Tag Archives: complementarity

Matrix of concepts

The structure of a matrix of concepts

The matrix of concepts is a structure that includes six concepts, which is suitable for modeling many common concepts, such as: courage, recklessness, irresolution, eclecticism, superficiality, clemency, instability, selfishness, objectivity, frankness, brusqueness, altruism, etc. Of the six concepts in the matrix:

  • two are neutral: A0 and Ā0
  • two are positive: A+ and Ā+
  • two are negative: A and Ā

These six concepts constitute the canonical poles of the matrix.

The six concepts of the matrix are in particular relationships with each other. Thus:

  • the neutral concepts A0 and Ā0 are dual
  • the positive concept A+ and the negative concept Ā are opposite (or contrary); similarly, the negative concept A and the positive concept Ā+ are opposite (or contrary)
  • the positive concepts A+ and Ā+ are complementary
  • lastly, the negative concepts A and Ā are extreme opposites
An instance of matrix of concepts

In the above instance of matrix of concepts:

  • the propensity to take risks and the propensity to avoid risks are dual
  • audacity and cowardice are contrary, opposite; in the same way, temerity and prudence are contrary, opposite
  • audacity and prudence are complementary
  • temerity and cowardice are extreme opposites

Moreover, the three concepts located on the left of the matrix constitute a half-matrix: it is the half-matrix associated with the pole A. In the same way, the three concepts located on the right of the matrix constitute the half-matrix associated to the pole Ā.


Franceschi, P., “Une classe de concepts” (in english), Semiotica, vol. 139 (1-4), 2002, pages 211-226.


Ambiguous images Arbitrary focus Bistable perception Complementarity relationship Conflict resolution Conflict resolution with matrices of concepts Conflict types relating to matrices of concepts Contrary relationship Dialectical contextualism Dialectical monism Dialectical monism in Aztec philosophy Dialectical monism in Heraclitus Dichotomic analysis Dichotomic analysis applied to paradox resolution Dichotomous reasoning Disqualification of one pole Disqualification of the positive Dualities Dual poles Extreme opposition General cognitive distortions Instance of one-sidedness bias Matrix of concepts Maximization Mental filter Minimization Bistable cognition Omission of the neutral One-sidedness bias One-sided viewpoint Opposition relationship Principle of dialectical indifference Requalification into the other pole Reference class Reference class problem Reference class problem in philosophical paradoxes Reference class problem in the Doomsday argument Reference class problem in Hempel’s paradox Reference class problem in the surprise examination paradox Selective abstraction Specific cognitive distortions System of taxa Two-sided viewpoint Viewpoint of a duality Viewpoint of a pole




Complementarity relationship

Within a concept matrix, a complementarity relationship exists between the concepts A+ and Ā+. For example, the concept of courage is the complementary of the concept of caution.

The idea of complementarity has a positive, appreciative nuance, and for this reason, the relationship of complementarity within a matrix of concepts is reserved for concepts of a positive nature, namely A+ and Ā+. Conversely, the relation of extreme opposition, which includes a negative, devaluing nuance, is reserved for concepts of a negative nature, i.e. A and Ā.


Franceschi, P., “Une classe de concepts” (in english), Semiotica, vol. 139 (1-4), 2002, pages 211-226.


Ambiguous images Arbitrary focus Bistable perception Complementarity relationship Conflict resolution Conflict resolution with matrices of concepts Conflict types relating to matrices of concepts Contrary relationship Dialectical contextualism Dialectical monism Dialectical monism in Aztec philosophy Dialectical monism in Heraclitus Dichotomic analysis Dichotomic analysis applied to paradox resolution Dichotomous reasoning Disqualification of one pole Disqualification of the positive Dualities Dual poles Extreme opposition General cognitive distortions Instance of one-sidedness bias Matrix of concepts Maximization Mental filter Minimization Bistable cognition Omission of the neutral One-sidedness bias One-sided viewpoint Opposition relationship Principle of dialectical indifference Requalification into the other pole Reference class Reference class problem Reference class problem in philosophical paradoxes Reference class problem in the Doomsday argument Reference class problem in Hempel’s paradox Reference class problem in the surprise examination paradox Selective abstraction Specific cognitive distortions System of taxa Two-sided viewpoint Viewpoint of a duality Viewpoint of a pole

How to Make a Dialectical Plan

My course (duration: 3h20) entitled “How to make a dialectical plan” is online on Udemy.

The course is a pedagogical and practical version of the notions contained in my articles On a Class of Concepts and The Dialectical Plan: For an Alternative to the Paradigm, published in the journal Semiotica. It is a step-by-step method, with exercises, to learn how to make a dialectical plan, using matrices of concepts.

A version of this course in French language is also available.