Category Archives: Glossary

System of taxa

The subject’s system of taxa consists of a taxonomy which allows the subject to evaluate and to classify the elements of the reference class, according to the criterion corresponding to a given duality A/Ā. These taxa can be considered as “what can see” the subject. It consists of a system of values that is inherent to the patient or of a filter through which the subject “sees” the elements of the reference class, i.e. the phenomena or the objects of reality.

The above figure represents an optimal system of taxa. The latter t is composed of 11 spheres which represent each a given taxon. The system of taxa is optimal, because all taxa are present.

It is worth noting that if the subject does not have some taxa, he cannot see nor count the corresponding elements. For example, if he/she lacks the taxa of the duality A/Ā corresponding to pole A, he cannot see the corresponding elements. In the same way, if the subject has no neutral taxon in his/her system of taxa, he cannot see the neutral elements of the reference class. More formally, let us consider then a series of n elements E₁, E₂, …, E_n such that each of them has, in a objective way, a degree d[E_i] in a duality A/Ā comprised between -1 and 1 (d ∈ [-1, +1]). We can consider then a series including 11 elements, E₁, E₂, …, E₁₁, which present an objective increasing degree (the choice of 11 elements is here arbitrary, and any other number would also do the job).

Franceschi P., Compléments pour une théorie des distorsions cognitives (in english), Journal de Thérapie Comportementale et Cognitive, 2007, 17, 2, 84-88.

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

Reference class

The reference class is constituted by a group of phenomena or objects. Several examples can be given here:

the class composed of the events and facts of the subject’s life
the class of the future events of the subject’s life
the class constituted by all the parts of the subject’s body
the class which is made up of the subject’s character’s traits

Franceschi P., Compléments pour une théorie des distorsions cognitives (in english), Journal de Thérapie Comportementale et Cognitive, 2007, 17, 2, 84-88.

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.

Maximization

Maximization is a general cognitive distortion that consists of assigning to an element of a given reference class, a taxon according to the A/Ā duality criterion that turns out to be greater than its objective value. Maximization is among the classically defined cognitive distortions. The subjective degree Δ[E] that is assigned by the subject to an event E is significantly greater than its objective degree d[E], so that |Δ[E]| > |d[E]|.

Franceschi P., Compléments pour une théorie des distorsions cognitives (in english), Journal de Thérapie Comportementale et Cognitive, 2007, 17, 2, 84-88.

Minimization

Minimization is a general cognitive distortion that consists of assigning to an element of a given reference class, a taxon according to the A/Ā duality criterion that turns out to be lower than its objective value. Minimization is among the classically defined cognitive distortions. The subjective degree Δ[E] that is assigned by the subject to an event E is significantly lower than its objective degree d[E], so that |Δ[E]| < |d[E]|.

Franceschi P., Compléments pour une théorie des distorsions cognitives (in english), Journal de Thérapie Comportementale et Cognitive, 2007, 17, 2, 84-88.

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.

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.

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.

Dialectical monism in Aztec philosophy

It is worth mentioning a form of dialectical monism in the ancient Aztec philosophy and especially in the concept of ” Teotl “, which is at the center of Aztec metaphysics and cosmology. Teotl is the expression of an endless alternation of continuous and cyclical oscillation between opposite poles. Teotl is thus characterized by a dual prominent structure, which results from the union of opposites , themselves characterized by complementarity. The dual pairs involved include : the masculine and the feminine, dark and light, order and disorder, hot and cold, life and death, being and non-being etc. The interdependence and higher union of the principles of life and death in Teotl, for example, was represented by Aztec artists of Tlatilco and Oaxaca in masks where one half is alive while the other half died, revealing the skull bones.

James Maffie, Aztec Philosophy, Internet Encyclopedia of Philosophy

Dichotomous analysis applied to paradox resolution

The dichotomous analysis as a methodology that can be used to search for solutions to some paradoxes and philosophical problems, results from the statement of the principle of dialectical indifference. The general idea underlying the dichotomous approach to paradox analysis is that two versions, corresponding to one and the other pole of a given duality, can be untangled within a philosophical paradox. The corresponding approach then is to find a reference class which is associated with the given paradox and the corresponding duality A/Ā, as well as the two resulting variations of the paradox that apply to each pole of this duality.

