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I propose to analyze the paradigmatic speech act of betting. I am concentrating specifically on the case of a linguistically explicit bet between two and only two distinct individuals, A and B, on the outcome of a bivalent proposition, P. Person A bets some valuable consideration Xa against person B’s Xb that some proposition P holds. It would no doubt require further analysis to capture the nuances of bets involving more participants (such as poker games or lotteries), or implicit bets (such as might be made with a nod or a hand signal), or bets for services rather than tangible property. I hope to present a set of necessary and sufficient conditions for a simple and central case of betting. For example, Bob bets his ham-on-rye against Jan’s pastrami sandwich that mayonnaise is really gross, if only you know what’s in it, and Jan accepts. In this example, Bob is A; his ham-on-rye is Xa; Jan is B; her pastrami sandwich is Xb; and the proposition that mayonnaise is really gross is P. Note that since the relative values of Xa and Xb may differ, my formulation is sufficiently rich to encompass bets that “give odds.”

The full process of betting is necessarily temporal, involving at least four discrete points in time. It will be useful in the following discussion to identify them as follows: At point T₀, A proposes a bet to B. The bet becomes effective at point T₁, which occurs if and when B accepts A’s bet. The outcome is determined at point T₂, which occurs when the truth value of the proposition P is settled. The process is complete at point T₃, which occurs when the loser has finished “paying up”.

I propose the following conditions, which I contend are individually necessary and jointly sufficient to constitute a bet:

1. Normal input and output conditions obtain, per Searle.

2. A bets Xa against some B’s Kb that F by way of some utterance Sa which establishes the terms of the bet. I am being intentionally vague here, intending only to establish that, in order for an explicit bet to occur, there must be some speech act Sa which expresses, at a minimum, both the embedded proposition F and the valuable consideration Xa and Xb. The precise referents of B and Xb need not necessarily be determined yet: Bob may say, “I’ll bet my sandwich against anyone’s that P”. Other terms of the bet besides Xa and Xb may also be specified in Sa. For example, it may be necessary to agree in advance on a particular way of settling P, e.g. by looking it up in an encyclopedia if P is some historical proposition, or by naming a referee, if P is the outcome of a future athletic contest.

3. B accepts A’s bet by way of some utterance, Sb, indicating acceptance of the terms expressed in Sa. In practice, the terms may be negotiated: if so, then some terms of Sa may actually be uttered by A and some by B. In order to apply condition 2 uniformly, we take B to be whichever person utters acceptance of the finalized terms, and A to be the other party, irrespective of who happened to be the first to propose a bet (I say “a bet” rather than “the bet” since the final version might be quite different from the initial proposal). If no one accepts A’s bet, the obligations entailed by the bet do not take effect.

4. In uttering Sa, A offers (and intends to offer) to undertake an obligation to B such that, if it turns out that not P, A must give Xa to B. In uttering Sb, B perfects A’s obligation to B, and B undertakes (and intends to undertake) a complementary obligation to A such that, if it turns out that P, B must give Xb to A. So, after the appropriate utterances, if it turns out that mayonnaise is not gross, Bob must give his ham-on-rye to Jan; otherwise Jan must give her pastrami to Bob.

5. In uttering Sa, A warrants that A has clear title to Xa. Similarly, in uttering Sb, B warrants that B has clear title to Xb. That is Bob cannot bet Phil’s sandwich: he can only bet his own sandwich. So A must own Xa and B must own Xb. Furthermore if Jan’s sandwich is already riding on a bet to Alice, she cannot (legitimately) accept Bob’s bet. In offering a bet, A warrants that there are no outstanding liens against Xa, and in accepting it, B similarly warrants Xb.

6. At the time T1 when the bet takes effect, it is not the case that A and B both know the truth value of P. Nonetheless, at most one of them may know the true value of P (Bob may have read Upton Sinclair’s The Jungle). In that case, the other must be either mistaken or uncertain about P. The crucial event that defines T2 is that A and B become aware of or come to agreement on the truth value of P, not necessarily that P then comes to be true or false (since P may be historical). Usually, we would expect to be able to say something stronger than merely that A and B do not both know the truth value of P: namely, we would ordinarily expect to be able to say that A believes that P is true (or likely) and that B believes that P is false (or unlikely), but as we shall see below, such is not necessarily the case.

