Author Archives: Paul

The Problem of the Relationships of Love-Hate-Indifference

English translation of a paper published in French in Semiotica, vol. 150(1-4), 2004 under the title “Le problème des relations amour-haine-indifférence”.

In On a class of concepts (2002), I described a theory based on the matrices of concepts which aims at constituting an alternative to the classification proposed by Greimas, in the field of paradigmatic analysis. The problem of the determination of the relationships of love/hate/indifference arises in this construction. I state then the problem of the relationships of love/hate/indifference in a detailed way, and several solutions that have been proposed in the literature to solve it. I describe lastly a solution to this problem, based on an extension of the theory of matrices of concepts.


This paper is cited in:

  • Isis Truck, Nesrin Halouani, & Souhail Jebali (2016) Linguistic negation and 2-tuple fuzzy linguistic representation model : a new proposal, pages 81–86, in Uncertainty Modelling in Knowledge Engineering and Decision Making, The 12th International FLINS Conference on Computational Intelligence in Decision and Control, Eds. Xianyi Zeng, Jie Lu, Etienne E Kerre, Luis Martinez, Ludovic Koehl, 2016, Singapore: World Scientific Publishing.

The Problem of the Relationships of Love-Hate-Indifference

Paul Franceschi

I shall be concerned in this paper with presenting a problem related to the proper definition of the relationships of the following concepts: love, hate and indifference. I will describe first the problem in detail and some proposed solutions. Lastly, I will present my own solution to the problem.

1. The problem

The problem is that of the proper definition of the relationships of the concepts love, hate and indifference. Let us call it the LHI problem. What are then the accurate relationships existing between these three concepts? At first sight, the definition of the relation between love and hate is obvious. These concepts are contraries. The definition of such a relation should be consensual. Nevertheless, the problem arises when one considers the relationship of love and indifference, and of hate and indifference. In these latter cases, no obvious response emerges.

However, the issue needs clarifying. In this context, what should we expect of a solution to the LHI problem? In fact, a rigorous solution ought to define precisely the three relations R, S, T such that love R hate, love S indifference and hate T indifference. And the definitions of these relations should be as accurate as possible.

It is worth mentioning that several authors must be credited for having mentioned and investigated the LHI problem. In particular, it is worth stressing that the difficulties presented within propositional calculus by some assertions of the type x loves y, x hates y, or x is indifferent to y have been hinted at by Emile Benzaken (1990)1:

Nevertheless, the difficulty can arise from pairs of words where the one expresses the contrary (negation) of the other; ‘to hate’ can be considered as the strong negation of ‘to love’, whereas ‘to be indifferent’ would be its weak negation.

The author exposes then the problem of the relationships of love/hate/indifference and proposes his own solution: hate is the strong negation of love, and indifferent is the weak negation of love.

However, it turns out that Benzaken’s solution is unsatisfying for a logician, for the following reasons. On the one hand, this way of solving the problem defines the relations between love and hate (strong negation, according to the author) and between love and indifference (weak negation, on the author’s view), but it fails to define accurately the relations existing between indifference and hate. There is a gap, a lack of response at this step. And mentioned above, a satisfying solution should elucidate the nature of the relationships of the three concepts. On the other hand, the difference between weak negation and strong negation is not made fully explicit within the solution provided by Benzaken. For these reasons, Benzaken’s solution to the LHI problem proves to be unsatisfying.

In a very different context, Rick Garlikov (1998) stresses some difficulties of essentially the same nature as those underlined by Benzaken:

In a seminar I attended one time, one of the men came in all excited because he had just come across a quotation he thought very insightful – that it was not hate that was the opposite of love, but that indifference was the opposite of love, because hate was at least still an emotion. I chuckled, and when he asked why I was laughing, I pointed out to him that both hate and indifference were opposites of love, just in different ways, that whether someone hated you or was indifferent toward you, in neither case did they love you.

Garlikov describes in effect the problem of the relationships of love/hate/indifference and implicitly proposes a solution of a similar nature as that provided by Benzaken. For this reason, Galikov’s account suffers from the same defects as those presented by Benzaken’s solution.

In what follows, my concern will be with settling first the relevant machinery, in order to prepare a few steps toward a solution to the LHI problem.

2. The framework

I will sketch here the formal apparatus described in more detail in Franceschi (2002). To begin with, consider a given duality. Let us denote it by A/Ā. At this step, A and Ā are dual concepts. Moreover, A and Ā can be considered as concepts that are characterized by a contrary component c {-1, 1} within a duality A/Ā, such that c[A] = -1 and c[Ā] = 1. Let us also consider that A and Ā are neutral concepts that can be thus denoted by A0 and Ā0.

Figure 1

At this point, we are in a position to define the class of the canonical poles. Consider then an extension of the previous class {A0, Ā0}, such that A0 and Ā0 respectively admit of a positive and a negative correlative concept. Such concepts are intuitively appealing. Let us denote them respectively by {A+, A} and {Ā+, Ā}. At this step, for a given duality A/Ā, we get then the following concepts: {A+, A0, A, Ā+, Ā0, Ā}. Let us call them canonical poles. It should be noted that one could use alternatively the notation α(A/Ā, c, p) for a canonical pole.2 In all cases, the components of a canonical pole are a duality A/Ā, a contrary component c {-1, 1} and a canonical polarity p {-1, 0, 1}. This definition of the canonical poles leads to distinguish between the positive (A+, Ā+), neutral (A0, Ā0) and negative (A, Ā) canonical poles. Lastly, the class made up by the 6 canonical poles can be termed the canonical matrix: {A+, A0, A, Ā+, Ā0, Ā}.

Let us investigate now into the nature of the relations existing between the canonical poles of a given matrix. Among the combinations of relations existing between the 6 canonical poles (A+, A0, A, Ā+, Ā0, Ā) of a same duality A/Ā, it is worth emphasizing the following relations: duality, antinomy, complementarity, corollarity, connexity, and anti-connexity. Thus, two canonical poles α1(A/Ā, c1, p1) and α2(A/Ā, c2, p2) of a same matrix are:

(i) dual if their contrary components are opposite and their polarities are neutral3

(ii) contrary (or antinomical) if their contrary components are opposite and their polarities are non-neutral and opposite4

(iii) complementary if their contrary components are opposite and their polarities are non-neutral and equal5

(iv) corollary if their contrary components are equal and their polarities are non-neutral and opposite6

(v) connex if their contrary components are equal and the absolute value of the difference of their polarities equals 17

(vi) anti-connex if their contrary components are opposite and the absolute value of the difference of their polarities equals 18

To sum up: {A0, Ā0} are dual, {A+, Ā} and {A, Ā+} are contraries, {A+, Ā+} and {A, Ā} are complementary, {A+, A} and {Ā+, Ā} are corollary, {A0, A+}, {A0, A}, {Ā0, Ā+} and {Ā0, Ā} are connex, {A0, Ā+}, {A0, Ā}, {Ā0, A+} and {Ā0, A} are anti-connex.

I shall focus now on the types of relations existing, under certain circumstances between the canonical poles of different dualities. Let us define preliminarily the includer relation. Let a concept α be an includer for two other concepts β and γ if and only if α = β γ. Such a definition captures the intuition that α is the minimal concept whose semantic content includes that of β and γ. To give an example concerning truth-value, determinate is an includer for {true, false}.

Let now A and E be two matrices whose canonical poles are respectively {A+, A0, A, Ā+, Ā0, Ā} and {E+, E0, E, Ē+, Ē0, Ē}. These matrices are such that E+, E0, E are the respective includers for {A+, Ā+}, {A0, Ā0}, {A, Ā} i.e. the two matrices are such that E+ = A+ Ā+, E0 = A0 Ā0 and E = A Ā.9

Figure 2

Let us denote this relation by A < E. One is now in a position to extend the relations previously defined between the canonical poles of a same matrix, to the relations of a same nature between two matrices presenting the properties of A and E, i.e. such that A < E. The relations of 2-duality, 2-antinomy, 2-complementarity, 2-anti-connexity10 ensue then straightforwardly. Thus, two canonical poles α1(A/Ā, c1, p1) and α2(E/Ē, c2, p2) of two different matrices are:

(i’) 2-dual (or trichotomic dual) if their polarities are neutral and if the dual of 2 is an includer for 1

(ii’) 2-contrary11 (or trichotomic contrary) if their polarities are non-neutral and opposite and if the contrary of α2 is an includer for α1

(iii’) 2-complementary (or trichotomic complementary) if their polarities are non-neutral and equal and if the complementary of α2 is an includer for α1

(vi’) 2-anti-connex (or trichotomic anti-connex) if the absolute value of the difference of their polarities is equal to 1 and if the anti-connex of α2 is an includer for α1

To sum up now: {A0, Ē0} and {Ā0, Ē0} are 2-dual, {A+, Ē}, {A, Ē+}, {Ā+, Ē} and {Ā, Ē+} are 2-contrary, {A+, Ē+}, {A, Ē}, {Ā+, Ē+} and {Ā, Ē} are 2-complementary, {A0, Ē+}, {A0, Ē}, {Ā0, Ē+} and {Ā0, Ē} are 2-anti-connex.

Lastly, the notion of a complement of a canonical pole also deserves mention. Let α be a canonical pole. Let us denote by ~α its complement, semantically corresponding to nonα. In the present context, the notion of a complement entails the definition of a universe of reference. I shall focus then on the notion of a complement of a canonical pole defined with regard to the corresponding matrix. In this case, the universe of reference is equal to {A+, A0, A, Ā+, Ā0, Ā} and then ~α = {A+, A0, A, Ā+, Ā0, Ā} – α. One has thus for example ~A+ = {A0, A, Ā+, Ā0, Ā} and a similar definition for the complements of the other canonical poles of the matrix. Consider now two matrices such that A < E. Under these circumstances, the universe of reference12 is equal to {A+, A0, A, Ā+, Ā0, Ā, Ē+, Ē0, Ē}. Call it the 2-matrix of α. It ensues that ~α = {A+, A0, A, Ā+, Ā0, Ā, Ē+, Ē0, Ē} – α. We have then the notion of a 2-complement of a canonical pole α, defined with regard to a universe of reference consisting of the 2-matrix of α. More generally, one has the notion of a ncomplement (n > 0) of a canonical pole with regard to the corresponding n-matrix.

3. A solution

With the relevant machinery in place, we are now in a position to present a solution to the LHI problem. Let us now analyze the problem in the light of the above framework. To begin with, let us analyze the relevant concepts in more detail. The concept love has a positive connotation. It is a meliorative concept that can be denoted by love+. Conversely, the concept hate has a negative connotation. It is a pejorative concept that can be rendered by hate. Similarly, the concept indifference also has a negative connotation. It can be considered a pejorative notion that can be denoted by indifference.

At this step, a difficulty emerges. In effect, it should be stressed that the three concepts are either meliorative or pejorative at a certain degree. And such a degree might be different from one concept to another. For example hate might be pejorative at a 0.95 degree, while indifference might be pejorative at a lesser degree of 0.7. Moreover, it could be said that such a degree might vary from culture to culture, from a given language to another. In sum, the meliorative or pejorative degree of the three concepts, so the objection goes, could be culture-relative.

Nevertheless, such difficulties can be avoided in the present context, since our reasoning will not bear upon the concepts inherent to a specific culture or language, but rather on the canonical concepts described above. Accordingly, we shall replace our usual concepts by the corresponding canonical concepts. There is room for variation in degrees, from culture to culture in the usual concepts of love, hate and indifference. But this point does not affect the current line of reasoning, since it only focuses on canonical concepts. The passage from the non-canonical concepts to the canonical ones goes straightforwardly as follows. Let d[α] be the pejorative or meliorative degree of a concept α. Hence if d[α] ]0.5; 1] then p[α] = 1 else if d[α] [-1; -0.5[ then p[α] = -1. At this point, one can pose legitimately that p[Love] = 1, p[Hate] = -1 and p[Indifference] = -113. As a result, the three concepts can be denoted by Love+, Hate, Indifference.

Figure 3

As noted from the beginning, the relationship of love/hate is unproblematic and identifies itself with the relation of contrary. This applies straightforwardly to the relationship of the canonical concepts Love+/Hate. Hence, the corresponding matrix has the following structure: {Love+, A0, A, Ā+, Ā0, Hate}. Now the next step is the reconstitution of the complete matrix. This task can be accomplished with the help of the definition of the relations of the canonical poles, namely: A is corollary to Love+, Ā+ is corollary to Hate, A0 is connex to Love+ and anti-connex to Hate, Ā0 is connex to Hate and anti-connex to Love+. Given these elements, we are now in a position to reconstitute the corresponding canonical matrix: {Love+, Attraction0, A, Defiance+, Repulsion0, Hate}.14

Let us examine now the case of the concept Indifference. Such a concept inserts itself into a matrix the structure of which is: {E+, E0, E, Ē+, Ē0, Indifference}. Just as before, it is now necessary to reconstitute the complete matrix. This can be done with the help of the corresponding definitions: Ē+ is corollary to Indifference, E is complementary to Indifference, E+ is contrary to Indifference, Ē0 is connex to Indifference and to the corollary of Indifference, E0 is anti-connex to Indifference and to the corollary of Indifference. The associated matrix is then: {E+, Interest0, E, Phlegm+, Detachment0, Indifference}.15

Figure 4

It should be observed now that Interest0 = Attraction0 Repulsion0 i.e. that Interest0 is an includer for Attraction0 and Repulsion0. At this step, given that {Love+, Attraction0, A, Repulsion+, Repulsion0, Hate} {E+, Interest0, E, Phlegm+, Detachment0, Indifference}, the relationship of Love+/Indifference and Hate/Indifference now apply straightforwardly. In effect, it ensues from the above definitions that, on the one hand, Love+ and Indifferenceare trichotomic contraries and on the other hand, Hate and Indifferenceare trichotomic complementaries. At this point, one is finally in a position to formulate a solution to the LHI problem:

(i) love is contrary to hate

(ii) love is 2-contrary to indifference

(iii) hate is 2-complementary to indifference

Hence, R, S, T identify respectively themselves with contrary, trichotomic contrary, trichotomic complementarity.

4. Concluding remarks

At this point, it is tempting not to consider the above analysis as a solution to the LHI problem per se. In effect, the concepts love, hate and indifference seem to be instances of a wider class of concepts whose relationships are of the same nature. This suggests that the same type of solution should be provided to the general problem of the definition of the relations of three given concepts , , . At first sight, certain concepts such as true, false and indeterminate, fall under the scope of the current analysis. Nevertheless, such a claim should be envisaged with caution. To what extent does the present analysis apply to other concepts? This is another problem that needs to be addressed, but whose resolution goes beyond the scope of the present account.16


References

Benzaken, Claude (1991). “Systèmes formels”. Paris, Masson

Franceschi, Paul (2002). “Une Classe de Concepts”. Semiotica, 139, pp. 211-26, English translation

Garlikov, Rick (1998). “Understanding, Shallow Thinking, and School”. At http://www.garlikov.com/writings.htm

1 My translation. The original text is as follows: ‘La difficulté cependant peut provenir de paires de mots dont l’un exprime le contraire (négation) de l’autre; “haïr” peut être pris comme la négation forte de “aimer” tandis que “être indifférent” en serait la négation faible. (p. 63).

2 With the latter notation, the matrix of the canonical poles is rendered as follows: {(A/Ā, -1, 1), (A/Ā, -1, 0), (A/Ā, -1, -1), (A/Ā, 1, 1), (A/Ā, 1, 0), (A/Ā, 1, -1)}.

3 Formally 1 and 2 are dual if and only if c[1] = – c[2] and p[1] = p[2] = 0.

4 Formally 1 and 2 are antinomical if and only if c[1] = – c[2] and p[1] = – p[2] with p[1], p[2] 0.

5 Formally 1 and 2 are complementary if and only if c[1] = – c[2] and p[1] = p[2] with p[1], p[2] 0.

6 Formally 1 and 2 are corollary if and only if c[1] = c[2] and p[1] = – p[2] with p[1], p[2] 0.

7 Formally 1 and 2 are connex if and only if c[1] = c[2] and │p[1] – p[2]│ = 1.

8 Formally 1 and 2 are anti-connex if and only if c[1] = – c[2] and │p[1] – p[2]│ = 1.

9 It should be observed that one of the three conditions is sufficient. In effect, E+ = A+ Ā+ entails E0 = A0 Ā0 and E = A Ā; E0 = A0 Ā0 implies E+ = A+ Ā+ and E = A Ā; E = A Ā entails E0 = A0 Ā0 and E+ = A+ Ā+.

10 The generalisation to n matrices (n > 1) of the present construction ensues, with the relations of n-duality, n-antinomy, n-complementarity, n-anti-connexity.

11 Or 2-antinomical.

12 In this context, E+, E0 and E can be omitted without loss of content, given their nature of includers.

13 The fact of considering alternatively p[indifference] > -0.5 and thus p[Indifference] = 0 also leads to a solution in the present framework. In this last case, the relations S and T both identify themselves with trichotomic anti-connexity.

14 In the process of reconstitution of the complete matrix, some concepts may be missing. The reason is that they are not lexicalized in the corresponding language. This is notably the case for A. This last concept semantically corresponds to inappropriate, excessive attraction.

15 As far as I can see, the concepts associated with E+ and E are not lexicalized. They respectively correspond to appropriate interest and inappropriate, excessive interest.

16 I thank Professor Claude Panaccio and Rick Garlikov for useful comments on an earlier draft.

The Dialectical Plan: an Alternative to the Paradigm

Posprint in English (with additional illustrations from wikimedia commons) of a paper published in French in Semiotica, vol. 146(1-4), 2003, 353-367, under the title “Le plan dialectique: pour une alternative au paradigme”. I apply the theory developed in On a Class of Concepts (2002) to the methodology for conceiving a plan. Regarding the dialectical plan, the paradigm is a plan whose structure is thesis-antithesis-synthesis. I describe a new type of matricial dialectical plan, which presents several advantages in regard to the classical dialectical plan and proposes to constitute an alternative to this latter.


This article is cited in:


 The Dialectical Plan: an Alternative to the Paradigm

In Franceschi (2002), I exposed a theory which aims to constitute an alternative to the classification proposed by Greimas in the field of paradigmatic analysis. In the present article, I proceed to draw the consequences of this latter theory by applying it to the technique of conception of a plan. Regarding the dialectic plan, the current paradigm is in effect a plan of the type thesis-antithesis-synthesis. This form of plan is very widespread and its use proves to be consensual. In what follows, I shall propose a novel type of dialectic plan as an alternative to the classical one. It consists of a type of plan which can be qualified as matrix-based, and which presents several advantages with regard to the classical dialectic plan.

