Vagueness and the Logical Substructure of Art
David Michael Wolach
There are problems for ‘truth-rule’ semantics as it applies to what we mean by meaning. Such problems are not often stressed in the philosophy of language because they do not generally stand in the way of successful (instrumental) theories regarding the normative aspects of public discourse, i.e., determinacy of meaning in context, of why we may be justified in claiming that a fellow speaker has erred, and so on. These problems do not concern the success of truth-rule semantics in the domain of constative communication, or speech acts elicited under the intention of direct and sincere communication. Rather, they concern the family of linguistic acts that we might call ‘performative'. These are acts of language that suggest, imply, or evoke rather than say something.
The performative actor depends not just upon an interpreter who will deduce her meaning by use of available criteria, but who will register discomfort upon encountering juxtaposed utterances so novel they threaten to extend beyond the walls of sense. Though parasitic upon accepted convention--insofar as they are built up from sentences in a ‘language game’ that are susceptible to analysis in terms of truth--literary tropes, being that they register at the skin, so to speak, are abstracted from reported, every day speech, and reach 'beyond' the merely propositional. All linguistic acts, it could be argued, bear to some degree a performative stamp, but the success of the literary utterance depends on communicative and also sensory aspects, and moreover is approached with the intention that it will deliver these.
I want to stress what traditional theories of meaning have not stressed and what truth-rule semantics cannot address: the integral role individual psychological histories play in the response to utterances and the determination of the extension of lexical items, and more generally, that to confront an utterance of another is to confront more than its truth-conditions, and therefore to understand the meaning of an utterance of another entails more than the mastery of its truth-rule (i.e., knowing what sentences the utterance materially implies and is implied by). This must be so for at least two reasons:
1) In the case of ordinary communication, it seems that learning generalizations such as 'p' is true iff G, is a sufficient condition for the mastery of a predicate, but the truth-rule says nothing about another major component of communication--having a procedure that decides whether something satisfies the right-hand side of the truth-rule. While it is true that in radical interpretation the extension predicates in a subject language is not a prerequisite for successful interpretation, we must realize that to succeed in translating one alien sentence into a home language does not imply that the translator and the alien speaker are having even similar thoughts (see Wittgenstein PI, "I express what I think, and for you to understand, you need not think what I think, or have the same thought as I.")
This, of course, is not news. But, as I will discuss below, it is the possibility of divergent thoughts, associations, dispositions in response to an utterance that performative and literary languages exploit; hence a thorough treatment of the relationship between meaning and effect, or between interpretation and response, will be needed to explore the functional difference between the language game of report and the language game of performance.
One way in which I may fail at successfully interpreting your utterance (in the case of communication between two speakers of the same language community) while nevertheless having full mastery of its truth-rule, is by having learned a vastly different extension for a predicate that you have learned, but which is used in the course of our exchange. This is to say that truth-rule semantics says nothing about what determines the extension of terms (we can be extensionalists, intentionalists, or neither in this respect), and I will here argue that a term's extension is determined by the spatio-temporal history of the speaker (the speaker is always encountering new uses of the term and accommodating them into her repertoire), and so strictly, there is always an important asymmetry between what I take myself to mean and what an interpreter takes me to mean, even in the case that I have mastered the truth-rules underpinning our exchange. Extending this further, there is also the possibility that the process of being interpreted recursively effects the stability of the utterance I have just made such that there is also an important asymmetry between what I think I took myself to mean (now) and what I took myself to mean (then). Stanely Cavell, for one, has noted this (see, The Politics of Art).
2) I take it to be a particular limitation of truth-rule semantics that its application ranges only over constative communication--utterances that report present, past, or possible states of affairs under a mutual assumption of sincere communication. Truth-rule semantics ought to be able to deal with implied meanings, context-sensitive modes of communication, as long as what is taken as evidence for an interpretation is wide-ranging enough so as to include time and place, the history and intentional relation of the speaker and so forth. But there is a performative aspect to ordinary speech acts that truth-rule semantics cannot handle, i.e., situations in which there is no evidence for or against the interpretation of a proposition, or, as in the case of fictional language, where the game that is played involves a frustration of norms and convention, and where another sense of "meaning"--that which results from the response evoked by an exchange--is tantamount and yet parasitic upon the rules and procedures of ordinary language.
