Definite Descriptions and the Argument from Inference

Abstract

This article discusses the “Argument from Inference” raised against the view that definite descriptions are semantically referring expressions. According to this argument, the indicated view is inadequate since it evaluates some invalid inferences with definite descriptions as “valid” and vice versa. I argue that the Argument from Inference is basically wrong. Firstly, it is crucially based on the assumption that a proponent of the view that definite descriptions are referring expressions conceives them as directly referring terms, i.e., the terms which contribute their referents into the semantic content of the sentences in which they occur. However, the framework of direct reference is not essential to the idea that descriptions might have semantic referential interpretation. Secondly, the Argument of Inference - if correct - suffices to establish an overgeneralized conclusion that even paradigmatically referring terms, like proper names, cannot be semantically referential. This fact indicates that the argument is flawed. In the final part of this article, I briefly consider what the source of the problem with the Argument of Inference might be.

Definite descriptions (i.e., the phrases of the form “the F”) have attracted a lot of attention of the philosophers of language. The reason why these specific phrases have invoked so many discussions is that it is not clear whether they are devices of reference or quantification, or whether they have both semantic roles (i.e., a particular description token can be a quantifier in one context and a referring expression in another context.) In effect, the problem of what truth conditions one should assign to the sentences of the form “The F is G” remains unsolved. An interesting aspect of this problem—which has not attracted much attention in literature—is the evaluation of various inferences containing sentences of the characterized form. With respect to this, an intuitive test for adequacy of a semantic theory of definite descriptions has been proposed by some theoreticians (see: Devitt 2004, p. 291 and especially Zouhar 2007). In brief, an adequate semantic theory of definite descriptions should provide a correct evaluation of inferences containing sentences with definite descriptions. That is to say, it should evaluate as “valid” these inferences which we intuitively take to be so, and it should evaluate as “invalid” these inferences which, according to our intuitions, are incorrect.

As Zouhar (2007) argues, the account which conceives definite descriptions as referring terms does not pass the test of inference-evaluation. It classifies some clearly invalid inferences as “valid” and vice versa. In my paper, I will argue that Zouhar’s test of inference-evaluation is wrong. Firstly, the author conducts his analysis of various inferences with definite descriptions in a specific semantic framework which is not essential to the view that definite descriptions are referring terms. That is to say, his critique applies at best only to a limited version of the targeted view. Secondly, Zouhar’s argumentation is an overkilling since it can be used to demonstrate that even paradigmatically referring terms cannot be semantically referential.

(I)

Let me start with Zouhar’s account of the targeted view and the reconstruction of his argumentation. The author introduces the term “referentialism” in order to denote the view which claims that descriptions¹ are “semantically referential and objects satisfying them enter their semantic content.” As the author explains, the referentialism respects Donnellan’s distinction between the attributive and the referential uses and it claims that only referentially used descriptions are semantically referential. So, in fact, the proponent of the view in question commits himself to the thesis that descriptions are semantically ambiguous as they have a different semantic function under both uses.

According to Zouhar, the referentialism ascribes the following truth conditions to an utterance of a subject-predicate sentence of the form “The F is G”:

• (R) “The F is G” is true iff d ∈ G,

where d is the referred object, and G is the extension of predicate “G”. Actually, Zouhar distinguishes the “radical” referentialism from the “moderate” one. Contrary to the former (which proposes analysis (R)), the latter view holds that the nominal “F” contributes to the proposition expressed. Namely, the moderate referentialism is, according to Zouhar, the view which ascribes the following truth conditions to the subject-predicate sentences:

• (MR) “The F is G” is true iff d ∈ F & d ∈ G.

In sum, the referentialism is the view that an utterance with a referentially used description expresses an object-dependent proposition, that is, it claims that the truth value of the proposition expressed depends—in some way or the other—on the condition of particular d which the speaker has in mind.