The classical dialectic plan

Hegel: Portrait by Jakob Schlesinger

The current paradigm regarding the dialectic plan is a plan of the thesis-antithesis-synthesis type1. This plan finds its origin in the dialectical approach2 developed by Hegel. The association of the three concepts thesis-antithesis-synthesis, which is now associated with the dialectical line of reasoning, was elaborated by Hegel and Marx3. The dialectical approach constitutes thus a process of reasoning that proceeds by the statement of two contradictory theses and by their reconciliation at the stage of the synthesis. According to Hegel4, every thesis presents then an inherently incomplete and partial nature, which gives then birth to its contrary, the antithesis. From Hegel’s standpoint, the contraries present, beyond the contradiction underlying them, an indissociable nature. This last property allows thus to make their final union, at a thought level which places itself beyond the one where the contradiction manifests itself. The contraries present thus by essence a genuine unity, from which it is worth grasping the fecund principle, allowing thus to reach, at a higher level, a genuine knowledge. This latter phase constitutes the synthesis, which can thus be considered as the step of reasoning which reconciliates veritably, at a greater level, the contradiction observed between the thesis and the antithesis. The synthesis allows thus to go beyond the conflict raised between the thesis and the antithesis, by further unifying the part of truth simultaneously contained in both of them. However, the process is not limited to that. For the synthesis thus obtained constitutes in turn a novel thesis, which itself yields a novel antithesis and then a novel synthesis, and so on… Within the current language, the dialectical approach designates now the general methodology which allows to go beyond and to solve the contradictions. It is in this dialectical approach that the classical plan of the thesis-antithesis-synthesis type finds its origin.

At this step, it is worth considering in turn each component of the thesis-antithesis-synthesis plan. Consider, to begin with, the thesis. This latter constitutes a standpoint expressed by a given author. It consists of the viewpoint on which the discussion is based, and toward which the structure of the plan is oriented. For simplicity, let us assimilate here the thesis to a given proposition. On the other hand, the antithesis is a standpoint which proves to be contrary to that of the thesis. Like the thesis, it is useful to reduce the antithesis, for the sake of simplicity, to a given proposition. At this step, the viewpoints expressed by the thesis and the antithesis are of an antinomical nature. Lastly, the synthesis constitutes the part of the discourse where the antagonist viewpoints developed in the thesis and the antithesis are overcome. The synthesis aims thus classically to go beyond the antinomy existing between the thesis and the antithesis and to encompass it.

In a general way, the advantage of the dialectic plan of the type thesis-antithesis-synthesis is to allow to apprehend the double aspect of a given problem or reality. By placing oneself alternatively from one side and from the other, by considering successively the thesis and then the antithesis, this type of plan allows to avoid a partial or truncated vision of the particular problem raised by the thesis. The aim of the classical dialectic plan is thus to apprehend the two-faceted nature of a given reality and to go beyond the contradiction which results from a preliminary study.

Matrices of concepts

mtcg-image1
A matrix of concepts

In Franceschi (2002), I described the structure of a matrix of concepts, the scope of which extends to many concepts. For the sake of the present discussion, it is not necessary to describe in a detailed way the structure of concepts put forth in this article. Nevertheless, the type of dialectic plan which will be proposed later derives directly from the notion of a matrix of concepts. It proves then necessary to present the main lines of the basic structure of a matrix of concepts.

Consider first a given duality. Let us denote it by A/Ā. At this step, A and Ā constitute dual concepts. One can then consider that A and Ā are concepts which characterize themselves by a contrary component c  {-1, 1} at the level of a given duality A/Ā, such that c[A] = -1 and c[Ā] = 1. One can also consider that A and Ā are neutral concepts which can thus be denoted by A0 and Ā0.

At this step, we are in a position to define the class of the canonical poles. It suffices to consider an extension of the preceding class {A0, Ā0}, such that A0 and Ā0 respectively admit of both a positive and a negative concept which are correlative. Such concepts possess a certain intuitive support. Let us denote them respectively by {A+, A} and {Ā+, Ā}. At this step, for a given duality A/Ā, we get the following concepts: {A+, A0, A, Ā+, Ā0, Ā}, which constitute the canonical poles. It is worth mentioning here that the notation α(A/Ā, c, p) could be used alternatively, for a given canonical pole5. In all cases, the components of a canonical pole are: a duality A/Ā, a contrary component c  {-1, 1} and a canonical polarity p  {-1, 0, 1}. This definition of the canonical poles leads to distinguish between the positive (A+, Ā+), neutral (A0, Ā0) and negative (A, Ā) canonicalpoles. Lastly, the class made up of the six canonical poles of a same matrix can be dubbed the canonical matrix: {A+, A0, A, Ā+, Ā0, Ā}.

Let us focus now on the nature of the relationships existing between the canonical poles of a given matrix. Among the combinations of relationships existing between the six canonical poles (A+, A0, A, Ā+, Ā0, Ā) of a same duality A/Ā, one will retain the following relations: duality, antinomy, complementarity, corollarity, connexity, anti-connexity. Thus, two canonical poles α1(A/Ā, c1, p1) and α2(A/Ā, c2, p2) of a same matrix are:

(a) dual if their contrary components are opposite and their polarities are neutral6

(b) contrary (or antinomical) if their components are opposite and their polarities are non-neutral and opposite7

(c) complementary if their contrary components are opposite and their polarities are non-neutral and equal8

(d) corollary if their contrary components are equal and their polarities are non-neutral and opposite9

(e) connex if their contrary components are equal and the absolute value of the difference of their polarities equals 110

(f) anti-connex if their contrary components are opposite and the absolute value of the difference of their polarities equals 111

To sum up: {A0, Ā0} are dual; {A+, Ā} and {A, Ā+} are contraries; {A+, Ā+} and {A, Ā} are complementary; {A+, A} and {Ā+, Ā} are corollary; {A0, A+}, {A0, A}, {Ā0, Ā+} and {Ā0, Ā} are connex; {A0, Ā+}, {A0, Ā}, {Ā0, A+} and {Ā0, A} are anti-connex.

To fix ideas, let us take the example of the matrix12 {eclecticism+, multi-disciplinarity0, dispersion, expertise+, monodisciplinarity0, compartmentalization}. One has then the following relationships:

(a’) {multi-disciplinarity0, monodisciplinarity0} are dual

(b’) {eclecticism+, compartmentalization}, {dispersion, expertise+} are antinomical

(c’) {eclecticism+, expertise+}, {dispersion, compartmentalization} are complementary

(d’) {eclecticism+, dispersion}, {expertise+, compartmentalization} are corollary

(e’) {multi-disciplinarity0, eclecticism+}, {multi-disciplinarity0, dispersion}, {monodisciplinarity0, expertise+}, {monodisciplinarity0, compartmentalization} are connex

(f’) {multi-disciplinarity0, expertise+}, {multi-disciplinarity0, compartmentalization}, {monodisciplinarity0, eclecticism+}, {monodisciplinarity0, dispersion} are anti-connex

Structure of a thesis

At this step, it is worth delving more deeply into the internal structure of the thesis to which the plan dialectical applies. I shall draw a distinction here between simple and complex theses.

Simples theses

In general, a simple thesis presents a structure which is that of an appreciation – negative, neutral or positive – relative to a given concept. Let α be such a concept; one denotes then by p(α) such structure of thesis, where p denotes a negative polarity, neutral or positive such that respectively p  {-1, 0, 1}. The negative appreciation can be assimilated to a blame and the positive appreciation to a praise. The blame of a given concept α is thus denoted by (α), the neutral appreciation by 0(α) and the praise by +(α). In a general way, the propositions corresponding to the simple theses present the following structure: p(α), with p  {-1, 0, 1} and α  {A+, A0, A, Ā+, Ā0, Ā}. By referring to the matrix notion, one notes that the different theoretical cases are the following, with regard to the six concepts of a given matrix: {(A+), (A0), (A), +), 0), ), 0(A+), 0(A0), 0(A), 0+), 00), 0), +(A+), +(A0), +(A), ++), +0), +)}. At this step, it appears that the neutral appreciation is somewhat rarely found. Thus, for the sake of simplicity, we shall be mainly concerned here with describing more accurately the theses which present the structure of a blame or of a praise.

Let us begin with the blame. A number of theses are thus composed of a depreciative appreciation, related to a behavior, a way of doing or apprehending things, a given situation. Such statements correspond to propositions that present the structure of a blame. Such propositions can be denoted by (s) where s designates a way of apprehending or of doing things.

Let us take, to fix ideas, a few examples. Consider the following thesis:

In the contempt of ambition is to be found one of the essential principles of happiness on earth. (Edgar Poe, The Domain of Arnheim)

(1) In the contempt of ambition is to be found one of the essential principles of happiness on earth.(Edgar Poe, The Domain of Arnheim)

The author considers here the “contempt of ambition” as a fundamental principle allowing to reach happiness. Such a viewpoint can be analyzed as a negative, depreciative judgment toward ambition. This latter concept can be considered as a neutral notion13. Hence, such a simple thesis presents the structure which is that of the blame of ambition0 and can be thus denoted by (ambition0).

Consider also this other thesis:

Love, the scourge of the world, atrocious folly. (Alfred of Musset, Premières poésies)

(2) Love, the scourge of the world, atrocious folly. (Alfred of Musset, Premières poésies)

The content of this latter thesis can be analyzed as a very pejorative appreciation formulated with regard to love+. Here also, such thesis presents a structure that can be analyzed as a blame of love+, that one can thus denote by (love+).

Conversely, one also frequently encounters some theses which are composed of a flattering appreciation with regard to a given behavior, a propensity to act, a situation or a way of apprehending things. The structure of the corresponding proposition is then that of a praise. One denotes such propositions by +(s) where s designates a way of considering things or a given behavior.

Consider then a few examples. To begin with, the following viewpoint illustrates this type of structure:

(3) Nothing of great importance came true in the world without passion. (Hegel, Introduction to the Philosophy of History)

The author formulates here a praise related to the passion, considering thus that “nothing of great importance” ever came true without this latter. One can consider here the passion as a neutral notion14. Such a viewpoint presents thus the structure of a praise of passion0, i.e. formally +(passion0).

One also encounters an identical type of structure, regarding the following affirmation:

Kant: “Passion is an illness that abhors all medication.”

(4) Passion is an illness that abhors all medication. (Kant)

which can be analyzed as a blame of passion0, i.e. formally ( passion0).

Lastly, the following simple thesis:

Oscar Wilde: “The worst vice of the fanatic is his sincerity.”

(5) The worst vice of the fanatic is his sincerity. (Oscar Wilde)

constitutes an example of praise of the negative concept of fanaticism, i.e. formally +(fanaticism).

At this step, we are in a position to determine the truth value of the simple theses. The truth value of each type of praise, of neutral appreciation or of blame indicates if the considered affirmation is plausible and coherent or not, given that the praise of a positive concept is true, in the same way as the neutral appreciation of a neutral concept and the blame of a negative concept. Conversely, the praise of a non-positive concept15, the neutral appreciation of a non-neutral concept or well the blame of a non-negative concept16 are false. Formally, the truth value [v] of propositions of the type P = pq), with p, q  {-1, 0, 1} and α  {A+, A0, A, Ā+, Ā0, Ā} can be calculated as follows: [v] = 1 (true) if p = q and [v] = -1 (false) if pq.17 Hence, among the different cases which have just been enumerated, those whose truth value is true are: {(A), ), 0(A0), 00), +(A+), ++)}. And those whose truth value is false are: {(A+), (A0), +), 0), 0(A+), 0(A), 0+), 0), +(A0), +(A), +0), +)}.

Complex theses

Whereas simple theses contain a judgment related to one single concept belonging to a given matrix, complex theses are composed of appreciations relative to several concepts of a same matrix. A complex thesis can thus be defined in a general way as the conjunction of several simple theses. A complex thesis can thus be composed of appreciations relative to two, three, …, n different concepts. One will use accordingly the term of n-complex thesis. Under these circumstances, the combinations prove to be numerous, without it being nevertheless necessary to enumerate them exhaustively. A given proposition P constituting a complex thesis presents thus the following structure: P = Q1  Q2  …  Qn, for n > 1, and Qi = piqi), with pi, qi  {-1, 0, 1} and α  {A+, A0, A, Ā+, Ā0, Ā}. We have then the 2-complex, 3-complex, …, n-complex theses.

At this step, it appears necessary to consider first the 2-complex theses, which constitute, among the complex theses, the most common case. The 2-complex theses are composed of some appreciations relative to two concepts of a same matrix. They present the structure: p1(A/Ā, c1, q))  r2(A/Ā, c2, s)). The following appreciation constitutes thus an example of 2-complex thesis:

(6) All theory is gray, but the golden tree of life is green. (Goethe)

This 2-complex thesis is in effect composed of both the blame of theory (“all theory is gray”) and the praise of pragmatism (“the golden tree of life is green”). It proves here that the concepts of interest for theory and of pragmatism belong to the following matrix: {capacity of abstraction+, interest for theory0, dogmatism, pragmatism+, interest for practise0, prosaicness}. The structure of the thesis is thus (interest for theory0)  +(pragmatism+) i.e. (A0)  ++).

In the same way, the following appreciation constitutes a case of 2-complex thesis:

Napoleon Bonaparte: “The art of being sometimes very audacious, sometimes very cautious is the art of success.”

(7) The art of being sometimes very audacious, sometimes very cautious is the art of success. (Napoleon Bonaparte)

This 2-complex thesis is composed of both the praise of boldness (“The art of being (…) very audacious (…) is the art of success”) and the praise of the cautiousness (“the art of being (…) very cautious is the art of success”). It appears that these latter concepts belong to the following matrix: {boldness+, propensity to take risk0, temerity, cautiousness+, propensity to avoid the risk0, cowardice}. The thesis is thus composed here of the praise of two complementary positive concepts of a same matrix. The particular structure of this type of complex thesis is thus composed of the praise of A+ and the praise of Ā+, i.e. formally +(boldness+)  +(cautiousness+).

Consider lastly the following thesis, which also constitutes a case of 2-complex thesis:

(8) Two excesses: to exclude reason, and to admit nothing else than reason.(Pascal, Thoughts)

This last thesis is in effect composed of both the blame of irrationality (“exclude the reason”) and the blame of hyper-rationalism (“to admit nothing else than reason”). The corresponding reconstituted matrix is the following: {imagination+, inspiration0, irrationality, rationality+, reason0, hyper-rationalism}. As we see it, we face here a 2-complex thesis whose structure is (irrationality)  (hyper-rationalism) i.e. (A)  ).

Lastly, the following 2-complex thesis:

(9) How can we tolerate that passion be placed on the same level than reason? (Sénèque, De Ira)

can be analyzed as a blame of passion0 and a praise of reason0, i.e. formally (passion0)  +(reason0), i.e. (A0)  +0) at the level of the matrix {motivation+, passion0, fanaticism, level-headedness+, reason0, lukewarmness}.

It is worth noting here that this last type of 2-complex thesis corresponds to a common case, for motives of internal coherence. It is in effect logical when one criticizes or depreciates such or such value or concept, of flattering its contrary. To blame such or such thing amounts naturally to praising its opposite, and conversely. For that reason, the 2-complex theses whose particular structure is (A)  ++) or well +(A+)  ) also constitute, among all possible combinations of 2-complex theses, a common case.

For what concerns the truth value of the 2-complex theses, it can be determined in the same way as for the simple theses. Let thus P  Q be a 2-complex thesis, such that P = pq) and Q = rs), with p, q, r, s  {-1, 0, 1} and α, β  {A+, A0, A, Ā+, Ā0, Ā}. Formally, the truth value [v] of a 2-complex thesis P  Q is true if v[P] = v[Q] = true, and false in other cases18. It is worth noting that the most common types of 2-complex theses are those whose truth value are true. Such is the case when the truth-value of each of the two propositions included within the complex thesis is true. Under this hypothesis, the two propositions reinforce themselves. It consists thus of the cases corresponding to: {+(A+)  (A), +(A+)  ++), +(A+)  ), (A)  ++), (A)  ), ++)  )}.

Dual theses

At this step, it is worth focusing on the notion of a dual thesis of a given thesis. This last notion applies both to the simple theses and to the complex ones. The dual thesis constitutes here an element of the dialectical discussion, which proves to be important since it is the basis of the discussion related to the thesis under consideration.

Let us focus, to begin with, on dual theses of simple theses. Let us begin by giving a general definition. Formally, a simple thesis p1(A/Ā, c, q)) admits of a dual thesis that corresponds to the following definition: p2(A/Ā, –c, q)). Thus, a dual thesis of a simple thesis presents the following characteristics: (i) the polarities of the appreciation of the dual thesis and of the simple thesis are identical; (ii) the contrary components of the concepts on which bear the appreciations of the dual thesis and of the simple thesis are opposite; (iii) the polarities of the concepts on which bear the appreciations of the dual thesis and of the simple thesis are identical.

Let us consider first the dual theses of the true simple theses. The types of true simple theses can be thus enumerated as follows: {+(A+), 0(A0), (A), ++), 00), )}. Formally, a true simple thesis p1(A/Ā, c, p)) presents a dual thesis which responds to the following definition: p2(A/Ā, –c, p)). Thus, the dual theses of the true simple theses are respectively: {++), 00), ), +(A+), 0(A0), (A)}.

To take an example, consider the following true simple thesis:

(10) What you can do, or dream you can do, begin it. Boldness has genius, power and magic in it. (Goethe)

which presents the structure +(boldness+) i.e. +(A+) at the level of the matrix {boldness+, propensity to take risk0, temerity, cautiousness+, propensity to avoid risk0, cowardice}. The thesis below whose structure is +(cautiousness+) i.e. ++) constitutes thus its dual thesis:

(11) Cautiousness is as much superior to the other virtues as sight is to the other senses. (Bion of Phlossa)

Consider also the dual theses of the false simple theses. The types of false simple theses are: {(A+), (A0), +), 0), 0(A+), 0(A), 0+), 0), +(A0), +(A), +0), +)}. And the dual theses of the false simple theses are respectively: {+), 0), (A+), (A0), 0+), 0), 0(A+), 0(A), +0), +), +(A0), +(A)}.

To take an example, the following false simple thesis:

(4) Passion is an illness that abhors all medication. (Kant)

presents the structure (passion0) i.e. (A0) at the level of the matrix {motivation+, passion0, fanaticism, level-headedness+, reason0, lukewarmness}. The following thesis whose structure is (reason0) i.e. 0) constitutes thus its dual thesis:

(12) If reason dominated on the earth, nothing would happen there. (Bernard Fontenelle)

It is worth considering now, on the other hand, the dual theses of the complex theses. These latter are such that the contrary components of the concepts on which bear the appreciations of the two simple theses, which are part of the dual thesis and of the considered thesis, are opposite19. Consider then the true 2-complex theses. Thus, the dual thesis of +(A+)  ) is ++)  (A). And also, the dual thesis of 0(A0)  +(A+) is 00)  ++). It is worth noting here in particular that the dual thesis of 0(A0)  00) is 00)  0(A0), that the dual thesis of +(A+)  ++) is + +)  +(A+) and that the dual thesis (A)  ) is (A)  ).