However, every duality is not well-suited to this approach, as for many dualities, the corresponding version of the paradox remains unchanged, regardless of the duality under consideration. In the dichotomous method, one focuses on finding a reference class and a relevant associated duality, such that the viewpoint of each of its poles actually lead to two structurally different versions of the paradox , or the disappearance of paradox from the point of view of one of the poles. Thus, when considering the paradox in terms of two poles A and Ā, and if it has no effect on the paradox itself, the corresponding duality A/Ā reveals itself therefore, from this point of view, irrelevant.

Franceschi, P., “Éléments d’un contextualisme dialectique ” (in english), in Liber Amicorum Pascal Engel, J. Dutant, G. Fassio & A. Meylan (éd.), Université de Genève, 2014, p. 581-608.

Dialectical monism in Heraclitus

In the antique Western world, dialectical monism appears not much widespread. But we notably find an elaborate form of dialectical monism in Heraclitus. Several fragments of the philosophy of Heraclitus reflect the expression of this unity that results from the joint presence of two dual principles. For example, the Eigth Fragment:

What opposes unites, and the finest attunement stems from things bearing in opposite directions, and all things come about by strife.

and also the Tenth Fragment:

Things grasped together: things whole, things not whole; being brought together, being separated; consonant, dissonant. Out of all things one thing, out of one thing all things.

Here we find the expression of dialectical monism , through the union of opposites . We see how the dialectic proceeds from the union of opposites : the consonant and dissonant . This dialectical approach that underpins the philosophy of Heraclitus is also illustrated in Fragment 51:

They do not understand how, while differing from it is in agreement with itself. There is a back turning connection, like that of a bow or a lyre.

One-sided viewpoint

When only the pole A (respectively the pole Ā) of a given duality is considered, it consists of a one-sided viewpoint. Things are seen exclusively from the perspective of one pole. It contrasts with the two-sided viewpoint, with takes into account both poles of a given duality.

The consequence of taking only into account one pole is that the other pole is ignored, or disqualified. In cognitive psychology, the resulting cognitive distortion applied to the positive/negative duality is termed ‘disqualifying the positive’.

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

One-sidedness bias

The one-sided bias consists in focusing on a given standpoint when considering a given object, and of neglecting the opposite view. In our framework, such fallacious reasoning consists, when considering an object o and the reference class associated with it, of taking into account the viewpoint of the A pole (respectively Ā), while completely ignoring the viewpoint corresponding to its dual pole Ā (respectively A) to define the reference class. We shall term one-sidedness bias such type of fallacy.
The conditions of this type of bias, in violation of the principle of dialectical indifference, needs however to be clarified. Indeed, in this context, we can consider that there are some cases where the two-sidedness with respect to a given duality A/Ā is not required. Such is the case when the elements of the context do not presuppose conditions of objectivity and exhaustiveness of views. Thus, a lawyer who would only emphasise the evidence in defence of his/her client, while completely ignoring the evidence against him/her does not commit the above-mentioned type of error of reasoning. In such a circumstance, in fact, the lawyer would not commit a faulty one-sidedness bias, since it is his/her inherent role. The same would go in a trial for the prosecutor, who conversely, would only focus on the evidence against the same person, by completely ignoring the exculpatory elements. In such a situation also the resulting one-sidedeness bias would not be inappropriate, because it follows well from the context that it consists well of the limited role assigned to the prosecutor. By contrast, a judge who would only take into account the evidence against the accused, or who would commit the opposite error, namely of only considering the exculpatory against the latter, would well commit an inappropriate one-sidedness bias because the mere role of the judge implies that he/she takes into account the two types of elements, and that his/her judgement is the result of the synthesis which is made.

