"Wisdom consists in the investigation of first causes or principles" (Descartes).
"All things that can be the object of knowledge are interwoven in the same way" (Descartes).
"The order of our thoughts must always go from the simplest to the most compound" (Descartes. Discourse of Method).
The Mathesis Universalis, by Descartes
René Descartes −philosopher, scientist and mathematician− is considered one of the great figures of Western thought. He was the founder of modern rationalist philosophy by basing it on the concept of the "thinking subject", in which reason becomes the ultimate criterion of truth. Descartes was an innovator, not only in philosophy, but also in physics (which was then called "natural philosophy"), by applying the rationality of mathematics to both disciplines.
Descartes was aware that there was a contrast between mathematics and philosophy. The philosophical field was uncertain, diffuse, opinionated, controversial. In mathematics, on the other hand, there was certainty and complete unanimity. Descartes therefore set out to reconstruct the whole edifice of knowledge by following a method analogous to that of mathematics, i.e., by applying the deductive and rational method. This universal mathematics (Mathesis Universalis) would make it possible to approach the study of reality in a much more solid and well-founded way, and would make it possible to create a true universal science.
Descartes used the term "Mathesis Universalis" in his work "Regulae ad directionem ingenii" (Rules for the direction of the spirit), begun in 1619, completed in 1628 and published posthumously in 1701. The word "mathesis" means teaching, study, science, knowledge. From its root comes the term "mathematics". For Descartes, mathesis universalis is a hypothetical universal science foundation of all particular sciences. This same denomination was later used by other philosophers, mainly Leibniz.
The Regulae is a key work of Cartesian thought. In it Descartes claims to have discovered a universal method, a method applicable to all sciences, the method of certainty and mathematical reason, the method with which the true science, the unique science, the universal science, the Mathesis Universalis can be constructed. Descartes was trying to "put order" in the diversity of particular knowledge that he himself possessed in mathematics, philosophy, physics, theology, etc. He then intuited the "admirable science" that would remedy this situation.
During his numerous travels, Descartes matured his idea of the true or universal science and of his method to elaborate it. But it was on November 10, 1619 (at the age of 23), while ill and bedridden, that he seems to have reached full and definitive consciousness of a new method, something he had been pursuing for a long time. He then had the conviction that all knowledge could be gathered into a single universal science, capable of solving in a general way all kinds of problems and of founding, not only science, but also philosophy.
The Cartesian method intended to replace the Aristotelian-scholastic philosophy by a total system based on a rationalist method to reach knowledge and truth from some primary principles or concepts.
The Discourse of Method
The "Discourse on Method," published in 1637, the full title of which was "Discourse on the Method for Conducting Reason Well and Seeking Truth in the Sciences," is Descartes' major work and one of the fundamental works of Western philosophy. From two letters he addressed to Mersenne (in the years 1636 and 1637), it is known that the title was to refer explicitly to his dream of a universal science: "Project of a universal science that could raise our nature to its highest degree of perfection". Descartes used the word "Discourse" and not "Treatise" to make it clear that his intention was not to create a formal doctrine or to reform the official teaching, but only to expose how he carried out the reform of his own thought.
The Discourse is a work of great mental lucidity, in which he deals with a great variety of subjects, among them: knowledge, the nature of reality, morality, the immortality of the soul and the existence of God. But what interests us here is the theme reflected in the title of the work.
Descartes exposes the problem of the foundation of knowledge: its lack of coherence and systematicity. He questions all the knowledge learned throughout all education, since the beliefs that are instilled in us from birth depend on the social environment and the people who educated us. And the sciences, having been made by multiple authors, each with their own opinion, cannot be the bearers of true knowledge. He criticizes the scholastic philosophy of his time, especially the Aristotelian syllogism, which he says serves only to explain things already known. Faced with this situation, he makes several general recommendations:
We must doubt everything systematically in order to find the truth. "In order to investigate the truth it is necessary to doubt, as far as possible, all things, once in a lifetime." Doubt is not an end in itself, but only a means to reach the truth. In this he agrees with his contemporary Francis Bacon: "Doubt is the school of truth", although Bacon sought truth through the inductive process.
We must renounce diversity of opinion and use reason to form our own beliefs. Reason must be detached from tradition and authority, and be autonomous, in the sense that its exercise is not conditioned by anything other than reason itself. Reason must be the supreme and only principle on which to base knowledge. What is true is what reason perceives with clarity. It is the thinking subject who has to determine when we are before a true or false knowledge. "Manage problems; do not accept anything as an article of faith, look for clear and distinct ideas, trust yourself." "It is true what my rational criterion decides what is true."
