and complex chains of reasoning. Today we would call the method symbolic algebra and Descartes, along with John Wallis, was its founder. Approximately seventeen years Descartes discovered how to apply his algebraic formulas to the expression of propositions of geometry. Analytic geometry not only replaced the drawings of “ruler and compass” proofs with more perspicuous (“certain and indubitable”) formulas, it also permitted the creations of deductive chains by virtue of substitutions in accordance with nothing more than basic logical laws.

While symbolic algebra is the most tangible result of the new method outlined in the Rules, we should not ignore other, broader aspects of his proposals for training the mind. One side of the Rules consists in no more than practical recommendations for thinking clearly and avoiding confusion and error. But another side contains substantive and controversial assertions about valid philosophical inference that Descartes would exploit in the Meditations. The practical recommendations sound a bit disingenuous at first blush, but they need to be seen in their proper role as a sort of preface to the later Rules that get into the technicalities of analysis, recursion and deduction. I see no reason not to take them at face value. One of the motives for dividing a problem into steps and securing the logical validity of each small step is to aid our finite memories. The moment of controversy arises when Descartes states that correct method and the road to indubitable certainty lies in discovering simple truths, namely truths whose truth is immediately clear and distinct, and other truths that are derived from simple truths by rules that are themselves clear and distinct. The methodological homilies and philosophically significant assertions are intertwined throughout the Rules. So let us list a few of the rules and try to sift the method from the madness:

Rules I and II: For my money the text gets off to a bad start by interpreting the product of science and the new learning as solid (Rule I) and clear (Rule III) judgments. Behind the initial impression of obvious simplicity, the terms “solid” and “clear” are nothing if not confusing. Just how meaningful are these concepts? “Solid” has to be a metaphor since the univocal meaning of “solid” clearly doesn’t apply. But as a metaphor it can give us no more than an intimation of Descartes’ intent; it requires other terms for clarification. “Clear” is not (or not necessarily) metaphorical, but is it a valid criterion for a valid scientific assertion? What constitutes clarity? What if one man’s clarity is another man’s muddle? Can an assertion be true and unclear? In fact, can it be a valid part of science and still be unclear? Almost every one of Descartes’ buddies in the Meditations - Objections and Replies found the concept of a most perfect substance to be very unclear and Descartes at no point was able to provide a satisfactory reply. And the good Locke professed to have no idea what “clear and distinct” meant (p. xix).

“Solid and clear judgments” is glossed in Rule II as being part and parcel of certain and indubitable knowledge. “Certain” and “indubitable” are appropriately meaningful in a way that “solid” and “clear” are not. Descartes introduces into what is today called “philosophy” and Descartes termed “first philosophy” a very high standard for validity. The experimental sciences cannot be held to the same standard because they involve experience which can be “deceptive,” as Descartes says, i.e. subject to revision. This comes roughly down to the same view as Bacon with his “degrees of certainty.” Descartes’ paradigm for a scientific truth is the conclusion of a geometric deduction, whereas Bacon's was the result of a table of comparisons and exclusions based on observation. The conclusion apparently is that the experimental sciences are not real science (“...il ne reste de toutes les sciences déjà connues que l'arithmétique et la géométrie....”p. 40) Descartes reconciles first philosophy to this standard of validity by asserting unconvincingly that his proofs in the Meditations are indeed geometrical proofs.

We should in addition be careful to distinguish between two separate criteria that Descartes establishes in these rules. The first is that science consists in certain knowledge. The second is that science consists in certain knowledge. The second criterion states that it is not good enough for a philosophical or scientific truth to be true. We must also know that it is true.

Descartes puts a novel and extraordinary emphasis on the certain knowledge of a true proposition in in addition to its simple truth. Can anything live up to this standard? Is it even meaningful? “Certain” appears to be equivalent to “indubitable”. “Indubitable,” as the Meditations would reaffirm, means “beyond all doubt.” All doubt. All doubt. The totalizing term “all” appears enfolded in the term “indubitable.” And whenever “all” is used without qualification, it threatens everything it touches with sure destruction.