Let us also give a few examples. Thus, the true 2-complex thesis corresponding to the following proposition:

Goethe: “All theory is gray, but the golden tree of life is green.”

(6) All theory is gray, but the golden tree of life is green. (Goethe)

presents the structure (A0)  ++) i.e. (interest for theory0)  +(pragmatism+) at the level of the matrix {capacity of abstraction+, interest for theory0, dogmatism, pragmatism+, interest for practice0, prosaicness}. The following thesis whose structure is 0)  +(A+) i.e. (interest for practice0)  +(capacity of abstraction+) constitutes thus its dual thesis:

(13) All practice is vile, but fecund and elevated is the quest of the genuine abstraction.

Similarly, the following proposition:

Pascal: “Two excesses: to exclude reason, and to admit nothing else than reason. “

(8) Two excesses: to exclude reason, and to admit nothing else than reason.(Pascal, Thoughts)

constitutes a true 2-complex thesis whose structure is (irrationality)  (hyper-rationalism) i.e. (A)  ) at the level of the matrix: {imagination+, inspiration0, irrationality, rationality+, reason0, hyper-rationalism}. The thesis below whose structure is +(imagination+)  +(rationality+) i.e. +(A+)  ++) constitutes thus its dual thesis:

(14) The art of being sometimes very imaginative, sometimes very rational is the art of success.

Lastly, it is worth noting that one has also analogous definitions for 3-complex, 4-complex, etc. theses. To take then an example, the dual thesis of the 3-complex thesis +(A+)  0(A0)  00) is ++)  00)  0(A0). In the same way, the dual thesis of the 3-complex thesis +(A+)  0(A0)  (A) is ++)  00)  ).

The matrix-based dialectic plan

The preceding developments allow now to describe the steps of the dialectical reasoning applicable to the analysis of a given particular thesis, from the above-mentioned principles. The first step consists thus in the accurate determination of the structure of the thesis under consideration. The second step, which results directly from it, is the attribution of a truth-value to this latter thesis. The following step consists then in the reconstitution of the whole matrix applicable to the concept(s) which are the object of the thesis. One is then in a position to determine the dual thesis of the considered thesis in the same way as the true simple theses other than the considered thesis and its dual thesis. Lastly, the final step is the synthesis which consists in the conjunction of the true simple theses relative to each of the 6 concepts of the considered matrix: +(A+)  0(A0)  (A)  ++)  00)  ). Such a synthesis allows to encompass a threefold antinomy: the one existing between A+ and Ā, A0 and Ā0, and A and Ā+. It should be observed here that one can eventually retain from the synthesis but a simplified form consisting of the conjunction of the true simple theses constituting a praise or a blame: +(A+)  (A)  ++)  ). In the same way, one may sometimes limit oneself to a truncated form of synthesis consisting in +(A+)  ++), which emphasizes the complementarity between A+ and Ā+.20

At this step, we are in a position to present the matrix-based dialectic plan. Such a plan results directly from the structure of matrix of concepts which has been just described. The corresponding matrix-based dialectic plan presents thus the following structure:21

(15) 1. From the viewpoint of A0

1.1 Praise of A+

1.2 Blame of A

2. From the viewpoint of Ā0

2.1 Praise of Ā+

2.2 Blame of Ā

3. Complementarity between A+ and Ā+ 22

Consider then, to take an example the following true simple thesis:

(16) Success was always a child of audacity. (Prosper Crebillon, Catilina)

whose structure is +(boldness+) i.e. +(A+) at the level of the matrix {boldness+, propensity to take risk0, temerity, cautiousness+, propensity to avoid risk0, cowardice}. It results then the following matrix-based plan:

(17) 1. From the viewpoint of risk taking0

1.1 The necessity of boldness+

1.2 The dangers of temerity

2. From the viewpoint of risk avoidance0

2.1 The advantages of the cautiousness+

2.2 The risk of cowardice

3. The necessary complementarity between boldness+ and cautiousness+

Consider also the following false simple thesis:

(12) If reason dominated on the earth, nothing would happen there. (Bernard Fontenelle)

whose structure is (reason0). The corresponding matrix is: {level-headedness+, reason0, lukewarmness, motivation+, passion0, fanaticism}. And the following matrix-based plan then ensues:

(18) Introduction: (i) structure of the thesis; (ii) truth value; (iii) matrix

1. From the viewpoint of reason0

1.1 The pitfall of lukewarmness

1.2 The necessity of level-headedness+

2. From the viewpoint of passion0

2.1 The dangers of fanaticism

2.2 The necessity of motivation+

3. The necessary complementarity between level-headedness+ and motivation+

Lastly, such a type of plan also proves to be adapted to a true 2-complex thesis such as the following:

(19) In the first place comes your profession, because doing just one thing well will procure a higher development for you than doing one hundred by halves. (Goethe)

This latter thesis can be analyzed as a 2-complex thesis whose structure is +(expertise+)  (superficiality) i.e. +(A+)  ) at the level of the matrix: {expertise+, monodisciplinarity0, compartmentalization, eclecticism+, multi-disciplinarity0, superficiality}. And the following matrix-based plan23 then ensues:

(20) 1. From the viewpoint of monodisciplinarity0

1.1 The advantages of expertise+

1.2 The risk of compartmentalization

2. From the viewpoint of multi-disciplinarity0

2.1 The necessity of eclecticism+

2.2 The dangers of superficiality

3. The necessary complementarity between expertise+ and eclecticism+

Conclusion

From the above developments, it should be noted that the matrix-based dialectic plan presents a number of advantages with regard to the classical dialectic plan. First, the dialectical approach which has just been described performs first an analysis of the structure of the thesis under consideration, which leads then to assign a truth value to it, on objective grounds.

Second, it appears that the matrix-based dialectic plan replaces the thesis or the main proposition in a context that comprises a greater number of concepts than the classical dialectic plan. In effect, the classical dialectic plan usually places the thesis in an environment comprising in general two, or even three concepts. By contrast, the matrix-based dialectic plan replaces the thesis in a context comprising six concepts which are related to this latter.

Third, one of the advantages of the matrix-based dialectic plan is that it also allows to take into account some concepts which are not lexicalized. In effect, a matrix of concepts describes six canonical concepts. But it is rare that the totality of these latter concepts are lexicalized. In effect, the most common situation is that only some concepts – in general two or three – among the six described by the corresponding matrix, are lexicalized. Here also, the advantage of the matrix-based dialectic plan is to allow to take into account exhaustively the six concepts of a same matrix and to incorporate them in the corresponding discussion.

It should also be noted that the step of the antithesis at the level of the classical dialectic plan is replaced here by the determination of the dual thesis, which presents an identical structure to that of the initial thesis. The dual thesis, which serves here as a basis for dialectical reasoning, presents by its simple or well n-complex structure a more elaborated nature than the traditional antithesis.

Lastly, it proves that the classical dialectic plan allows to overcome an antinomy existing between two concepts, which serve respectively as a support to the thesis and to the antithesis. It consists most often of A+ and Ā, of A0 and Ā0, or well of A and Ā+. Most of the time, it consists of a dual or antinomical pair of concepts which present the property of being lexicalized. Conversely, the matrix-based dialectic plan constitutes the expression of a dialectical move of the thought which allows to go beyond a threefold antinomy: the one existing at the same time between A+ and Ā, A0 and Ā0, and finally A and Ā+, whether these concepts are lexicalized or not.


References

Franceschi, Paul (2002). Une classe de concepts. Semiotica 139 (1-4), 211-226. English translation.

Hegel, Georg Wilhelm Friedrich (1812-1816). Wissenschaft der Logik. Science de la logique, trad. Bourgeois, Paris, Aubier Montaigne, 1972.

Hegel, Georg Wilhelm Friedrich (1817). Die Encyclopädie der philosophischen Wissenschaften im Grundrisse. Précis de l’encyclopédie des sciences philosophiques, trad. J. Gibelin. Vrin, Paris, 1978


1 One also finds the antithesis-thesis-synthesis variant.

2 Platon envisaged dialectic under the form of a dialogue between two persons, based on alternate questions and responses. One also finds a dialectical approach in Kant, but also in Fichte and Schelling.

3 In the context of dialectical materialism, the dialectic finds its expression on the social terrain, through the conflict or the struggle, which are viewed as the manifestation, at a material level, of the contradiction. Historical progress and social advances ensue once this conflict has been overcome. For Marx also, the dialectical objective situates itself veritably at the level of the reality, finding thus its expression in the facts and the phenomena. Conversely, the dialectical move observed at the level of human thought only constitutes the subjective reflect of the essential dialectic, a simple transposition of the latter at the level of the humain brain.

4 Cf. Hegel (1812-1816) and (1817).

5 With this last notation, the matrix of the canonical poles is rendered as follows: {α(A/Ā, -1, 1), α(A/Ā, -1, 0), α(A/Ā, -1, -1), α(A/Ā, 1, 1), α(A/Ā, 1, 0), α(A/Ā, 1, -1)}.

6 Formally α1 and α2 are dual if and only if c1] = – c2] and p1] = p2] = 0.

7 Formally α1 and α2 are antinomical if and only if c1] = – c2] and p1] = – p2] with p1], p2]  0.

8 Formally α1 and α2 are complementary if and only if c1] = – c2] and p1] = p2] with p1], p2]  0.

9 Formally α1 and α2 are corollary if and only if c1] = c2] and p1] = – p2] with p1], p2]  0.

10 Formally α1 and α2 are connex if and only if c1] = c2] and │p1] – p2]│ = 1.

11 Formally α1 and α2 are anti-connex if and only if c1] = – c2] and │p1] – p2]│ = 1.

12 For a more comprehensive list of matrices of concepts, see Franceschi (2002).

13 Personal ambition could be fruitful (ambition+) or well excessive, or even immoderate (ambition).

14 A passion could be positive (passion+) or well excessive, destructive (passion).

15 Negative or neutral.

16 Positive or neutral.

17 One could as well distinguish here degrees of truth value, by making use of degrees of appreciation, with p  [-1, 1]. An approach by degree of the truth value ensues, by calculating thus this latter with regard to the absolute value of the difference between p and q: [v] = 1- |(pq)/2|.

18 Such a definition generalizes to the determination of the truth values of the 3-composed theses, …, n-composed.

19 Formally, let thus P  Q be a 2-composed thesis, such that P = p11(A/Ā, c1, q1)) and Q = P22(A/Ā, c2, q2), with p1, p2, q1, q2  {-1, 0, 1}, c1, c2  {-1, 1} and α, β  {A+, A0, A, Ā+, Ā0, Ā}; then the dual thesis of P  Q is of the form: p11 (A/Ā, –c1, q1))  P22 (A/Ā, –c2, q2). Such definition generalizes easily to the dual theses of the n-composed theses.

20 The description of the different steps of the dialectical process thus defined also suggests other types of plans than the one which has been emphasized here. Alternative plans can notably highlight a part related to the step of determination of the truth value of the considered thesis, or well to the dual thesis of this latter.

21 Alternatively, one could also consider the following variation:

1. From an analytic point of view

1.1 From the viewpoint of A0

1.1.1 Praise of A+

1.1.2 Blame of A

1.2 From the viewpoint of Ā0

1.2.1 Praise of Ā+

1.2.2 Blame of Ā

2. From a synthetic point of view: the complementarity between A+ and Ā+ and between A and Ā

22 A variation of this type of plan consists evidently in assimilating the part 3 with the conclusion.

23 For this last type of thesis whose structure is +(A+)  ), it is also possible to recur to another type of plan which emphasizes more the dual thesis ++)  (A). Such a type of plan proves to be close to the classical dialectic plan and stresses on the dual thesis of the considered thesis, e.g. +(eclecticism+)  (compartmentalization). Such a type of plan presents then the following structure:

1. Thesis

1.1 The advantages of expertise+

1.2 The dangers of superficiality

2. Dual thesis

2.1 The necessity of eclecticism+

2.2 The risk of compartmentalization

3. The necessary synthesis between eclecticism+ and expertise+, and superficiality and compartmentalization

The Simulation Argument and the Reference Class Problem: the Dialectical Contextualist’s Standpoint

Postprint. I present in this paper an analysis of the Simulation Argument from a dialectical contextualist’s standpoint. This analysis is grounded on the reference class problem. I begin with describing in detail Bostrom’s Simulation Argument. I identify then the reference class within the Simulation Argument. I also point out a reference class problem, by applying the argument successively to three different reference classes: aware-simulations, imperfect simulations and immersion-simulations. Finally, I point out that there are three levels of conclusion within the Simulation Argument, depending on the chosen reference class, that yield each final conclusions of a fundamentally different nature.

This article supersedes my preceding work on the Simulation argument. Please do not cite previous work.


The Simulation Argument and the Reference Class Problem : a Dialectical Contextualism Analysis

Paul FRANCESCHI

www.paulfranceschi.com

English postprint of a paper initially published in French in Philosophiques, 2016, 43-2, pp. 371-389, under the title L’argument de la Simulation et le problème de la classe de référence : le point de vue du contextualisme dialectique

ABSTRACT. I present in this paper an analysis of the Simulation Argument from a dialectical contextualist’s standpoint. This analysis is grounded on the reference class problem. I begin with describing in detail Bostrom’s Simulation Argument. I identify then the reference class within the Simulation Argument. I also point out a reference class problem, by applying the argument successively to three different reference classes: aware-simulations, imperfect simulations and immersion-simulations. Finally, I point out that there are three levels of conclusion within the Simulation Argument, depending on the chosen reference class, that yield each final conclusions of a fundamentally different nature.

1. The Simulation Argument

I shall propose in what follows an analysis of the Simulation Argument, recently described by Nick Bostrom (2003). I will first describe in detail the Simulation Argument (SA for short), focusing in particular on the resulting counter-intuitive consequence. I will then show how such a consequence can be avoided, based on the analysis of the reference class underlying SA, without having to give up one’s pre-theoretical intuitions.

The general idea behind SA can be stated as follows. It is very likely that post-human civilizations will possess a computing power that will be completely out of proportion with that of ours today. Such extraordinary computing power should give them the ability to carry out completely realistic human simulations, such as ensuring that the inhabitants of these simulations are aware of their own existence, in all respects similar to ours. In such a context, it is likely that post-human civilizations will devote part of their computer resources to carrying out simulations of the human civilizations that preceded them. In this case, the number of simulated humans should greatly exceed the number of authentic humans. Under such conditions, taking into account the simple fact that we exist leads to the conclusion that it is more likely that we are part of the simulated humans, rather than of the authentic humans.

Bostrom thus points out that the Simulation Argument is based on the following three hypotheses:

(1)it is very likely that humanity will not reach a post-human stage
(2)it is very unlikely that post-human civilizations will carry out simulations of the human races that preceded them
(3)it is very likely that we are currently living in a simulation carried out by a post-human civilization

and it follows that at least one of these three assumptions is true.

For the purposes of the present analysis, it is also useful at this stage to emphasize the underlying dichotomous structure of SA. The first step in the reasoning consists then in considering, by dichotomy, that either (i) humanity will not reach a post-human stage, or (ii) it will actually reach such a post-human stage. The first of these two hypotheses corresponds to the disjunct (1) of the argument. We consider then the hypothesis that humanity will reach a post-human stage and thus continue its existence for many millennia. In such a case, it can also be considered likely that post-human civilizations will possess both the technology and the skills necessary to perform human simulations. A new dichotomy then arises: either (i) these post-human civilizations will not perform such simulations — this is the disjunct (2) of the argument; or (ii) these post-human civilizations will actually perform such simulations. In the latter case, it will follow that the number of simulated humans will greatly exceed the number of humans. The probability of living in a simulation will therefore be much greater than that of living in the shoes of an ordinary human. The conclusion then follows that we, the inhabitants of the Earth, are probably living in a simulation carried out by a post-human civilization. This last conclusion constitutes the disjunct(3) of the argument. An additional step leads then to the conclusion that at least one of the hypotheses (1), (2) and (3) is true. The dichotomous structure underlying SA can thus be described step by step as follows:

(4)humanity will either not reach a post-human stage or reach a post-human stagedichotomy 1
(1)humanity will not reach a post-human stagehypothesis 1.1
(5)humanity will reach a post-human stagehypothesis 1.2
(6)post-human civilizations will be able to perform human simulationsfrom (5)
(7)post-human civilizations will either not perform human simulations or will perform themdichotomy 2
(2)post-human civilizations will not perform human simulationshypothesis 2.1
(8)post-human civilizations will perform human simulationshypothesis 2.2
(9)the proportion of simulated humans will far exceed that of humansfrom (8)
(3)it is very likely that we are currently living in a simulation carried out by a post-human civilizationfrom (9)
(10)at least one of the hypotheses (1), (2) and (3) is truefrom (1), (2), (3)

It is also worth mentioning an element that results from the very interpretation of the argument. For as Bostrom (2005) points out, the Simulation Argument must not be misinterpreted. This is not an argument that leads to the conclusion that (3) is true, namely that we are currently living in a simulation carried out by a post-human civilization. The core of SA is thus that one of the hypotheses (1), (2) or (3) at least is true.

This nuance of interpretation being mentioned, the Simulation Argument is not without its problems. Because SA leads to the conclusion that at least one of the assumptions (1), (2) or (3) is true, and that in the situation of ignorance in which we find ourselves, we can consider the latter as equiprobable. As Bostrom himself notes (Bostrom, 2003): “In the dark forest of our current ignorance, it seems sensible to apportion one’s credence roughly evenly between (1), (2) and (3)”. However, according to our pre-theoretical intuition, the probability of (3) is nil or at best extremely close to 0, so the conclusion of the argument has the consequence of increasing the probability that (3) is true from zero to a probability of about 1/3. Thus, the problem with the Simulation Argument is precisely that it shifts — via its disjunctive conclusion — from a zero or almost zero probability concerning (3) to a much higher probability of about 1/3. Because a probability of 1/3 for the hypotheses (1) and (2) is not a priori shocking, but is completely counter-intuitive as far as hypothesis (3) is concerned. It is in this sense that we can talk about the problem posed by the Simulation Argument and the need to find a solution to it.

