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

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.

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

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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 ▣ Courage ▣ 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 ▣ Doctrine of the mean ▣ Doomsday argument ▣ Dualities ▣ Dual poles ▣ Extreme opposition ▣ General cognitive distortions ▣ Instance of one-sidedness bias ▣ Liar paradox ▣ 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 ▣ Sorites paradox ▣ Specific cognitive distortions ▣ Surprise examination paradox ▣ System of taxa ▣ Two-sided viewpoint ▣ Viewpoint of a duality ▣ Viewpoint of a pole