Against the presented view, Zouhar formulates the argument which he calls “the Argument from Inference”. That is to say, he invites us to investigate what the consequences of accepting (R) (or (MR)) are for an evaluation of some simple inferences which contain sentences of the form “The F is G”. As Zouhar maintains, the verdicts delivered by referentialism—in either of its versions—are unsatisfactory. It evaluates some clearly incorrect inferences as “valid”, or it does not show the validity of some inferences which are intuitively correct.

Firstly, according to Zouhar, the radical referentialism must evaluate an inference of the form

• (1) The F is G. Hence, some Fs are G,

as invalid. The reason for this is that the radical version conceives (1)—as Zouhar maintains—as an inference from the proposition that d ∈ G to the proposition that F ∩ G ≠ ∅ , which is obviously invalid. The problem does not concern the moderate version. However, this position must, in turn, agree that an instance of the following inference is valid:

(2) The F is G. Hence d is G.²

The acceptance of (2) is, according to Zouhar, a result of acceptance of analysis (MR). Namely, a proponent of the moderate referentialism takes the premise to express the proposition that d ∈ F & d ∈ G, while he takes the conclusion to express that d ∈ G, and the former proposition clearly entails the latter. However, as Zouhar observes, this verdict is again unsatisfactory. In conclusion, since neither the radical referentialism nor the moderate one provides a correct account of the aforementioned inferences, the referentialism fails as a semantic theory of descriptions.

Having presented the core of Zouhar’s argumentation against referentialism, I will now proceed to my critical remarks. Two main objections of mine will be considered separately, in section (II) and (III) respectively.

(II)

The first major objection is, roughly, that Zouhar’s argument does not actually aim the core of the view that descriptions may be referring terms. Before I explain my objection, let me observe first that Zouhar does not carefully distinguish all possible positions concerning the semantics of descriptions which are presented in the literature. For example, he does not take into consideration a theory presented by Sainsbury (2004), according to which descriptions are referring expressions and so the sentences of the form “The F is G” have a simple logical form, though they have “Russellian” truth conditions (such an interpretation is possible in virtue of applying a free negative logic as a basis of formal semantic theory). Additionally, Zouhar ignores the proposal of Elbourne (2005) who conceives descriptions as complex referring terms and assigns “Fregean” truth conditions to the sentences with descriptions. What is characteristic for both aforementioned positions is that they claim that descriptions in their attributive use are devices of reference. It is important to note that such a view is immune to the Argument from Inference because we can account for inferences (1) and (2) properly on the ground of the theory of Sainsbury or Elbourne.

The fact that Zouhar does not take into consideration the aforementioned theories is not, however, a problem for his critique as yet. As it was noted, the author clearly targets the position that when the use of a description is referential (in Donnellanian sense), the description acquires a referential semantic content which cannot be captured by Russell’s quantificational analysis. However, the problem is that Zouhar relates this position to a conception of reference which is not accepted by all advocates of the position in question and which is, moreover, not essential to the idea that the referentially used descriptions have a different semantic interpretation than the attributively used ones. Let me explain this now.

As we may observe, analyses (R) and (MR) stipulate the truth conditions of subject-predicate sentences with descriptions. On the other hand, when Zouhar proceeds to his Argument from Inference, he starts to talk about the “propositions” expressed by such sentences. Obviously, this shift is understandable provided that we conceive validity of inferences in terms of the entailment-relation between the propositions expressed by the premise(s) and the conclusion(s). But what Zouhar simply does is to take—as the proposition expressed by “The F is G”—what stands on the right-hand of biconditionals (R) (or (MR) respectively.) Accordingly, the view that the referentially used descriptions are semantically referential has been related to the view that the proposition expressed by a referential statement has simply object d as a constituent: it has d as a constituent and ascribes G-hood to d (radical referentialism), or has d as a constituent and ascribes F-hood and G-hood to it (moderate referentialism).