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

Franceschi, P., “Éléments d’un contextualisme dialectique ” (in english), in Liber Amicorum Pascal Engel, J. Dutant, G. Fassio & A. Meylan (éd.), Université de Genève, 2014, p. 581-608.

Bistable perception

Bistable perception is a phenomenon caused by a visual stimulus, which generates two different perceptions in the subject who sees it. Bistable perception instances result in particular from:

The Necker cube
the Rubin’s vase
the duck / rabbit illusion

Cases of bistable perception attract the interest because they raise questions about the causes that lead to the bistable phenomenon of perception, but also because there are individual differences in this type of sensitive perception. In particular, the frequency changes or the duration of one of the alternative perceptions vary considerably among individuals. This raises questions about the factors that induce this or that particular response with regard to this phenomenon, in a given individual.

The bistable perception can also be regarded as a special case of multi-stable perception, where only two different views are possible from the same stimulus.

One can also consider the two types of resulting alternative perceptions as two interpretations of the same visual stimulus. The bistable perception most commonly studied are visual ones, but there also exists instances of bistable perception in other sensory modalities: auditory, olfactory, etc.

Requalification into the other pole

The requalification into the other pole is a general type of cognitive distortion. It is characterized by a reasoning which consists in re-qualifying an event belonging to a given duality A, in the other duality Ā.

The requalification into the other pole is part of the general cognitive distortions, as well as the disqualification of one of the poles, the omission of the neutral, the arbitrary focus, the minimization, the maximization.

A characteristic instance of requalification in the other pole consists in the specific cognitive distortion which applies to the class of the events of the subject’s life and to the Positive/Negative duality. This consists typically in re-describing as negative an event which should be objectively considered as positive.

By requalifying positive events in a negative way, the person can reach the conclusion that all events of his/her life are of a negative nature. For instance, by considering the past events of his/her life, the subject notes that he/she made no act of violence. He/she considers this to be “suspect”.

Another instance of requalification in the other pole consists in the specific cognitive distortion which applies to the class of the parts of the person’s body and to the Nice+/Ugly- duality. Typically, the subject re-qualifies as “ugly” a part of his/her body which is objectively “nice”.

Franceschi P., Compléments pour une théorie des distorsions cognitives (in english), Journal de Thérapie Comportementale et Cognitive, 2007, 17, 2, 84-88.

Omission of the neutral

The omission of the neutral is a type of general cognitive distortion. It results from the absence, in the patient’s system of taxa, of the neutral taxon. It follows that the elements of the reference class which can objectively be defined as neutral with regard to a given duality A/Ā, are not taken into account by the patient.

The omission of the neutral sometimes plays an important role, notably when there is a gaussian distribution of the elements of the reference class, where the elements objectively corresponding to the neutral taxon are precisely those which are the most numerous.

The omission of the neutral is part of the general cognitive distortions, as well as the disqualification of one of the poles, the requalification in the other pole, the arbitrary focus, the minimization, the maximization.

Franceschi P., Compléments pour une théorie des distorsions cognitives (in english), Journal de Thérapie Comportementale et Cognitive, 2007, 17, 2, 84-88.

Dual pole

A dual pole is one of the components of a pair of concepts that make up a given duality. Among the dualities, we can mention: quantitative/qualitative, static/dynamic, external/internal, unique/multiple, etc.
Thus, quantitative, quantitative, static, dynamic,… are dual poles. It should be noted that their nature is neutral, that is, they do not carry a positive or negative connotation. Thus, concepts that have a positive connotation are: audacity, courage, ardor, merit, combativity, etc. Similarly, concepts that have a negative connotation are: cowardice, pessimism, timidity, irresolution, etc.

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

Duality

Dualities are pairs of concepts that are dual, antinomic. The pairs of concepts, i.e. the dual poles that make up the dualities are concepts that are neutral in nature. They have no positive or negative connotation, unlike concepts like courage or pessimism, which have a positive or negative nature respectively.