As a preliminary point, it is worth considering what constitutes the paradoxical aspect of SA. What indeed gives SA a paradoxical nature? For SA differs from the class of paradoxes that lead to a contradiction. In paradoxes such as the Liar or the sorites paradox, the corresponding reasoning leads to a contradiction1. However, nothing of the sort can be seen at the level of SA, which belongs, from this point of view, to a different class of paradoxes, including the Doomsday Argument and Hempel’s problem. It is indeed a class of paradoxes whose conclusion is contrary to intuition, and which comes into conflict with the set of all our beliefs. In the Doomsday Argument then, the conclusion that taking into account our rank within the class of humans who have ever existed has the effect that an apocalypse is much more likely than one might have initially thought, offends the set of all our beliefs. Similarly, in Hempel’s problem, the fact that a blue umbrella confirms the hypothesis that all crows are black comes in conflict with the body of our knowledge. Similarly within SA, what finally appears paradoxical at first analysis is that SA leads to a probability of the hypothesis that we are currently living in a simulation created by post-humans, which is higher than that resulting from our pre-theoretical intuition.

2. The reference class problem and the Simulation Argument

The conclusion of the reasoning underlying SA, based on the calculation of the future ratio between real and simulated humans, albeit counter-intuitive, nevertheless results from a reasoning that appears a priori valid. However, such reasoning raises a question, which is related to the reference class that is inherent to the argument itself2. Indeed, it appears that SA has, indirectly, a particular reference class, which is that of human simulations. But what constitutes a simulation? The original argument implicitly refers to a reference class which is that of virtual simulations of humans, of a very high quality and by nature indistinguishable from authentic humans. However, there is some ambiguity about the very notion of a simulation and the question arises as to the applicability of SA to other types of human simulations3. Indeed, we are in a position to conceive of somewhat different types of simulations which also fall intuitively within the scope of the argument.

As a preliminary point, it is worth specifying here the nature of the simulations carried out by computer means referred to in the original argument. Implicitly, SA refers to computer simulations carried out by means of conventional computers composed of silicon chips. But it can also be envisaged that simulations are carried out using computers built from components using DNA properties and molecular biology. Recent research has shown that it is possible to implement high-performance algorithms (Adleman 1994, 1998) and to produce computer components (Benenson & al. 2001, MacDonald & al. 2006) based on bio-calculation techniques that exploit in particular the combinations of the four components (adenine, cytosine, guanine, thymine) of the DNA molecule. If such a field of research were to expand significantly and make it possible to produce computers at least as powerful as conventional computers, this type of bio-computers could legitimately fall within the scope of SA as well. Because the fact that the simulations are carried out using conventional or biological computers4 does not alter the scope of the argument. In any case, the result is that the proportion of simulated humans will be much higher than that of real humans, due to the properties of simulated reality using digital means, because the computer does not know the physical limits that are those of matter.

It can also be observed preliminarily that Bostrom explicitly refers to simulations carried out using computer means. However, the question arises as to whether simulated humans could not consist of perfectly successful physical copies of real humans. In such a case, simulations5 could be extremely difficult to discern. A priori, such a variation also constitutes an acceptable version of SA. However, there is a difference with the original argument, which also highlights Bostrom’s preferential choice of computer simulations. Indeed, in the original argument there is a very significant disproportion between humans simulated by computer means on the one hand and real humans on the other. This is the premise (9) of the argument: “the proportion of simulated humans will far exceed that of humans”. As Bostrom points out, the former would then be much more numerous than the latter, due to the very nature of computer simulations. It is this disproportion that then allows us to conclude (3) “we most probably live in a simulation carried out by a post-human civilization”. With simulations of a physical nature, one would not a priori have such a disproportion, and the scope of the conclusion would be somewhat different. Suppose, for example, that post-humans manage to perform simulations of a physical nature, the number of which would be equal to that of real humans. In this case, the proportion of simulated humans would be 1/2 (whereas it is close to 1 in the original argument). Premise (9) would then become: “the proportion of simulated humans and actual humans will be 1/2”. And this would only allow us to conclude (3) “the probability that we are simulations performed by a post-human civilization is equal to 1/2”. As can be seen, this would result in a significantly attenuated version of SA. The difference with the original version of SA is that the simulation argument for physical simulations applies with less force than the original argument. However, if the conditions were to change and this would result in the future in a disproportion of the same nature as with computer simulations for physical simulations, SA would then apply with all its force. In any event, the following analysis would then apply in the same way to this last category of simulations.

With these preliminary considerations in mind, we shall focus in turn on different types of human simulations, which are likely to be part of the SA reference class, and the ensuing conclusions at the argument level. Because the very question of defining the reference class for SA leads to questions about whether or not several types of simulations should be included within the SA scope. However, the question of the definition of the reference class for SA thus appears closely related to the nature of the future taxonomy of the beings and entities that will populate the Earth in the near or distant future. There is no question here of claiming exhaustiveness, given the speculative nature of such an area. However, it is possible to determine to what extent SA can also be applied to simulations of a different nature from those mentioned in the original argument, but which have equal legitimacy. We shall examine then in turn: conscious simulations, imperfect simulations, and immersion simulations.

3. The reference class problem : the caseof conscious simulations

At this step, it is not yet possible to really talk about the problem of the reference class within SA. To do so, it must be shown that the choice of one or the other reference class has completely different consequences at the level of the argument, and in particular that the nature of its conclusion is affected, i.e. fundamentally modified. In what follows, we will now focus on showing that depending on which reference class is chosen, radically different conclusions ensue at the level of the argument itself and that, consequently, there is a reference class problem within SA. For this purpose, we will consider several reference classes in turn, focusing on how conclusions of a fundamentally different nature result from them at the level of the argument itself.

The original version of SA implicitly depicts simulations of humans of a certain type. These are virtual simulations, almost indistinguishable from real humans and that present thus a very high degree of sophistication. Moreover, these are a type of simulations that are not aware that they are themselves simulated and are therefore convinced that they are genuine humans. This is implicit in the terms of the argument itself and in particular, the inference from (9) to (3) which leads to the conclusion that ʻweʼ are currently living in an indistinguishable simulation carried out by post-humans. In fact, these are simulations that are somehow abused and misled by post-humans regarding their true identity. For the purposes of this discussion, we shall term quasi-humans the simulated humans who are not aware that they are human.

At this stage, it appears that it is also possible to conceive of indistinguishable simulations that have an identical degree of sophistication but that, on the other hand, would be aware that they are being simulated. We shall then call quasi-humans+ the simulated humans who are aware that they are themselves simulations. Such simulations are in all respects identical to the quasi-humans to which SA implicitly refers, with the only difference that they are this time clearly aware of their intrinsic nature of simulation. Intuitively, SA also applies to this type of simulation. A priori, there is no justification for excluding such a type of simulation. Moreover, there are several reasons to believe that quasi-humans+ may be more numerous than quasi-humans. For ethical reasons (i) first of all, it may be thought that post-humans might be inclined to prefer quasi-humans+ to quasi-humans. For the fact of conferring an existence on quasi-humans constitutes a deception as to their true identity, whereas such an inconvenient is absent in the case of quasi-humans+. Such deception could reasonably be considered unethical and lead to some form of prohibition of quasi-humans. Another reason (ii) is that simulations of humans who are aware of their own simulation nature should not be dismissed a priori. Indeed, we can think that the level of intelligence acquired by some quasi-humans in the near future could be extremely high and in this case, the simulations would very quickly become aware that they are themselves simulations. It may be thought that from a certain degree of intelligence, and in particular that which may be obtained by humanity in the not too distant future (Kurtzweil, 2000, 2005; Bostrom, 2006), quasi-humans should be able — at least much more easily than at present — to collect evidence that they are the subject of a simulation. Furthermore (iii), the very concept of “unconscious simulation that it is a simulation” could be inherently contradictory, because it would then be necessary to limit one’s intelligence and therefore, it would no longer constitute an indistinguishable and sufficiently realistic simulation6. These three reasons suggest that quasi-humans+ may well exist in greater numbers than quasi-humans — or even that they may even be the only type of simulation implemented by post-humans.

At this stage, it is worth considering the consequences of taking into account the quasi-humans+ within the simulation reference class inherent to SA. For this purpose, let us first consider the variation of SA (let us term it SA*) that applies, exclusively, to the class of quasi-humans+. Such a choice, first of all, has no consequence on the disjunct (1) of SA, which refers to a possible disappearance of our humanity before it has reached the post-human stage. Nor does this has any effect on the disjunct (2), according to which post-humans will not perform quasi-humans+, i.e. conscious simulations of human beings. On the other hand, the choice of such a reference class has a direct consequence on the disjunct (3) of SA. Certainly, it follows, in the same way as for the original argument, the first level conclusion that the number of quasi-humans+ will far exceed the number of authentic humans (the disproportion). However, the second level conclusion that “we” are currently quasi-humans no longer follows. Indeed, such a conclusion (let us call it self-applicability) no longer applies to us, since we are not aware that we are being simulated and are completely convinced that we are authentic humans. Thus, in this particular context, the inference from (9) to (3) no longer prevails. Indeed, what constitutes SA’s worrying conclusion no longer results from step (9), since we cannot identify with the quasi-humans+, the latter being clearly aware that they are evolving in a simulation. Thus, unlike the original version of SA based on the reference class that associates humans with quasi-humains, this new version associating humans with quasi-humans+ is not associated with such a disturbing conclusion. The conclusion that now follows, as we can see, is quite reassuring, and in any case very different from the deeply worrying7 conclusion that results from the original argument.

At this stage, it appears that a question arises: should we identify, in the context of SA, the reference class to the quasi-humans or the quasi-humans+?8 It appears that no objective element in SA’s statement supports the a priori choice of the quasi-humans or the quasi-humans+. Thus, any version of the argument that includes the preferential choice of the quasi-humans or the quasi-humans+ appears to be biased. This is the case for the original version of SA, which thus contains a bias in favor of the quasi-humans, which results from Bostrom’s choice of a class of simulations that is exclusively assimilated to quasi-humans, i.e. simulations that are not aware of their simulation nature and are therefore abused and misled by post-humans about the very nature of their identity. And this is also the case for SA*, the alternative version of SA that has just been described, which includes a particular bias in favor of quasi-humans+, simulations that are aware of their own simulation nature. However, the choice of the reference class is fundamental here, because it has an essential consequence: if we choose a reference class that associates simulations with quasi-humans, the result is the worrying conclusion that we are most likely currently experiencing in a simulation. On the other hand, if a reference class is chosen that identifies simulations with quasi-humans+, the result is a scenario that reassuringly does not include such a conclusion. At this stage, it is clear that the choice of the quasi-humans i.e., non-conscious simulations — in the original version of SA, to the detriment of conscious simulations, constitutes an arbitrary choice. Indeed, what makes it possible to prefer the choice of quasi-humans, compared to quasi-humans+? Such justification is lacking in the context of the argument. At this stage, it appears that SA’s original argument contains a bias that leads to the preferential choice of quasi-humans, and to the alarming conclusion associated with it9.

4. The reference class problem : the case of imperfect simulations

The problem of the reference class within SA relates, as mentioned above, to the very nature and to the type of simulations referred to in the argument. Is this problem limited to the preferential choice, at the level of the original argument, of unconscious simulations, to the detriment of the alternative choice of conscious simulations, which correspond to very sophisticated simulations of humans, capable of creating illusion, but endowed with the awareness that they themselves are simulations? It appears not. Indeed, as mentioned above, other types of simulations can also be envisaged for which the argument also works, but which are of a somewhat different nature. In particular, it is conceivable that post-humans may design and implement simulations that are identical to those of the original argument, but that are not as perfect in essence. Such a situation is quite likely and does not have the ethical disadvantages that could accompany the indistinguishable simulations staged in the original argument. The choice to carry out such simulations could be the result of the necessary technological level, or of deliberate and pragmatic choices, designed to save time and resources. These could be, for example, simulations of excellent quality such that the scientific inhabitants of the simulations could only discover their artificial nature after, for example, ten years of research. Such simulations could be carried out in very large numbers and, given their less resource-intensive nature, could occur in even greater numbers than quasi-humans. For the purposes of this discussion, we will call imperfect simulations this category of simulations.

At this stage, one can ask oneself what are the consequences on SA of taking into account a reference class that identifies itself with imperfect simulations? In this case, it follows, in the same way as the original argument, that the first level conclusion that the number of imperfect simulations will far exceed the number of authentic humans (the disproportion). But here too, however, the second level conclusion that “we” are currently imperfect simulations (self-applicability) no longer follows. The latter no longer applies to us and a reassuring conclusion replaces it, since we are clearly aware that we are not such imperfect simulations. Finally, it turns out that the conclusion that results from taking into account the class of imperfect simulations is of the same nature as that which follows when considering the class of the quasi-humans+.

5. The reference class problem : the caseof immersion simulations

As we have seen, extending the SA reference class to conscious simulations leads to a conclusion of a different nature from the one that results from the original argument. The same applies to another category of simulations — imperfect simulations — which lead to a conclusion of the same nature as conscious simulations, and which in any case turns out to be different from that resulting from taking into account the simulations mentioned in the original argument. At this stage, the question arises as to whether the reference class can not be assimilated to other types of simulations relevant from the point of view of SA and whose consideration would lead to a conclusion that is inherently different from that which follows when considering the simulations of the original argument, or conscious or imperfect simulations.

In particular, the question arises as to whether human simulations, which would be such as to apply to ourselves — in a sense that may differ from the original argument — and which would include the conclusion of self-applicability inherent in SA, could not exist in a more or less near future. Some answers can be provided by considering an evolution of the concepts of virtual reality that are already being implemented in different fields such as psychiatry, surgery, industry, military training, entertainment, etc. In psychiatry in particular, virtual universes are used to implement techniques related to behavioral therapies, and offer advantages over traditional in vivo scenarios (Powers & Emmelkamp, 2008). In this type of treatment, the patient himself is simulated using an avatar and the universe in which he evolves is also simulated in the most realistic way possible. Convincing results have been obtained in the treatment of some phobias (Choy & al., 2007, Parsons & Rizzo, 2008), as well as post-traumatic stress disorder (Cukor & al., 2009, Baños & al., 2011).

In this context, it is conceivable that developments in this concept of virtual reality could lead to the realization of simulated humans, which would require a high degree of realism. This would require, in particular, the completion of current research, particularly on the simulation of the human brain. It is possible that significant progress may be made in the near future (Moravec, 1998; Kurzweil, 2005; Sandberg and Bostrom, 2008; De Garis et al. al., 2010). It is also conceivable that we will then have the ability to immerse ourselves in simulated universes by borrowing the personalities of humans thus simulated, while really having — the time of immersion — the impression that this is our real existence10. In addition, the same human simulation could take the form of multiple variations that would correspond to the purpose — therapeutic, scientific, playful, utilitarian, historical, etc. — sought during the immersion. For example, it is conceivable that some variations may only include important elements of the simulated personality’s life, neglecting uninteresting details. For the purposes of this discussion, we can term this type of simulation: immersion simulations. In this context, humans could thus frequently resort to immersion in a simulated anterior human personality. It is also possible that individuals may use simulations of themselves: they could be simulations of themselves at earlier times in their lives, with eventual slight variations, however, depending on the purpose sought for the immersion in question. In such circumstances, it is conceivable that very large quantities of this type of simulation could be carried out by computer means. In any case, it appears that the number of simulations at our disposal would be much greater than the inhabitants of our planet. In this context, it appears that SA functions in the same way as the original argument if we reason in relation to a reference class that identifies itself with this type of immersion simulations.

At this point, it is worth considering the effect on SA of assimilating the reference class to immersion simulations. In such a context, it appears that the first-level consequence based on the humans/simulations disproportion would apply here, in the same way as the original argument. Secondly, and this is an important consequence, the second level conclusion based on self-applicability would now apply, since we can conclude that “we” are also, in this extended sense, simulations. On the other hand, it would no longer follow the alarming conclusion, which is that of the original argument and which manifests itself at a third level, that we are unconscious simulations, since the fact that we are in this sense simulations does not imply here that we are mistaken about our first identity. Thus, unlike the original argument, the result is a reassuring conclusion: humans are occasionally immersion simulations, while being aware that they use them.

Could we not object here that we have not yet reached the state where we can identify, even if only temporarily, with such immersion simulations and that this does not make the above developments relevant to SA? Strictly speaking, the virtual reality implemented in our time can indeed be considered too coarse in nature to be assimilated to the very realistic simulations hinted at by Bostrom. However, it can be assumed that only high-quality immersion simulations, which would give the illusion at least the time of their use that they are a real existence, could be carried out, for such simulations to become relevant for the SA reference class. The hypothesis that such a technological level, based on an explosion of artificial intelligence, could be achieved within a few decades has thus been put forward (Kurzweil, 2005; Eden et al. al., 2013). If such a technological evolution were to occur within, for example, a few decades, could we not then legitimately consider that such simulations also fall within the reference class of SA? Given this possible temporal proximity, it seems appropriate to take into account the case of immersion simulations and to evaluate their consequences for SA11.

6. The different levels of conclusion according to the chosen reference class

Finally, the preceding discussion emphasizes that if SA is considered in light of its inherent reference class problem, there are actually several levels in the conclusion of SA: (C1) disproportion; (C2) self-applicability; (C3) unconsciousness (the worrying fact that we are fooled, deceived about our primary identity). In fact, the previous discussion shows that (C1) is true regardless of the chosen (by restriction or extension) reference class: quasi-humans, quasi-humans+, imperfect simulations and immersion simulations. In addition, (C2) is also true for the original reference class of quasi-humans — and for immersion simulations, but is false for the class of quasi-humans+ and imperfect simulations. Finally, (C3) is true for the original reference class of quasi-humans, but it proves to be false for quasi-humans+, imperfect simulations and immersion simulations. These three levels of conclusion are represented in the table below:

levelconclusioncasequasi-humansquasi-humans+imperfect simulationsimmersion simulations
C1the proportion of simulated humans will far exceed that of humans (disproportion)C1Atruetruetruetrue
the proportion of simulated humans will not significantly exceed that of humansC1Āfalsefalsefalsefalse
C2we are most likely simulations (self-applicability)C2Atruefalsefalsetrue
we are most likely not simulationsC2Āfalsetruetruefalse
C3we are unconscious simulations of their simulation nature (unconsciousness)C3Atruefalsefalsefalse
we are not unconscious simulations of their simulation natureC3Āfalsetruetruetrue

Figure 1. The different levels of conclusion within SA

as well as in the following tree structure:

Figure 2. Treeof the different levels of conclusion of SA

While SA’s original conclusion suggests that there is only one level of conclusion, it turns out, however, as just pointed out, that there are in fact several levels of conclusion in SA, when the argument is examined from a broader perspective, in the light of the reference class problem. The conclusion of the original argument (C3A) is itself worrying and alarming, in that it concludes that there is a much higher probability than we had imagined a priori that we are humans simulated without being aware of it. However, the above analysis shows that, depending on the chosen reference class, some conclusions of a very different nature can be inferred by the simulation argument. Thus, a completely different conclusion is associated with the choice of the reference class of the quasi-humans+ or imperfect simulations. The resulting conclusion is that we are not such simulations (C2Ā). Finally, another possible conclusion, itself associated with the choice of the immersion simulation class, is that we are eventually part of such a simulation class, but we are aware of it and therefore it is not a cause for concern (C3Ā).