We must look for the foundation of a science outside science itself; its foundation must be at a higher level. "No science is qualified to demonstrate scientifically its own basis." This position is the same one that centuries later John Wheeler would hold with respect to physics: "No physical theory that deals only with physics will ever explain physics."
We must unify all the dispersed knowledge and thus reform our global understanding of the world, in order to create a universal science. By doing so, we will be able to discover the hidden and make easy what is apparently difficult.
The method
Descartes proposes a new method to obtain a sure knowledge based on the power of human reason. The main ideas of this new method, based mainly on his works "Regulae" (1628), "Discourse on Method" (1637), "Principia Philosophiae" (Principles of Philosophy, 1647), "Metaphysical Meditations" (1641) and "Passions of the Soul" (1649), are, in essence, the following:
Starting from total and absolute doubt, and given that doubt is a form of thought, Descartes finds a philosophical principle that serves him as a starting point to base his project: "Cogito, ergo sum" (I think, therefore I am). The consciousness of the self or the subject as thinking substance becomes the principle of everything.
We must first seek the universal or central principles of all sciences, and then descend to the particular. It is a centrifugal movement: from the universal or nuclear to the particular or peripheral.
Philosophy is the ultimate foundation of all sciences. The universal science, the science that must investigate the principles or foundations of knowledge, is philosophy, and more specifically, metaphysics. Descartes mentions Plato and Aristotle as the main authors who initiated this path.
The body of knowledge is like a tree: its roots are metaphysics, the trunk is physics (or natural philosophy), and the branches are the other sciences (principally, medicine, mechanics, and morals).
Human understanding is based on two actions (or fundamental operations of the mind): intuition and deduction. Intuition is applied for the discovery of the first truths, which are the roots of the tree of knowledge, metaphysics. And deduction is applied for the discovery of particular truths, relying on reasoning, mathematical style.
Mathematics is the most perfect knowledge and the model of knowledge. In the same way that mathematics produces truths from premises, the task of science is to deduce truths from first principles. Thus a true and universal science would be constructed.
There is an intrinsic unity in all sciences, although externally they seem different. The unifying factor of the sciences is reason, for all the sciences are the consequence or the result of applying reason, which is always one and the same in all men, regardless of the field of application. Reason is what is common to all the particular sciences. Reason is the essential knowledge and the foundation of universal science.
All knowledge must always be certain and evident, without possibility of doubt. Otherwise, it is not true knowledge. Truth and knowledge must be the same thing. In mathematics there is no room for doubt, hence its value. Mathematical reason is the foundation of all science.
There are three different and completely separate "substances", which are: 1) the mind or thinking substance (res cogitans); 2) the body (res extensa); 3) God, the res infinita. These substances correspond to 3 fundamental innate ideas: self, world and God.
A substance is that which exists by itself, which is self-sufficient, which does not need anything else to exist. In this sense, only God can be substance. But Descartes admits that mind and body are substances because they are independent of each other. Each substance has attributes (essential properties) and modes (non-essential properties).
The mental and bodily substances are united and interact with each other in man through the pineal gland. It is the famous "Cartesian dualism", which has had so much influence throughout history and which is now considered to have been overcome, since it is believed that everything has a common origin or foundation.
The attribute of the thinking substance is thought. And its modes are: to desire, to know, to will, to hate, to admire, and so on. The attribute of extensive substance is extension (or spatiality) and the modes its various manifestations in the three dimensions. The nature of physical reality is its extension in space, its geometrical character, so that the principles of physics must rest on mathematics.
The first principles are "simple natures" (naturae simplices). They belong to the ideal order. They are innate ideas, possessed by all men by the fact that they are rational. They are not acquired by experience and do not depend on cultural or social context. They are self-evident truths that are in our minds, independent of time, place and person. They cannot be demonstrated but are the basis of all demonstration. There are 3 distinct groups of simple natures: 1) material (figure, extension, motion, etc.); 2) mental (thinking, knowing, willing, doubting, hating, etc.); 3) common to both (existence, unity, duration, etc.).
Descartes' formal method, founded on logic and mathematics, consists of 4 rules:
Evidence. "Do not admit as true anything that is not known with evidence that it is true".
Evidences are the simple natures: the innate, intuitive, immediate, simple, clear, distinct and unprovable ideas. They are the fundamental pillars of knowledge on which complex truths or new truths are built.
Analysis. "To divide every difficulty into as many parts as possible and into as many as its best solution requires."
Any subject or problem we have to study is an interrelated set of more or less complex ideas. This phase consists of analyzing these ideas until we find the evidence. To analyze is to decompose the complex into its simple natures.