This is why, much like Cavell, I claim that there are multiple senses of ‘meaning’, two of which predominate this discussion once we cross over from everyday speech acts to the literary language game: the first concerns the rules and conventions of ordinary language, consative communication, and enables us to determine the content of the literary utterance. In this sense of "meaning," the literary language is no different from ordinary speech acts, hence the interpretation of literary language should be no different from the interpretation of an ordinary speech act. But the second sense does not concern truth or falsity, and so escapes the notice of truth-rule semantics: it is open-textured, relies on and exploits the variable histories of its interpreters, vagueness, and in this sense we can say that the work's second meaning is subjective, a matter of how it effects the interpreter, how it makes her act, not of what it enables her to report.
In this second sense, there is no normative component to the meaning of the literary utterance. The meaning of the utterance exists as a possible response (or in the language of simulation theory, it involves an ‘imaginative play’); the utterance itself is mediated by the interpreter's history; and the interpreter's active translation of the utterance into a response recursively effects the pattern of future responses. If this is so, it makes no sense to say that an interpretation of a literary utterance is correct or incorrect, replete with error or otherwise. This is not to say that the subjective meaning is inaccessible or private, but that its reference point is an interpreter who has a unique spatio-temporal grounding, a unique perceptual point of view, and so any disagreement over the interpretation of a literary trope will literally change the meaning of that trope. To disagree over the meaning of the utterance would be to talk around the utterance, to say: "Step into my shoes, see what I see"--which is not to re-experience the utterance from a different point of view, but to re-experience the utterance with the additional information of someone else's report of their point of view.
I will briefly review Davidson's truth-rule semantics, baring in mind that his project is not mine, his concerns not my concerns. I do think, however, that if we can pinpoint the limitations of Davidson's thesis on radical translation, we can also more clearly grapple with the problem of meaning as it pertains to art.
Truth-Rules and Ordinary Language
Any truth-rule semantics for natural languages is parasitic upon what Davidson refers to as "an establishment of a ground for objective thought" (“Triangulation,” 21). That is, when we ask the question 'how can we come to know the meaning of another's utterance?' we arrive at the conclusion that, to link the object language with the subject language in the case of two conversant creatures, there must be some meta-language that gives us a rule for translating the expressions of one into the expressions of another--a truth-rule. But, no matter what rule we choose (or has been chosen for us), underlying it must exist a way of confirming that the rule works, that what has been interpreted has been interpreted correctly or otherwise. The result of the project, if successful, is that of analyzing the meaning of a sentence in terms of what sentences make it true, and what sentences it makes true.
We ask: what grounds the success of the truth-rule? The Tarskian theory of truth, the starting point of truth-rule semantics, says that for every sentence s of the object language, there is a sentence such that s is true iff p. Supposing, for instance, that s is "Davidson is a philosopher," the Tarskian sentence would yield 'Davidson is a philosopher' is true iff Davidson is a philosopher. Here meaning is equated with truth, where truth is defined as logical satisfaction. For the Tarskian model, what grounds the success of the truth-rule is the assumption that the truth-conditions for a sentence are preserved on the right side of the bi-conditional formula. But for natural languages we cannot assume the carrying over of truth-values because we cannot assume translation. Davidson points out that what is left is to turn Tarski's theory of truth on its head: rather than assuming translation and deriving truth from it, we "take truth as basic and… extract an account of translation or interpretation" (“Radical Interpretation,” 134).
As language users we approach the world, Davidson says, with Tarskian sentences already at hand. In the event that I am trying to translate an alien utterance, I have sentences of the form:
P is true in L when spoken by x at t iff P is S
And I am naturally confronted by evidence, common to both speakers, such as where x is from, whether x holds S to be true at such and such a time, in such and such a place, etc., all of which may narrow what began (in the case of radical translation) as an infinite string of possible interpretations (the possible relation of an infinite number of sentences in the subject language to an infinite sequence of objects in the object language). I thus consider such information as evidence that (T) is true--I weigh the utterance against a background of "massive agreement" (136). What grounds the truth-rule for P, then, is evidence that is available both to the speaker and to the interpreter. In "Triangulation," Davidson further stipulates that such evidence (in the case of radical translation), in order that we may make sense of the possibility of error, must be available perceptually--it must be in the form of a "proximal stimulus."
