How Paradoxical Is the Liar Paradox?
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Maria J. Frápolli, How Paradoxical is the Liar Paradox? in LOGOS ARCHITEK- TON, Journal of Logic and Philosophy of Science, Topic: Paradoxes, Edited by Virgil Draghici, Vol. 2, No. 2, Autumn - Winter 2008, Cluj University Press, 2008, Cluj-Na- poca, Romania, pp. 7 - 34.
HOW PARADOXICAL IS THE LIAR PARADOX?
María J. Frápolli
Department of Philosophy I
University of Granada (Spain)
1. THE PROBLEM
Few philosophical puzzles have been more damaging for the development of a discipline than the so-called “Liar Paradox” for semantics. The Paradox has been taken seriously by most part of the philosophical world, and many different strategies have been proposed to solve it. But the Liar Paradox is just this, a paradox, a game with words, a sophisticated joke. It is not a contradiction, it does not suppose any threat for the study of meaning and neither shows it the limits of language and thought. As most paradoxes, it has meant a challenge that has led theorists to improve their instruments, successfully in this case, and now a day linguistics and the philosophy of language have the tools to analyzing it away and explain why it has seemed so frightening for centuries.
It is a basic piece of logical knowledge that if from a set of assumptions a contradiction follows, something goes wrong with the set of assumptions. Nevertheless, which one of the assumptions is responsible for the troubles is usually something that cannot be derived from the contradiction alone. Behind the many different versions of the paradox there are a handful of suspicious postulates. In the case of Tarski’s version of the paradox, these postulates include the interpretation of quotation marks known as the “logical block” view and the classical objectual interpretation of quantifiers. Both assumptions can be challenged from the present state of the philosophy of logic and of language. Self-reflexivity is another and there are others. But the only assumption which is common to all the different versions of the Liar is the thesis that sentences are the bearers of truth. Tarski blamed the notion of truth and the universality of natural languages and proposed a hierarchy of languages in each of which the semantic apparatus of the previous one was included, although its own semantic remained outside. Tarski’s solution has become a sort of dogma in analytic philosophy. As a piece of theory, it is in principle unobjectionable. A theoretical proposal is at most useful or idle, illuminating or obstructive, explicative or paralysing. What Tarski’s proposal is for sure is unnecessary and, to say the least, misguiding.
The paradox is historically related to Epimenides, the Cretan prophet who lived in the VI century BC, who allegedly declared that all Cretans were liars. With the structure of a paradox, it was formulated by Eubulides of Miletus in IV century BC. St. Paul, in the letter to the Cretans, reproduced Epimenides’ opinion about his co-citizens and from then on it has been repeated over and over again across centuries. In 1930, Tarski converted it in the main argument that led him to the claim that natural languages were inconsistent, since the concept of truth leads inevitably to contradictions. Tarski offers the following diagnostic:
“In § 1 [of his (1930)] colloquial language is the object of our discussion. The final conclusion is totally negative. In that language it seems to be impossible to define the notion of truth or even to use this notion in a consistent manner and in agreement with the laws of logic.” (Tarski 1930/1983: 153) A few pages later, he insists:
“ A characteristic feature of colloquial language (in contrast to various scientific languages) is its universality. It would not be in harmony with the spirit of this language if in some other language a word occurred which could not be translated into it; it could be claimed that ‘if we can speak meaningfully about anything at all, we can also speak about it in colloquial language’. If we are to maintain this universality of everyday language in connexion with semantical investigations, we must, to be consistent, admit into the language, in addition to its sentences and other expressions, also the names of these sentences and expressions, and sentences containing these names, as well as such semantic expressions as ‘true sentence’, ‘name’, ‘denote’ etc. But it is presumably just this universality of everyday language which is the primary source of all semantical antinomies, like the antinomy of the liar or of heterological words. These antinomies seem to provide a proof that everyday language which is universal in the above sense, and for which the normal laws of logic hold, must be inconsistent.” (Tarski 1930/1983: 164). Thousands of pages have been written on Tarski’s diagnostic on natural languages, on his derivation of the Liar paradox and on his solution. Thousands of pages have been written too assessing the paradox and its scope and offering alternative solutions to that of Tarski. We will not be concerned with Tarski’s historical neither is it our purpose to offer a new solution to the paradox to be placed on the shelf besides the rest of alleged ways out. What is to be presented in what follows is an exercise of data crossing. It will consist in placing the customary claims defended when one is explaining, evaluating, or attempting to solve the liar paradox in the context of the contemporary studies of language. This way, it will be shown that the background assumptions behind the derivation of the paradox cannot be sustained in the current state of the language studies. More specifically, no contemporary theory of language recognizes sentences as the bearers of truth and falsity. What is semantically evaluable is what is said by the use of a particular utterance. No discussion is provoked by this last claim, although there are lively debates about how what is said is reached at and the contribution of context in its constitution, debates that aim at drawing the relative boundaries between semantics and pragmatics. On the other hand, any derivation of the paradox makes essential use of sentences as truth bearers. The view of language required to derive the paradox no longer represents a defendable view, even though it was the best scientific theory available in Tarski’s times.
