I. Semantics vs. pragmatics

Bulletin of the Section of Logic Volume 14/4 (1985), pp. 150–155 reedition 2007 [original edition, pp. 150–157]

Marek Tokarz

GOALS, RESULTS AND EFFICIENCY OF UTTERANCES Abstract This is an abstract of a lecture read at the Logic Symposium, Sofia, October 1985.

I. Semantics vs. pragmatics Suppose that we are given two objects, L and U, the first being a set, called the set of declarative sentences of some language L, the second being a poset, U = < U, ≤>, elements of which are called situations. If a ≤ b, a, b ∈ U , we say that situation a is a part of situation b. (We do not pay much attention on what a situation exactly is. It is enough for our purposes that the specialists do know that: the theory of situations is well developed nowadays.) Of all aspects of logic, the semantics is one interested in functions O : L → U, which assign to each declarative sentence of L a situation of U. Where α ∈ L, O(α) is supposed to be the fact (situation) described by α; O(α) is said to be the objective of α. From the point of view of pragmatics the objective of a sentence is not absolute. It depends on the circumstances, i.e., on the situation in which the sentence is uttered. Thus pragmatics is interested in functions O : U → U L. For a ∈ U, α ∈ L, Oa (α) is then the objective of α, provided that the speaker used α in situation a.

Goals, Results and Efficiency of Utterances

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Example. L = {d I am thirstye }, U = < {a, b, c, d, . . .}, ? >, a = the situation consisting in that the speaker is M. Tokarz, b = the situation consisting in that the speaker is R. W´ojcicki, c = the situation consisting in that M. Tokarz is thirsty, d = the situation consisting in that R. W´ojcicki is thirsty. Then: Oa (d I am thirstye ) = c; Ob (d I am thirstye ) = d.

II. Results To begin with our subject let us observe that in the standard pragmatic approach sketched above there is no room, unfortunately, for some evidently pragmatic phenomena connected with speech acts. One of them is that uttering a sentence, we not only describe a situation, but also create a new one. Utterances have not only their objectives, but also, and always, their results. If I talk to John about Mary and say: “She doesn’t love you at all, she loves me”, the objective of the sentence is simply the situation that Mary loves Marek Tokarz, but not John. Still the result of the sentence may be very complex: the utterance considered might make John buy a gun, or a knife, or some poison to kill me, or Mary, or both, or to kill himself. Or he would drank to death, or he would come back to his wife – depending on many components of the situation. Being interested in results, we are relived from reflection on whether the sentences under question are true. Even uttering a tautology, say “May be she loves you, may be she doesn’t”, may have non-trivial consequences. What is more, the objectives are assigned not to all sentences, while all the utterances, commands, questions etc., have some results. Let us thus suppose that the considered language L is the union L ∪ L∗ of two sets: of declarative and non-declarative sentences, respectively. If the situation in which some α ∈ L is uttered can be ignored, the result of α is denote by R(α); and otherwise it is Ra (α) – the situation which arises when α is uttered in situation a. The function R is similar in type to O: R : L → U, or, “more pragmatically”: R : U → U L.

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III. Intentions In the real life, if we speak, we always intend to cause some special situation. For example, my wife says: “It is awfully raining”, intending to make me stay home, or to take the umbrella; or a poet writes “Why the cucumber does not sing?” intending to shock the reader. We may assume that the intended result is always to be described by a declarative sentence, which is no more than the assumption that we think in the language. Thus we may say α, intending to cause a situation described by β; in such a case we simply want O(β) to be R(α); exactly speaking, we want O(β) to be at least a part of R(α): O(β) ≤ R(α). The intended result, or the goal, of a speech act is one story, and the actual result is another. May be the speaker does secure his object, may be he does not. Clearly, as we all know, intentional locutions are sometimes effective, sometimes they are not; as an example consider the sentence “Lend me money!” with the obvious goal that the listener lends me money. And in this way the problem of intentions (goals) leads to the analysis of efficiency.

IV. Efficiency ’ On the ground of what was said till now we con realize that an intentional, or goal-oriented, locution is no longer a single sentence. It is more like a pair of sentences < α, β >∈ L × L, where α is the expression just uttered and β describes the goal the speaker wants to be realized. The notion of a model for the intentional language L × L was also intuitively described above: it should consist of a structure of situations U = < U, ≤> and of two functions: O and R, where O : L → U, R : L → U . Models of the form P = < U; O, R > will be called basic models. An intentional locution z = < α, β >∈ L × L is effective in the model P, in symbols EP (z), if O(β) ≤ R(α). The class of all basic models is denoted by B. Example. Let us consider an intentional language L × L such that L = L ∪ L∗ , L∗ = {α}, L = {β}, where