To doubt is to act. The truth of an utterance is doubted if someone says, “I doubt that.” If someone says, “John Holmes coked up,” you can doubt the truth of his utterance by saying, “I doubt whether John Holmes coked up.” How about, “Either John Holmes coked up or it is not the case that John Holmes coked up.” This utterance is an instantiation of a logical law so if anything is indubitable, this is it. But if Tim Leary were to  say, “I doubt that either John Holmes coked up or it is not the case that John Holmes coked up,” we might think that Tim is tripping again, but in what way is he not doubting? The most we can say is that his doubt makes no sense to us. So if anyone says, “Tim, you weren’t sincerely doubting it deep in your heart. You were just play acting to try to make a point,” he could answer, “Try me. And try Pyrrhus and even Locke and Mill.” Even if a person’s reasons for doubting an utterance turned out to be wrong or incoherent, he could still have sincerely doubted that utterance. In any event Descartes’ rule doesn’t say “cannot be sincerely doubted.” “It says “indubitable.” For a case of truly sincere doubt consider, “I doubt whether I can conclude ‘I am’ from ‘I think.’” Moreover, we would not be entirely secure in claiming that, even if a person's doubt were insincere, he were not in some sense doubting.

Perhaps “indubitable” has a factual meaning. Perhaps, it means, “never has been doubted or never will be doubted.” We can wipe that off the slate. I now hereby doubt every utterance past, present or future in this or any other universe. (I say this with some regret since everything Axel Rose says is probably true.) Maybe we should restrict genuine doubters to qualified people, perhaps white males with a certain fixed income. Under almost any such qualification a lot of things we thought were untrue suddenly become indubitable. For example, “Dred Scott is sub-human.” This approach would also lead to the conclusion that either the Cogito is not indubitable or that every single author of the Objections to the Meditations would have to be excluded from the group of qualified people.

A pragmatist gloss could be given as follows. There are certain truths that people begin to accept after examining the proofs in favor of those truths vs. the reasoning behind any objections to those truths. People conclude that the proofs in favor of these truths are satisfying and reject the objections. Once enough people accept these truths, then they can be called “indubitable.” Marvelously vague as most pragmatist glosses are, this view still has problems. Either it reduces “indubitable” to “good enough for me,” or it reduces “good enough for me” to “indubitable.” In the first case, there is no independent meaning for “indubitable” and Descartes might as well not have written these rules. In the second case, the consequence is that one cannot argue to change generally held opinions because they are indubitable.

Another approach would be to argue that Descartes got off on the wrong foot by substituting “known” for “true” and “indubitable” for “necessarily true.” There is some merit to this approach although “necessarily true” has its own problems. Discussion along these lines would take us too far astray from Descartes and would more fruitfully be pursued in another context.

The fact is (an indubitable fact if there ever was one) is that Descartes never really explains in a satisfactory way what it means for a truth to be indubitable. He throws out “clear and distinct” and “self-evident,” but those terms have next to no explanatory value. Other than that Descartes gives us examples. These are (1) Mathematical truths, and (2) The metaphysical claims from the Meditations, viz the Cogito, the existence of God and the substantiality of the soul (which he occasionally states are the results of geometrical style reasoning). Concerning the metaphysical claims, it is circular to use them as examples to prove that there are such things as indubitable truths, because the argument for these claims is based on the assumption that there are such things as indubitable truths and the philosopher who accepts those metaphysical claims already understands what an indubitable truth is. Indeed the objectors to the Meditations did not find the idea that mind is a separate substance or the idea that God is a substance containing every perfection to be so self-evident or clear and distinct. In the end Descartes’ only answer to their objections was along the lines of, “Well, you must be some sort of nincompoop.” Concerning mathematical truths, it is a profound insight on the part of Cartesian philosophy that mathematical proofs have a validity that at the very least rivals logical proofs (or at least well-formed syllogisms). Still, some more recent views of mathematics hold that mathematical laws are to one degree or another the product of convention and so they are not compelling in any way Descartes would have found acceptable. Descartes does not directly address this issue in either the Rules or the Meditations. Obviously it is not enough to just repeat over and over the mantras of “clear and distinct” and “self-evident.”  Descartes further muddies the waters by stating or implying that the reasoning behind the Cogito and his proof of the existence of God is not just self evident like mathematical reasoning, but that it is a type of mathematical reasoning. A propos, Cartesian algebra is effectively a universalization of individual acts of calculation. But even with regard to purely algebraic formulas, the problem of indubitability remains. Breakthrough that it was, Descartes does not explain why, for example, a simple law like volume = height x width x length is indubitable and why it applies to every case in which we want to calculate an object’s volume.