It is quite obvious now that Zouhar places the idea that descriptions might have a semantic referential interpretation in the framework of the so-called “direct reference”. The idea standing behind this label is that a referring term (a name, an indexical etc.) contributes directly its referent to the proposition expressed—that is to say—the term contributes an element of the world to the semantic content of the sentence containing this term.³ In fact, Zouhar explicitly commits himself to the direct-reference approach in some passages (e.g., he notes that the referentialism “has it that ‘the F’ contributes, to the proposition expressed […], an individual” (p. 31) and furthermore: “according to Devitt, Reimer, et al., it is what the description is used to refer to that enters to the proposition expressed by an utterance involving the description.”, p. 36, ft. 9).⁴ With respect to this, it is important to emphasize that even the “moderate” referentialism—which Zouhar identifies with Devitt’s position—is forced into the framework of the direct reference. The only difference with respect to the radical referentialism is that the former claims that not solely the individual referred contributes to the proposition expressed, but also the property from the description.

To sum up, the Argument from Inference targets specifically the direct-reference approach to the semantics of referentially used descriptions. Let me proceed now to an explanation why I think this is problematic for Zouhar’s critique. First of all, not every theorist who claims that referentially used descriptions have a referential semantic interpretation explain their semantics in terms of direct reference. For instance—contrary to Zouhar’s remarks—Devitt distances himself from the view in question (he rejects it in many places, see: et al. 2012).⁵ Setting his declaration aside, it is quite easy to recognize that his conception of referential meanings of descriptions is far from the direct-reference approach. Devitt identifies three elements which constitute the meaning of a referential description token. The core of the meaning is its reference-determining relation to the particular object that the speaker has in mind. This relation is, in turn, explained in terms of causal perceptual links to the object, in virtue of which a given thought is about that object. Secondly, Devitt acknowledges that nominal “F” also contributes to the meaning of a referential description token; however, he becomes neutral on the issue what this contribution is precisely. Finally, he observes that the convention of using “the F” referentially is somehow different from the one related to indefinite descriptions, and this convention ought to be taken into a full account of referential meanings. (Compare: Devitt 2004, pp. 290–5.)

In other words, in Devitt’s theory, the object referred is not taken to be a constituent of the referential meaning of a description token. Since, in general, what contributes to the proposition expressed by a sentence of the form “The F is G” is the meaning of “the F”, we cannot agree with Zouhar that “according to Devitt, what the description is used to refer to enters to the proposition expressed.” The individual referred does not enter the proposition expressed simply because it is not a constituent of the embedded description’s meaning. Presumably, the reason why Zouhar relates Devitt to the direct-reference approach is that Devitt uses the term of a “singular thought”—and by “singular propositions”, philosophers usually mean exactly the propositions which have individuals as their constituents. Nevertheless, Zouhar should not be misled by this fact, since Devitt explains what he means by “singularity” of a thought (2004, p. 290) and, surely, it has nothing to do with the direct-reference view.

So far, we have seen that the Argument from Inference does not actually target all possible versions of the view that referentially used descriptions have a referential semantic interpretation. However, one may say that this observation is irrelevant as an objection to Zouhar’s position, since his critique can be actually regarded as an attack on a particular version of the view in question, namely, the direct-referential kind. Moreover, this particular kind is not that unusual since there are philosophers who describe the “referentialism” about descriptions in a similar vein as Zouhar does, namely, they take it to be a position that a referentially used description introduces the referred object to the semantic content of the sentence (for example, Neale (1990, p. 65) seems to endorse a characterization of “referentialism” equivalent to Zouhar’s characterization of “radical referentialism”). So, as one may conclude, Zouhar’s argument can still be found as relevant in the debate on the semantics of the referentially used descriptions.

