The Role of Truth-Values in Indirect Meanings

The present study was supported by the Russian Science Foundation; project Nr 16-18-10202. The authors would like to express their gratitude for those who have helped them in their study, especially to Elena Chepel, Eleonora Khudoshina, Elena Ludilova, and Nadezhda Panchenko.

In our previous article [35], we have shown this, among others, with a demonstration borrowed in the so-called theorem of Putnam [45]. Putnam’s result in his demonstration by contradiction of the untenability of the Fregean semantics (Putnam’s example: the sentence “a cat on a mat” is true if and only if there is a cherry on a tree) ceases to be absurd if we replace, in his demonstration, the Montague intentions with the meaning lines: there could be a metaphorical sense in what this result is meaningful, e.g., if Cherry is a name of a cat. This fact proves that the meaning lines are not possible in the Fregean semantics where the denotation of a sentence is its truth-value. Therefore, the meaning lines belong to situational semantics, where the denotation of a sentence is the situation it refers to. We have demonstrated further that, in the case of indirect meanings, this semantics is similar to the situational semantics by Roman Suszko (cf. [54]) but even weaker. Moreover, the so-called “metaphorical logic” proposed by Vladimir Vasjukov [57] for formalising the ontology by Alexis Meinong is applicable to the poetical tropes of the natural language. If Hintikka and Sandu are right in insisting that the sentences containing indirect meanings and those that do not have the same formal semantics (we agree with them on this point), then, the semantics of natural language as a whole is non-Fregean and situational. See Appendix for a more formal summary.

We can consider this nick as a metaphor regardless of its possible usage as a personal name of a pet, because, in the case of the cat called Cherry, the metaphor is certainly not dead, in contrast with so-called dead metaphors such as “hot dog”.

“Impossible world” is a kind of possible worlds where are broken the logical laws that are presumed to be in force in this world.

Here we avoid a discussion of semantics of natural language in general and a detailed distinction between direct and indirect meanings. In our previous paper [35], we have briefly discussed incompatibility of Hintikka—Sandu’s approach with the Fregean semantics of natural language (in the wake of Richard Montague and David Lewis), despite their own intention to overcome a “crisis” in this discipline.

Cf. his hypothetical “Thesis of Extensionality” [8, pp. 245–247].

Unless humour and jokes become a constituent part of the therapist’s technics, serving, most often, to reduce patient’s paranoid sadistic impulses and aggression. In such cases, humour and jokes are used for restoring patient’s personality (transforming the transference-countertansference relationship between him and the therapist). If this succeeds, the patient starts to realise the humoristic nature of therapist’s words. For a discussion of this complicated matter, s. [4].

In his 1927 article “Humour” (“Der Humor”) [16]. For placing the Freudian psychoanalytic approach to the humour into the context of the 20^th-century interdisciplinary humour studies, s. [38].

For a larger than Freudian psychoanalytic approach to the humour, s. [41]. This approach, inspired, in a large part, by Ignacio Matte Blanco, could be the most interesting for a logician.

From his 1905 book “Jokes and their relation to the unconscious” (“Der Witz und seine Beziehung zum Unbewußten”) [17, p. 120].

The corresponding chapter is entitled “Freud’s Rhetoric and Symbolics” [56, pp. 247–254].

Cf. a detailed and rich monograph [6].

This Grice’s seminal paper has been written in 1967 and first published in 1975; cf. also its 1987 continuation [23, pp. 53–54].

Ralph Müller [40] provides a concise introduction to the problem, albeit without any specific logical theories and attention to the truth-values either. Salvatore Attardo [3] implies a cognitive (Lakoff-styled) theory of metaphor, which undermines its interest to our purpose.

Ivan Panaev’s poem Будто из Гейне (As if from Heine), a parody on the Russian poetical translations from and imitations of Heinrich Heine. With the music by N. D. Dmitriev (1848)—which Panaev himself called “beautiful” in 1855,—it became a famous romance Густолиственных кленов аллея… (The alley of thick-foliage maples…), and this despite its obviously humoristic wording, alliterations, and paronomasias. Paradoxically, as a parody, the poem was unusually successful: it “killed” (as contemporary critics said) the epigonous lyrics it was aimed at. See, for the text and a commentary, [26, pp. 650, 1040]. We are grateful to Eleonora I. Khudoshina for having pointed us out this story.