Davidson's way of analyzing meanings in terms of truth may give us a theory that tells us under what conditions an utterance is true, and goes part way in describing why, in the event of error, we are justified in telling a speaker that he is mistaken. But I now want to highlight another aspect of Davidson's thesis, and more generally, of truth-rule semantics. This aspect can best be seen as a follow-up to Davidson's question 'how can I come to know the meaning of another's utterance?' The question comes out: 'to what degree do I know the meaning of another's utterance once I have applied a truth-rule analysis to it?'
We must not, as Davidson notes, move from conditions for truth to the assumption that identification of the truth-rule gives us the meaning of an utterance: "if truth values were all that mattered," he states, "the T-sentence for 'Snow is white' could as well say that it is true if and only if grass is green" (“Radical Interpretation,” 135). There are two points to be made regarding this. First, even in the case of ordinary speech acts, we may have mastered a procedure for truth and yet, because of the open-texture of a predicate, we may still not know whether the right-hand side of the Tarskian sentence is satisfied. For instance, I may have the following truth-rule:
x is a bird is true iff x is an animal with beak and feathers
and I may know that birds have a beak and feathers and still not know whether this object satisfies the right side of the bi-conditional, i.e., if the object is such an instance of "beak" and "feathers" such that it satisfies the predicate 'is a bird'. Such indeterminacy, or logical vagueness, may not be because we do not have enough evidence, but because the predicate ranges over an evolving set of objects (i.e., the extension of a predicate changes with the use of the predicate); such is the case not only with evaluative terms, but also in practice with everyday lexical items such as 'chair', 'person', 'bald', ‘tall’ and so on.
Regardless of what does determine the extension of a predicate, we note immediately that while learning truth rules may be a necessary condition for learning a language, it is not a sufficient one. But for my purposes it is more important to note that, roughly, extensions are rather (perhaps artificially) like dispositions to apply a certain name in the sense that, just as I may be disposed to call something an x but not call something else an x, I may be disposed to include under the extension 'is a bird' x, say, while you may not. Though it is through verbal exchange that the extension of terms settles to a state of uniformity, there will always be some disagreement as to the range of objects a term covers, especially in the case of infrequently employed utterances, or utterances made outside their usual context.
Not only does our rough and ready way of gathering evidence in truth-rule semantics ignore the possibility for fine-grained lexical differences between speakers even in the case that wholesale disagreement is absent, these fine-grained differences become magnified and exploited in literary speech acts, where the history of the interpreter (that which determines the extension of terms) becomes the locus for interpretation. But there is a second point regarding Davidson's claim above. This concerns the difference between the language game of reporting and the language game of evoking.
Literary Language and Subjectivity
As in the case with performative speech acts, the role of the utterance may not be that of reporting. If this is so, then the truth-rule becomes less important, if not irrelevant to the nature of the interpreter's response. Consider the sentence:
(S) John's face is a wall.
If we interpret S according to Davidson's semantics, we approach it with Tarskian sentences of the form:
(T) 'John's face is a wall is true' iff John is expressionless.
And then we begin by gathering contextual evidence surrounding the utterance. We might consider that x claimed S in the context of a performative act, and we might also use as evidence the inference that under such circumstances, x usually makes identity claims such as S to draw a connection between two items generally taken to be categorically distinct. We may add further evidence that elsewhere John was described as a ‘poker face’, that he was often 'blank', etc. The result may be something like:
(x)(t)(c) (if x utters S in circumstance c then x holds true 'John's face is a wall' at t iff John is expressionless.
But, though it is likely a plausible interpretation of the sentence, any such Tarskian sentence, using truth as a guide, as it were, will fail to capture what is important in a literary utterance: the response of the interpreter over and above the interpretation (the bodily reaction of the interpreter, including the mnemonic associations S evokes in the context of other performative utterances, i.e., the specific response of that interpreter). Put another way, what Davidson's heuristic will give us is the publicly agreed upon content of S, but will fail to shed any light on what I call (for lack of a more suitable term) the disputation of S, the particular response to S of an interpreter given the interpreter's unique history as an agent moving through the world.