Nonetheless, I think that the above attempt of defending Zouhar’s argument is unconvincing. The first general point is that an equation of the “referentialism” about the semantics of referentially used descriptions with the direct-reference account of them—even if not specific to Zouhar alone—is simply incorrect. The problem concerning Donnellan’s “attributive/referential” distinction is whether the latter use determines a different semantic convention, that is, whether a referentially used token of a description has a kind of a “referential” meaning which is not captured by Russellian quantificational interpretation. If someone accepts this thesis, he may describe this “referential” meaning in various ways and the direct-reference approach is just one of the options. Hence, if Zouhar’s goal is to target specifically the direct-reference account of the referentially used descriptions, his argument misses the core of the problem concerning their semantics. Secondly, I believe that it would be inadequate to interpret Zouhar’s intention as if he wanted to reject only a particular variant of the view that the referential use is semantically significant. Observe that the author has not even made the slightest suggestion that among various versions of the view in question, he is targeting only specific one(s). On the contrary, he assumes that his argument has an essentially wider application. As we have seen, Zouhar argues that even a causal-perceptual conception of reference (like the one of Devitt)—which he erroneously puts in the framework of direct reference—does not deliver an adequate account of the semantics of the referentially used descriptions. In other words, it is not a problem that the Argument from Inference has a narrow application; the point is that it has much more limited application than its author assumes it to have.

Finally, I think that the most problematic issue in Zouhar’s adoption of the direct-reference framework is that his analysis implies a quite implausible version of this view with regards to the referentially used descriptions. Observe that the letter “d”—as its stands on the right-hand of the biconditionals (R) and (MR)—functions like a proper name or an individual constant referring to an object the speaker has in mind by using “the F”. If it is an expression of this kind, then it refers to the same object no matter which particular context we consider. But this is plainly wrong. Obviously, the speaker may use “the F” to refer to different objects in various contexts and the analyses provided by Zouhar do not actually account for this fact. In other words, it would be equally wrong to ascribe the following truth conditions to an utterance of “I am tall”:

• (3) “I am tall” iff James ∈ TALL,

where “TALL” denotes the set of tall individuals and “James” is a constant name denoting a certain man. Presumably, what Zouhar should consider is the following way of specifying the truth conditions of utterances with referentially used descriptions:

• (R*) An utterance of ‘The F is G’ is true relative to context C iff the object that the utterer of ‘The F’ has in mind in C ∈ G.

• (MR*) An utterance of ‘The F is G’ is true relative to context C iff the object that the utterer of ‘The F’ has in mind in C ∈ G and it ∈ F.

With respect to this, observe that when it comes to conducting a test in order to check whether the theory based on (R*) and (MR*) can distinguish valid inferences from the invalid ones, we should firstly consider a particular context of use, since it is the context which helps us determine the proposition which is expressed by a referential utterance. Afterwards, i.e., once we establish what particular propositions are expressed in a given context, we should ask ourselves whether the proposition(s) expressed by the premise(s) entail(s) (or not—depending on what the theory predicts) the proposition expressed by the conclusion.

In sum, the first major problem with the Argument from Inference is that it targets specifically the direct-referential approach to the semantics of referentially used descriptions. As I have argued, this fact is problematic for Zouhar’s consideration in several ways. Firstly, the direct-reference approach is irrelevant to the idea that the referentially used descriptions are referring terms. Secondly, Zouhar assumes that his Argument has an essentially wider application than it really does. Thirdly, by ignoring context-sensitivity of descriptions, Zouhar identifies their semantics with the standard semantics of proper names or individual constants. The resulting account is highly improbable given the direct-reference framework.

(III)

The second major problem with the Argument from Inference is that it is overgeneralized reasoning. That is to say, given that we accept it in the case of descriptions, we are legitimated to conclude that various other expressions—even paradigmatically referring ones—cannot be semantically referential. This means clearly that there must be something wrong with this argument. In the second part of this section, I will indicate two elements of the Argument from Inference which may be responsible for the overgeneralized conclusion.

Firstly, let me demonstrate some undesirable consequences of Zouhar’s reasoning. I will use proper names as an example. Suppose that the name “Mark Twain” denotes an individual d. Certainly, not only do we use this expression in order to refer to d, but it designates this individual by means of certain linguistic conventions. We may call this claim “referentialism about proper names”. Since d is a semantic referent of “Mark Twain”, the truth conditions of a simple subject-predicate sentence containing this name are as follows:

• (RN) “Mark Twain is G” is true iff d ∈ G

Let us check now how the referentialism about names evaluates some inferences. In particular, let us consider Zouharian example:

• (3) Mark Twain is a writer. Hence d is a writer,

where “d” is a referential term which refers exactly to d. According to the Argument from Inference, (3) must be then valid since it is simply an inference from the proposition that d ∈ writers to the proposition itself. However, this verdict is clearly unsatisfactory. Consider, for example, the following instance of the above inference:

• (4) Mark Twain is a writer. Hence, Samuel Clemens is a writer.