By way of historical speculation, I surmise that the requirement for indubitable certainty is or could be a felt desire on the part of a certain group, in this case the burgeoning scientific community or some members of that community. It is not a requirement of successful observation, experiment or even mathematical invention. Non-philosophical scientists like Galileo and Harvey clearly produced successful results without worrying whether those results were or were not indubitable. Descartes' standards and his attempts to meet those standards should be seen as a relic of scholastic efforts to prove indubitably the existence of God. The way Descartes ties his (failed) proof of the existence of God to the validity of any scientific results whatsoever shows this. Passages in the Discourse intimate that Descartes was deeply affected by the silencing of Galileo. His system was an attempt to tie the new science and the old religion together into one seamless form of reasoning. His life was marked by constant efforts to be able to say what he wanted without fear of harrassment.

Rule III: Knowledge is divided into clear and evident intuitions and what we can deduce from clear and evident intuitions. “Evident” clearly does not add anything to the discussion.

Rules IV and V: To solve problems it is necessary to order and dispose things properly. We need to reduce complicated and obscure propositions to simpler ones. Then we can start with our intuition of the simpler propositions to prove the more complicated ones. The division into parts and simplification has a great deal of practical value. The problem lies in the idea that we can have an intuition of the simpler propositions or the rules by which we can move from simpler to more complex propositions. Descartes states that these simple intuitions are the product of “the light of reason.” They cannot be taught: Method “…ne peut aller en effet jusqu’à enseigner aussi comment ces operations mêmes doivent être faîtes, car elles sont les plus simples et les premières de toutes….” (Pléiade p. 47) Well, that’s a fine state of affairs!

Rules VII, IX, XI and XIII: Sufficient enumeration is an example of practical advice. It allows one to review and retain the steps of a proof. Focusing on the easiest things is supposed to help us grow accustomed to what it means to have a clear and distinct intuition of truth. The idea of acquiring more certainty, however, is a bit disturbing. The example of the magnet in Rule XIII serves two purposes. First it shows that Descartes’ methodological recommendations are not limited to pure arithmetic. Secondly, it promises to show how in his method deduction might differ from syllogistic deduction. (Whenever I say “syllogistic deduction” I refer to well-formed and mostly simple syllogisms. For Descartes’ denunciations of the Schoolmen are in fact directed against syllogisms that are either ill-formed or where the subject matter is confused with the form of reasoning. Since the Schoolmen applied their syllogisms to highly abstract and largely invented concepts, the confusion of content and form could easily be obscured. In these cases Descartes’ dismissals, just like those of Bacon and Hobbes were right on.) What Descartes delivers, however, is somewhat wanting. Method (presumably deductive method) is supposed to consist of three elements: (1) Something unknown, (2) the designation of what is unknown, and (3) the designation of what is unknown by what is known. All of this has practical value, for clearly stating the problem you wish to solve or what exactly you are looking for goes a long way to furthering your research. Rule XVII talks about the mutual dependence of propositions in a chain of proof but does not tell us what constitutes mutual dependence. (Note, the interactive proofs of the Meditations really do differ from both syllogistic reasoning and algebraic deductions.) The significance will emerge only later with the actual creation of symbolic algebra.