The above analysis finally highlights what is wrong with the original version of SA, which is at a twofold level. First, the original argument focuses on the class of simulations that are not aware of their own simulation nature. This leads to a succession of conclusions that there will be a greater proportion of simulated humans than authentic humans (C1A), that we are part of simulated humans (C2A) and finally that we are, more likely than we might have imagined a priori, simulated humans unaware of being (C3A). However, as mentioned above, the very notion of human simulation is ambiguous, and such a class can in fact be defined in different ways, given that there is no objective criterion in SA for choosing such a class in a way that is not arbitrary. We can indeed choose the reference class by identifying the simulations with unconscious simulations, i.e. quasi-humans simulations. But the alternative choice of a reference class that identifies itself with simulations that are conscious of being simulations themselves, i.e. quasi-humans+, has equal legitimacy. In the original argument, there is no objective criterion for choosing the reference class in a non-arbitrary way. Thus, the fact of favoring, in the original argument, the choice of quasi-humans — with the alarming conclusion associated with them — over quasi-humans+, constitutes a bias, as well as the choice of a reference class that identifies itself with quasi-humans+, leads this time to a reassuring conclusion.

Secondly, it appears that the reference class of SA can be defined at a certain level of restriction or extension. The choice in the original argument of the quasi-humans — occurs at a certain level of restriction. But if we now move to a certain level of extension, the reference class now includes imperfect simulations. And if we place ourselves at an even greater level of extension, simulations include not only imperfect simulations, but also immersion simulations. But depending on whether the class is chosen at a particular level of restriction or extension, a completely different conclusion will follow. Thus, the choice, at a higher level of extension, of imperfect simulations leads to a reassuring conclusion. Similarly, at an even greater level of extension, which this time includes immersion simulations, there also follows a new reassuring conclusion. Thus, the above analysis shows that in the original version of SA, the choice is made preferentially, by restriction, on the reference class of quasi-humans, to which is associated a worrying conclusion, as well as a choice by extension, also taking into account imperfect simulations or immersion simulations, leads to a reassuring conclusion.

Can we not object, at this stage, that the above analysis leads to a change in the original scenario of SA and that it is no longer the same problem12? To this, it can be replied that the previous analysis is based on variations in SA that preserve the very structure of the original argument. What this analysis shows is that this same structure is likely to produce conclusions of a very different nature, as long as the reference class is varied within reasonable limits that correspond to the context of SA, and even though the original SA statement suggests a single type of conclusion. Bostrom himself emphasizes that it is the structure of the argument that constitutes its real core: “The structure of the Simulation Argument does not depend on the nature of the hypothetical beings that would be created by the technologically mature civilizations. If instead of computer simulations they created enormous numbers of brains in vats connected to a suitable virtual reality simulation, the same effect could in principle be achieved.” (Bostrom, 2005). In addition, the different levels of extension used here to highlight variations in the SA reference class are intended to illustrate how different levels of conclusion can result. But if we wish to preserve the very form of the original argument, we can then limit the variation of the reference class to what really constitutes the core of this analysis, by considering only a reference class that identifies itself with the quasi-humans. The reference class is then made up of both quasi-humans and quasi-humans+. This is sufficient to generate a reassuring conclusion — which is not taken into account in the original argument — and thus modify the general conclusion resulting from the argument. In this case, it is the same reference class as the one underlying the original argument, with the only difference that simulations knowing that they are simulated are now part of it. Because the latter, whose possible existence is not mentioned in the original argument, nevertheless have an equal right to legitimacy in the context of SA.

Finally, the preferential choice in the original argument of the quasi-humans class, appears to be an arbitrary choice that no objective criterion justifies, while other choices deserve equal legitimacy. For the SA statement does not contain any objective element allowing the choice of the reference class to be made in a non-arbitrary manner. In this context, the worrying conclusion associated with the original argument also turns out to be an arbitrary conclusion, since there are several other reference classes that have an equal degree of relevance to the argument itself, and from which a quite reassuring conclusion follows.13 14

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MacDonald J., Li Y., Sutovic M., Lederman H., Pendri K., Lu W., Andrews B. L., Stefanovic D., Stojanovic M. N. « Medium Scale Integration of Molecular Logic Gates in an Automaton », Nano Letters, 6, 2006, p. 2598–2603.

Moravec, Hans « When will computer hardware match the human brain? », Journal of Evolution and Technology, 1998, vol. 1.

Parsons T.D., Rizzo A. « Affective outcomes of virtual reality exposure therapy for anxiety and specific phobias: A meta-analysis », Journal of Behavior Therapy and Experimental Psychiatry, vol. 39, no. 3, 2008, p. 250–261.

Powers M. B., Emmelkamp P. « Virtual reality exposure therapy for anxiety disorders: A meta-analysis », Journal of Anxiety Disorders, vol. 22, no. 3, 2008, p. 561–569.

Sandberg, Anders et Bostrom, Nick Whole Brain Emulation: a Roadmap, Technical Report #2008-3, Future of Humanity Institute, Oxford University, 2008.

Walton, Douglas, One-Sided Arguments: A Dialectical Analysis of Bias, Albany, State University of New York Press, 1999.

1 The Liar is thus both true and false. In the sorites paradox, an object with a certain number of grains of sand is both a heap and a non-heap. Similarly, in Goodman’s paradox, an emerald is both green and grue, and therefore both green and blue after a certain date. Finally, in the Sleeping Beauty paradox, the probability that the piece fell on heads before the awakening of the Sleeping Beauty is 1/2 by virtue of one reasoning mode, and only 1/3 by virtue of an alternative reasoning.

2 William Eckhardt (2013, p. 15) considers that — in the same way as the Doomsday Argument (Eckhardt 1993, 1997, Franceschi, 2009) — the problem inherent in SA comes from the use of retrocausality and the problem related to the definition of the reference class: “if simulated, are you random among human sims? hominid sims? conscious sims?”.

3 We will leave aside here the question of whether an infinite number of simulated humans should be taken into account. This could be the case if the ultimate level of reality were abstract. In this case, the reference class could include simulated humans who identify themselves, for example, with matrices of very large integers. But Bostrom answers such an objection in his FAQ (www.simulation-argument.com/faq.html) and points out that in this case, the calculations are no longer valid (the denominator is infinite) and the ratio is not defined. We will therefore leave this hypothesis aside, focusing our argument on what constitutes the core of SA, i.e. the case where the number of human simulations is finite.

4 The same would be true if simulations were carried out using quantum computers.

5 I thank an anonymous referee for highlighting this point, as well as the point about computers built from components using DNA properties and molecular biology.

6 It seems difficult to rule out here the case where quasi-humans discover, at least fortuitously, that they are simulated humans, thus becoming quasi-humans+ from that moment on. However, in order to advantage the paradox, we will consider here that the very notion of an indistinguishable simulation is not plagued with contradiction.

7 Bostrom (2003) considers that the fact that we live in a simulation would only moderately affect our daily lives: “Supposing we live in a simulation, what are the implications for us humans? The foregoing remarks notwithstanding, the implications are not all that radical”. However, it may be thought that the effect should be much more profound, given that the fundamental level of reality is not where the simulation subjects believe it to be and that, as a result, many of their beliefs are completely erroneous. As David Chalmers (2005) points it out: “The brain is massively deluded, it seems. It has all sorts of false beliefs about the world. It believes that it has a body, but it has no body. It believes that it is walking outside in the sunlight, but in fact it is inside a dark lab. It believes it is one place, when in fact it may be somewhere quite different”.

8 For the purposes of this discussion, we present things as an alternative between quasi-humans and quasi-humans+. However, one could conceive that post-humans – perhaps different post-human civilizations – create both quasi-humans and quasi-humans+. We would then have a tripartite situation involving humans, quasi-humans and quasi-humans+. For the sake of simplicity, we can assimilate here such a situation to the one that prevails when post-humans only create quasi-humans since it is sufficient that the latter are present in very large numbers to create the worrying effect inherent to SA.

9 This type of bias can be analyzed in one instance of the one-sidedness bias (Walton, 1999, p. 76-81, Franceschi, 2014, p. 587-592) where the reference class is that of the simulations and the associated duality is consciousness/unconsciousness.

10 A complete simulation of a human brain is also called an upload. One definition (Sandberg & Bostrom, 2008, p. 7) is as follows:  : “The basic idea is to take a particular brain, scan its structure in detail, and construct a software model of it that is so faithful to the original that, when run on appropriate hardware, it will behave in essentially the same way as the original brain.”

11 The above also shows that when examining SA carefully, it can be seen that the argument contains a second reference class. This second reference class is that of post-humans. What is a post-human? Should we assimilate this class to civilizations far superior to ours, to those that will evolve in the 25th century or the 43th century? Should the descendants of our current human race who will live in the 22nd century be counted among the post-humans if they were to make considerable technological progress in the field of simulations? In any case, the definition of the post-human class appears to be closely linked to that of simulations. Because if we are interested, in a broad sense, in immersion simulations, then post-humans can be assimilated to a generation of humans not very far from us. If we consider imperfect simulations, then they should be associated with a more distant time. On the other hand, if we consider, in a more restrictive sense, simulations of humans that are completely indistinguishable from our current humanity, then we should be interested in post-humans from a much more distant era. Thus, the class of post-humans appears to be closely correlated with that of simulations, because the degree of evolution of simulations is related to the level reached by the post-human civilizations that implement them. For this reason, we shall limit the present discussion to the reference class of the simulations.

12 I thank an anonymous referee for raising this objection.

13 The resulting double weakening of SA finally makes it possible to reconcile SA with our pre-theoretical intuitions, because the worrying scenario of the original argument now coexists with several scenarios of a quite reassuring nature.

14 The present analysis is a direct application to the Simulation Argument of the form of dialectical contextualism described in Franceschi (2014).

I thank two anonymous referees for Philosophiques, for very useful comments on an earlier version of this article.

An Introduction to Analytic Philosophy

In this book, Paul Franceschi provides us with an introduction to analytic philosophy. In a concrete way, he chooses to describe forty paradoxes, arguments or philosophical issues that represent so many challenges for contemporary philosophy and human intelligence, for some paradoxes of millennial origin—such as the Liar or the sorites paradox—are still unresolved in the present day. Some other philosophical puzzles, however—such as the Doomsday argument—appeared only recently in the literature. The author strives to introduce us clearly to each of these problems as well as to major attempts that have been formulated to solve them.

In 2021, “An Introduction to Analytic Philosophy” entered the “64 Best Analytic Philosophy eBooks of All Time” list established by the bookauthority.org site.

“I’m really impressed by this very neat and stimulating book. I highly recommend it both to students for pedagogy and general culture (prisoner’s dilemma, twin-earth, etc.), and to professionals as well for the reference tool and even more generally to those who like to think.”

Julien Dutant, Philotropes, Philosophical blog


The Kindle version is also available.

Complements to a Theory of Cognitive Distortions

English preprint of a paper published in French under the title “Compléments pour une théorie des distorsions cognitives”, in the Journal de Thérapie Comportementale et Cognitive, 2007, 17-2, pp. 84-88.

The purpose of this study is to describe a conceptual framework for cognitive distortions, which notably allows to specify more accurately their intrinsic relationships. This conceptual framework aims at inserting itself within the apparatus of cognitive therapy and of critical thinking. The present analysis is based on the following fundamental concepts: the reference class, the duality and the system of taxa. With the help of these three notions, each cognitive distortion can be defined. A distinction is also made between, on the one hand, general cognitive distortions and on the other hand, specific cognitive distortions. The present model allows then to define within the same conceptual framework the general cognitive distortions such as dichotomous reasoning, disqualifying a given pole, minimisation and maximisation. It also allows to describe as specific cognitive distortions: disqualifying the positive, selective abstraction and catastrophism. Furthermore, the present model predicts the existence of two other general cognitive distortions: the omission of the neutral and requalifying in the other pole.


This paper is cited in:

  • Paul Franceschi, Théorie des distorsions cognitives : application à l’anxiété généralisée, Journal de Thérapie Comportementale et Cognitive, Volume 18, Issue 4, December 2008, Pages 127-131, English translation
  • Paul Franceschi, Théorie des distorsions cognitives : la sur-généralisation et l’étiquetage, Journal de Thérapie Comportementale et Cognitive, Volume 19, Issue 4, December 2009, Pages 136-140, English translation
  • Pramod Pandey, On the Nature of Reason in the present-day research, in Hasnain, Imtiaz, S. and Chaudhary, S. C. (eds.), Problematizing Language Studies: Cultural, Theoretical and Applied Perspectives- Essays in Honour of of Rama Kant Agnihotri. New Delhi: Aakar Books. Pp. 387-97, 2010.
  • Paul Franceschi, Traitement cognitif différentiel des délires oolythématiques et du trouble anxieux généralisé, Journal de Thérapie Comportementale et Cognitive, Volume 21, Issue 4, November 2011, Pages 121-125, English translation
  • Lisa Wake, Karl Nielsen, Nandana Nielsen & Catalin Zaharia, Depression symptom clusters, in “The Clinical Effectiveness of Neurolinguistic Programming”, Routledge 2013, edited by Lisa Wake, Richard M. Gray and Frank S. Bourke
  • Masoumeh Nozari, Ali Razipour Jouybari, Azam Nozari, Roya Raoufi Ahmad (2013) The Relationship between Moral Intelligence and Cognitive Distortions among Employees, Journal of Basic and Applied Scientific Research, 3(9), pages 345-348.
  • Lizet Fernandez-Jammet, Evaluation longitudinale de l’efficacité d’une prise en charge cognitivo-comportementale de groupe destinée à des patients atteints de fibromyalgie, dissertation doctorale, 2016
  • Hélène Richard-Lepouriel, Trouble bipolaire, auto-stigmatisation et restructuration cognitive : une première tentative de prise en charge, Journal de Thérapie Comportementale et Cognitive, Volume 27-4, November 2017, Pages 177-183
  • Valérie Pennequin & Nicolas Combalbert, L’influence des biais cognitifs sur l’anxiété chez des adultes non cliniques, Annales Médico-psychologiques, Volume 175, Issue 2, February 2017, Pages 103-107
  • Anita Robert, Nicolas Combalbert, Valérie Pennequin, Etude des profils de distorsion cognitive en fonction des états anxieux et dépressifs chez des adultes tout-venant, Annales Médico-Psychologiques 176 (2018) 225–230
  • Nawal Ouhmad, Nicolas Combalbert, Wissam El-Hage, Cognitive distortions and emotion regulation among post traumatic stress disorder victims, in Psychological Applications and Trends, Ed. by C. Pracana & M. Wang, InScience Press, 2019
  • Paul Franceschi, For a Typology of Auditory Verbal Hallucinations Based on their Content, Activitas Nervosa Superior, volume 62, pages 104–109, 2020
  • A.Robert, N.Combalbert, V.Pennequin, R.Deperrois, N.Ouhmad, Création de l’Échelle de Distorsions Cognitives pour adultes (EDC-A) : étude des propriétés psychométriques en population générale et association avec l’anxiété et la dépression, Psychologie Française, 2021
  • Deperrois Romain & Nicolas Combalbert, Links between cognitive distortions and cognitive emotion regulation strategies in non-clinical young adulthood, in Psychological Applications and Trends, Ed. by C. Pracana & M. Wang, InScience Press, 2021
  • Ouhmad, Nawal & El-Hage, Wissam & Combalbert, Nicolas. (2022), Maladaptive cognitions and emotional regulation in PTSD, 3-7, Conference: International Psychological Applications Conference and Trend, doi:10.36315/2022.

Complements to a Theory of Cognitive Distortions

Paul FRANCESCHI

The cognitive distortions, introduced by Aaron Beck (1963, 1964) and Albert Ellis (1962) are traditionally defined as fallacious reasoning that plays a crucial role in the emergence of certain mental disorders. The cognitive therapy in particular is based on the identification of these cognitive distortions within the everyday way of thinking of the patient, and their replacement by alternative reasoning. Traditionally, the cognitive distortions are represented as one of the twelve following irrational modes of reasoning: 1. Emotional reasoning 2. Overgeneralization 3. Jumping to conclusions (or arbitrary inference) 4. Dichotomous reasoning 5. Should statements (Ellis 1962) 6. Fortune telling or mind reading 7. Selective abstraction 8. Disqualifying the positive 9. Maximisation and minimisation 10. Catastrophism 11. Personalisation 12. Labelling.

Under their classical form which is that of an enumeration, the cognitive distortions plays a central role within the field of cognitive therapy. Considering also their widespread nature in normal reasoning, one can think however that an accurate understanding of the cognitive distortions proves also to be useful outside the field of psychopathology. In particular, the cognitive distortions can also be seen as part of the apparatus which constitutes critical thinking. For these reasons, it appears that a conceptual framework, notably allowing to define the relationships between the different cognitive distortions, could also turn out to be useful. In what follows, we shall set out to present a general theory of the cognitive distortions, which brings a certain number of supplementary elements in comparison with classical theory.

1. Main notions

The present framework allows to represent several classical cognitive distortions: dichotomous reasoning, disqualification of one of the poles, selective abstraction, minimisation and maximisation. To these, one can add two other cognitive distortions of which the present model allows to predict the existence and which are closely related to the classical cognitive distortions, although they do not appear, to the knowledge of the author, to the number of these last. It consists of the omission of the neutral and the requalification in the other pole.

The cognitive distortions can be constructed, in the present model, from three main notions: the reference class,the duality and the system of taxa. It is necessary, in a preliminary way, to set out to describe these three notions. The reference class, above all, 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 patient’s life; the class of the future events of the patient’s life; the class constituted by all the parts of the patient’s body; the class which is made up of the patient’s character’s traits.

The notion of duality, second, corresponds to a pair of concepts such as Positive/Negative, Internal/External, Collective/Individual, Nice/Ugly, etc. A duality corresponds then to a criterion under the angle of which the elements of the reference class can be considered or evaluated. Let us denote by A/Ā a given duality, where A and Ā constitute then dual concepts. An enumeration (necessarily partial) of the dualities is as follows: Positive/Negative, Internal/External, Quantitative/Qualitative, Visible/Invisible, Analytical/synthetic, Absolute/Relative, Abstract/Concrete, Static/Dynamic, Unique/Multiple, Aesthetics/Practice, Definite/Vague, Finite/Infinite, Simple/Composite, Individual/Collective, Implicit/Explicit, Intentional/Unintentional.

