fourfolds, linear logic, logic, Philosophy

J.-Y. Girard’s Transcendental Syntax

March 7, 2012 Martin K. Jones 1 Comment

With the recent release of the paper found at the link below, logician Jean-Yves Girard has updated his program for a transcendental syntax to version 2.0. The first version was available last year only in French, but this new manuscript is available in English. Girard is known for his refinement of classical and intuitionistic logic, Linear Logic, and his exploration into the mechanisms of logic, Ludics.

In this new paper, Girard describes four levels of semantics, his infernos: alethic, functional, interactive, and deontic. They descend into the depths of meaning, and thus are numbered from -1 to -4. The negatively first, alethic, is the layer of truth or models. The negatively second, functional, is the layer of functions or categories. The negatively third, interaction, is the layer of games or game semantics. The negatively fourth, deontic, is the layer of normativity or formatting.

The Four Fundamental Forces of Physics

February 9, 2012 Martin K. Jones 5 Comments

References:

http://en.wikipedia.org/wiki/Fundamental_interaction

http://www.the-electric-universe.info/welcome.html

http://hyperphysics.phy-astr.gsu.edu/hbase/forces/funfor.html

http://www.pbs.org/wgbh/nova/teachers/activities/3012_elegant_09.html

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fourfolds, Science

Thermodynamics and the Four Thermodynamic Potentials

January 27, 2012 Martin K. Jones 2 Comments

References:

http://johncarlosbaez.wordpress.com/2012/01/23/classical-mechanics-versus-thermodynamics-part-2/

http://en.wikipedia.org/wiki/Thermodynamic_potential

http://en.wikipedia.org/wiki/Maxwell_relations

http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/thepot.html

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fourfolds, ontology

Philippe Descola’s Four Ontologies

January 26, 2012 Martin K. Jones Leave a comment

References:

Philippe Descola / Par-delà nature et culture

Structuralist Diagram of Philippe Descola’s Lecture, “Anthropology and Ontology”

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epistemology, fourfolds

Stances Towards Truth

December 9, 2011 Martin K. Jones 1 Comment

What are the different stances towards truth? I can think of four: relativism, pluralism, dogmatism, and skepticism.

In Relativism, truths are relative to the individual, and may be associated with their personal perspective. Truths are necessarily different as individuals are different and cannot be ranked as to their correctness between individuals.

In Pluralism, truths are separate and may be combined but usually cannot be unified under one overarching truth. Truths are pragmatically different and are true in principle or function.

In Dogmatism or Absolutism, there is one truth, whether we have access to it or not. Truth is absolute and necessarily consistent with itself.

In Skepticism, there may be no absolute truths. Truth is always in doubt and there is no certainty.

I believe that few if any of us are purists with respect to any of these stances towards truth. Each of us combines these four stances into a filter that we use to adopt and maintain our personal ensemble of truths. Some of us may be highly skeptical, with a little dogmatism about our skepticism, plus a bit of relativism and pluralism thrown in for good measure. And so on. Our filter will change depending on how we perceive the current truth of those stances.

Similarly, social organizations may also operate the same way as individuals in constructing a filter towards truth. Whether the organization’s filter arises as an average of the individual’s filters, or from some inherent property of the organization, remains open.

Whether there is one transcendent truth or possibly no absolute truths depends on your valuation of dogmatism and skepticism, respectively. And thus it doesn’t depend on what you or anyone thinks at all.

Notes:

Perhaps Absolutism would be a better choice than dogmatism in the diagram.

The post The One and the Many may be used to develop these stances better.

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architectonics, epistemology, fourfolds, hermeneutics, ontology, Philosophy

Walter Watson and David Dilworth’s Archic Matrix

December 2, 2011 Martin K. Jones 11 Comments

Throughout the history of philosophy, there have been many conflicting stances both towards claiming what exists (ontology), and how we can know our claims are valid (epistemology). There are the oppositions between idealism and realism, between rationalism and empiricism, between thinking all is change and all is changeless, between all is many and all is one, and so on. One approach to overcome these oppositions is to combine them to form their Hegelian synthesis. Another is to deconstruct them à la Derrida. Another pluralistic approach is to consider that there is a germ of truth on each side of the conflicting stance, an aspect of reality for which that stance is valid. Some might think that pluralism is the same as relativism, but it is not. Relativism and pluralism form yet another philosophical opposition like others mentioned above.

