Logical mechanisms of tabooing discourse

Abstract

The paper presents the semantic model of logical content processing in the environment of tabooed sentences. Such sentences occur both in academic and colloquial discourses. They can be interpreted as infected formulas with the value of an insult. The proposed model assumes that the inferential mechanism of argumentative activities realised in discourses in the environment of such formulas is based on Bochvar's logical matrices and Kripke’s possible worlds semantic structures. This mechanism is determined by semantic consequence operators of three types. The presented theory can be viewed as a formal tool for reconstructing the logical mental mechanism which stops deductive actions aiming at the development of narrative worlds in discourse practices during epistemic wars. It postulates that these practices, which occur in processes of developing science, are governed by special logical mechanisms of inference.

KEYWORDS:

• Consequence operators
• Bochvar’s matrix
• epistemic wars
• infectious logic
• taboo

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 The author of this article was accused in academic disciplinary proceedings for publicly presenting arguments during logic classes in favour of the conclusion that female breasts are functionally used for sex rather than for feeding infants. The author referred to the facts that in his country, on average, a woman gives birth to 1.5 children, which determines the lactation period of about 2 years. This number clearly contrasts with the average length of women's sexual activity. A disciplinary case against the author was initiated at the request of a left-wing member of the Polish parliament. One can imagine a situation that in the future, publishing this type of logically correct argumentation on the Internet will be algorithmically banned by AI systems due to violating certain taboos. Ideological guards will then not have to take actions on the discourse aimed at punishing participants who violate the taboo. Artificial intelligence systems will be able to do this for them. They will be able to play the role of ideological guards, consisting in controlling the political correctness of produced discourses. Therefore, the aim of this text is to initiate a discussion among logicians on the risk of implementing taboo logical mechanisms into AI systems.

2 The phenomenon of forbidding language users, under a penalty, to express certain meanings or refer to various fragments of reality is known as a linguistic taboo. Currently, the number of scientific papers on taboos in various research contexts can be estimated at several hundred items. Linguists point out that the taboo phenomenon appears in the use of euphemisms and dysphemisms (Allan & Burridge, 2006, pp. 29–54; Allan, 2018; Pedraza Pizarro, 2018), in swearing and slurring (Jay & Janschewitz, 2008; Croom, 2011; Croom, 2014; Allan, 2015; Archer, 2015), and in derogatory speech (Hom, 2010). Other studies concern the ways of expressing taboo meanings or the ways of referring toward tabooed reality. Here are some examples: sexual preferences (Crespo-Fernández, 2018), homophobia (Sabatini, 2018), gender or sex (De Klerk, 1992; Crespo-Fernández, 2019), menstruation (Agyekum, 2002; Crespo-Fernández, 2019), death and diseases (Wildfeuer et al., 2015), ageing (Benczes et al., 2018), political correctness (Haslanger, 2010; Anderson et al., 2012), ideology (Humphfrey, 2005; Allan, 2019), and others. The taboo phenomenon is multidimensional.

3 Masterman (1970) distinguishes at least twenty-one different meanings of the term ‘paradigm’ used by Kuhn in The Structure of Scientific Revolutions. Shapere (1964) asserts that the notion of a paradigm is vague, mysterious, and too general. Kuhn (1974) agreed that he had used the term too widely. The category of the paradigmatic level of discourses, used in this article, refers to the meta-beliefs that instruct scholars on how to construct axioms and hypotheses, deductively or hermeneutically derive theorems, establish facts empirically, interpret them, and justify or reject theories, concepts, hypotheses, theorems, and even descriptions of facts. The paradigmatic level of theory also includes axiological instructions that determine both the hierarchy of research tasks and the area of what is forbidden in scientific and humanities research (mental censors).

4 The title of Andrew Dickson White’s book (1896), A History of the Warfare of Science with Theology in Christendom directly indicates that the phenomenon of paradigmatic wars was noticed in the 19th century. A little earlier, Draper (1875) wrote: ‘Religion must relinquish that imperious, that domineering position which she has so long maintained against Science. There must be absolute freedom for thought. The ecclesiastic must learn to keep himself within the domain he has chosen, and cease to tyrannise over the philosopher, who, conscious of his own strength and the purity of his motives, will bear such interference no longer’ (p. 367). Perhaps the first spectacular paradigmatic war was a conflict between the Pythagoreans and the proponents of irrational geometric objects. Legend has it that Hippasus of Metapontum was expelled from the Pythagorean League for publicly stating that the length of the diagonal of a square is an irrational number, and then punished by the gods with death in a shipwreck. Serres (1982, p. 129) comments on this legend: ‘The authors of this legend wanted to speak through allegory. Everything that is irrational and deprived of form must remain hidden, that is what they were trying to say. That if any soul wishes to penetrate this secret region and leave it open, then it will be engulfed in the sea of becoming, it will drown in its restless currents'. A historically documented case of paradigm warfare is the condemnation of Galileo by the Holy Office which prohibited him from maintaining, defending, and teaching heliocentric astronomy. Galileo's writings on heliocentrism were included in the Index of banned books. In Poland, K. Łyszczyński was decapitated in 1689 for uttering sentences about the chimerical nature of God in his treatise De non existentia dei (Skoczyński & Woleński, 2010, p. 126; Nowicki, 1989). Kołakowski (1976, pp. 136–142) asserts, that under Stalinism, in the Soviet Union, the ideological guardians of Leninism denounced scientists as enemies of the people, the state, and the party for claiming that simultaneity is not absolute from the point of view of the theory of relativity or for supporting the Copenhagen interpretation of quantum mechanics. The practice of hunting taboo breakers consisted in searching for sentences in texts, inconsistent with the Stalinist interpretation of Leninism. Such incorrigible authors were often subject to police bashing and dismissal from their positions at work. A current example of a paradigm war in the scientific discourse is the conflict between the defenders and opponents of the hypothesis saying that the Covid-19 vaccination is effective. Publications of opponents of this hypothesis are often banned from social media sites. Some doctors questioning the effectiveness of the Covid-19 vaccine have been fired from their jobs in many countries. The defenders of this hypothesis are also attacked by its opponents using, for example, hate speech. Such practices can be interpreted as establishing oppositional language taboos. A drastic example of the tabooing of artistic discourse is the death sentence of the poet Ashraf Fayadh for apostasy and preaching atheism in 2015 in Saudi Arabia. Earlier, for the same reasons, Khomeini imposed a fatwa on the writer Salman Rushdie.