Instances of dualities are the following:

Internal/External
Quantitative/Qualitative
Visible/Invisible
Absolute/Relative
Abstract/Concrete
Static/Dynamic
Diachronic/Synchronic
Single/Multiple
Extension/Restriction
Aesthetic/Practical
Precise/Vague
Finite/Infinite
Single/compound
Individual/Collective
Analytical/Synthetic
Implicit/Explicit
Voluntary/Involuntary

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

Franceschi P., Compléments pour une théorie des distorsions cognitives (in english), Journal de Thérapie Comportementale et Cognitive, 2007, 17, 2, 84-88.

Viewpoint of a pole

Let us define the concept of point of view related to a given pole of an A/Ā duality: we get then, for example (at the level of the extension/restriction duality) the standpoint by extension, as well as the viewpoint by restriction. Similarly, the qualitative viewpoint or perspective results from it, as well as the quantitative point of view, etc.. (at the level of the qualitative/quantitative duality). Thus, when considering a given object o (either a concrete or an abstract object such as a proposition or a reasoning), we may consider it in relation to various dualities, and at the level of the latter, relative to each of its two dual poles.

The underlying idea inherent to the viewpoint relative to a given duality, or to a given pole of a duality, is that each of the two poles of the same duality, all things being equal, deserve an equal legitimacy. In this sense, if we consider an object o in terms of a duality A/Ā, one should not favour one of the poles with respect to the other. To obtain an objective point of view with respect to a given duality A/Ā, one should place oneself in turn from the perspective of the pole A, and then from that of the pole Ā. For an approach that would only address the viewpoint of one of the two poles would prove to be partial and truncated. The fact of considering in turn the perspective of the two poles, in the study of an object o and of its associated reference class allows to avoid a subjective approach and to meet as much as possible the needs of objectivity.

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

Principle of dialectical indifference

(PRINCIPLE OF DIALECTICAL INDIFFERENCE) When considering a given object o and the reference class E associated with it, from the angle of duality A/Ā, all things being equal, it should be given equal weight to the viewpoint of the A pole and the viewpoint of the Ā pole.

The principle of dialectical indifference can be enunciated as follows: if we consider an object o under the angle of a given A/Ā duality, there is no reason to favour the viewpoint from A with regard to the viewpoint from Ā, and unless otherwise resulting from the context, we must weigh equally the viewpoints A and Ā. A direct consequence of this principle is that if one considers the perspective of the A pole, one also needs to take into consideration the standpoint of the opposite pole Ā (and vice versa). The need to consider both points of view, the one resulting from the A pole and the other associated with the Ā pole, meets the need of analysing the object o and the reference class associated with it from an objective point of view. This goal is achieved, as far as possible, by taking into account the complementary points of view which are those of the poles A and Ā. Each of these viewpoints has indeed, with regard to a given duality A/Ā, an equal relevance. Under such circumstances, when only the A pole or (exclusively) the pole Ā is considered, it consists then of a one-sided perspective. Conversely, the viewpoint which results from the synthesis of the standpoints corresponding to both poles A and Ā is of a two-sided type. Basically, this approach proves to be dialectical in essence. In effect, the step consisting of successively analysing the complementary views relative to a given reference class, is intended to allow, in a subsequent step, a final synthesis, which results from the joint consideration of the viewpoints corresponding to both poles A and Ā. In the present construction, the process of confronting the different perspectives relevant to an A/Ā duality is intended to build cumulatively, a more objective and comprehensive standpoint than the one, necessarily partial, resulting from taking into account those data that stem from only one of the two poles.

Further reading: Elements of dialectical contextualism

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Paul Franceschi

Philosophy and Concepts

Category Archives: Glossary

System of taxa

Reference class

Extreme opposition

Maximization

Minimization

Complementarity relationship

Contrary relationship

Opposition relationship

Dialectical monism in Aztec philosophy

Dichotomous analysis applied to paradox resolution

Dialectical monism in Heraclitus

One-sided viewpoint

One-sidedness bias

Bistable perception

Requalification into the other pole

Omission of the neutral

Dual pole

Duality

Viewpoint of a pole

Principle of dialectical indifference