Synthesis. "To conduct my thoughts with order, beginning with the simplest and easiest objects to know, in order to ascend little by little, gradually, to the knowledge of the most composite."
Once the problem has been decomposed into its simple natures, we must reconstruct it in all its complexity, deducing and constructing all the ideas and consequences that derive from those simple natures. And at the same time that we reconstruct the complex, we also expand our knowledge with new truths.
Verification or enumeration. "And the last, in making in everything such comprehensive accounts and such general reviews, that I would come to be sure of omitting nothing."
It is a matter of going over the previous steps in detail to be sure that there has been no mistake and that we have not forgotten anything. It is the return to intuition, to contemplate the totality in an intuitive and global way. It starts with intuition and ends with intuition.
MENTAL vs. Mathesis Universalis
There are remarkable parallels between the Mathesis Universalis sought by Descartes and MENTAL:
Consciousness.
Descartes started practically from scratch. He suppressed all his old beliefs in order to seek a new foundation on which to build the new beliefs. He then discovered and adopted his fundamental principle, "I think, therefore I am." This principle can be interpreted to mean that the principle that underlies everything is consciousness.
MENTAL is also the result of questioning everything, searching for universal principles (as in the case of Descartes), a search that culminated in the archetypes of consciousness.
Universality.
Descartes proposes a universal science and a universal method.
MENTAL is a universal language, a universal method and the foundation of universal science.
Foundation of the sciences.
Descartes tried to found all the sciences by means of a universal science in order to put order in the knowledge of his time. Today we find that mathematics lacks solid foundations since (in 1931) Gödel proved his famous incompleteness theorem, a theorem that shows that it is not possible to found mathematics from the superficial, from itself (from a formal axiomatic system). This result confirmed Descartes' intuition that a science cannot be founded from science itself.
MENTAL pretends to be the answer to this situation, since it is the foundation of mathematics, and is not affected by Gödel's theorem.
The first concepts.
Descartes' first concepts, which should be the basis of all sciences, should be simple, evident, innate, intuitive and certain principles, in which there can be no doubt. There being separation between mind and body, there are simple corporeal, mental and common natures.
In MENTAL the first concepts (the archetypes of consciousness or the philosophical categories) are also innate, simple, evident and intuitive concepts. They are abstract in character and common to the internal and external world. In MENTAL, ontology is equal to epistemology.
The new truths.
The Cartesian method is based on some first concepts from which all new truths can be generated. Descartes sought with his method to discover new truths, beyond the simply deductive, a method for invention and discovery. The universal science, the union and the construction of knowledge must be done from the primitive concepts, which are simple, and then gradually ascend to the complex to generate new truths.
The archetypes of MENTAL are semantic axioms from which all possible expressions can be constructed. The primary archetypes are of the utmost simplicity and the highest level of abstraction. Everything is constructed from the primary archetypes. Simplicity goes together with truth and consciousness. In the expressions derived from MENTAL we find new truths. These are not only deductions, but constructions that reveal new relationships between the first concepts.
Problem solving.
According to Descartes, universal science might be able to solve in a general way all kinds of problems.
With MENTAL, problems are simplified, clarified or solved because they are contemplated from a higher level.
The union of philosophy and mathematics.
Descartes believed that universal science should be built from philosophical principles. Descartes united philosophy and mathematics. It was this synthesis that allowed him to envision the development of a universal science in which all knowledge would be given in "order and measure," as it is given in mathematics.
In MENTAL, philosophy and mathematics go together. The primary archetypes are philosophical categories and abstractions of a meta-mathematical type.
The union of opposites.
Descartes united intuition and deduction, for he claimed that human understanding is based on these two actions. In his method he united analysis and synthesis. He tried to unite the universal with the particular. He united algebra and geometry with his system of geometric representation of algebraic expressions to create analytic geometry. This unification was one of the greatest intellectual achievements of modern science. The Cartesian system can be interpreted today as the union of the two modes of consciousness associated with the cerebral hemispheres: rational (or analytical) and intuitive (or synthetic) consciousness.
MENTAL, as the language of consciousness, unites all pairs of opposites.
Diffusion.
Descartes wrote the Discourse in French −it is the first book of philosophy written in this language − instead of the scientific and learned language of his time, which was Latin. He did this so that it would be open to all who would use only their natural reason, without prejudice.
MENTAL is a simple, clear, accessible to everyone, democratic language. It demystifies the sometimes cryptic official knowledge.
Personal transformation.
