Abstract
We use here the analytical tools of contemporary logic and pragmatics to propose a study of veridicity , seen as the set of all attitudes expressed by a speaker about the truthfulness of what he/she is saying. Combining the logical operators that bear on propositional content (affirmation and negation) with the pragmatic operations (asserting, considering, denying, estiming), we construct an axiomatic system (as alternative interpretation of hexagon of opposition) with its syntactical and semantical presentations. Such a system provides a formal structure !formal that holds not only for veridictional speech acts, but also for the belief attitudes associated with them.
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- 1.
The acts in question are directives, commissives, and declaratives; see Vernant (1997, Chap. III).
- 2.
See my article, Vernant (2005a, Chap. XIII, pp. 267–288).
- 3.
- 4.
See my article (Vernant 2006).
- 5.
D. Vanderveken’s illocutionary logic introduces illocutionary denial for all types illocutionary acts; see Searle and Vanderveken (1985, pp. 74, 152–155). Here, I will deliberately confine my analysis solely to Denial as a veridictional operator opposing Assertion . One can thus consider my veridictional pragmatics as part of general illocutionary logic. This is why I will use its operators whenever possible. But I will make use of a system (equivalent to modal system T) that is less powerful than the one (S5) employed by illocutionary logic (T ⊂ S5).
- 6.
I use this term to refer to “expressing an opinion about”. It is closely tied to judgment, but in natural language, its “expressive” dimension remains implicit.
- 7.
Ockham had already made the distinction between judgment (assent or dissent) and simple apprehension, which he named neutral proposition: “Someone can apprehend a proposition and yet not give it one’s assent or dissent, as is patent with neutral propositions”, De Ockham (1979, I, prol. qu. 1, p. 16). Recall also that in the traditional disputatio, three attitudes were possible: concedo, nego, dubito.
- 8.
The reader will find my axiomatization of the relations between the veridictional operators in the Appendix of my Vernant (2009).
- 9.
We get the excluded quarter: (A ∨ D ∨ C).
- 10.
\(\vartriangleright \) is the symbol for illocutionary commitment between two acts; see Searle and Vanderveken (1985, Chap. IV, p. 81): “\(A_{1} \vartriangleright A_{2}\) iff it is not possible for the speaker to realize A 1 without being committed to A 2”. This relation is reflexive, non-anti-symmetric, and transitive; see p. 141. ≈ is the symbol for congruence of two illocutionary acts; see Searle and Vanderveken (1985, Chap. IV, p. 82): “Two illocutionary acts are congruent iff each one commits the speaker to the other”. This equivalence relation is definable: A 1 ≈ A 2 iff \(A_{1} \vartriangleright A_{2}\) and \(A_{2} \vartriangleright A_{1}\) (where A is any illocutionary act).
- 11.
It does not hold for exclusive negation, which means we do not have \(A\mathbf{P} \vartriangleright DD\mathbf{P}\).
- 12.
This axiomatic system includes axioms for proving theorems and counter-axioms for proving counter-theorems. Regarding this bipolarity, see Vernant (2010a).
- 13.
Of course, pragmatic assertion is the illocutionary act of a given speaker, which does not imply the truth, and all the less so, the validity of the proposition in question. It is not to be confused with logical assertion (demonstration) as defined by Russell and Frege, nor with what can be regarded as established, i.e., proven. This latter interpretation is the one that Jean de La Harpe adopted in (1950, pp. 26–31).
- 14.
This corresponds to what Karl Otto Apel called “pretension to truth” (Apel 1994, p. 46).
- 15.
Here we find Russell’s “Principle of assertion ” (see our article “The Limits of a Logical Treatment of Assertion”). Unlike epistemic !epistemic logic, which poses the question of omniscience \([K\mathbf{P}\&(\mathbf{P} \rightarrow \mathbf{Q})] \rightarrow K\mathbf{Q}\), there is no risk of omnidiction here since we do not have to assert all of the consequences of our assertions: \(\neg \{[\vdash \mathbf{P}\&(\mathbf{P} \rightarrow \mathbf{Q})]\vartriangleright \vdash \mathbf{Q}\}\).
- 16.
To simplify my presentation, I will not bring to bear the rules and counter-rules of transformation.
- 17.
As we shall see in the next section, a more sophisticated formalization that incorporates the speaker is possible; it gives us A a p.
- 18.
Unlike Searle, who ignores the specificity of metadiscursives and unduly classifies “I assert that it’s raining” among the assertives; see Searle (1982, p. 61).
- 19.
Daniel Vanderveken, who formalized Searle’s theory, relies on a system equivalent to modal system S5; see Vanderveken (1990).
- 20.
Here, any illocutionary act is a proposal made by the speaker to the addressee, a proposal that must be negotiated to give rise to a jointly assumed “interact”; see Vernant (1997, Chap. VIII) and Vernant (2009, Chap. X, Sect. 4.1.1).
- 21.
Formally, a Model is any triplet < W, S, V > in which W is a proposed set of discursive worlds W 0, W 1, …; R is the accessibility relation, which is reflexive (x)(xRx) and thus serial (x)Ez(xRz); and V is the function that attributes the values {1, 0}. V (A) thus reads as follows: For all P and W i , V (A P, W i ) = 1 if for all W j such that W i RW j , V (P, W j ) = 1, else V (A P, W i ) = 0. Likewise, V (I) reads: for all P and W i , V (I P, W i ) = 1 if for at least one W j such that W i RW j , V (P, W j ) = 1, else V (I P, W i ) = 0.
- 22.
- 23.
The counter-position corresponds to the formula ¬A → E, which is not included in our axiomatic system since it is equivalent to the inclusive disjunction: A ∨ E.
- 24.
For greater clarity, I again use letters of the alphabet to symbolize veridictional acts.
- 25.
The strictly epistemic dimension can only intervene in the framework of our Dialogical Logic of Veridicity , Vernant (2010b) which accounts for agreement (or disagreement) about the truth in question. Knowledge is necessarily dialogically mutualized.
- 26.
On this crucial distinction, see Vernant (2009, Chaps. I and VII).
- 27.
See \(R1:\vdash \mathbf{P} \Rightarrow \vdash A\mathbf{P}\), where \(\vdash \) is the metalogical symbol for deduction and A, that of the act of assertion .
- 28.
This praxiological dimension is analyzed in Vernant (2009, Chap. XI).
- 29.
See Vernant (1997, Chap. IV).
- 30.
See Vernant (1997, Chap. VIII) and Vernant (2009, Chap. X, Sect. 4.1.1.1).
- 31.
By themselves, assertions are pure abstractions. An assertion assumes a particular function in a dialogue only as a response, a reply, an inquiry, a questioning, etc. See Vernant (2009, Chap. IX).
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Vernant, D. (2014). Pragmatics of Veridicity. In: Rebuschi, M., Batt, M., Heinzmann, G., Lihoreau, F., Musiol, M., Trognon, A. (eds) Interdisciplinary Works in Logic, Epistemology, Psychology and Linguistics. Logic, Argumentation & Reasoning, vol 3. Springer, Cham. https://doi.org/10.1007/978-3-319-03044-9_11
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