Intuitively, we cannot derive the conclusion from the premise without any additional knowledge. Validity of inferences is a matter of logical or analytic connections between the premise(s) and the conclusion, while in the case of (3) / (4), the truth of the conclusion is guaranteed by the truth of the premise together with a purely empirical fact that both expressions—the one from the premise and the one from the conclusion—refer to one individual. To sum up, by applying Zouhar’s argument, we have demonstrated that the referentialism about proper names cannot distinguish valid inferences from the invalid ones. Since such a theory does not pass the test of inference-evaluation, it must be wrong. In brief—names cannot be semantically referential.

The presented reasoning may raise a doubt. As we may observe, I have considered a theory according to which “Mark Twain”—and, respectively, “Samuel Clemens”—contribute only their referents to the proposition expressed in a sentence. But what happens when we consider a theory according to which proper names in general contribute something more than merely their referents to the proposition expressed, e.g., some conceptual elements? It seems that such a theory would pass the test of inference-evaluation, since “Mark Twain” and “Samuel Clemens” may obviously contribute different concepts to the sentences in which they occur and so the premise in (4) would no longer entail the conclusion. Based on this observation, one may conclude that the Argument from Inference does not lead to the undesirable consequence by itself, but its result depends on the choice of the theory.

I cannot fully agree with the aforementioned objection to my claim that the Argument from Inference suffices to reject the referentialism about names. Let me explain why. My claim was that provided we agree that Zouhar’s argument works for descriptions, we should also agree that it works for proper names. However, the problem with the aforementioned objection is that it undermines the Argument from Inference when it is already applied to descriptions. According to Zouhar, the referentialist must acknowledge that an inference of the form

• (2) The F is G. Hence d is G,

is valid. However, one may observe that this verdict is legitimate only if we additionally assume that the referential term “d” does not contribute anything more than its referent to the proposition expressed; for if “d” introduces a kind of a conceptual element into the proposition expressed—the one which is not involved in the semantic content of “the F”—the premise would no longer entail the conclusion.⁶

In other words, it seems that Zouhar’s argument is so constructed that it actually assumes that a referential term “d” which is used in the conclusion (in inference (2)) must only contribute its referent to the proposition expressed; otherwise, the argument does not work. But this assumption—when applied to the case of (3)—suffices naturally to preserve the conclusion that proper names cannot be referential, since it guarantees that “d” does not introduce anything more to the propositional content of the statement than “Mark Twain” does, and so (3) must be unfortunately classified as valid.

Let me turn back to the main point. The presented reasoning concerning proper names indicates that the Argument from Inference can be used for rejecting the referential treatment of almost any kinds of terms.⁷ That is to say, if Zouhar’s argument is correct, there are probably no referential terms in the natural language(!) By reductio ad absurdum, I have demonstrated then that the Argument from Inference fails at some point. Let me now consider what its problem may be.

In my opinion, there are two difficulties in Zouhar’s argumentation. (I am not sure which one is the real source of the problem.) The first one is, not surprisingly, an adoption of the framework of direct reference. One may say that what really vitiates the argument is the direct-reference approach taken throughout the whole argumentation. As we have seen, the conclusion that the referentialism about descriptions / proper names cannot properly evaluate inference (2) / (3) comes from the assumption that a description / name contributes its referent to the proposition expressed and, moreover, that “d” contributes nothing more to the proposition expressed than its referent. So, perhaps at least one of these “direct-reference” assumptions should be abandoned. In sum, one might suspect that it is, in fact, the direct-reference framework which makes the test of inference-evaluation incorrect.