The disputation of S, though parasitic upon the content of S--which is, like any other utterance, available for the kind of truth-rule scrutiny outlined by Davidson--makes the truth-rule analysis somewhat irrelevant (this is the case of climbing the latter in order to shove it away). This is not because the disputation of S is private or inaccessible, but because the meaning arriving at an inevitable dispute, rather than an agreement or triangulation, concerns the effect S has on a particular interpreter, i.e., because one object of the literary language game is not to report but to evoke, to resonate particularly with particular interpreters, and to cause argument—a meaning-generating dispute.
As in the case of metaphor, double entendre, repetition, and other liteary conventions, performative speech acts seek not only to disrupt ordinary language use and bend its limits (thus evoking at first awkward associations) but also seek to exploit the often wildly varying histories of its interpreters. Certainly without a general procedure which effects the determination of the extension of predicates we would be lost as to the content of the literary utterance--and so lost, such sentences would evoke nothing (this is Davidson's point about the importance of truth-rules in radical interpretation). But this should not prejudice the notion that embedded in our exchange of gestures, even on the level of everyday communication, is the possibility that one utterance may evoke vastly different associations amongst interpreters. The ideal in everyday communication, one would assume, would be to stifle this possibility; but in the literary language game it is encouraged, even exploited. Davidson recognizes this in "The Myth of the Subjective." He states:
The grasp of meanings is determined only by the terminal elements in the conditioning process and is tested only by the end product: use of words geared to appropriate objects and situations. This is perhaps best seen by noticing that two speakers who "mean the same thing" by an expression need have no more in common than their dispositions to appropriate verbal behavior; the neural networks may be very different… Two speakers may be alike in all relevant physical respects, and yet they may mean quite different things by the same words because of differences in the external situations in which the words have been learned. (164)
Though Davidson concedes this point, since his work is to show that meanings are not private, he does not relish in it. I will relish in it, as what interests me is the possibility of logical vagueness as a precursor to disputation, performative acts—behaviors that are meant to disrupt and do violence to the individual, to set up a debate that results in the necessary disagreement over whether, and how, to agree.
Notes and Examples of de re Vagueness:
If Γ, α⇒β is valid, then Γ, ¬β⇒¬α is valid
Assuming 6 feet to be a borderline case of "is tall."
a) John is tall⇒John is higher than six feet (valid)
But:
b) John is not higher than six feet⇒John is not tall (not valid)
Counter example: John is 6 feet. There is no admissible valuation in (a) that would give the conclusion the value "F" and yet the premise "T." But the inference does not go through, because there is a precisification for "is tall," (6 feet) that would make John under six feet high, yet tall.
If Γ, α⇒β is valid, then Γ⇒α→β is valid
Assuming 18 years old is a borderline case of "is a child."
a) X is a child therefore X is less than 18 years old (valid)
But from implication to the conclusion:
b) if X is a child, then X is less than 18 years old (not valid)
Using substitution of connectives, we turn (b) into:
c) X is not a child or X is less than 18 years old. (not valid)
Counter example: Suppose X is 18 years old. Thus, there is an admissible valuation of "is a child" (hence, "is not a child") such that both disjuncts come out false (X is a child and X is not less than 18 years old.) Therefore, the implication only holds locally, under precisifications of the predicate that would exclude X from its extension.
If Γ, α⇒β and Γ, α′⇒β are valid, then Γ, α∨α′⇒β is valid.
A therefore C (valid)
B therefore C (valid)
A or B therefore C (not valid)
Counterexample: A is indeterminate and B is determinate. Therefore, definitely B, but not-definitely A. Hence: the inference to C is valid only where A is T, and not globally valid otherwise. From not-definitely A, we cannot infer definitely C--although C might be infered at local points. Therefore, the inference is not globally valid.
iv) If Γ, α⇒β and α⇒¬β are valid, then Γ⇒¬α
David is a child⇒David is less than 18 years old (valid)
David is a child⇒David is not less than 18 years old (valid)
⇒David is not a child. (not valid)
Counterexample: Suppose David is 18 years old and that 18 years is a borderline case of "is a child." The predicate "is a child" has variable admissible valuations, such that the conjunction (a and b) of globally valid but mutually exclusive inferences does not imply the global falsity of c. On one admissible valuation, child may be precisified to include 18 years old, and on another in may exclude 18 years. In the first cases the inference is valid, whereas in the third it is not. In a and b the conclusions are globally valid, whereas in c the conclusion is only locally valid--validity here depends on the precisification of "is a child," hence not-p does not imply definitely not-p.