In condition 4 of his analysis of promising, Searle claims that “H [hearer] would prefer S’s [speaker’s] doing A to his not doing A, and S believes H would prefer his doing A to his not doing A” [Searle, “What is a Speech Act?” in Martinich The Philosophy of Language, 2nd ed., p. 122, Searle’s notation differs from mine: his “A” is an act]. In comparing my analysis of betting to Searle’s analysis of promising, I am tempted to say that in order for A to bet that P, A must believe that P (or maybe that A must have a certain confidence level in P, perhaps corresponding to the ratio of the values of Xa and Xb). But A’s belief in P cannot be a precondition for betting, since that would preclude the possibility of “hedging one’s bet” by making contrary bet, perhaps at inverse odds. For the same reason, it cannot be a precondition for betting that A would prefer P to not P, or that B would prefer not P to P. And since it does not matter whether B would prefer not P, it cannot matter whether A believes B would prefer not P. By a similar argument, it cannot matter whether B believes A would prefer P. The point is essentially that A and B incur their respective obligations simply by agreeing to the bet, not by preferring or believing one thing or another.

Instead, the chain of reasoning goes the other way: the fact that A bets that P may be taken as evidence (though not as incontrovertible evidence) that A believes or expects that P.

Nor does betting have any corollary to Searle’s condition 6 for promising, such as that “A intends to give Xa to B if it turns out that not P” (and mutatis mutandi for B). I think it does not matter whether either Bob or Jan actually intends to surrender a sandwich if proved wrong. Bob incurs the obligation to give up his sandwich if proved wrong, regardless of his intention to do so: even if he fully intends to welch on the bet he no less obligated. Furthermore, I do not think it helps to substitute some corollary of Searle’s amended condition 6a, such as that “A intends that the utterance of Sa will make him responsible for intending to give Xa to B if it turns out that not F,” (and mutatis mutandi for B). Rather, I think that making the bet obligates A to actually give Xa to B if A loses, whether or not he intends to do so, and this obligation is already expressed in condition 4.

As with condition (1), I include the remaining conditions mainly because Searle does, and because I have no argument with them. They apply, with the suitable obvious alterations, to any performative speech act.

7. A intends that the utterance of Sa will produce in B a belief that conditions (4) and (5) obtain by means of the recognition of the intention to produce that belief, and he intends this recognition to be achieved by means of the recognition of the sentence(s) Sa as sentence(s) conventionally used to produce such beliefs. This is the Gricean condition, which mainly ensures that the terms of the bet are communicated by linguistic means.

8. The semantical rules of the dialect spoken by A and B are such that Sa is correctly and sincerely uttered if and only if conditions (1)-(7) obtain. This condition mainly ensures that the utterances Sa and Sb consist of well-formed sentences in a language spoken and understood by both A and B, and that Sa conventionally expresses what come to be the terms of the bet.

An utterance which failed to meet conditions (1), (7), or (8) could hardly count as a performative speech act at all. For each of the remaining conditions (2)-(6) that I have proposed as being specific to betting, it seems clear that some speech act that failed to meet any one of them would either not be a bet, or would be a defective one. Condition (2) requires that A actually say the terms of the bet. Condition (3) requires that B agree to those terms. Condition (4) describes the obligations undertaken by A and B. Condition (5) requires that A and B have the right to bet with Xa and Xb, respectively. Condition (6) essentially says that A and B do not already agree on P. If it is then agreed that a speech act that meets all these conditions must be a bet, then this set of conditions is both necessary and sufficient for a bet to take place.

Essay

Title

PARADIGMATIC BETTING

Synopsis

An excruciatingly formal theoretical analysis of the speech act of betting

Topic

Philosophy of Language

ShortTitle

Paradigmatic Betting

Date

October 31, 1991

Professor