The second problematic step concerns the issue of “validity”. Zouhar’s argument brings the conclusion that (2) / (3) must be valid according to the referentialism about descriptions / names, since the proposition expressed by the premise in (2) / (3) entails the proposition expressed by the conclusion in (2) / (3). However, we may consider a different notion of validity by introducing the entailment relation between the logical forms of the sentences (and not between the propositions expressed by them.) We would say that sentence A entails sentence B iff for any interpretation I: if the logical form of A is true with respect to I, then the logical form of B is true with respect to I. (Accordingly, an inference from A to B is valid iff A entails B.)⁸ Given such a notion of validity, (2) and (3) come out as invalid from the viewpoint of the referential interpretation of proper names and descriptions. It is because there is an interpretation under which the logical form of “The F is G” (which the referentialist would like to represent as “G(the F)”) is true, while the logical form of “d is G” (that is, “G(d)”) is false, and there is an interpretation under which the logical form of “Mark Twain is a writer” is true and the logical form of “d is a writer” is false. In sum, provided we choose an alternative notion of validity, i.e., the one which concerns the logical form of sentences and not their propositional contents, the referentialism (about proper names, descriptions etc.) would formulate correct evaluations of the presented inferences.

(IV)

Throughout this paper, I have argued that Zouhar’s test of distinguishing valid inferences from the invalid ones—designed for the view that descriptions (in their referential use) are semantically referring expressions—is incorrect. Firstly, his argument is constructed in such a way that it solely targets the direct-reference approach to the semantics of the referentially used descriptions and this approach is not essential to the aforementioned view. Moreover, I have noted that Zouhar does not take into account context-sensitivity of the referentially used descriptions, which makes the position he targets quite peculiar. The second objection of mine was reductio ad absurdum. As I have argued, Zouhar’s reasoning can be used to demonstrate that proper names (in general, paradigmatically referring expressions) cannot be semantically referential. In the final part of my critique, I have identified two premises underlying the reasoning of Zouhar which may be responsible for its incorrectness. Firstly, we may reject the framework of direct reference assumed throughout the argument, which enables us to block the conclusion that the semantic content of the premise in inference (2) / (3) entails the semantic content of the conclusion. Secondly, we may adopt another notion of validity which enables us to say that (although the premise in (2) / (3) entails the conclusion) the inference is, nevertheless, invalid in the refined sense.

In the light of my consideration, one may attempt to conceive the Argument from Inference as reasoning directed not against the referential treatment of descriptions but rather against the direct-reference approach in general. That is to say, the argument shows that a theory of descriptions, names etc.—settled in the framework of direct reference—leads to a confusion of valid inferences with invalid ones. Nevertheless, a defender of the approach in question has some resources in order to provide adequate evaluation of the aforementioned type of inference. In particular, he may wish to apply another notion of validity (e.g., the one concerning the logical forms of sentences) according to which (2) / (3) is invalid.⁹ Yet he should justify his choice, that is, he must explain why we should not regard propositions as the entities which enter the relation of entailment essential to validity of inferences.

The fact that Zouhar’s Argument from Inference is vitiated does not mean, nevertheless, that the idea of testing a semantic theory of descriptions by checking its evaluations of various inferences with descriptions is wrong. On the contrary, it is important that the semantic theory makes correct predictions about (in)validity of inferences we make. As far as I know, no theorist has ever subjected Russell’s theory to a general test for distinguishing valid inferences from invalid ones.¹⁰ In particular, we may wish to investigate whether the uniqueness claim (i.e., the claim that there exists exactly one F) becomes, as Russell sees it, a part of the semantic analysis of a sentence of the form “The F is G”.¹¹ If this is true, then the following inference would be valid:

• (5) The table is covered with books. Hence, there is only one table.

However, I doubt whether the competent users of English would classify the above inference as valid. (Perhaps, this guess could be tested empirically.) If my intuition is right, then the proponent of Russell’s theory of descriptions owes an explanation why the users of language reject the above kind of inference.