Archive for January, 2011

The Tetralemma and Semiotic Square

January 28, 2011

The Tetralemma is a list that is supposed to exhaust all logical possibilities. Something is either X, or not X, or both X and not X, or neither X nor not X. Nagarjuna’s Fourfold Negation expresses a paradox by negating the Tetralemma, and asking what is not X, nor not X, nor both X and not X, nor neither X nor not X.

The Semiotic Square is an analytical tool to explore relationships between two semiotic signs, usually considered opposites of each other. The S1 and S2 in the figure are the signs in opposition, so that S2 is the dual of S1. S1+~S2 (S1 and not S2) would be X, ~S1+S2 would be not X, S1+S2 would be both X and not X, and ~S1+~S2 would be neither X nor not X.


[*4.84, *5.182]


Richard McKeon’s Aspects of Knowing

January 16, 2011

Richard McKeon’s system of Philosophical Semantics arises from the sixteen pairwise and ordered relations between his four aspects of knowing or cognates: knower, knowledge, the known, and the knowable. These sixteen relations can be sorted in four groups of four elements each: methods, interpretations, principles, and selections.

Between knower and knowledge, and between the knowable and the known, arise the four methods of two each: the universal and the particular.

  • From knower to knowledge, the operational method.
  • From knowledge to knower, the dialectical method.
  • From the knowable to the known, the logistic method.
  • From the known to the knowable, the problematic method.

Between knower and the known, and between the knowable and knowledge, arise the four interpretations of two each: the phenomenal and the ontic.

  • From knower to the known, the existential interpretation.
  • From the known to knower, the essential interpretation.
  • From the knowable to knowledge, the entitative interpretation.
  • From knowledge to the knowable, the ontological interpretation.

Between knower and the knowable, and between knowledge and the known, arise the four principles of two each: the meroscopic and the holoscopic.

  • From knower to the knowable, the actional principle.
  • From the knowable to knower, the simple principle.
  • From knowledge to the known, the comprehensive principle.
  • From the known to knowledge, the reflexive principle.

Between each of the aspects of knowing with itself, arise the four selections.

  • From knower to itself, the perspectival selection.
  • From knowledge to itself, the transcendental selection.
  • From the knowable to itself, the reductive selection.
  • From the known to itself, the functional selection.

Each method can be associated with a discursive process: operational with debate, dialectical with dialogue, logistic with proof, and problematic with inquiry. Each method is also associated with a mode of thought which in turn has two moments and one dependency or assumption: the operational method is debate by discrimination and postulation dependent on chosen theses, the dialectical method is dialogue by assimilation and exemplification dependent on changeless models, the logistic method is proof by construction and decomposition dependent on indivisible constituents, and the problematic method is inquiry by resolution and question dependent on discoverable causes.


Richard McKeon / On Knowing–The Natural Sciences

Richard McKeon / Freedom and History and Other Essays: an introduction to the thought of Richard McKeon

Sadly, the following pages are no longer available:

[*4.47, *5.184-*5.187, *6.20, *6.106]


Arthur M. Young’s Fourfold Theory of Process

January 2, 2011

I have recently come across the philosophical work of Arthur M. Young (AMY). This is an initial impression of that work since I have only read what is available from the web links below, and even then there is a great deal to digest. In addition, there is difficulty in presenting a summary of his theory because of similarities to my ideas as well as substantial differences. I am sure I will need to return to AMY’s theory after more consideration.

I have hinted at a correspondence between several double duals presented in this blog, but I have steered away from claiming that they are all linked to each other – that they are essentially equivalently exchangeable. AMY’s theory links the four elements, the four causes, Jung’s functions of the psyche, geometrical elements and transformations, as well as several other fourfolds into a cosmic theory of reality.

Some of these same fourfolds are present in my theory, and I am considering how others may be introduced. Some not mentioned by AMY are only mentioned in earlier entries on this blog, without presentation. However, from many of these same fourfolds I have reached substantially different conclusions from AMY. I believe this is because AMY’s theory of process is essentially dualistic, whereas my theory appears to be physicalistic, although one might also say it is a process and/or relational theory.

Below is a table of some of the correspondences for AMY’s theory of process:

of the Psyche
Elements of
Purpose Final Intuition Fire Rotation Spirit
Value Material Emotion Water Scale Soul
Form Formal Intellect Air Inversion Mind
Object Efficient Sensation Earth Translation Body

Below is a table of some of the correspondences for my theory:

Four Elements
of Empedocles
The Here and
the Now
Four Causes
Duality of
Time and
Fire Before Efficient Change time Substance
of content
Water After Final Bear time Form of
Air Above Formal Bear
Form of
Earth Below Material Change
of expression


Arthur M. Young / The Reflexive Universe

Arthur M. Young / The Geometry of Meaning

[*6.84-*6.89, *7.78, *7.79, *8.62, *8.63]