Rules XII, XIV, XV, XVI and XVIII: These rules really contain in germ the idea of mathematical symbolism and algebra by way of geometrical figures. Simplifying symbols take advantage of all the help the understanding, imagination, senses and memory can give us to form a distinct intuition of simple propositions and compare the results we seek with the things we already know.

Rule XIII: The concept of abstracting out what is superfluous sets the stage for the mathematical symbolism of the following rules.

Denunciations of syllogistic logic and the substance/accident model (discussed below) did not spring fully armed from the heads of either Descartes or Bacon. While not quite a commonplace, this line of attack became more and more familiar as a kind of Platonist revival took hold of post-Renaissance intellectuals and as scholastics, those representatives of Aristotelianism and the worst in syllogistic logic, made fools of themselves by doggedly attacking the heliocentric view of the universe as illogical (because it was non-Aristotelian). As early as 1580 Montaigne was taking aim at Aristotle and the schoolmen and Théophile de Viau’s hysterically funny burlesque of scholastic disputes about the nature of substance (Première journée, pp 15 ff. ) predates the Règles by about six years.

Descartes’ rhetoric (“…les doctes se servent souvent de distinctions si subtiles, qu’ils éteignent la lumière naturelle et trouvent des ténèbres même en ce qui est bien connu des gens sans culture…,” Pléiade, p. 98) echo some of Bacon’s more memorable phrases. However, Descartes and Bacon take two not entirely parallel paths away from the schoolmen. Bacon seizes on the poverty of the philosophical schools to promote direct research of nature the world. It was only by looking at the world around him with fresh eyes that the scientist could escape the pointless niggling about meaningless terms that made a mockery of scholastic philosophy. Bacon himself was an enthusiastic investigator of nature and made it part of his life’s work to promote state sponsored associations for the furthering of science. But he was not a mathematician and had no insight into the value of systematizing results. Descartes was a mathematician and spent limited time on the sort of empirical research that so fascinated Bacon. Accordingly, he proposes not so much to disregard as to reform methods of deductive reasoning. His symbolic algebra and analytic geometry are just such reforms. Science would require research and experimentation as well as mathematical techniques. Without the former thought descends into fantastical scholasticism. Without the latter it is a jumble of isolated and unrelated observations.

Descartes’ stress on mathematical method distinguished him from others who during the Renaissance were beginning the replace Aristotle by Plato as the point of classical philosophical reference. For whatever the faults of scholasticism may have been, the intuitive analogistic metaphysics of Renaissance Platonists like Marsilio Ficino or the disorganized research methods of Bacon were not a satisfactory replacement. Rather, mathematics, specifically symbolic algebra and analytic geometry, would aid scientists in organizing their results in into a finite set of coherent laws.  And, as Descartes would explore in the Meditations many sorts of arguments could be adapted from Plato and Platonic philosophers to provide, in Descartes’ view, a firm foundation for first philosophy as well as science. But in one other respect there is a sharp distinction between Descartes and the previous generation of Renaissance Platonists. Descartes unequivocally rejected what could be termed the ontological anarchy of Ficino (not to mention Plotinus and Anselm). For it is one of the hallmarks of Platonic philosophers that they believe nonmaterial objects of one sort or another really exist. If you don’t agree, that’s just because you’re still trapped in the cave. Even though Descartes abstracts from individual calculations in the creation of symbolic algebra, he stresses that these abstractions are no more than an aid to memory. Extension, for example, is not something separate and distinct from extended objects.

