Abstract
We will deal here only with the presupposition of existence of the assertion by adopting a pragmatic approach. Our subject will thus be to report logically this operation of presupposition of existence and to consider a pragmatic solution to the Fregeo-Russellian problem of the failure of the precondition of existence. We propose, by using the trivalent logic of Dmitrii Bochvar, to construct a logic of the presupposition of existence for assertions.
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Notes
- 1.
On Russell’s complex treatment of existence, see [17], pp. 51–87.
- 2.
The “existence” at stake here is the logical kind which assumes only that a domain of application provides an individual value which satisfies the predicate in question, ∃x(Hx) → Ha. Depending on the domain, this individual may be a number, an empirical object, a star, a fictional character, etc. In this purely logical sense, we would say that Odysseus exists. Rules of universal and existential instantiation are therefore subject to conditions of existence, so we have [∃x(Hx) • E!a] → Ha. In contrast, free logics allow for individual variables that may not refer to any individual in the domain; see [5].
- 3.
Note that the definition of existence of Principia Mathematica *10.01 (∃x)Fx =Df ¬(x)¬Fx supposes (as does the rest, in fact) that we assume the existence of at least one individual; see [8], Intro. Chap. 1, p. 20.
- 4.
See [4], p. 33. “Daher ist es uns auch gleichgültig, ob der Name ‘Odysseus’ z. B. eine Bedeutung habe, solange wir das Gedicht als Kunstwerk aufnehmen. Das Streben nach Wahrheit also ist es, was uns überall vom Sinn zur Bedeutung vorzudringen treibt.” The primary distinction between sense and reference allows us to consider objects which have no denotation but do have a sense, such as “The least rapidly convergent series,” ibidem, p. 28. Such objects are simple “Bilder,” p. 109:
- 5.
See [11] p. 20. and also p. 20 in which Strawson discusses the opposition between two approaches – falsity theory and truth-value gap theory – and concludes that both are defensible but that the second “is apt to seem more intuitively attractive in some instances than it does in others,” ibidem, p. 71. Strawson’s example has the merit of reminding us that the presupposition of existence also applies to questions – as well as all other types of illocutionary acts. As our focus here is on the logical square, we are dealing only with assertions. However, we note that from a dialogue perspective, a question is first of all a proposal made by the speaker to the addressee who, in turn, must validate it as “interact” as an effectively asked question or on the contrary an unasked one, disqualifying its illocutionary value. On the concept of “interact,” see [13], Chap. 8, § 4.
- 6.
See also [18], 6.5, “Zu einer Antwort, die man nicht aussprechen kann, kann man auch die Frage nicht aussprechen. Das Rätsel gibt es nicht. Wenn sich eine Frage überhaupt stellen läßt, so kann sie Auch beantwortet werden,” p. 114. Pragmatically, answering a loaded question consists in challenging the presupposition it contains.
- 7.
This symbol’s form is meant to highlight the shift from the implicit to the explicit. Note that here we deal the presupposition of existence of the subject of the assertion, and not the general pragmatic presupposition operator.
- 8.
- 9.
This spelling is the simplification of the character wu which means, inter alia, “absence” and which is used as a response in some Zen Buddhist gong’an (kōans in Japanese), such as “A monk asked Joshu: ‘Does a dog have Buddha-nature?’. Joshu replied: ‘Does a dog have Buddha-nature?’ This is the most important question of all. If you answer yes or no, you lose your own Buddha nature.”
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Vernant, D. (2022). Existential Presupposition and Logical Square. In: Béziau, JY., Desclés, JP., Moktefi, A., Pascu, A.C. (eds) Logic in Question. Studies in Universal Logic. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-94452-0_27
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