Story I, 12 [44, pp. 105–111].

For an orientation in the ocean of literature on the riddle by folklorists and anthropologists, s., e.g., [1]. The most of this literature could be of only tangential interest for a logician. Among the recent most comprehensive studies, s. especially those of Savely Senderovich [52, 53].

In the most archaic structures of riddle, there are not two but three situations involved, thus establishing the transworld connexion between three possible worlds; cf. more on them below, Sect. 8.

[55, pp. 203.26–204.2]: αἰνίγματός τε γὰρ ἰδέα αὕτη ἐστί, τὸ λέγοντα ὑπάρχοντα ἀδύναται συνάψαι· κατὰ μὲν οὖν τὴν τῶν ἄλλων ὀνομάτων σύνθεσιν οὐχ οἷόν τε τοῦτο ποιῆσαι, κατὰ δὲ τὴν μεταφορῶν ἐνδέχεται.

Beside Senderovich’s monorgaphs [52, 53], the most interesting, from a logical point of view, is the chain of three articles [5, 27, 37] by Ian Hamnet, who elaborated the topic on the role of inconsistency and ambiguities in various kinds of human interaction, not only the riddles. He specified, moreover, that the kind of ambiguity involved here is not vagueness but indetermination: it results not from lack of specification, as vagueness, but because the text or ritual “fails to indicate which of two (or more) references is intended, though each possible reference may be fairly specific in itself” [27, p. 383]. In this way, Hamnet distinguished, even though without strict logical terminology, between the subcontrary and contrary oppositions, stating that only the first is involved in the archaic rituals, riddles etc.

We will quote the first publication [15]; cf. French and German translations [13, 14].

Who does not mention [15] in his [52, 53].

“…вопрос загадки и ее ответ суть тавтологии, но построенные таким образом, что обе тавтологические части разнонаправлены (по крайней мере на поверхностном уровне): разведение этих двух структур на максимально возможное расстояние не только «скрывает» аспект тождества, но и представляет собой своего рода аналог выведения смысла мира вовне или, точнее, удержание предельно большого расстояния между смыслом (ответом загадки) и вопросом о нем, в других терминах — сохранение такого максимального напряжения между тавтологическими членами, когда сама тавтологичность предельно скрыта” [15, pp. 16–17]. “Из этого принципа вытекает, что, по сути дела, решением загадки должен считаться не просто ответ (загадка вообще менее всего связана с угадыванием и импровизацией, но со знанием и искусством его порождения), а ответ как свернутый знак всей процедуры экспликации скрытого тождества обеих частей загадки” [15, p. 38, n. 7]. The passage starts in the main texts and continues in an endnote, but we do not interrupt the textual flow in our translation.

See, for details, [27, 52, 53].

See Martin Gardner’s note 5 to ch. 7 in [9, pp. 71–73]. Lewis Carroll himself wrote about his answer (ibid.): “This, however, is merely an afterthought; the Riddle, as originally invented, had no answer at all.” Our question is whether this “at all” means to be absolute (ontological) or merely epistemological.

For the transworld meaning lines, we can postulate a specific (im)possible world, where the meaning lines belonging to the “anti-humour” of type (2) do not exist.

Cf. a comparative study of several hermeneutic traditions: [58].

Origen, On the Principles, books III and IV; cf., on this feature of the traditional Christian exegesis, Henri de Lubac’s studies, starting from [11].

For the use in the exegesis, s. [22].

For a logical analysis, s. especially [48‐50].

In the context of the present paper, the most relevant literature on Sarbiewski are [19, 30, 34, 43].

For the sake of brevity, we apply, in Table 1, truth-values “true” and “false” to the situations and the relations, taking in mind that they are applicable to the propositions that describe situations and relations.

For a detailed explanation, s. [35].

See, for a detailed bibliography, [12].