Conditionals in context
This book may appear on the surface to be a dry treatise on a topic that is of greater interest for a philosopher than an everyday working linguist: the formal semantics of conditional sentences. But what its author, Cincinnati philosopher Christopher Gauker, is after is nothing less than a paradigm shift in the way we think and theorize about meaning in language. The standard view in formal semantics, based on a view of language as a picture of the world (or rather, of many possible worlds), is to be thrown out and replaced with a theory of semantics that takes seriously LANGUAGE USE IN CONTEXT. G's previous book (Gauker 2003) presented the framework forming the basis of the theory of conditionals presented here. The main point of this book is to use the semantics of conditional sentences as a case study to show the advantages of G's basic framework, which we might call CONTEXT-LOGICAL SEMANTICS (CLS).
Central to any formal semantics is the notion of logical validity, which serves to distinguish valid arguments from invalid ones. According to the prevailing model-theoretic conception of logical validity, a speaker's aim in asserting a sentence in a context is to express a proposition P, whose interpretation [P] in a model can be formalized as a set of possible worlds in which the proposition is true. Logical validity is defined in terms of truth preservation: an argument is valid iff for every possible world where the premises are true, the conclusion is also true. If you are a believer in the model-theoretic account, you will have to suspend many of your central semantic notions in order to grasp what G is up to. Propositions are eschewed in favor of sentences, and possible worlds are replaced by contexts (which are in some respects similar to partial possible worlds but also different in important respects). Truth is replaced by ASSERTIBILITY, which entails relevance to the goals of the conversation.
Reference is thrown out altogether, except as a useful notion in conversations dealing with repair (Who are you referring to?). The need for a theory of reference is avoided in G's account by positing the CONTEXT PERTINENT TO THE CONVERSATION (CPC)-a linguistic structure comprising what is relevant (and thus assertible) in a conversation. In a conversation with the goal of building a fence, the sentence Socrates is mortal is most likely neither assertible nor deniable. The CPC is also OBJECTIVE in the sense that it depends in part on how the world is, apart from what we happen to believe. It is a product of the goals of the conversation and the environmental circumstances in which the conversation takes place. The CPC is contrasted to the various subjective TAKES on (i.e. mental representations of) the context that individual interlocutors may have. Whereas what an interlocutor DOES depends on her take on the context, what she OUGHT to do depends on the objective context.
G makes the standard distinction between two basic types of conditional sentences: indicatives, such as If he is in Paris, then he is happy, and subjunctives, such as If he were in Paris, then he would be happy. In CLS the semantic value of a conditional sentence depends on the RELEVANT PROSPECTS provided by the context where the conditional is uttered. For example, the indicative sentence If you turn left at the next corner, you will see a blue house at the end of the street (call this sentence C) is assertible in a context if in each of the relevant prospects where the hearer turns left on the next corner, the hearer sees a blue house at the end of the street. It is important to distinguish 'relevant prospects' from mere possibilities, simply because in some situations we are entitled to ignore some possibilities. For example, we are usually entitled to ignore the possibility of a bird swooping down and pecking out the hearer's eyes before he has a chance to lay eyes on the aforementioned blue house; even if this is indeed possible, C is assertible.
A useful notion of logical validity should either confirm our intuitions concerning the validity of various forms of argument, or explain why our intuitions are mistaken. G's account does both of these, and in addition argues that no other account has gotten it right-especially no account based on the model-theoretic account. G finds two fundamental flaws in the latter. First, it commits one to a theory of reference, which would be fine if only someone could explain what [End Page 201] reference is. Unfortunately, on G's view, no one has succeeded in doing this. Second, and perhaps more convincingly, accounts of conditionals on the classical model-theoretic conception of validity consistently give counterintuitive judgments for some arguments. The root cause of this is the stipulation that conditionals are material implications, that is, that 'if P then Q' is equivalent to 'either not-P or Q'. An example of such an argument is the so-called 'contraposed marbles argument'. Imagine a situation where you are about to draw a marble from an urn. Now have a look at the argument in 1.
(1) It is not the case that (if I do not draw a red marble, then I will draw a blue marble).
I will draw neither a red marble nor a blue marble.
This argument is invalid, since there may be other marbles in the urn besides the red and blue ones. In that context, it is not true that if I do not draw a red marble, then I will draw a blue marble-it might be that I do not draw a red marble but a yellow one. So denying this conditional is correct, and thus the premise is true. In this context, however, the conclusion is false since I might well draw a red marble or a blue marble; after all, there are both red and blue marbles in the urn (as well as yellow ones). Unfortunately, this argument is judged valid by the model-theoretic account, where conditionals are interpreted as material implications. G offers a careful examination of what he refers to as THE RECEIVED VIEW of the semantics of conditionals-a combination of ideas formulated within the model-theoretical framework by Lewis and Stalnaker,1 intended to avoid the problems indicated by the contraposed marbles argument. G's main objection to the received view is that it gets the logic of conditionals wrong. Specifically, in abandoning material implication it throws the proverbial baby out with the bathwater by also rendering 'disjunctions-to-conditionals' (the inference from 'not-p or q' to 'if p then q') invalid, even though this argument has no intuitive counterexamples.
