Public debate becomes impossible in the Twilight of the State. Diverse political and ideological currents – critical of the failings of modern State--, directly demand the erasure of the separation of powers, the political utilization of justice and the privilege of politics over law. The functional separation of economy, religion, law, and politics not only … Continue reading The Modern State as Concrete Universal

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

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 Philosophical Remarks, L. Wittgenstein wrote prophetically: "I predict a time when there will be mathematical investigations of calculi containing contradictions, and people will actually be proud of having emancipated themselves from contradictions." The import of this statement is deeper than you may think, because it puts into question not only what is the … Continue reading Dialetheism and Multipolarity

Here is a new version of an article I published in 2006 in my old web site. I have expanded the article with more recent material pointing to the idea of the "completenes" of action and the need for new conceptual foundations for Information Security. The original article did not explain the need for new … Continue reading What is an Error?

The Aristotelian "square of oppositions" is at the centre of recent developments in the geometry of logic. The image below is a modified representation of the logical tetra-icosahedron defined by Regis Pellisier [2004, 2009]. I have moved the nodes and edges around to better show the standard logical square (depicted in red). The labels "Immediate", … Continue reading Mapping the Logic of Action

Are you interested in Actor-Oriented-Programming or the "logic of agency"? If the answer is yes, then you will benefit from studying the XII Century work by Anselm of Canterbury (St. Anselm). The works of Sara Uckelman and Douglas Walton (see notes in the Mind Map) gave me surprising insights into the achievement of this "old" … Continue reading St. Anselm of Canterbury: Logic of Action

The Aristotelian "square of oppositions" is at the centre of recent developments in the geometry of logic. The image below is a modified representation of the logical tetra-icosahedron defined by Regis Pellisier [2004, 2009]. I have moved the nodes and edges around to better show the standard logical square (depicted in red). The labels "Immediate", … Continue reading Logic of Action II (2009)