(2) The substance-accident model of basic concepts related closely to the way knowledge was gathered and organized in the centuries following Aristotle. Things in the world of whatever kind that could in some way be considered independently from other things were called substances and the qualities of substances – Qualities being whatever could not be considered independently from the substances of which they were qualities – were called accidents. Science, such as it was, consisted in organizing and categorizing substances, partly on the basis of accidents shared or not shared with other substances, into groups. The members of some groups, it was discovered, were included in other more inclusive, groups. More inclusive groups had a generic relation to their sub-groups. The former were called genera and the latter species of the genus of which they were a sub-group. Strictly speaking, the substance-accident model is not an ontology, if ontology be understood loosely as an assertion about what really exists vs. what we may have a shorthand name for even though the name does not refer to anything real but only in an indirect way to other things that really are real. Hence the substance-accident model can equally accommodate scientists or philosophers who believed that accidents were real and scientists or philosophers who did not believe that accidents were real and that accidents were merely a shorthand way of pointing out certain interesting facts about other, truly real things. Equally the term “substance” could be used without a great deal of ontological discrimination. Examples from Aristotle and scholastics mix inanimate objects, biological entities, people and various non-spatial or ideal entities as examples of substances. There was, in fact, not much that could conceptually differentiate between “substance” and “thing” or “individual” except in contexts where “substance” is used in its strictly defined sense as a thing that is qualified by accidents and that could be considered independently of any other thing. It is this looseness that allowed the substance-accident model to linger in philosophers' minds even after Galileo and others replaced the categorizing approach to science, without which the substance-accident model had no real scientific purpose, with an approach based on measurement. In the famous wax example of the Meditations Descartes demonstrates among other things how the idea that there are absolutely independent, non-context dependent substances literally melts under close examination. One does not need to accept his conclusion that individual substances like the ball of wax are products of the understanding (although the conclusion that substances are arbitrarily denominated is important for the replacement of the concept of substance, and perhaps natural kinds as well, by figure, extension and motion) to see how the idea of substances as entities strictly and completely independent of their accidents and indeed of any context was not very clearly defined. The consequence is that the distinction between “substance” and the shady background terms used to define “substance” (“thing,” “individual,” “entity”) also melts and with it the entire substance-accident model. The Rules shines a light on a few basic concepts, viz. extension, figure and motion, whose varying proportions and relations – proportions and relations that the scientist could measure – stood in a direct, apparently one-to-one, relation with what had been called a substance’s qualities (or, more accurately, a physical substance’s qualities). All sorts of neat consequences follow from this shift. The Cartesian model was conceptually more economical because it replaces a potentially infinite number of qualities with a few concepts and the proportions and relations between those concepts. Also measurability was tied in a wonderful way with predictability, and along with predictability comes the possibility of regularities which scientists would call laws of nature. Scientists could set up trials or experiments to verify whether a proposed regularity or law was indeed repeatable such that a new basis for agreement within the scientific community, one not solely dependent on concept creation and logical deduction, was established. For example, if mass, velocity and attractive force in two different experiments are held constant, then a law might state that the acceleration of the body should be the same in each experiment. Descartes did not push very far into the realm of experimental science because, as Leibniz would later observe, he did not yet have access to much of the experimental data that would have been collected by the end of the century.

Extension, figure, etc. are not a genuine substitute for the category of accident since they are applicable only to a limited range of objects or only to objects understood in a certain limited way. However, attention to these phenomena points to weaknesses in the substance-accident model as a categorical framework also. Addressing those weaknesses, a task that Descartes never undertook, would require a reconsideration of the subject-predicate model of language that is tightly bound to the substance-accident model of objecthood. Since this important issue is outside the realm of Descartes’ philosophizing, it will not be considered here.

Descartes does not provide actual arguments for the conceptual shift away from substance-accident to extension-figure-motion as he would provide arguments for his existence and for the existence of God. So since, there are no arguments, there are no arguments for us to find right or wrong. The relation of these models of the constitution of things to the structure of language or to some models of the structure of language would potentially provide such an argument, but Descartes did not take that route. Likewise, because of the generality at which the reconceptualization takes place, the recourse to experiential verification is not a clear option (Perhaps examples of accidents not reducible to extension etc. would count as such a verification or falsification.) The arguments in the Rules for replacing syllogistic deduction with mathematically based types of reasoning deal with rules for logical deduction and induction and not with the concepts that are the content of logical reasoning. So any reasons for accepting the extension-figure-motion model over the accident model comes down to preference and utility. As we have seen the advantages of Descartes’ model, particularly as a means of organizing research in the physical sciences, are noteworthy.

