Tag Archives: opposition

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 ▣ 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




Extreme opposition

An extreme opposition relationship exists within a matrix of concepts, between the two negative concepts, i.e. A– and Ā–. This relationship is the counterpart of the complementarity relationship, which concerns the positive concepts A+ and Ā+. Two different terms are used to designate these two relationships, because the notion of complementarity has a positive nuance, while the extreme opposition has a depreciative nuance.

For example, the concept of temerity is the extreme opposite of the concept of cowardice.

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 ▣ 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

Contrary relationship

A contrary (or opposition) relationship exists within a matrix of concepts, between:

  • on the one hand the concepts A+ and Ā-
  • and on the other hand, the concepts A- and Ā+


For example, the concept of courage is the contrary of the concept of cowardice. And similarly, the concept of temerity is the contrary of the concept of prudence.

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 ▣ 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

Opposition relationship

An opposition (or contrary) relationship exists within a matrix of concepts, between:

  • on the one hand the concepts A+ and Ā-
  • and on the other hand, the concepts A- and Ā+


For example, the concept of courage is the opposite of the concept of cowardice. And similarly, the concept of temerity is the opposite of the concept of prudence.

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 ▣ 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