Finally, thepatient’s system of taxa consists of a taxonomy which allows the patient 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 patient. It consists of a system of values that is inherent to the patient or of a filter through which the patient “sees” the elements of the reference class, i.e. the phenomena or the objects of reality. The figure below represents an optimal system of taxa.

Fig.1. The optimal system of taxa

This last is composed of 11 spheres which represent each a given taxon. The system of taxa is optimal, because all taxa are present. On the other hand, if the patient 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 patient 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, …, En such that each of them has, in a objective way, a degree d[Ei] in a duality A/Ā comprised between -1 and 1 (d Î [-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). Let us pose then: d[E1] = -1, d[E2] = -4/5, d[E3] = -3/5, d[E4] = -2/5, d[E5] = -1/5, d[E6] = 0, d[E7] = 1/5, d[E8] = 2/5, d[E9] = 3/5, d[E10] = 4/5, d[E11] = 1. Let us also define a subjective degree D[Ei] such that it is attributed by the patient to each of the Ei. So, E1-E5 corresponds to the pole A of duality A/Ā, E6 to the neutral taxon and E7-E11 corresponds to the pole Ā. Moreover, this optimal system of taxa can be assimilated with one Likert scale with 11 degrees.

At this stage, we are in a position to define the main cognitive distortions, and it is worth considering them in turn. The cognitive distortions can be defined as a type of reasoning which leads to favour, without objective grounds, a subset of the taxa applicable to a given duality A/Ā, in order to qualify a given reference class. It also proves to be useful to draw a distinction, in a preliminary way, between the general cognitive distortions and the specific cognitive distortions. The general cognitive distortions relate to all reference classes and all dualities. By contrast, the specific cognitive distortions are mere instances of the general cognitive distortions which are inherent to a given reference class and to a given duality.

2. The cognitive distortions

2.1 Dichotomous reasoning

In the present context, dichotomous reasoning (or all-or-nothing thinking) can be defined as a general cognitive distortion which leads the patient to consider a given reference class only according to the two extreme taxa which relate to every pole of a given duality. With this type of reasoning, the patient ignores completely the presence of degrees or of intermediate steps. In his/her taxa system, the patient has as well the two extreme taxa corresponding to poles A and Ā. The defect in that way of considering things is that facts or objects corresponding to intermediary taxa are not taken into account. So it results from it a reasoning without nuances nor gradation, which proves to be maladapted to properly apprehend the diversity of human situations. Formally, dichotomous reasoning consists in taking into account only the elements of the reference class such as|d[Ei]| = 1, ord[E1] = 1 ord[E11] = -1, by ignoring all the others.

Fig. 2. Dichotomous reasoning

2.2 The disqualification of one of the poles

In the present model, the disqualification of one of the poles is the general cognitive distortion which leads to grant an arbitrary priority in one of the poles of a given duality, in order to qualify the elements of a reference class. It consists then in the fact of attributing more importance to one of the poles rather than to the other one, in the lack of objective motivation. The taxa corresponding to one of the poles of a given duality are lacking in the patient’s system of taxa. So, the patient sees things only through the prism of pole A (respectively Ā), by ignoring completely the viewpoint of the opposed pole Ā (respectively A). Formally, the disqualification of one of the poles leads to consider only the Ei such that d[Ei] ≤ (respectivelyd[Ei] ≥ 0), by ignoring any events such thatd[Ei] > 0 (respectivelyd[Ei] < 0).

Fig. 3. The disqualification of one of the poles

An instance of the disqualification of one of the poles consists in the disqualification of the positive. This last can be analysed, in the present context, as a specific instance of the disqualification of one of the poles, which applies to the Positive/Negative duality and to the reference class including the facts and events of the patient’s life. The patient tends then to ignore positive events, by considering that they do not count, for any reason. Such instance finds to apply in the cognitive therapy of depression.

Another instance of the disqualification of one of the poles also applies to the Positive/Negative duality and to the reference class which comprises the character’s traits of the patient. This one completely ignores his/her positive character’s traits (qualities) and only directs his/her attention to his/her negative character’s traits (defects). This encourages then him/her to conclude that he/she “is worth nothing”, that he/she is “a failure”. Such instance also applies in the cognitive therapy of depression.

2.3 Arbitrary focusing on a given modality

Another type of cognitive general distortion consists in arbitrary focusing on a modality of a given duality. In the present context, this type of general cognitive distortion leads to favour one taxon in the patient’s system of taxa, by ignoring all the others. In arbitrary focusing, the taxon being discussed is present in the patient’s system of taxa, and is affected to an unique element of the reference class. There is eclipsing (in general temporary) of others taxa and other elements of the reference class, so that the patient is haunted by this specific element.

Fig. 4. Arbitrary focusing

A particular instance of this type of general cognitive distortion, relates to the reference class of the facts of the patient’s life, and to the Positive/Negative duality. It is a specific cognitive distortion, which consists in focusing on a negative event of the patient’s life. It is then one of the classical cognitive distortions, defined as selective abstraction (Mental filter), which consists in the fact of choosing one detail with a negative connotation and to focalise on it. Suchlike, the patient sees only this detail, and his/her vision{view} of reality is darkened because it is entirely tinted with this particular event. Such instance applies in the cognitive therapy of depression.

One can also mention another instance of arbitrary focusing, which also applies to the Positive/Negative duality, but relates to the class of reference composed of the hypothetical future events of the patient’s life. In that case, the patient focalises on the possible happening of a very negative event. Such instance finds to apply in the cognitive therapy of generalised anxiety disorder.

Another specific instance of arbitrary focusing applies to the Nice/Ugly duality and to a reference class which identifies itself with all the parts of the patient’s body. The patient focalises then on a detail of his/her anatomy which he considers to be ugliness. The patient has well, in his/her system of taxa the Ugly taxon in question. Moreover, he/she affects this taxon to an unique part of his/her body, while all the others taxa are temporarily eclipsed. Such specific cognitive distortion finds to apply in the cognitive therapy of body dysmorphic disorder (Neziroglu and Yaryura-Tobias 1993, Veale and Riley 2001, Veale 2004).

2.4 The omission of the neutral

The present model also leads to predict the existence of another type of general cognitive distortion, which consists in the omission of the neutral. This latter cognitive distortion 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. Formally, the patient omits to consider the Ei such that d[Ei] = 0. 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.

Fig. 5. The omission of the neutral

2.5 The requalification in the other pole

The present model also leads to predict the existence of another type of general cognitive distortion. That is the reasoning which consists in re-qualifying an event belonging to a given duality A, in the other duality Ā. Formally, the subjective degree attributed by the patient to a given event E is the opposite of its objective degree, so that: D[E] = (-1) x d[E].

Fig. 6. The requalification into the other pole

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 patient’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 patient 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 patient notes that he/she made no act of violence. He/she considers this to be “suspect”. This type of instance also finds to apply within the cognitive therapy of depression.

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

2.6 Minimisation and maximisation

This general cognitive distortion consists in attributing to an element of the reference class, a taxon according to the criterion of a duality A/Ā which proves to be lower (minimisation) or greater (maximisation) than its objective value. It consists here of a classical cognitive distortion. The subjective degree D[E] which is attributed by the patient to an event E differs significantly from its objective degree d[E]. In minimisation, this subjective degree is distinctly less than, so that |D[E]| < |d[E]|. In maximisation, by contrast, the subjective degree is distinctly greater, such that |D[E]| > |d[E]|.

Fig. 7. Maximisation and minimisation

A specific instance of minimisation relates to the class of the facts of the patient’s life and to the Positive/Negative duality. The patient tends to consider certain facts of his/her existence as less positive than they in reality are. In maximisation, he/she considers certain facts of his/her life as more negative than they really are. In the present context, the classical cognitive distortion of catastrophism (or dramatisation) can be considered as a specific cognitive distortion, which consists of a maximisation applied to the negative pole of the Positive/Negative duality. The patient attributes then a subjective degree D[E] in the Positive/Negative duality to an event, while the absolute value of its objective degree d[E] is very distinctly lesser. Such instance applies to the cognitive therapy of depression.

3. Conclusion

As we see it, the present theory provides several elements, in comparison with classical theory, that allow to define and to classify the classical cognitive distortions, within the same conceptual framework. These last are considered, either as general cognitive distortions, or as specific cognitive distortions, i.e. as instances of the general cognitive distortions which relate to a given reference class and duality. Thus, dichotomous reasoning, maximisation and minimisation constitute general cognitive distortions. In addition, disqualification of the positive, selective abstraction, selective negative focus and catastrophism constitute then specific cognitive distortions. Besides, the present analysis allowed to describe two additional general cognitive distortions: the omission of the neutral and the requalification in the other pole.

References

Beck AT.: 1963, Thinking and depression: Idiosyncratic content and cognitive distortions. Archives of General Psychiatry 9, 324-333.

Beck AT.: 1964, Thinking and depression: Theory and therapy, Archives of General Psychiatry 10, 561-571.

Ellis A.: 1962, Reason and Emotion in Psychotherapy, Lyle Stuart, New York.

Neziroglu FA et JA. Yaryura-Tobias: 1993, Exposure, response prevention, and cognitive therapy in the treatment of body dysmorphic disorder. Behav Ther 24, 431-438.

Veale D et S. Riley: 2001, Mirror, mirror on the wall, who is the ugliest of them all? The psychopathology of mirror gazing in previous termbody dysmorphic disorder.next term. Behaviour Research and Therapy 39, 1381-1393.

Veale D.: 2004, Advances in a cognitive behavioural model of body dysmorphic disorder. Body Image 1, 113-125.

Viewpoint of a duality

Viewpoints relative to a given duality are viewpoints that concerne a given duality A/Ā.

For example, one can place oneself under the angle of the Static/Dynamic duality. Or, one can place oneself according to the point of view of the Absolute/Relative duality.

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


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

A Solution to the Doomsday Argument

doomsday

Un article publié en français dans the Canadian Journal of Philosophy Volume 28, Juillet 1998, pages 227-46.

Cet article présente une solution pour l’Argument de l’Apocalypse (DA). Je montre tout d’abord qu’il n’existe pas de critère objectif pour le choix en général d’une classe de référence: dans ce cas, le calcul inhérent à DA ne peut pas prendre place. En second lieu, j’envisage le choix particulier d’une classe de référence donnée, ainsi que Leslie le recommande. Mais le caractère arbitraire de la sélection rend légitime de multiples possibilités de choix, soit par extension, soit par restriction: DA peut alors être établi en particulier pour le genre Homo, pour l’espèce Homo sapiens, pour la sous-espèce Homo sapiens sapiens, … , pour une classe définie de manière restreinte correspondant aux humains n’ayant pas connu l’ordinateur, etc. Finalement, il apparaît que DA “fonctionne”, mais sa conclusion se révèle inoffensive.

The Doomsday Argument and Hempel’s Problem

Posprint in English (with additional illustrations from wikimedia commons) of a paper published in French in the Canadian Journal of Philosophy Vol.29, July 1999, pp. 139-56 under the title “Comment l’Urne de Carter et Leslie se Déverse dans celle de Hempel”.
I begin by describing a solution to Hempel’s Problem. I recall, second, the solution to the Doomsday Argument described in my previous Une Solution pour l’Argument de l’Apocalypse (Canadian Journal of Philosophy 1998-2) and remark that both solutions are based on a similar line of reasoning. I show thirdly that the Doomsday Argument can be reduced to the core of Hempel’s Problem.


This paper is cited in:

Koji Sawa, Junki Yokokawa and Tatsuji Takahashi (2013) Logical Equivalence: Symmetric and Asymmetric Features, Symmetry: Culture and Science, Vol. 24, No. x.

Milan M. Cirkovic, A Resource Letter on Physical eschatology, Am.J.Phys. 71 (2003) 122-133

Nick Bostrom, Anthropic Bias: Observation Selection Effects in Science and Philosophy, Routledge (2002)

Alasdair Richmond, The Doomsday Argument, Philosophical Books Vol. 47 No. 2 April 2006, pp. 129–142


The Doomsday Argument and Hempel’s Problem

Postprint – with additional illustrations from Wikimedia commons) – of a paper originally pubslihed in French in the Canadian Journal of Philosophy under the title « Comment l’urne de Carter et Leslie se déverse dans celle de Carter », vol. 29, March 1999, pages 139-156.

Paul Franceschi

I Hempel’s Problem

Hempel’s Problem (thereafter, HP) is based on the fact that the two following assertions:

(H) All ravens are black

(H’) Everything that is non-black is a non-raven

are logically equivalent. The logical structure of (H) is:

(H1) All X are Y

that is to say x (Xx  Yx), whereas that of (H’) has the form:

(H1′) All non-Y are non-X

Carl Gustav Hempel.jpg
Carl Hempel

that is to say x (~Yx  ~Xx). In fact, the structure of the contrapositive form (H1′) is clearly equivalent to that of (H1). It follows that the discovery of a black raven confirms (H) and also (H’), but also that the discovery of a non-black thing which is not a raven such as a pink flame or even a grey umbrella, confirms (H’) and thus (H). This last conclusion appears paradoxical. The propositions (H1) and (H1′) are based on four properties X, ~X, Y and ~Y, respectively corresponding to raven, non-raven, black, and non-black in the original version of HP. These four properties determine four categories of objects: XY, X~Y, ~XY and ~X~Y, which correspond respectively to black ravens, non-black ravens, black non-ravens and non-black non-ravens. One can observe here that a raven is defined with precision in the taxonomy within which it fits. A category as that of the ravens can be regarded as well defined, because it is based on a set of precise criteria defining unambiguously the species corvus corax and allowing the identification of its instances. It also appears that one can build without difficulty a version of HP where a variation with regard to the X class is operated. If one replace the X class with that of the tulips or that of the dolphins, etc. by adapting correlatively the Y property, one still obtains a valid version of HP. It appears thus that changes can be operated at the level of the X class without loosing the problem inherent to HP.

Corvus corax

Similarly, the black property can be specified with precision, on the basis of a taxonomy of colours established with regard to the wavelengths of the light.1 Moreover, one can consider variations with regard to the Y property. One will thus be able to choose properties such as whose length is smaller than 50 cm, living less than 10 years, etc. Such variations also lead to acceptable versions of HP. Lastly, it should be noted that the non-black property can be the subject of a definition which does not suffer from ambiguity, in particular with the help of the precise taxonomy of colours which has been just mentioned. Similarly, if one takes into account variations of the Y property such as smaller than 40 cm, or whose diameter is larger than 25 cm, etc, one arrives to definitions of the non-Y property which just as non-black are established with precision and lead in addition to versions of HP presenting the same problem as the original version. Thus, the X class, just as the properties Y and non-Y can be the subject of a precise and nonambiguous definition. Moreover, variations operated at the level of these classes lead to acceptable versions of HP. In contrast, the situation is not the same for the non-X class.

II The reference class Z

The concept of non-raven present in the original version of HP leads to highlight an important problem. What constitutes an instance of a non-raven? Intuitively a blue jay, a pink flame, a grey umbrella and even a natural integer constitute non-ravens. One is thus confronted with the definition of a new reference class – call it Z – including X and non-X. The Z class allows defining complementarily the class of non-X, and in the original version of Hempel, the class of non-ravens. Thus Z is the implicit reference class with regard to which the definition of the X class allows that of non-X. Does one have then to consider a Z class that goes until including abstract objects? Is it necessary to consider a concept of non-raven including abstract entities such as natural integers and complex numbers? Or is it necessary to limit oneself to a Z class, which only embraces concrete things? Such a discussion has its importance, because there are infinitely many abstract objects, whereas there are only finitely many individualised concrete objects. This fact is likely to influence later importantly the possible application of a bayesian reasoning. One could thus have a reference class Z including at the same time abstract objects (natural integers, real and complex numbers, etc.) and concrete objects such as artefacts but also natural entities such as humans, animals, plants, meteorites, stars, etc. Such a reference class is defined very extensively. And the consequence of such a choice is that the discovery of any object confirms (H’) and thus (H). At this stage, anything2 confirms (H). It should be noted that one can also have a definition of Z including all concrete objects that have been just mentioned, but excluding this time the abstract objects.

Larus audouinii

The instances of this class are now finitely denumerable, just as the cardinal of the corresponding set: the reference class Z then includes animals, plants, stars, etc. But alternatively, one could still consider a Z class associating the ravens (corvus corax) and the Audouin’s gulls3 (larus audouinii). In this case, the instances of the X class (corvus corax) are in a number larger than those of the non-X class (larus audouinii). And we always face the corresponding version of HP.4

Lastly, nothing seems to prohibit, at a very restrictive level, to choose a Z class made up of the X class, only added with one single element such as a red tulip. With this definition of Z, we still face a minimal version of HP. Of course, any object, added to the class of X and constituting the non-X class will be appropriate and then confirm at the same time (H’) and (H). Thus, any object ~X~Y will lead to confirm (H). The remarks which have just been made call however an immediate objection. With various degrees, it is allowed to think that the choice of each reference class Z that has been just mentioned is arbitrary. Because it is allowed to reject on those grounds extreme definitions of Z such as the one defined above and including all abstract objects. Similarly, a Z class including the natural integers or the complex numbers can also be eliminated. The X class is defined with regard to the concrete objects that are the ravens and there is not particular reason to choose a Z class including abstract entities.

A red tulip

Similarly, one will be able to reject a definition of Z based on a purely artificial restriction, simply associating with X a determinate object such as a red tulip. Because I can choose arbitrarily, the object that constitutes the complement of X, i.e. I can define Z as I wish. Such an extreme conception appears as without relationship with the initial definition of X. A Z class thus defined is not homogeneous. And there is no justification to legitimate the association of a red tulip to the class of the ravens to build that of Z. The association within a same Z class of the ravens and the Audouin’s gulls, appears analogously as an illegitimate choice. Why not then the association of the ravens and the goldfinches? Such associations are symptomatic of a purely artificial selection. Thus, the choices of reference classes Z mentioned above reveal an arbitrary and artificial nature. Indeed, shouldn’t one make one’s possible to find a Z class which is the most natural and the most homogeneous possible, taking into account the given definition of X? One can think that one must attempt to operate a determination of the Z class, which is the most objective possible. In the original version of HP, doesn’t the choice of the ravens for the X class implicitly determine a Z class which is directly in connection with that of the ravens? A Z class naturally including that of the ravens such as that of the corvidae, or that of the birds, seems a good candidate. Because such a class is at least implicitly determined by the contents of the X class. But before analysing versions of HP built accordingly, it is worth considering before some nonparadoxical versions of HP.