Descartes clearly believed that one group of real things could be fully characterized in terms of extension, figure and motion. In other texts, where he would argue for the existence of God and the substantiality of mind he opened up the possibility, and in his view the actuality, of substances that are not fully characterized by extension etc. Materialism is the doctrine that there are no other such substances and that candidates such as mental events could also be fully characterized in terms of extension etc. Descartes’ actual arguments that minds form a sort of reality that cannot be characterized by extension are thin and quite unconvincing.

It is an open question as to whether dropping the concepts of substance and accident as a model for scientific research in favor of the concepts of measurable extension, figure and motion (Another open question is whether a reconceptualization for scientific purposes really took place, for, as Bacon observes, the scholastics did not really use substance/accident as a framework for scientific research at all) is in fact also a strong ontological claim. Heidegger (Sein und Zeit, pp. 89 ff.) asserts that this mathematicization of nature is a nearly exhaustive definition of what exists and not simply a theoretically useful list of some characteristics of some things that exist. Descartes did not address a systematic ontology head on. Of course, in addition to material objects, he admitted the existence of the mind and of God but not the independent existence of numbers. Nor does he assert that the concepts of extension, figure and motion are the only way to characterize material objects. If there is going to be value to Heidegger's fairly apocalyptic accusation, he would need to show that Descartes intended to exclude alternative characterizations of existing objects (alternatives such as Zuhandensein, for example).

3) Descartes did not introduce the notion of faculties to philosophy. Those can be traced as least as far back as Aristotle. And even Socrates tended to confuse truth with knowability and possibility with conceivability. But the specific view of mental faculties and the place of that view in an overall philosophical project that we recognize today is largely the creation of Descartes and Hobbes. Despite introducing his faculties (There are four of them: understanding, imagination, the senses and memory) in the guise of what appears to be no more than practical advice for correct scientific method, Descartes in fact employed the theory of faculties largely to explain a couple of phenomena. The first is error. The second is how the mind can intuit items that do not really exist in the spatio-temporal world (Items such as extension, limit etc.) It is worth noting that Descartes does not tie his views on mental faculties directly either to his criterion of indubitability for genuine philosophical knowledge or to any of his supposedly indubitable proofs, namely the Cogito, the proof of the existence of God or the proof of the non-corporeal existence of the soul. In the Meditations Descartes introduces the sense-understanding distinction in order to explain perceptual error. Likewise the faculties in the Meditations are part of what the mind is; there is no role played by the specific faculties in the proof that mind is not corporeal and extended. So, while the theory of faculties is significant for Descartes, it is not instrumental in his fundamental metaphysical proofs or even in his views on scientific method. Hobbes inaugurated the practice of beginning a philosophy book by discussing the human mind with an eye toward using that discussion as a basis for further philosophical conclusions (In Descartes’ Règles, the faculties are not introduced till Rule XII). Hobbes, as we know, always moved directly from his chapters on mind to address political issues. The world would have to wait for Locke for the faculty theory to really go to town.

Note that the role of Descartes’ theory of faculties is by and large to explain perceptual error and errors of judgment. The faculties are not limited to that role in, for example, Aristotle’s De Anima. Aristotle’s conclusions about the faculties are, as he tells it, the result of observation, just as his views on biology come from observing animals and his views on rhetoric come from observing orators. Although Aristotle does discuss error and opinion, his observations occur within the context of creating a corpus of knowledge about the soul. The same can be said about the data collecting stage of empirical psychology. Descartes’ theory of faculties is not observational. It is explanatory. It is meant to provide a framework for understanding simple concepts as well as perceptual and judgmental error. A comparison to universal gravitation is not out of place. The theory of universal gravitation is also explanatory and not observational. No one has ever seen or otherwise perceived gravity. The observations to which the theory of universal gravitation related are what 17^th century scientists noted in their experiments and through the lenses of their telescopes. One relevant observational theory is the theory of planetary motion. The theory of universal gravitation is meant to explain the observations encoded in the theory of planetary motion. Likewise Descartes’ theory of faculties is meant to explain instances of observed error in perception or judgment.