5 Classical logic cannot be used to check the correctness of mathematical inferences in which there are formulas which lose meaning because they are composed of terms that do not make sense for certain values of variables. This situation is revealed in mathematical theories, where functions are defined conditionally, and they do not satisfy the condition of existence and uniqueness for some numbers (Hałkowska, 1979; Hałkowska, 1989). Mathematical formulas which contain functional terms that do not meet this condition are understood as having no truth value, as having a truth value gap, or as neither false nor true. The inferential properties of such formulas are studied in the framework of nonsense logics (Halldén, 1949; Åqvist, 1962; Segerberg, 1965; Piróg-Rzepecka, 1977; Hałkowska, 1979). Based on this approach, logicians construct semantic models for nonsense logics that, in certain circumstances, allow for the logical correctness of inferences, in which there occur nonsensical formulas with truth value gaps.

6 The question of the truth conditions of derogatory speech is widely discussed in philosophy. Regarding this problem, the following positions can be distinguished: expressivism, externalism, and inferentialism. Each of them has its own different versions (Hom, 2010; Anderson et al., 2012; Anderson & Lepore, 2013a, 2013b; Hedger, 2012, 2013; Jeshion, 2013; Croom, 2014; Lycan, 2015). The problem of the logical correctness of inferences involving derogatory expressions is not considered in detail. Even the inferentialists do not address the question of the logical correctness of derogatory inferences. They claim, following Dummett, that the meanings of slurs are determined by non-logical, fine-grained rules of their use (Whiting, 2008, 2013; Williamson, 2009; Macagno & Rossi, 2021).

7 If the proponents of their world give up defending a tabooed sentence because of an attack by opponents, then they will construct a new world. For example, if Galileo rejected the theorem The Earth revolves around the Sun in his theory, he would have constructed a geocentric world. Metaphorically speaking, he would have found himself in a different world. Goodman (1978) was perhaps the first to pose the question of distinguishing between versions of the world. Is the world where a point is defined as the intersection of two straight lines in the same plane a version of the world where a point is defined as the intersection of a plane by a straight line in three-dimensional space? Similarly, in physics one can ask: is the world in which rest motions are only normal motions (the world of Aristotelian physics) the same world in which rest motions and, additionally, uniformly rectilinear motions are normal motions (world of Newtonian physics)? If Newton rejected Aristotle's assumption that motion at rest fall under the category of normal motion, would such a kinetic theory construct a version of the world described by the theory he actually created, or would it construct a different world? Fortunately, the statement that motion at rest belongs to the category of normal motion was not tabooed in Newton's time. It was in line with Aristotle's vision of the Absolute as the first immovable mover, which was often invoked by Thomists of the time.

8 The value 1/2 in Bochvar’s matrices is interpreted in different ways. Besides understanding it as nonsense or off- topic, logicians propose interpretations of this value in the spirit of phenomenological and Meinongian ontologies (Woodruff, 1970, pp. 121–122). For example, a sentence has logical value 1/2 when its logical subject is a term denoting the so-called non-existent objects, or a sentence has a logical value 1/2 when it attributes the accidental property to the content of the idea (Kaczmarek, 2003). Phenomenologists assume that irreal objects (golden mountains, pegasi, heroes from novels, and ideas) are indeterminate in terms of certain content. They have ontic gaps. Sentences in which such content is predicated of such objects have the logical value 1/2. Therefore, logicians call this way of understanding the value 1/2 gappy interpretation (Beall, 2016). From this perspective, the practice of tabooing could be defined as the activity of attributing peculiar ontic gaps to objects. Penalties for breaking taboos would appear as penalties for filling ontic gaps with forbidden content.

Additional information

Funding

This work was supported by Narodowe Centrum Nauki: [grant no 2016/21/B/HS1/00821].