The Mathesis Universalis and Neoclassical Economics

As Edward Fullbrook highlights in his recent book Narrative Fixation in Economics, the Cartesian view of human reality has deeply shaped the way Neoclassical Economics theorizes about the economic and social existence (2016, p. 45). Indeed, while emphasizing the relevance of the pure thought of a disembedded human subject,  Neoclassical Economics has reinforced the relevance of the Cartesian method of inquiry  that moved the so called scientific (true) knowledge  out of the general flux of experience.

In the second part of the Discourse of Method, Descartes presented some principles that should be followed in order to acquire knowledge: 1) human beings cannot  admit any ideas that are not absolutely clear; 2) human beings must divide each problem in so many parts as appropriate for its best resolution; 3) human beings should apply deductive reasoning to organize their  thoughts from the simplest to the most complex ones 4) the analytical-synthetic process of reasoning leads to true knowledge.

According to Descartes, the first principle of his method focuses the importance of “never accepting something as true that I clearly don’t know as such” (Discourse of Method, Part II). Indeed, Descartes inspired himself in Geometry as a model of Science. As a result, he considered the postulates of Geometry not only as universal and necessary but also as clear and distinctive ideas related to intellectual intuition. Only these clear and distinctive ideas  are considered to be the pillars of true knowledge.

Based on the second principle, Descartes builds his research method of analysis that isolates the clear and distinctive ideas from the most complex ones. His emphasis on the order of thoughts strengthens the role of Mathematics in the Cartesian method of pure inquiry. Moreover, the third principle of his method leads to a special kind of organization of thoughts. In his own words, the organization of thought should start “with the simplest and easier to gradually rise, as if by means of steps, to the knowledge of the more composed, and assuming an order between the ones that don’t precede naturally each other” (Discourse of Method, Part II).

Departing from the mathematical method of reasoning, Descartes arrives at the notion of order in scientific thought, that is to say, once the human subject knows the simple elements of a problem, he can assume all the consequences that derive from those first ideas considered as absolutely certain. Those first ideas have the characteristics of clarity and distinction. Besides, they are known intuitively and constitute the pillars on which relies true knowledge.

Finally, Descartes reinforced the analytical-synthetic process of reasoning. Following the deductive method of pure inquiry, human knowledge grows throughout a rigorous chain of ideas. As a consequence, new thoughts arise while the human subject applies deductive reasoning so as to create a chain of ideas that links the most simple to the most complex ones. In this attempt, true knowledge can be obtained.

As a matter of fact, the Cartesian method presents the intellectual intuition and the deductive reasoning as crucial elements of the discovery and construction of true knowledge. Moreover, clarity, distinction and order overwhelmed the mathesis universalis that turned out to be considered as the pinnacle of the epistemo-ontological construction of Cartesian thinking.  The mathesis universalis is, according to the Cartesian epistemology, a general method of pure inquiry able to explain everything, regardless of the nature of the objects to be studied.

As E. Gilson (1945) highlighted, the Cartesian method represents an attempt to extend the mathematical method of inquiry to all of human knowledge in the form of the mathesis universalis.  Indeed, this extension is at the center of the a priori foundations of scientific knowledge in Neoclassical Economics.





DESCARTES, René.  Discurso do Método. São Paulo: Abril Cultural, 1973.

FULLBROOK, E. Narrative Fixation in Economics, WEA Books, 2016.

WILLIAMS, Bernard. Descartes: The Project Of Pure Enquiry. UK: Penguin, 1978

  1. Since the a prior method starts from certainties and uses certain logic to proceed, the process leads to certainties and is immune to the possibility of learning from experience. This is exactly the case with economists. Keynes criticized his fellow economists for being “unmoved by the lack of correspondence between the results of their theory and the facts of observation.”

    • Maria Alejandra Madi said:

      Thanks for your comment. I completely agree. The Cartesian true knowledge does not depend on being validated
      by real-life experience. This philosophical perspective lacks a Phenomenology that could found a realistic approach to economic thinking.


  2. David Chester said:

    Who is it to dare actually follow Descartes into the science of macroeconomics? Few indeed! There are lots of complaints about this subject not being sufficiently scientific, but how many minds are able to build (or to accept) a new theory which actually meets this need and specifically explains about of what our social system comprises and HOW IT WORKS?

    I wish to show that such an explanation is possible and my recent book provides proof of this vital matter. The old dismal pseudo-science of macroeconomics now is replaced by a better one than is truly scientific!

    Write to me for an e-copy, and update your past ways to the new facts, discoveries and thinking processes. I am not writing this in order to make a financial gain of any kind, but for the sake of the joyful sharing of new scientific knowledge, which, as in the days of Michael Faraday and other pioneers, was freely and happily given.

    Description of book:

    “Consequential Macroeconomics–Rationalizing About How Our Social System Works”

    In the past the subject of theoretical macroeconomics has been treated badly and in an incomplete unscientific manner. The basic model for representing the general social system of a nation has never been properly developed. The results previously obtained, from the over-simplified models of the past, are unsatisfactory and they sometimes even conflict with common sense. When the alternative of computer-modeling is used, the detailed results are too complex, difficult to follow and they are unsuitable for students and teachers to appreciate, interpret and understand what really is involved.
    The aim of this book is to correct this situation and to provide a very logical and compact, but sufficiently complete, theoretical presentation about how our social system actually works. The emphasis is on viewing the system from sufficient a distance so as to be able to envisage it as a whole, in order to provide an improved and better perception and understanding of the full structure of our social system. It also introduces some original aspects of analysis into the subsequent methodology.