Descartes underwent a profound personal transformation as he progressed in the construction of his method. He sensed that the knowledge of that universal science elevated consciousness, as he expressed in the initial title he had envisioned for the Discourse: "Project of a universal science that could raise our nature to its highest degree of perfection". That transformation implies a unified consciousness: "There being but one true knowledge of each thing, he who possesses it knows all that can be known". And the need to "reform the understanding" can be understood as reforming our conscience, our vision of the world.
With MENTAl, the author has also made an inner journey of self-discovery and personal transformation.
The Mathesis Universalis was intuited by Descartes, but was partially developed. Descartes did not clearly and fully identify the first concepts (the simple natures), did not formalize them, and did not specify how they combined to generate new truths. Nor did he configure a universal language of reality, science and consciousness.
MENTAL is precisely the set of those first concepts, whose combinatorics (by means of the first concepts themselves) constitute the universal language and the foundation of universal science.
We can consider, therefore, that MENTAL is the Mathesis Universalis pursued by Descartes, although MENTAL goes beyond the objective that Descartes proposed, since by its supreme level of abstraction, it is the foundation of the possible worlds.
Addenda
Descartes and the existence of God
Descartes strove to understand, with the help of "divine truth," the foundation of the cosmos. He claimed that the knowledge obtained by his method could lead to the "ultimate religion" by demonstrating with conclusive rational arguments the existence of God and the immortality of the soul. He proposed 3 arguments to demonstrate the existence of God:
The gnoseological. In the mind of the subject, which is finite and imperfect, appear the ideas of perfection and infinity. It is impossible that from an imperfect being can arise the idea of the absolutely perfect. And it is impossible that from a finite being can arise the idea of infinity. Therefore, there must be a perfect and infinite being in itself that puts in our mind these ideas.
The ontological. If in the mind of the subject there is the idea of a perfect and infinite being, it must exist, because if it did not exist it would lack one of the perfections which is existence, and that would be contradictory. Therefore, God, the perfect being, exists.
The causal. I am not the cause of myself, nor have I always existed, nor do I owe my existence to causes less perfect than God. It would be necessary to go back to an infinite number of causes, so we must admit an ultimate cause, God, who is the cause of his own existence.
"Descartes' error", by Antonio Damasio
The neurologist Antonio Damasio believes only in biology and does not believe in anything that has no material basis. All aspects of the mind and emotions must be studied from a biological point of view:
Biological structures regulate the body, emotions and cognitive processes. It locates the mind in the upper brain layers, and emotions in the lower layers.
Mental activity requires the brain and the body. The body contributes to the functioning of the mind and is part of the mind. The mind is "embodied" and not just "brained".
It is not only the mind that thinks. The body and emotions play a key role in the way we think. Rationality requires emotional input.
Emotions are bodily perceptions of the degree of fit between body and circumstances. There are some "somatic markers", which influence rationality.
According to Damasio [2006], Descartes' error was threefold:
To affirm that being is derived from thinking, for it is the opposite: in the beginning was being and then thinking. "We are, and then we think, and we think only insofar as we are, because the structures and operations of being cause thinking." Therefore, Descartes' statement should have been "I am, therefore I think."
Separate body and mind, for the mind is as much a part of the body as it is of the brain. The mind has a biological root.
Separate reason from feelings, for feelings influence reason. There is possibly a common thread connecting reason, feelings and body.
Regarding the former, Damasio misinterprets Descartes' philosophical principle as a logical derivation or implication. It is evident that being is above mind and thought. Descartes was surely referring to thought being subordinate to existence. Without existence there can be no thought. And if there is thought it is because there is existence. The statement "I exist, therefore I think" is redundant, because if this sentence can be said it is because there is thought. But not everything that exists, thinks. In fact, the root of the human being, the soul, does not think; it perceives.
Regarding the second, Descartes was indeed wrong in separating mind and body, because the physical and the psychic are manifestations of the primary archetypes (the hypothesis held by Jung and Pauli). It is the simplest hypothesis, the one that follows the principle of Occam's razor.
Regarding the third thing, it must be said that mind, body and emotions are interrelated because they are manifestations of Being. Physical body, mental body and emotional body are three different levels (or dimensions), but they are interrelated to each other. The brain is an instrument of the mind; the mind is not an epiphenomenon of the brain.
Bibliography
Aczel, Amir D. El cuaderno secreto de Descartes. Una historia verdadera sobre matemáticas, misticismo y el esfuerzo por entender el universo. Biblioteca Buridán, 2005.
Damasio, Antonio. El error de Descartes. La emoción, la razón y el cerebro humano. Crítica, 2006.
Descartes, René. Discurso del método. Espasa-Calpe, 2001.
Descates, René. Discurso del método. Estudio preliminar, traducción y notas de E. Bello Reguera. Tecnos, 2003.