2. WHAT DOES “INCONSISTENCY” MEAN?
Before going into the details, let us indulge in a general reflection prompted by the Tarskian texts just quoted. Arguments, valid or not, are commonly defined as set of propositions. Propositions and sets of propositions are the bearers of logical properties; they are the entities capable of being consistent or contradictory. Theories can also be said, in a derivative way, to be consistent or inconsistent. What would it possibly mean to predicate consistency or inconsistency of a language, which is after all only an instrument of information transmission? A language can undergo fraudulent usages, but fraudulent usages don’t convert the instrument in inconsistent ─ bad workers always blame their tools. This is nevertheless the astonishing claim that Tarski made of natural languages, and that after him everybody seems to have swallowed. It might be replied that what Tarski in fact proclaimed to be inconsistent is the notion of truth in natural languages. Let us explore what might be the real import of such a claim. The claim that a notion is contradictory can only mean that there is a tension between its application conditions and its consequences. If a notion’s “introduction rules” have consequences that are not justified by the kind of situation that entitles us to apply it, then it is appropriate to declare the notion inconsistent. But inconsistency applied to a notion is not identical to inconsistency applied to sets of propositions. A notion is inconsistent when its use is not conservative, i. e. when the consequences of its application exceed the conditions that enable its introduction. A well known example of inconsistent notion is the case of “tonk” introduced by A. Prior (Prior 1960). “Tonk” is allegedly a sentential connective which has the introduction rules of the disjunction and the elimination rules of the conjunction. This way, it permits to draw conclusions that are not justified by the set of assumptions we have began with. Is truth a notion of this kind? The answer is in the negative, and there are several reasons that support it.
The main reason to reject that truth is inconsistent is that there is no tension between the situations in which we are allowed to apply the notion and the consequences that derive from this application. For the conditions for the application of a truth ascription are the same as the conditions for the assertion of the proposition which is its content. And the consequences of a truth ascription are the consequences derived from the assertion of its content. If there were tension between introduction and consequences in the case of truth, it would infect the notion of assertion itself ─ an extreme thesis for which there is no justification. Consider the following two examples, (1) and (2),
(1) China is an astonishing country [said by Victoria in context C]
(2) Obama is a promising candidate [said by Victoria in context D]
(3) What Victoria said [in a particular context] is true.
Example (3) is a truth ascription in which the speaker ascribes true to what Victoria said (in a particular context). If the utterer of (3) refers to an occasion in which Victoria had uttered sentence (1), then he would expressed exactly the same proposition as the proposition expressed in (1). The same sentence (3), “What Victoria said is true”, can be used to recover any other proposition provided that it has been said by Victoria in some context to which the speaker links his truth ascription. In particular, if the utterer of (3) refers to context D, the content of his truth ascription would have been the proposition expressed by (2).