    The 320 page book is presented in parts 6 named:”getting started”,”model”,”analysis”, “decisions”, “money” and “consequences”. It contains an introduction and a set of 7 appendices, a list of references and an index. This is an original engineering approach to this subject, where the ideas of Jean Says, Adam Smith, Henry George, David Ricardo, Leon Walras, Wassley Leontief, Henry Hazlitt, and several others are combined into well-knit scientific framework.
    The approach taken here starts from scratch. After the introduction and general review of the overall problems in representing our social system, a series of assumptions and early considerations are provided, along with the necessary definitions. From this standing, there is built up a base model (see diagram) that is logical in its development and which is virtually complete, whilst not being more complicated than is absolutely necessary–to provide for the subsequent analysis in a scientific manner.

    The model is expressed in three ways, by this diagram, by equations and by a matrix using W.W. Leontief’s “Input-Output” method. Its various parts are then described and used for analysis and explanation about the circulation of money, goods, services, valuable documents, etc. This leads an examination of the general equilibrium and stability of the system.

    Short-term disturbances to the steady-state result in the need for decision-making, which is carefully described in detail and illustrated by four simplified numerical (hand-calculated) examples, three being about taxation and the short-term dynamics. These calculations show that compared to the benefits in progress that result from an increment in income-tax (yes, it is beneficial overall), a tax on land-value is about 3 times better! The decision-making depends on some properties of the system, which are introduced to complete the descriptions of this process.

    Theories about money and banking are given which lead to a discussion about the functions of government over longer periods of time. There follows a development about the limitations to growth of the system, related to George’s description of the “savanna” in “Progress and Poverty”. The book concludes with a long review and summary that provides a better and somewhat new understanding of what macroeconomics really is all about.

    The book is suitable for students of economics who wish to avoid the confusion of past explanations or are new to this subject. They should have a small acquaintance with economics and some high-school mathematics to include elementary (square) matrices and the notation of the calculus. This book is useful for teaching purposes, particularly because it uses a more general terminology (with full definitions) than is often the case. However the development also opens the way for research, since it provides a new and easy-to-use tool for analysis of short-term policy changes within the whole of a nation’s social system.

    • Maria Alejandra Madi said:

      The Cartesian true knowledge does not depend on being validated by real-life experience. Its subjective idealism is still relevant in neoclassical economics. This philosophical perspective lacks a Phenomenology that could found a realistic approach to economic thinking.

      I am interested in reading your ebook. We certainly need to consider real-life experience- how the world works – in realistic macroeconomic approaches.


      • If you will kindly send me your e-mail address I will be able to send you the e-copy of my book that you are interested in seeing. I am David Harold Chester

  3. Two of my mathematics professors wrote a book entitled “Descartes Dream: The World According to Mathematics.” Two points interest from that book. First, how did Descartes create the notion to mathematize everything and call it a unified method for science? The answer: as the result of a psychotic dream, or a series of dreams. Might be better to call them nightmares. The dreams were so disturbing for Descartes that he sought safety in the Church. A strange event, considering he was about to reduce the Church’s doctrines and rituals to mathematics. Second, the authors spend the rest of the book pointing out and illustrating the many limitations and misuses of mathematics. One chapter is particularly relevant for social scientists, “The Social Tyranny of Numbers.” Two passages seem prudent to consider.

    “Mathematization is upheld as the only way for a field of study to attain the rank of a science. Mathematization means formalization, casting the field of study into the axiomatic mode and thereby, it is supposed, purging it of the taint of rhetoric, of the lawyerly tricks used by those who are unable to let facts and logic speak for themselves. For those who want to assert the claim of rhetoric as a necessary and valid aspect of any human endeavor, mathematics appears as the dragon which must be slain.
    . . . .
    The introduction of mathematical methods in biology, economics, psychology, and other branches of the so-called behavioral sciences has always been accompanied by controversy. The opponents to mathematization may have had good grounds for the resistance, but the arguments could be discounted by raising the suspicion that they didn’t understand the mathematical methods they were challenging. For this reason, it is important to state publicly that among professional mathematicians the skepticism about behavioral-science mathematics and even about mathematical biology is much stronger than it is among non-mathematical behavioral scientists and biologists. This skepticism is rarely stated in print. Unlike philosophers and literary critics, mathematicians dislike controversy. They are not used to it and will usually keep their mouths shut to avoid it. (A famous instance was Gauss’ suppression of his own discovery of non-Euclidean geometry, for fear of a clamor from the ‘Boeotians.’)”

    Following the mathematics is no way to develop any social science, including economics!

    • Maria Alejandra Madi said:

      Hi Ken

      Good comment! Many thanks for the literature recommendation. The book seems interesting to deep the epistemological understanding about the role of maths in economics.


  4. Ernesto Vaihinger said:

    Estimo que el método de Descartes va más allá de los instrumentos que se puedan utilizar. Está claro que su método se inspira en la búsqueda de la verdad. Lo que hay que discutir es la “verdad” apodíctica que pretende la economía neoclásica abusando del cartesianismo. Su mundo ideal sin protagonistas y actores actuando en sociedad no existe.

  5. Maria Alejandra Madi said:

    Gracias Ernesto. Muy oportuno tu comentario. Hay que extender la crítica a la idea de verdad absoluta y a la concepción a-temporal del “sujeto que piensa” en un vacío ! Hay que reforzar que la filosofía de la teoría neoclássica es el idealismo subjetivo que no considera la realidad como existencia.


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