III The analogy with the urn

It is notoriously admitted that certain versions5 of HP are not paradoxical. Such is in particular the case if one considers a reference class Z associated with boxes, or a set of playing cards. One can also consider a version of HP associated with an urn. An X class is thus considered where the objects are finitely denumerable and which only includes balls and tetrahedrons. The Y class itself is reduced to two colours: red and green. One has thus four types of objects: red balls, green balls, red tetrahedrons and green tetrahedrons. In this context, we have the following version of HP:

(H2) All balls are red

(H2′) All non-red objects are non-balls

It appears here that the case of red tetrahedrons can be ignored. Indeed, their role is indifferent and one can thus ignore their presence in the urn. They can be regarded as parasitic objects, whose eventual presence in the urn does not have importance. One is thus brought to take into account an urn containing the significant objects consisting in red balls, green balls and green tetrahedrons. And the fact that non-red objects can only be green, and that non-balls can only be tetrahedrons leads to consider equivalently:

(H3) All balls are red

(H3′) All green objects are tetrahedrons

that clearly constitutes a nonparadoxical version of HP. Indeed, the draw of a red ball confirms (H3) and (H3′) whereas the draw of a green tetrahedron confirms (H3′) and (H3).

Consider now the case where the urn contains six significant objects.6 One has just drawn three red balls and one green tetrahedron (the draw is 3-0-17) and one makes then the hypothesis (H3). At this stage, the probability that all balls are red corresponds to three draws (3-0-3, 4-0-2 and 5-0-1) among six possible draws (3-0-3, 3-1-2, 3-2-1, 4-0-2, 4-1-1, 5-0-1). Similarly, the probability that all green objects are tetrahedrons is identical. Thus, P(H3) = P(H3′) = 1/2 and also P(~H3) = P(~H3′) = 1/2. These initial probabilities being stated, consider now the case where one has just carried out a new draw in the urn. Another red ball is drawn (the draw is 4-0-1). This corresponds to three possible compositions of the urn (4-0-2, 4-1-1, 5-0-1). Let E be the event consisting in the draw of a red ball in the urn. We have then the probability of drawing a red ball if all the balls of the urn are red, i.e. P(E, H3) such as P(E, H3) = 2/3, since two cases (4-0-2, 5-0-1) correspond to the fact that all balls are red. In the same way, P(E, ~H3) = 1/3. The situation is identical if one considers P(E, H3′) and P(E, ~H3′). One is then in a position to calculate the posterior probability that all balls are red using Bayes formula: P'(H3) = [P(H3) X P(E, H3)] / [P(H3) X P(E, H3) + P(~H3) X P(E, ~H3)] = (0,5 X 2/3) / (0,5 X 2/3 + 0,5 X 1/3) = 2/3. And P'(~H3) = 1/3. There are identical results concerning P'(H3′) and P'(~H3′). Thus, P'(H3) > P(H3) and P'(H3′) > P(H3′), so that the hypothesis (H3) just as the equivalent hypothesis (H3′) are confirmed by the draw of a new red ball.

Let us examine finally the situation where, instead of a red ball, one draws a green tetrahedron (the draw is 3-0-2) in the urn. Let thus F be the event consisting in the draw of a green tetrahedron. In this case, we have three possible combinations (3-0-3, 3-1-2, 4-0-2). But among these, two (3-0-3, 4-0-2) correspond to a situation where hypotheses (H3) and (H3′) are confirmed. Thus, P(F, H3) = P(F, H3′) = 2/3 and P(F, ~H3) = P(F, ~H3′) = 1/3. A bayesian calculation provides the same results as on the preceding hypothesis of the draw of a red ball. Thus, on the hypothesis of the draw of a green tetrahedron, one calculates the posterior probabilities P'(H3) = P'(H3′) = 2/3 and P'(~H3) = P'(~H3′) = 1/3. Thus, the draw of a green tetrahedron confirms at the same time (H3′) and (H3). It should be noted that one can easily build versions of HP allowing to establish nonparadoxically the preceding reasoning. Consider a cubic mineral block of 1m on side. Such an object of 1m3 is divided into 1000 cubic blocks of 1 dm3, consisting either of quartz, or of white feldspar. One examines fifty of these blocks, and one notes that several of them consist of white feldspar of gemmeous quality. One is brought to make the hypothesis that all blocks of white feldspar are of gemmeous quality. We have then the following version of HP:

(H4) All blocks of white feldspar are of gemmeous quality

(H4′) All blocks of non-gemmeous quality are not white feldspar

that is equivalent to:

(H5) All blocks of white feldspar are of gemmeous quality

(H5′) All blocks of non-gemmeous quality are quartz

where we have in effect the equivalence between (H5) and (H5′) and where a correct bayesian reasoning can be established. Such an example (call it the mineral urn) can also be transposed to other properties X and Y, since identical conditions are preserved.

IV A solution to the problem

One must, taking into account the above developments,8 attempt to highlight a definition of the Z class that does not present an arbitrary and artificial nature, but proves on the contrary the most natural and the most homogeneous possible, with regard to the given definition of X. Consider accordingly the following9 version of HP:

(H6) All Corsican-Sardinian goshawks have a wingspan smaller than 3,50 m

(H6′) All birds having a wingspan larger than 3,50 m are not Corsican-Sardinian goshawks

In this particular version of (H’), the X class is that of the Corsican-Sardinian goshawks,10 and the reference class Z is that of the birds. This last class presents an obvious relationship with that of the Corsican-Sardinian goshawks. It is allowed to think that such a way of defining Z with regard to X is a natural one. Indeed such a definition does not present an arbitrary nature as obviously as that was the case with the examples of Z classes mentioned above. Of course, one can observe that it is possible to choose, in a more restricted but so natural way, a Z class corresponding to the accipiter genus. Such a class presents a homogeneous nature. It includes in particular the species accipiter gentilis (northern goshawk) but also accipiter nisus (European sparrowhawk), accipiter novaehollandiae (grey goshawk), accipiter melanoleucus (black and white goshawk).

Accipiter gentilis

However, alternatively and according to the same viewpoint, one could also extend the Z class to the instances of the – wider – family of accipitridae11 including at the same time the accipiter genus which have been just mentioned, but also the milvus (kite), buteo (buzzard), aquila (eagle), etc. genus. Such a class includes in particular the species milvus migrans (black kite), milvus milvus (red kite), buteo buteo (common buzzard), aquila chrysaetos (golden eagle), etc. These various acceptable definitions of the Z class find their justification in the taxonomy within which the Corsican-Sardinian goshawk inserts itself. More systematically, the latter belongs to the subspecies accipiter gentilis arrigonii, to the species accipiter gentilis, to the accipiter genus, to the family of accipitridae, to the order of falconiformes, to the class of birds, to the subphylum of vertebrates, to the phylum of chordates,12 to the animal reign, etc. It ensues that the following variations of (H’) are acceptable, in the context which has just been defined:

(H7′) All northern goshawks having a wingspan larger than 3,50 m are not Corsican-Sardinian goshawks

(H8′) All goshawks having a wingspan larger than 3,50 m are not Corsican-Sardinian goshawks

(H9′) All accipitridae having a wingspan larger than 3,50 m are not Corsican-Sardinian goshawks

(H10′) All falconiformes having a wingspan larger than 3,50 m are not Corsican-Sardinian goshawks

(H11′) All birds having a wingspan larger than 3,50 m are not Corsican-Sardinian goshawks

(H12′) All vertebrates having a wingspan larger than 3,50 m are not Corsican-Sardinian goshawks

(H13′) All chordates having a wingspan larger than 3,50 m are not Corsican-Sardinian goshawks

(H14′) All animals having a wingspan larger than 3,50 m are not Corsican-Sardinian goshawks

There are thus several versions of (H’) corresponding to variations of the Z class which themselves are made possible by the fact that the Corsican-Sardinian goshawk belongs to n categories, determined by the taxonomy to which it belongs. And in fact, when I meet one northern goshawk belonging to the nominal form (accipiter gentilis gentilis), it is at the same time a northern goshawk (accipiter gentilis) non- Corsican-Sardinian (non-accipiter gentilis arrigonii), a goshawk (accipiter) non-Corsican-Sardinian goshawk, an accipitridae non-Corsican-Sardinian goshawk, a falconiformes non-Corsican-Sardinian goshawk, a bird (aves) non-Corsican-Sardinian goshawk, but also a vertebrate non-Corsican-Sardinian goshawk, a chordate non-Corsican-Sardinian goshawk, an animal non-Corsican-Sardinian goshawk. Thus, the instance of accipiter gentilis gentilis that I have just observed, belongs at the same time to all these categories. And when I meet a grey whale, it is not a bird non-Corsican-Sardinian goshawk, but it is indeed a vertebrate non-Corsican-Sardinian goshawk, as well as a chordate non-Corsican-Sardinian goshawk, and also an animal non-Corsican-Sardinian goshawk.

In general, a given object x which has just been discovered belongs to n levels in the taxonomy within which it fits. It belongs thus to a subspecies, 13 a species, a sub-genus, a genus, a super-genus, a subfamily, a family, a super-family, a subphylum, a junction, a reign… One can assign to the subspecies the level14 1 in the taxonomy, to the species the level 2…, to the super-family the level 8, etc. And if within (H), the class X is at a level p, it is clear that Z must be placed at a level q such as q > p. But how to fix Z at a level q which is not arbitrary? Because the reference class Z corresponds to a level of integration. But where must one stop? Does one have to attach Z to the level of the species, the sub-genus, the genus…, the reign? One does not have an objective criterion allowing the choice of a level q among the possibilities that are offered. I can choose q close to p by proceeding by restriction; but in a so conclusive way, I am authorised to choose q distant from p, by applying a principle of extension. Then why choose such class of reference restrictively defined rather than such other extensively defined? One does not have actually a criterion to legitimate the choice, according to whether one proceeds by restriction or by extension, of the Z class. Consequently, it appears that the latter can only be defined arbitrarily. And it follows clearly here that the determination of the Z class and thus of the non-X class is arbitrary. But the choice of the reference class Z appears fundamental. Because according to whether I choose such or such reference class Z, it will result from it that a given object x will confirm or not (H). For any object x, I can build a Z class such as x belongs to non-X, as I can choose a Z class such as x does not belong to non-X. Thus, this choice is left to my arbitrary.

For a given object x, I can build a Z class such as this object confirms (H) and another Z class such as this object does not confirm (H). Of course, if Z is selected arbitrarily, the bayesian reasoning inherent to HP “works”, but corresponds to an arbitrary and artificial point of view: having found an object x, (H) is confirmed. But one can as well choose, in a so artificial and more restrictive way, a Z class where x misses and where x does not confirm (H). Thus, one is not enabled to conclude objectively that the discovery of the object x confirms (H). Because to reason thus would amount to conferring a universal and general value to a viewpoint which is only the expression of an arbitrary choice.

How this result can be reconciled with the facts mentioned above,15 concerning the existence of nonparadoxical versions of HP? It is worth noting here that the bayesian reasoning can be established in each case where the Z class is finite, and where this fact is known before the experiment.16 One can then show a bayesian shift. But at this stage, it is worth distinguishing the cases where the Z class is determined before the experiment by an objective criterion and the cases where it is not the case. In the first case, the contents of the Z class are given before the experiment and the Z class is thus not selected arbitrarily, but according to an objective criterion. Consequently, the bayesian reasoning is correct and provides relevant information. Such is in particular the case when one considers a version of HP applied to an urn, or a version such as the mineral urn. On this last hypothesis, the composition of the Z class is fixed in advance. There is then a significant difference with Nicod’s criterion:17 an object ~X~Y confirms (H) and an object XY confirms (H’).

Conversely, when the Z class is not fixed and is not determined before the experiment by an objective criterion, one can subjectively choose Z at any level of extension or restriction, but the conclusions resulting from the bayesian reasoning must be regarded as purely arbitrary and do not present thus an objective value. Because one then does not have a base and a justification to choose such or such level of restriction or extension. Thus, in this case, Nicod’s criterion according to which any object ~X~Y is neutral with respect to (H) and any object XY is neutral with respect to (H’), can apply itself. It should be observed that the present solution has the effect of preserving the equivalence of a proposition and its contraposition. And similarly, the principle of the confirmation of a generalisation by each of its instances is also preserved.

V A common solution to Hempel’s Problem and the Doomsday Argument

The Doomsday Argument (thereafter, DA) attributed to Brandon Carter, has been described by John Leslie (1992).18 DA can be described as follows. Consider an event A: the final extinction of the human race will occur before year 2150. One can estimate at 1 chance from 100 the probability that this extinction occurs: P(A) = 0,01. Let also ~A be the event: the final extinction of the human race will not occur before 2150. Consider also the event E: I live during the 1990s. In addition one can estimate today at 50 billions the number of humans having existed since the birth of humanity: let H1997 be such a number. In the same way, the current population can be evaluated to 5 billions: P1997 = 5×109. One calculates thus that one human from ten, if event A occurs, will have known the 1990s. The probability that humanity is extinct before 2150 if I have known the 1990s, is thus evaluated: P(E, A) = 5×109/5×1010 = 0,1. On the other hand, if the human race passes the course of the 2150s, one can think that it will be destined to a much more significant expansion, and that the number of humans will be able to rise for example to 5×1012. In this case, the probability that the human race is not extinct after 2150 if I have known the 1990s, can be evaluated as follows: P(E, ~A) = 5×109/5×1012 = 0,001. This now makes it possible to calculate the posterior probability of the human race extinction before 2150, using Bayes formula: P'(A) = [P(A) x P(E, A)] / [P(A) x P(E, A) + P(~A) X P(E, ~A)] = (0,01 x 0,1) / (0,01 x 0,1 + 0,99 x 0,001)  0,5025. Thus, the fact of taking into account the fact that I live currently has made the probability of the human race extinction before 2150 shift from 0,01 to 50,25.

640px-Dmanisi-D3844._Homo_erectus_or_Homo_georgicus
Homo erectus’ skull (photo by Ryan Somma)

I have presented in my paper ‘Une Solution pour l’Argument de l’Apocalypse’19 a solution to DA, whose main lines can be described as follows. The DA reasoning is based on a single reference class, which is that of the humans.20 But how this reference class has to be defined? Should it be limited to the only representatives of our current subspecies Homo sapiens sapiens? Or does one have to extend it to all the representatives of the species Homo sapiens, by including this time, in addition to Homo sapiens sapiens, Homo sapiens neandertalensis…? Or is it necessary to include in the reference class the entire Homo genus, including then all the successive representatives of Homo erectus, Homo habilis, Homo sapiens, etc? And isn’t it still necessary to go until envisaging a wider class, including all the representatives of a super-genus S, made up not only of the Homo genus, but also of the new genus Surhomo, Hyperhomo, etc. which will result from the foreseeable evolutions from our current species? It appears thus that one can consider a reduced reference class by proceeding by restriction, or apprehend a larger class by making the choice of a reference class by extension. One can thus operate for the choice of the reference class by applying either a principle of restriction or a principle of extension. And according to whether one applies one or the other principle, various levels of choice are each time possible.

But it appears that one does not have an objective criterion, which makes it possible to legitimate the choice of such or such a reference class. And even our current subspecies Homo sapiens sapiens cannot be regarded as a natural and an adequate choice for the reference class. Because isn’t it allowed to think that our paradigmatic concept of human has to undergo evolutions? And in addition, the fact of excluding from the reference class a subspecies such as Homo sapiens neandertalensis or the future evolutions of our species, doesn’t it reveal an anthropocentric viewpoint? Since one does not have an objective selection criterion, one can choose arbitrarily one or the other of the classes that have been just described. One can for example identify the reference class to the species Homo sapiens, and observe a bayesian shift. There is indeed then an increase in the posterior probability of the extinction of Homo sapiens. But this bayesian shift is worth as well for a still more restricted reference class, such as our subspecies Homo sapiens sapiens. There too, the application of Bayes formula leads to an appreciable increase in the posterior probability of the nearest end of Homo sapiens sapiens. However identically, the bayesian shift also applies to a still more reduced reference class, which is that of the representatives of Homo sapiens sapiens having not known the computer. Such a reference class will certainly face a nearest extinction. There however, such a conclusion is not likely to frighten us, because the evolutionary potentialities of our species are such that the succession of a new species to those which preceded them, constitutes one of the characteristics of our evolution mode.

It should be mentioned that this solution leads here to accept the conclusion (the bayesian shift) of Carter and Leslie for a given reference class, while placing it in comparison with conclusions of comparable nature relating to other reference classes, completely inoffensive. The fact of taking into account various levels of restriction, made legitimate by the lack of an objective criterion of choice, leads finally to the harmlessness of the argument. Thus, it appears that the argument based on the reference class and its arbitrary choice by restriction or extension constitutes a common solution to HP and DA. HP and DA are ultimately underlain by the same problem inherent to the definition of the Z class of HP and the single reference class of DA. One thus has a solution of comparable nature for the two paradoxes. It is worth here concluding by presenting an element that tends to confirm the common source of the two problems. One will observe first that one is not able to highlight a version of DA corresponding veritably to the original version of HP, a reference class such as that of the ravens being not transposable in DA. The inherent argument in DA is indeed based on the use of the anthropic principle and requires obviously a reference class made up of intelligent beings. When Leslie21 considers the extension of the reference class, he specifies expressly that the condition for the membership of the reference class is the aptitude to produce an anthropic reasoning. On the other hand it is possible to describe a version of HP made up from the elements of DA. If one takes X for our current subspecies Homo sapiens sapiens and Y for are alive only before 2150, one obtains the following version of HP:

(H15) All Homo sapiens sapiens will be alive only before the year 2150

(H15′) All those which will live after 2150 will be non-Homo sapiens sapiens

In this context, an alive human being in 1997 constitutes an instance confirming (H15). In parallel, the discovery of an Homo sapiens sapiens after 2150 leads to refute (H15). Lastly, the discovery of an alive non-Homo sapiens sapiens after 2150 constitutes a confirmation of (H15′) and thus of (H15). Taking into account this particular formulation, it is clear that one currently only observes instances confirming (H15). On the other hand, after 2150, one will be able to have instances refuting (H15) or instances confirming (H15′).

It is worth noting here that (H15) does not allow veritably to be used as support of a version of DA. Indeed, the reference class identifies itself here precisely as Homo sapiens sapiens, whereas in the original version of DA, the reference class consists in the human race. Consequently, one has not, strictly speaking, an identity between the event underlie by (H15) and A, so that (H15)-(H15′) does not constitute a joint version22 of DA and HP.