The application conditions of a truth ascription such as (3) are exactly the same as the assertion condition of its content. If a speaker wants to ascribe truth to the content of (2), the enabling conditions of his truth ascription would be the same as the assertion condition that his act of asserting that Obama is a promising candidate would have. If a speaker wants to ascribe truth to the content of (1), the enabling conditions of his truth ascription would be the same as the assertion conditions of his act of asserting that China is an astonishing country. The use of a truth ascription is acceptable always that asserting the proposition (or set of propositions) which is its content is acceptable. This is a general description of a truth ascription’s application conditions. The particular conditions of particular truth ascriptions depend on their particular contents and contexts. A speaker endorses a content by means of a truth ascription when he considers that the content is or should be part of the assumed information, inside the scope determined by the context. Truth is applied to a content when the content is assumed to be safe enough to be used as a step in the derivation of some other contents, or safe enough to be considered part of the shared knowledge. The consequences of qualifying a content as true are identical to the consequences that an act of direct assertion of the content would have in the context at issue. An asserted content, be it the product of a direct act of assertion or of a second order act, as it is in the case of truth ascriptions, is a “usable” content. The particular consequences of asserting a particular content depend on its particular composition and on the characteristics of the context concerned. When a speaker highlights a content by ascribing truth to it, he is performing several acts; one of them is partaking with his audience a part of the web of his beliefs, another is stressing the character of the content as part of the (the speaker’s or shared) background assumptions; a content put forward as true is something ready to be used as a premise in inferential acts, a content highlighted to be part, or welcome for the first time to be a part, of settled information. There is thus no conflict between the circumstances that allow a speaker to introduce the notion and the consequences that the introduction may have. If from the notion of truth a contradiction follows, the only reason for it has to be misuse. We will show that the Liar Paradox is the product of an incorrect use of a truth ascription. It is in fact the product of a categorical mistake in Ryle’s sense.
A minor remark from a more run-of-the-mill perspective will serve to present a further reason to reject the inconsistency of truth. If truth were a contradictory notion, as many have defended, or if it were a useless piece of language, as the followers of the theory of redundancy have thought, it would be a real theoretical difficulty for a general naturalistic account of language and rationality, i.e. for a scientific account, to explain its pervasiveness in natural languages. All natural languages we know of include a notion or a family of notions that are equivalent to the English truth apparatus. From the perspective of the language users, it would be a deeply mysterious phenomenon the fact that ordinary speakers in all languages are able to understand and make use of the truth terms without difficulty and with sound results, something that Tarski himself acknowledges (1930/1983: 153). A theory of truth that defends the inconsistency of the notion should account for the consistent uses, which in terms of frequency are an immense majority. The redundancy defenders should, on their turn, explain how truth is probably one of the most recurrent notions in any language.
3. TRUTH BEARERS
There has traditionally been a range of entities postulated as the bearers of truth: judgments, thoughts, beliefs, sentences, propositions, and utterances are amongst them. Psychological entities, such as judgments, beliefs and thoughts, were more common in the xix century; analytical philosophers typically embraced sentences due to their generalized reluctance to deal with abstract entities, a reluctance that counted off propositions for the alleged difficulties derived from their identification criteria and from their ontological status. The move of declaring sentences the primary truth bearers has led the theory of truth to a dead end, a situation for which the generalized success of the Quinean attacks against intensional entities are in part responsible. Classical analytic philosophy is not the only position to be blamed: the developments of formal logic and formal semantics are not innocent either. The point at which formal sciences have their share of responsibility rests on the confusion between formulae in artificial languages, which in fact represent propositional structures, and sentences in natural languages, which are syntactic strings of signs plus their conventional meanings.