Accordingly Descartes’ theory is subject to the sort of validation that is appropriate for explanatory theories. Namely: Does it explain the observations, and does it provide the best explanation of the observations? Like gravity, sense and imagination and so forth are not things one would ever expect to see. Rather they are hypostatized as a framework for understanding observed phenomena.

For this reason, Descartes’ theory does not suffer from the same infelicities as those theories of mind that are designed to set logical limits on what can be known and consequently on what can count as a philosophical truth. The mental theories proposed by the empiricists and by Kant, for example, must be unassailable just as the axioms of logic are unassailable since they are used for the purpose of drawing metaphysical conclusions (or rather cpnclusions about the limits of metaphysics). Since Descartes’ view on faculties are not part of his metaphysical proofs, they need not be idées claires et indubitables in quite the same way.

The status of the theory of faculties in Descartes’ philosophy throws some light on why he never subjects the existence of the faculties (as a separate issue from the general doubt of his own existence) to the kind of systematic doubt he practices in the Meditations. They are not items he observes in the same way he observes the ball of wax or the scarecrow. As a framework for explanation, the Cartesian faculties are not properly the object of systematic doubt. They are subject to the more focused doubt as to whether they provide the best explanation for error.

Freud introduced his theory of mental systems in Chapter VII of Traumdeutung for pretty much the same reason. The phenomenon he wanted to explain was how an item could stay in the mind and yet not be the object of conscious awareness. Furthermore, some items can be recalled voluntarily to consciousness while others seem to force their way into consciousness without such a voluntary mental act. It is worth noting that the theory of gravitation would have had very little explanatory power if it did not include a means for measuring gravitational force and so predicting the motions of the heavenly bodies. Without some sort of mechanism for prediction and even measurement, these theories of mind won’t ever really explain very much.

The Cartesian faculties are not discovered by introspection in the same way that many objects defined by Husserlian phenomenologists seem to be. And for that reason the faculties (though not necessarily the proofs of the Meditations) are not the proper target of those who would question the validity or communicability of scientific observations based solely on introspection.

Note: There is something of an academic urban legend abroad that mathematicians are Pythagoreans by nature and that they and physicists all believe fiercely in the reality of ideal objects (“Otherwise there would be no point to our research.” Stop whining.). In point of fact between Plato and Frege the ontological status of mathematical objects was hardly ever an issue. Descartes, for one, never thought there were such things. From about pp. 98 ff. whenever Descartes introduces a new idea for symbolism or shows how to generate a previously unknown arithmetical relation from two known relations, he emphasizes that the objects in question are no more than a shorthand for dealing with relations between real objects in the spatio-temporal world. When we abstract out a mathematical object like a point or a number, it is beneficial to use our imagination to find a symbol or a “true idea” of the abstraction so the understanding can concentrate on its properties and discover new properties that might be hidden by the density of real world objects or groups of things.  These pages (p. 100) contain an interesting criterion of existence: to be representable in the imagination. On this page Descartes effectively equates “conçue par l’imagination” and “impliquent en réalité.” Even though we abstract from any individual subject when we imagine mathematical objects, this does not mean that mathematical objects are real and distinct entities (p. 100).  If we succumb to the illusion that numbers are real, then we are likely to attribute to them marvelous properties and illusory qualities. Those who put so much faith in these things do so because they perceive numbers as distinct from numbered things (p.101). (Cf. also Discours de la méthode, p. 150.)