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α =d How many roads must a man walk down before you can call him a man?”e , β =d Somebody makes me know how many roads must a man walk down before you can call him a mane . Let us further consider a structure of situations U = < U, ≤> such that U = {a, b, c, d}, }, where a = the situation consisting in that somebody makes me know how many roads must a man walk down before you can call him a man, b = the situation that Dostoyevsky makes me know how many roads must a man walk down before you can call him a man, c =the situation that everybody considers me an idiot, d =? Let us finally put P1 = < U; O, R1 >, P2 =< U; O, R2 >, where O(β) = a, R1 (α) = b, R2 (α) = c, R1 (β) = R2 (β) = d. Then the locution < α, β > is effective in P1 and not in P2 . In basic models neither the objectives nor the results depend on the situation in which locutions are performed. A more realistic sort of models are pragmatic ones. By a pragmatic model we mean any triple of the form P = < U, O, R >, where U = < U, ≤> is a poset, O : U → U L , R : U → U L . An intentional locution z = < α, β >∈ L × L is effective in the pragmatic model P in a (z), if Oa (β) ≤ Ra (α). The class of all situation a ∈ U , in symbols EP pragmatic models is denoted by P.

V. Logic The logic of intentional locutions must differ from the usual one, for, as was already said, where goals are dealt with, the problem of truth is inessential according to plan. It is the efficiency alone that we are interested in. It is easy to observe that there should be no tautology in our system: for no locution is absolutely effective, i.e., effective in any circumstances. The

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system of logic of goal-oriented locutions should describe the intentional entailment; it should tell us which sentences are effective provided that some other are effective. Let P be a basic model and let X ⊆ L × L. Then EP (X) abbreviates “for every < α, β >∈ X, EP (< α, β >)”. For P being pragmatic, the a meaning of EP (X) is analogous. Let K ⊆ B. Then the relation |=K , or the relation of intentional entailment based on the class K, is defined as follows: for every X ⊆ L × L and for every z ∈ L × L. X |=K z iff ∀P ∈ K[EP (X) ⇒ EP (z)]. Analogously, the relation |=K is defined for K ⊆ P: a X |=K z iff ∀P ∈ K∀a ∈ U (P)[EP (z) ⇒ EaP (z)], where U (P) is the universe of the structure of situations of the model P. Theorem 1. Every consequence relation on L × L is of the form |=K for some K ⊆ B. Theorem 2. The strength of B ie equal to that of P. Corollary 3. |=B =|=P =3.

Both |=B and |=P are the identity entailments, i.e.,

VI. Compatibility The models examined up to now did not distinguish between the consequence relations in L × L; each of the consequence relations could be an intentional entailment, Theorem 1 says, owing to the fact that the description of the language presented above was somewhat unrealistic. We considered declarative sentences of L as if they formed a pure set, as if they were related in no essential way. But it is not so in the real life. We never use a “pure” language, there is always a logic we accept. The communication would be impossible if the speaker and the listener had no logic in common. In fact we should ask one another “Do you use this logic?” just as we ask “Do you dance this?”. Logics describe the entailments between sentences and pragmatic reasonings have clearly to be consistent with the accepted logic. Accepting a particular logic we automatically make a supposition that the entailment relations given in it are determined by the nature of the world supposed to be possible, i.e., by the relations between possible situations. If it is so, we say that the worlds are compatible with the logic. Let us try to give a formal approach to the problem of compatibility.


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Suppose that our common logic is represented by a consequence operation C : 2L → 2L . Let P = < U, O, R > be a basic model for some language L = L ∪ L∗ . We say that P is compatible with C if for every α, β ∈ L α ∈ C(β) implies O(α) ≤ O(β). As an example consider the ordinary logic in the ordinary language with the ordinary semantics (imagine, if you can – as usual people do – that there is such a thing!). In this logic the sentence “John drank too much” is one of the consequences of the sentence “John drank too much and he kicked his boss”. Thus the situation consisting in that John drank too much must be a part of the situation consisting in that John drank too much and he kicked his boss. Observe that the converse implication is not generally true: the situation consisting in that I am a jet co-pilot contains as its part the fact that I am at least 15 years old” still the sentence “I am at least 15 years old” is not a logical consequence of the sentence “I am a jet co-pilot”, if the logical consequence is given its standard meaning. The notion of compatibility for pragmatic models is defined analogously: a pragmatic model P = < U, O, R > is compatible with a logic C if for all α, β ∈ L, for all a ∈ U α ∈ C(β) implies Oa (α) ≤ Oa (β). The class of all basic (resp. pragmatic) models compatible with C will be denoted by B(C) (resp. P(C)). We conclude with presenting the following theorem: Theorem 4. (a) For every consequence operation C in L, |=B(C) is the smallest of all consequence relations ` on L × L which satisfy the condition if β ∈ C(α) then for every γ ∈ L, {< γ, α >) ` < γ, β >; (b) For every X ⊆ L, for every α ∈ L, β ∈ L X |=B(C) < α, β > iff ∃γ ∈ L[< α, γ >∈ X&β ∈ C(γ)]; (c) |=B(C) =|=P(C) .

Section of Logic and Methodology Silesian University Katowice, Poland