But this version of HP being made up with the elements of DA, one must be able, at this stage, to verify the common origin of the two problem, by showing how the argument raised in defence of DA with regard to the reference class, can also be used in support of HP. One knows the response made by Leslie to the objection that the reference class for DA is ambiguous or, due to the evolutions of Homo sapiens sapiens, leads to a heterogeneous reference class, of composite nature. It is exposed in the response made to Eckhardt:

How far should the reference class extend? (…) One can place the boundary more or less where one pleases, provided that one adjusts one’s prior probability accordingly. Exclude, if you really want to, all future beings with intelligence quotients above five thousand, calling them demi-gods and not humans23.

and developed in The End of the World24:

The moral could seem to be that one’s reference class might be made more or less what one liked. (…) What if we wanted to count our much-modified descendants, perhaps with three arms or with godlike intelligence, as ‘genuinely human’? There would be nothing wrong in this. Yet if we were instead interested in the future only of two-armed humans, or of humans with intelligence much like that of humans today, then there would be nothing wrong in refusing to count any others25.

For Leslie, one can go until including in the reference class, the descendants of humanity become very distant from our current species due to the fact of evolution. But Leslie also accepts liberally that one limits the reference class to the only individuals close to our current humanity. One is thus free to choose the reference class that one wishes, while operating either by extension, or by restriction. It will be enough in each case to adjust the initial probability accordingly. It appears here that this type of answer can be transposed, literally, to an objection to HP of comparable nature, based on the reference class of (H15)-(H15′). One can fix, so the objection goes, the Z class as one wishes, and assign to “all those” the desired content. One can for example limit Z to the species Homo sapiens, or well associate it to the whole of the Homo genus, including then the evolutions of our species such as Homo spatialis, Homo computeris, etc. What is important – could continue this defender – is to determine preliminarily the reference class and to conserve this definition when the various instances are then met. Thus, it proves that the arguments advanced in support of the reference class of DA can be transposed in defence of HP. This constitutes an additional element, going in the direction of the common origin of the two problems, dependent on the definition of a reference class. DA and HP need consequently a same type of answer. Thus, the urn of Carter and Leslie flows in that of Hempel.26

References

ECKHARDT, W. 1993. “Probability Theory and the Doomsday Argument.” Mind, 102 (1993): 483-8
FRANCESCHI, P. 1998, “Une Solution pour l’Argument de l’Apocalypse.” Canadian Journal of Philosophy, 28 (1998): 227-46
GOODMAN, N. 1955. Fact, Fiction and Forecast. Cambridge: Harvard University Press.
HEMPEL, C. 1945. “Studies in the logic of confirmation.” Mind, 54 (1945): 1-26 et 97-121
LESLIE, J. 1992. “Time and the Anthropic Principle.” Mind, 101 (1992): 521-40
—. 1993. “Doom and probabilities.” Mind, 102 (1993): 489-91
—. 1996. The End of the World: the science and ethics of human extinction. London and New York: Routledge.
PAPINEAU, D. 1995. “Methodology: the Elements of the Philosophy of Science.” In Philosophy A Guide Through the Subject, ed. A.C. Grayling. Oxford: Oxford University Press.
SAINSBURY, M. 1988. Paradoxes. New York: Cambridge University Press.
THIBAULT, J-C. 1983. Les oiseaux de Corse. Paris: De Gerfau.

1 It is known that a monochromatic light, of single wavelength, meets practically only in laboratory. But the natural colours can be modelled in terms of subtraction of lights of certain wavelengths, starting from the white light of the Sun.

2 Any object ~X~Y in the Z class thus extensively defined.

3 The total population of Audouin’s gulls is evaluated with approximately 3000 couples (cf. Thibault 1983, 132).

4 This incidentally makes it possible to verify that HP does not find its origin in a disproportion of the X class compared to that of the non-X. The fact that the instances of the X class are in a number larger than those of the non-X does not prevent the emergence of a version of HP.

5 Properly speaking, these are not thus versions of HP, since they are nonparadoxical. But the corresponding propositions have the logical structure of (H) and (H’).

6 The red tetrahedrons possibly found in the urn are regarded as nonsignificant objects.

7 With the notation: npq (red balls – green balls – green tetrahedrons).

8 Cf. § II.

9 This particular version of HP is chosen here because it is based on an X class corresponding to the subspecies accipiter gentilis arrigonii. Conversely, the original version of HP is grounded on the species corvus corax. The choice of a subspecies for the X class allows simply here a supplementary level of integration.

10 The Corsican-Sardinian goshawks (accipiter gentilis arrigonii) constitute a subspecies of the northern goshawk, specific to Corsica and Sardinia. This endemic subspecies differs from the nominal form of the northern goshawk by the following characteristics (cf. Thibault 1983): the colouring of the head is blackish instead of brown blackish; the back is brown; the lower part is darker.

11 The ornithologists still distinguish the class of the accipitriformes, corresponding to all accipitridae, to which are added the pandlionidae, such as pandlion haliaetus (osprey), etc.

12 The phylum of chordata includes all vertebrates and some invertebrates, which present the property of having a dorsal chord, at least at a given period of their life.

13 It is possible to consider alternatively, if one wishes, another taxonomy that our current scientific taxonomy. That does not affect the current reasoning, since the conclusions are identical, since the principles of classification are respected.

14 It is obviously possible to take into account finer taxonomies and including additional subdivisions starting from the various subspecies. Obviously, that does not affect the current line of reasoning.

15 Cf. § III.

16 As we have seen, the bayesian reasoning cannot take place when one considers a Z class including infinite sets such as natural integers, real numbers, etc.

17 Nicod’s criterion is defined as follows (Hempel 1945, 11), with S1 = (H) and S2 = (H’): ‘(…) let has, B, C, D Be furnace objects such that has is has raven and black, B is has raven goal not black, C not has raven goal black and D neither has raven NOR black. Then, according to Nicod’ S criterion, has would confirm S1, goal Be neutral with respect to S2; B would disconfirm both S1 and S2; C would Be neutral with respect to both S1 and S2, and D would confirm S1, goal Be neutral with respect to S2.’

18 John Leslie, ‘Time and the Anthropic Principle.’ Mind, 101 (1992): 521-40.

19 Canadian Journal of Philosophy 28 (1998) 227-46.

20 Leslie uses the terms of human race.

21 ‘How much widening of the reference class is appropriate when we look towards the future? There are strong grounds for widening it to include our evolutionarily much-altered descendants, three-armed or otherwise, as ‘humans’ for doomsday argument purposes – granted, that’s to say, that their intelligence would remain well above the chimpanzee level.’ (1996, 262)

22 I.e. comprising simultaneously the two problems.

23 W. Eckhardt, ‘Probability Theory and the Doomsday Argument.’ Mind, 102 (1993): 483-8; cf. John Leslie, ‘Doom and probabilities.’ Mind, 102 (1993): 489-91

24 This point of view is detailed by Leslie, in the part entitled ‘Just who should count have being human?’ (The End of the World, 256-63).

25 Cf. Leslie (1996, 260).

26 I thank two anonymous referees for the Canadian Journal of Philosophy for their comments, concerning an earlier draft of this paper.

Paradigmatic Analysis of a Corpus of Proverbs with the help of Matrices of Concepts

A paper appeared in French in Semiotica, 2007, vol. 167, pp. 271-282 under the title “Analyse paradigmatique d’un corpus de proverbes à l’aide des matrices de concepts“.

In On a Class of Concepts (2002), I presented a theory based on matrices of concepts which aims to constitute an alternative to the classification proposed by Greimas, in the field of paradigmatic analysis. I proceed here to apply the matrices de concepts to the analysis of a corpus made up of Corsican proverbs.

An analysis of French word ‘très’

According to our analysis, the word ‘très’ is likely to occur in the following grammatical types:

  • Adjective modifier: here, ‘très’ modifies the meaning of an adjective: très beau (very beautiful, biddisimu), très content (very happy, cuntentissimu)
  • Adverb modifier: ‘très’ here modifies the meaning of an adverb: ‘très rarement’ = very rarely, raramenti; ‘très souvent’ = very often, mori à spessu
  • Adverb (i.e. in our terminology, a Verb modifier): ‘very’ modifies here the meaning of a verb: ‘j’ai très faim’ = I am very hungry, t’aghju mori fami; ‘il avait très soif’ = he was very thirsty, t’aia mori seti: where the verb is here the verbal locution ‘avoir faim’ = to be hungry, avè a fami; avoir soif = to be thirsty, avè a seti

Leaving ambiguity unresolved

Disambiguation is an essential process in machine translation. Sometimes, however, it seems more rational and logical to leave an ambiguity in the translation. This is the case when (i) there is an ambiguous word in the sentence to be translated; and (ii) the context does not provide an objective reason to choose one of the two occurrences. It seems that in this case, the best translation is the one that leaves the ambiguity intact.

Let’s take an example. Consider the following French sentence: ‘Son palais était en feu.’. The French word ‘palais’ is ambiguous, because it corresponds in English and in Corsican to two different words (palace, palazzu and palate, palatu).

Thus, we have 3 possibilities of translation:

  • His palate was on fire
  • His palace was on fire
  • His palace/palate was on fire

The third translation, in my opinion, is better, because it points out that the context is insufficient to choose one of the two alternatives.

Consider now, on the one hand, the following sentence: ‘Il avait mangé du piment fort. Son palais était en feu.’ Now the context provides an objective motivation to choose one of the two occurence. This yields the following translation: He had eaten some hot pepper. His palate was on fire.

On the other hand, consider the following sentence: ‘Les ennemis du prince avaient lancé des engins incendiaires. Son palais était en feu.’ We also have here an objective reason to choose the other alternative. It translates then: The prince’s enemies had thrown incendiary devices. His palace was on fire.

Dictionary = Corpus?

As far as machine translation is concerned, it seems that the best thing is to combine the best of the two approaches: rule-based or statistic-based. If it were possible to converge the two approaches, it seems that the benefit could be great. Let us try to define what could allow such a convergence, based on the two-sided grammatical approach. Let us try to illustrate this with a few examples.
To begin with, u soli sittimbrinu = ‘le soleil de septembre’ (the sun of September). In Corsican language, sittimbrinu is a masculine singular adjective that means ‘de septembre’ (of September). In French, ‘de septembre’ is–from an analytic perspective–a preposition followed by a common masculine singular noun. But according to the two-sided analysis ‘de septembre’ (of September) is also–from a synthetic perspective–a masculine singular adjective. This double nature, according to this two-sided analysis of ‘de septembre’, allows in fact the alignment of ‘de septembre’ (of September) with sittimbrinu.
More generally, if we define words or groups of words according to the two-sided grammatical analysis in the dictionary, we also have an alignment tool, which can be used for a translation system based on statistics, in the same way as a corpus. Thus, if it is sufficiently provided, the dictionary is also a corpus, and even more, an aligned corpus.

Grammatical taxonomy again: the case of prepositions

Let’s look at the translation of the word ‘whose’. Depending on the case, ‘whose’ can be a

  • relative pronoun: ‘la difficulté dont je t’ai parlé’ (the difficulty I told you about), ‘voilà le professeur dont j’apprécie beaucoup les cours’ (this is the teacher whose classes I really enjoy.)
  • or, more rarely, a preposition: ‘il y avait cinq couleurs, dont le rouge et le bleu’. (there were five colours, including red and blue.)

It is the latter case that we will be looking at. In this case, ‘dont’ is translated into English as ‘including’. In Corsican, the translation is: c’eranu cinque culori, frà i quali u rossu è u turchinu. But if we translate ‘il y avait cinq plantes, dont le ciste et la bruyère’ (‘there were five plants, including cistus and heather’), we get: c’eranu cinque piante, frà e quale u muchju è a scopa. Thus the translation of ‘dont’ (including) as a preposition is either frà i quali (masculine plural, culore being masculine in Corsican) or frà e quale (feminine plural), depending on which noun ‘dont’ refers to.

Thus ‘dont’ is translated into the masculine plural or the feminine plural, depending on the noun – either masculine or feminine – to which it refers. This casts doubt on the ‘prepositional’ nature of ‘dont’, and leads to further analysis to determine whether there might not be a more suitable grammatical type.

It is worth noting that ‘dont (including) can be replaced by ‘parmi lequels’ (among which, frà i quali) or ‘parmi lesquelles’ (among which, frà e quale) depending on whether the noun to which ‘whose’ refers is in the masculine plural or the feminine plural. This suggests that ‘whose’ could be conceived of as a preposition followed by a pronoun. In the spirit of this analysis, the BDL site notes: ‘Dont’ is probably the relative pronoun whose use is the most delicate. To use it correctly, one must know that dont always ‘hides’ the preposition ‘de’; ‘dont’ is equivalent to ‘de qui’, ‘de quoi’, ‘duquel’, etc. This link between ‘dont’ and ‘de’ goes back to the Latin origin of ‘dont’, which is from ‘unde’ “from where”.

More generally, this suggests that further analysis of some prepositions may be needed.

Creating new grammatical types

Italian has ‘prepositions followed by articles’ (preposizione articolate). This is a specific grammatical type, which refers to a word (e.g. della) that replaces a preposition (di) followed by an article (la):

	il	lo	l’	la	i	gli	le
di	del	dello	dell’	della	dei	degli	delle
a	al	allo	all’	alla	ai	agli	alle
da	dal	dallo	dall’	dalla	dai	dagli	dalle
in	nel	nello	nell’	nella	nei	negli	nelle
su	sul	sullo	sull’	sulla	sui	sugli	sulle

This specific grammatical type also corresponds to:

  • in French: du = de le, des = de les
  • in Corsican and especially in the Sartenese variant: ‘llu = di lu, ‘lla = di la, etc.

This raises the general problem of the number of grammatical types we should retain. Should we create new grammatical types beyond the classical ones, in order to optimise translators and NLP in general? What is the best grammatical type to retain for ‘prepositions followed by an article’: a new primitive one or a compound one (always keeping Occam’s razor in mind)? A preposition followed by an article behaves like a preposition for words on its left, and like an article for words on its right.

Evaluation of the performance after changes

Just performed a series of open tests, using the (pseudo-random) article of the day from wikipedia in French.The results are the following, concerning the Taravese version of the Corsican language:
95,76
95,76
94,34
95,76
99,25
95,04
95,48
that is to say an average of about 95%, taking into account that the ‘cismuntinca’ version generally obtains a slightly lower result, because of the masculine and feminine plurals which are different (whereas they are identical in Taravese).

Grammatical word-disambiguation again and again

The main difficulty here seems to lie in the adaptation of the grammatical disambiguation module. Indeed, for the French language, such a module performs disambiguation with respect to about 100 categories. The number of pairs (or 3-tuples, 4-tuples, etc.) of disambiguation, for French, is about 250. The question is: when we change languages, how many categories of n-tuples of disambiguation does this result in? In particular, when one switches from French to Italian, does this result in a big change in the categories to be disambiguated?

Let’s take an example, with a particular category of words to disambiguate. One such category is for example AQfs/Vsing3present (feminine singular adjective or verb in the 3rd person singular present tense). A word in Italian that belongs to this type is ‘stanca’. So we have both uses:

  • ‘è stanca’ (she is tired): AQfs
  • stanca il cavallo’ (it tires the horse): Vsing3present
    In French, we don’t have this kind of disambiguation category directly because the category concerned is broader than that: it includes at least the 1st person singular of the present. Thus we have the word ‘sèche’, which belongs to this type of disambiguation category:
  • ‘la feuille est sèche’ (the leaf is dry): AQfs
  • ‘je sèche mes cheveux’ (I dry my hair): Vsing1present
  • ‘il sèche sa chemise’ (he dries his shirt): Vsing3present

Of course, the code that allows the disambiguation of AQfs/Vsing1present/Vsing3present should also allow the derivation of the disambiguation of AQfs/Vsing3present. But this gives an idea of the kind of problems that arise and the adaptation needed.

If the types of disambiguation are very different from one language to another, it will be necessary to have a disambiguation module which is capable of adapting to many new types of disambiguation and which is therefore very flexible. This appears to be a considerable difficulty for the creation of an eco-system. It seems that Apertium, faced with this difficulty, has chosen a statistical module as a solution for its eco-system. However, the question of whether such a flexible module, adaptable without difficulty from one language to another, is feasible in the context of rule-based MT, remains an open question.

First feasability test: dictionary morphing

The first test carried out to transform the dictionary (in the extended sense) based on the French-Corsican pair, into a dictionary related to the Italian-Gallurian pair, shows that it is feasible. The result – of an acceptable but perfectible quality – is obtained in 21 minutes (with 16 GO RAM & Intel core i7-8550U CPU). We start with a multi-lingual dictionary based on French entries, and the final result is an Italian-Gallurese dictionary.

Translation from Italian to Gallurese

Our new project will be to try to implement the translation from Italian into Gallurese. For this is an essential pair for the Gallurese language, which is a priority. The major difficulty in doing this is:
– on the one hand, to (automatically) transform the dictionary (in the extended sense) based on the French-Corsican pair, into a dictionary related to the Italian-Gallurese pair
– on the other hand, to implement automatically (without having to rewrite them entirely) the other modules, and in particular the one based on grammatical disambiguation.

The stakes here seem high. It is a question of transforming a system that can translate one pair of languages (i.e. French into Corsican) into an eco-system that can translate several pairs of languages (the target language of which being an endangered language).

Adjective modifiers again

We will consider again a category of words such as ‘very’, when they precede an adjective. Traditionally, this category is termed ‘adverbs’ or ‘adverbs of degree’, but we prefer ‘adjective modifier’, because (i) analytically, they change the meaning of an adjective and (ii) synthetically, an adjective modifier followed by an adjective is still an adjective. A more complete list is: almost, absolutely, badly, barely, completely, decidedly, deeply, enormously, entirely, extremely, fairly, fully, greatly, hardly, highly, how, incredibly, intensely, less, most, much, nearly, perfectly, positively, practically, pretty, purely, quite, rather, really, scarcely, simply, somewhat, strongly, terribly, thoroughly, totally, utterly, very, virtually, well.

If we look at sentences such as: il est bien content (he is very happy, hè beddu cuntenti), ils étaient bien contents (they were very happy, erani beddi cuntenti), elle serait bien contente (she would be very happy, saria bedda cuntenti), elles sont bien contentes (they are very happy, sò beddi cuntenti), we can see that the modifier of the adjective ‘bien’ is rendered as very in English and in Corsican as:

  • bellu/beddu: singular masculine
  • belli/beddi: plural masculine
  • bella/bedda: feminine singular
  • belle/beddi: feminine plural

This shows that the adjective modifier is invariable in French and English, but varies in gender and number in Corsican. Thus, in Corsican grammar, it seems appropriate to distinguish between:

  • singular masculine adjective modifier
  • plural masculine adjective modifier
  • singular feminine adjective modifier
  • plural feminine adjective modifier

On the other hand, such a distinction does not seem useful in English and French, where the category of ‘adjective modifier’ is sufficient and there is no need for further detail.