To correctly classify this argument as not valid, G argues, a three-valued logic admitting 'lack of truth value' is needed. No account of lack of truth value proposed in a model-theoretical semantics is able to correctly deal with the contraposed marbles argument, at least not insofar as it keeps the notion of validity as preservation of truth in a model. This is not the first time this problem is demonstrated, nor the first time the 'received view' is challenged. G reviews previous attempts by Barwise (in the framework of situation semantics; see Barwise 1986) and Lycan (2001) at providing an account of conditionals that avoids the problems of the received view. G finds both of these theories similar in some respects to his own, but unfortunately neither theory provides for the validity of disjunctions-to-conditionals.
So, how does G handle the contraposed marbles argument? On the CLS account, the premise may be assertible while the conclusion fails to be assertible since the context may include the prospect that I draw a yellow marble, as well as prospects where I draw a blue marble or a red marble. The conclusion, however, is not deniable either, so the conclusion is neither assertible nor deniable. According to the context-logical conception of validity, an argument is valid iff for every context where the premises are assertible, the conclusion is assertible too. Since there is a context where the premise of the contraposed marbles argument is assertible, but the consequent is not, the argument is not valid.
In CLS, conditional sentences are CONTEXT-SPECIFIC RULES OF INFERENCE whose function is to narrow down the number of available prospects in the context to those in which the conditional is assertible. In a context where, for example, some choice needs to be made, the available prospects (choices) are themselves represented as contexts, and the CPC is thus a MULTICONTEXT, that is, a set of contexts. Using these concepts, G offers a careful formalization of the semantics of indicative conditionals encompassing not just one but two kinds of validity (strong and weak). Using this theory, G can explain why some invalid arguments nevertheless appear valid to us, and thus account for many purported counterexamples to argument forms considered valid by G. This is complemented by a formalization of the semantics of subjunctive conditionals inspired [End Page 202] by ideas from Stalnaker. Briefly put, subjunctives are evaluated in relation to complex structures composed of multicontexts representing not only the immediately relevant prospects, but also some less relevant prospects.
Some aspects of G's formal theory may be controversial; for example, one may take issue with his intuitions on the validity of some argument form or other. The associated philosophical ideas, however, are outright provocative. So, could one accept fully the formal account while refusing at least some of the philosophical ideas connected to it? In at least some cases, the answer is probably yes. The formal theory seems to work equally well if we understand the context to be an interlocutor's subjective 'take', or if we understand it to be the 'objective' CPC. So one might want to dispose of one or the other type of context, or even introduce a third notion of context. It seems entirely possible to introduce into G's framework a revamped version of 'common ground' (a notion that G argues against), fulfilling the formal requirements on contexts. This notion could perhaps be called the 'shared take' on the context, and would consist, roughly, of all sentences that the interlocutors both take to be in both their takes on the context. Such a notion could also help to explicate the notion of 'going without saying', which is not formalized in the present account.
I would also like to air three further worries concerning the notion of 'objective context'. First, there is the risk (acknowledged by G) that the concept of reference, despite efforts to the contrary, will rear its ugly head once we try to explain the relation between the context and the 'environmental circumstances'. Second, the notion of 'reliably achieving a goal', which is crucial in the definition of objective context, is left unexplained. Third, the language relativity of the objective context begs the question: Whose language? This is a problem insofar as interlocutors have (if ever so slightly) different languages. In conversation, these differences are dealt with by continuous mutual alignment with respect to language use, regulated by feedback signals indicating understanding and acceptance, or lack thereof. But in the case of 'objective context', there seems to be no such practice to rely on. Still, the assumption of a static and perfectly shared language is pervasive in formal semantics, so perhaps it is unfair to criticize G on this point.
In the long run, it falls on G (and anyone he can convince to join him in the fray) not only to show that his theory gets everything right that the received view got wrong, but also that it gets right everything that the received view got right. Given the amount of work carried out in the received view, this is quite a momentous task. The jury will be out for a long time yet. Meanwhile, I strongly recommend that anyone with a serious interest in formal semantics (let alone conditionals) read this book.
Department of Philosophy, Linguistics and Theory of Science
University of Gothenburg
1. For literature pertaining to the Lewis and Stalnaker framework, see Lewis 1973 and the various papers by Stalnaker in Stalnaker et al. 1981.