In “La Libertad en la Filosofía de la Cuadratura de Heidegger,” Alejandro Rojas Jiménez continues his analysis of the Quadrature as follows: “Empezaré por exponer el sentido simbólico de los Mortales como los que son capaces de la muerte como muerte. El sentido fundamental de esta definición es que sólo él vive ante la presencia … Continue reading A.R. Jiménez on the Quadrature

The Quadrature has been formulated and discovered or re-discovered many times in history. A book might be written to explain how and when the Quadrature is forgotten or recedes into the background. Perhaps the least understood formulation is that of Martin Heidegger. As M. Robitaille notes, following the studies by Jean-Francois Mattéi, Heideger´s “quadrature” (Geviert … Continue reading The Quadrature : Le Quadriparti – La Cuadratura

The Quadrature is the “halo” described here by Ludwig Wittgenstein: “Thought is surrounded by a halo. Its essence, logic, presents an order, in fact the a priori order of the world: that is, the order of possibilities. which must be common to both world and thought. But this order, it seems, must be utterly simple. … Continue reading Wittgenstein: “Thought is Surrounded by a Halo”

The work of R. Jung, especially the paper quoted below, shows the key turn we should take to re-define systems theory. This would be positive for Science in general, and certainly for all specialties dealing with social and technical systems. The conventional view criticised by Jung –one centred around mechanical metaphors—must be overcome. The key … Continue reading Richard Jung: “Surfaces Of Systems”

If we don’t think and speak Being, then we think and speak in oppositions and remain in oppositions. Our action then is self-defeating, banal and incomplete. Now, human thinking and speech necessarily blossoms and opens up as a series of differentiations, each one presenting us with a fragment of of the world. The basic differentiations … Continue reading The Fourfold Thoughts Of Being

The painting Les Deux Carrosses by Claude Gillot presents a scene of street-level conflict where two carts pulled by servants are blocking each other. The characters in the painting, arranged around the binary opposition of the cart pullers (who are almost touching) gesticulate grotesquely. One of them is masked, and all are dressed in rich … Continue reading Les Deux Carrosses by Claude Gillot (circa 1707)

In  “Recent Contributions to the Mathematical Theory of Communication”  (University of Illinois Press, Urbana, 1964) Warren Weaver summarised the paradoxical character of Information Theory (as formulated by C. Shannon): “2.2 Information “The word information, in this theory, is used in a special sense that must not be confused with its ordinary usage. In particular, information … Continue reading Information Theory

In these  pages I frequently refer to and build upon a structure with four “modes” or “terms” – namely those of Person, Subject, Agent and Object. At its core, this model is not original, and stems from the work of many disparate authors, in different areas of knowledge. For the sake of rigour and completeness, … Continue reading Quadratures: Person, Subject, Agent and Object

More support for the logical basis of the geometry of cognition comes from the American mathematician W.H. Gottschalk (a fact noted by Alessio Moretti in his PhD thesis published in 2009. Gottschalk writes: “It is well-known that every involution in a logical or mathematical system gives rise to a theory of duality; for example, negation … Continue reading The Theory of Quaternality

George Spencer-Brown –the creator of a very original “logic of distinctions”—wrote an interesting statement about the Law of Complementarity: “There is no stronger mathematical law than the law of complementarity. A thing is defined by its complement, i.e by what it is not. Ant its complement is defined by its uncomplement, i.e. by the thing … Continue reading The Law of Complementarity

The correlated terms of intensive and extensive abstraction have another antecedent in the reflections of G.W.F Hegel on intensive and extensive “magnitude.”  The following fragments can be found in Hegel’s “Science of Logic- Identity of Intensive and Extensive Magnitude” – sections 480, 481 and 483: “480. The determinateness of intensive magnitude is, therefore, to be … Continue reading Hegel: Intensive And Extensive Magnitude

One of the most important insights made in the realm of Systems Theory was due to Kent D. Palmer in a paper published in  2010. (Source: http://holonomic.net/sd01V04.pdf ). The key paper, under the title “Advanced Meta-Systems Theory For MetaSystems Engineers,” presents a radical reformulation of the relations between the concepts of “system” and “meta-system.” Palmer … Continue reading K. Palmer: “The Inverse Dual Of a System”

Careless discussion tends to ignore important philosophical criteria, as noted in previous notes and articles in this blog. One of these is the distinction between two basic types of negative statements: true negations, and complements of the predicate. Daniel J. Castellano, a mathematician and historian from MIT and Boston University covers these points in his … Continue reading Distinctions: Two Kinds of Negative Statements

In his “A Preface to Metaphysics,” (Fourth Lecture, section 10) Jacques Maritain writes: “I have already spoken of the most important distinction which the ancient drew between abstractio totalis, which I will call extensive visualisation, and abstractio formalis, which I will call intensive or characterising and typifying visualisation. At first intellectual visualisation is as yet … Continue reading J. Maritain on Extensive and Intensive Visualisation

Discontinuity  is manifest in language in the sense that there is a complete separation between the signifier and the signified, between the symbolic and that for which the symbol stands for. This is also called the “arbitrariness of the signifier” (see the work of Ferdinand de Saussure - http://www.revue-texto.net/Saussure/Saussure.html ) The term “arbitrariness” means here … Continue reading Discontinuity in Language

“When reflection, turning to the comprehension of chaotic experience, busies itself about recurrences, when it seeks to normalise in some way things coming and going, and to straighten out the causes of events, that reflection is inevitably turned toward something dynamic and independent, and can have no successful issue except in mechanical science. When on … Continue reading Intensive and Extensive Abstraction

When reading the Bhagavad Gita, among the teachings on human action we find a lesson which could not be more contrary to “common sense” as it is conceived today: “The world is imprisoned in its own activity, except when actions are performed as worship of God. Therefore you must perform every action sacramentally, and be … Continue reading Complete and Incomplete Action

To what extent is human life natural? To what extent is it natural life? This is the fundamental un-answered question of anthropology. On all sides, on all related sciences there is an assumption that human life is different –either superior or inferior—but essentially different to nature. The presumption is that human life is either extraordinary … Continue reading Human Life And Natural Life

In the Monadologie (1714), G. W. Leibniz writes: “And there must be simple substances, since there are compounds; for a compound is nothing but a collection or aggregatum of simple things.” -  tr. Robert Latta.  (“Einfache Substanzen muß es geben, weil es zusammengesetzte gibt; denn das Zusammengesetzte ist nichts, als eine Anhäufung oder ein aggregatum … Continue reading A Logical Argument

In “Against Philosophical Appeasement” ( http://www.reocities.com/Athens/Thebes/dcs11.htm ) Anthony and Mary Mansueto write a magnificent indictment of nihilism, which starts as follows: “Nothing is harder for this sceptical age than to believe that the universe ultimately has meaning –except, perhaps, the idea that such a belief is not only warranted, but is in fact commanded, by … Continue reading Nihilism and Meaning Come Together

Anthony Mansueto has done original and very valuable work on the philosophy of religion, and he has done this while linking his reflection to social and historical questions normally avoided by academics. In the essay “Once Again on the Religious Question” ( www.reocities.com/Athens/Thebes/1593 ) Mansueto restates and explains the essence of his theses also published … Continue reading Theories of Abstraction