Regardless of the validity of pluralism, it can be very useful to analyze what philosophical stances are possible and how they relate to one another. The philosopher Richard McKeon created a rich schema for philosophical semantics that deserves greater recognition. This schema was both simplified and elaborated on by Walter Watson and David Dilworth in their books about the Archic Matrix. There are four main aspects, all exemplified by ancient philosophers: the Sophists, Democritus, Plato, and Aristotle. Everything else is a combination of these original aspects, or essentially a rehashing of them. The main aspects are perspective from the Sophists, reality from Democritus, method from Plato, and principle from Aristotle. These partition “what is”, however it is conceived, into four aspects, each of which can be interpreted in four different ways.

Considering Whitehead’s Criteria, note that perspective has consistency, method has coherency, reality has applicability, and principle has adequacy.

The Cynefin Framework

November 8, 2011 Martin K. Jones 2 Comments

From Wikipedia:

The Cynefin framework is a model used to describe problems, situations and systems. The model provides a typology of contexts that guides what sort of explanations and/or solutions may apply.

There are actually five domains in the framework, with the fifth one being disorder. It is not shown here. The domains are different in how cause and effect relate to one another within them. They are in the order of light transmission through the four elements: bright, light, dim, and dark.

For each domain, there is a common approach, each containing sense and respond. Simple: Sense – Categorize – Respond. Complicated: Sense – Analyze – Respond. Complex: Probe – Sense – Respond. Chaos: Act – Sense – Respond. For Simple and Complicated, sense comes first, and for Complex and Chaos, sense comes second. Respond ends the approach for each domain. Can one say the Simple and Complicated are a priori, and Complex and Chaos are a posteriori? Or that Simple and Complicated are rational, and Complex and Chaos are empirical?

Interestingly, if we examine the element of the approach that is not sense or respond, they have a close approximation to the fourfold of the Scientific Method.

References:

http://en.wikipedia.org/wiki/Cynefin

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cycle, fourfolds, Science

The Scientific Method

November 4, 2011 Martin K. Jones 4 Comments

The Scientific Method (SM) is often shown as a cycle of four steps: Observation, Hypothesis, Prediction, and Experiment. This cycle is somewhat similar to Kolb’s Learning Cycle, but there are important differences. Experiment is in both, but in Kolb Experience is the result of Experiment, and in the SM, Experiment follows Prediction. I think that Prediction would ideally be a part of both, and in the SM, Experience could be included in Observation. Perhaps Kolb’s Active Experimentation is really SM’s Prediction and Kolb’s Experience is SM’s Experiment.

References:

http://en.wikipedia.org/wiki/Scientific_method

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fourfolds, linear logic, logic

Linear Logic: the dualities

October 26, 2011 Martin K. Jones Leave a comment

The meaning of the logical rules is to be found in the rules themselves.

— J. Y. Girard in “On the Meaning of Logical Rules I: syntax vs. semantics”

There are two types of dualities in linear logic. Linear negation (^⊥) carries the conjunctions to the disjunctions and back again, as equivalences (≡), like De Morgan’s laws in classical logic.Additionally, the exponentials ? and ! link the additives and the multiplicatives, as linear biconditionals (o—o).

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fourfolds, Metaphysics, Philosophy

Lucretius: On the Nature of Things

October 10, 2011 Martin K. Jones 3 Comments

But, now again to weave the tale begun,
All nature, then, as self-sustained, consists
Of twain of things: of bodies and of void
In which they’re set, and where they’re moved around.
For common instinct of our race declares
That body of itself exists: unless
This primal faith, deep-founded, fail us not,
Naught will there be whereunto to appeal
On things occult when seeking aught to prove
By reasonings of mind. Again, without
That place and room, which we do call the inane,
Nowhere could bodies then be set, nor go
Hither or thither at all- as shown before.

— From On the Nature of Things by Lucretius

A book on the rediscovery of the ancient Epicurean poem “On the Nature of Things” by Lucretius has recently been published. “The Swerve: how the world became modern” by Stephen Greenblatt looks quite interesting. The fourfold above was inspired by the previous fourfold Spacetime. A very nice NPR review can be found below.