The option of sentences as primary truth bearers is not supported by contemporary linguistics and philosophy of language, as it will be showed below, but it is also unacceptable from the point of view of pragmatism of all times. On truth bearers, Ramsey, for instance, says:
“First we have to consider to what class of things the epithets “true” and “false” are primarily applied, since there are three classes that might be suggested. For we use “true” and “false” both for mental states, such as beliefs, judgments, opinions or conjectures; and also of statements or indicative sentences; and thirdly according to some philosophers we apply these terms to “propositions”, which are the objects of judgments and the meaning of sentences, but themselves neither judgments nor sentences. […] The third class consisting of statements or indicative sentences is not a serious rival, for it is evident that the truth and falsity of statements depends on their meaning, that is on what people mean by them, the thoughts and opinions which they are intended to convey. And even if, as some say, judgments are no more than sentences uttered to oneself, the truth of such sentences will still not be more primitive than but simply identical with that of judgments.” (Ramsey 1927/1991: 6-7) This “not a serious rival” has been the option chosen by the widest part of the analytic philosophy of the xx century. The election of sentences as truth bearers has contorted the perspective from which truth has been analyzed. The manifest lack of understanding of the phenomenon of truth is shown in the interest and weight still given to the Liar Paradox.
The classical way in which the question of truth bearers has been formulated consists in asking for the entity of which the property of truth is predicated. And the answer should have helped to determine the kind of property truth is and its meaning. Nevertheless, as early as in 1884, Frege already advised “never to ask for the meaning of a word in isolation, but only in the context of a proposition” (1884: x). Applied to the analysis of truth, the principle amounts to the assumption that the minimal piece of language in which the enquiry about the meaning of truth makes sense is the whole sentence. Shorter pieces carry out combinatorial or procedural tasks whose complete import cannot be assessed unless the level of the speaker’s performance is taken into account. The Fregean principle is the first step, but other steps are needed. It is crucial for the right assessment of the sophisticated issues of meaning and content to address the attention to complete speech acts. The standard speech acts in which truth is essentially put to work are those that ascribe truth to a propositional content by the use of a specific kind of sentence, a truth ascription. Truth ascription, as (3) above, recovers a proposition already asserted, as (1) and (2), or assumed to be assertable. Thus, the relation between the truth ascription and its content is not that of subject and predicate, or substratum and property, something that Frege clearly saw (Frege 1892: 64). The grammatical predicate “is true” does not predicate anything of a subject, its contribution to the proposition expressed by the sentences in which appears is assumed by propositional variables and the quantifiers that bind them. There is no truth-conditional content attached to the truth predicate. In contemporary terms, we would say that truth terms have procedural1, as opposed to truth-conditional meaning. For these reasons, the
1 For a discussion about non truth conditional meaning, see Wilson (1975), Blakemore (1987), Bezuidenhout (2004). classical terms in which the issue of truth bearers has been stated no longer makes sense.
In contemporary philosophy of language there are two2 main theories in competition, both heirs of Grice’s spirit: “Minimalism” or “Literalism”, on the one hand, and “Contextualism”, on the other. Minimalism assumes that what is said by the utterance of a sentence, such as (4),
(4) You are not got to die3, is the proposition derived from the literal meaning of the words that occurred in it. Even if sometimes these meanings fall short of yielding a semantically evaluable entity, minimalism considers that what is literally said is the minimal reachable entity capable of being true or false. In the case of (4), what is said is that the referent of “you” is not going to die, full stop. Imagine an appropriate context for (4): a mother reassuring a child after a small domestic accident in which the child has suffered an innocuous cut. In this context, what a standard hearer understands is that the mother is saying to the child that he is not going to die because of this cut. The minimalist explanation is the usual Gricean one. What is literally said is that the child is not going to die whereas the more restricted information, that the child is not going to die because of the cut, is inferred as a conversational implicature in which the maxim of quality that ask the speaker not to say what he considers patently false is flouted. Minimalism acknowledges a role for the context, but restricted to the saturation of indexicals and the disambiguation of ambiguous items and structures.
Contextualists, such as Recanati and Carston4, offer a different analysis that complies with a general intuition, also attributed to Grice, which Recanati has dubbed as the “Availability Principle” (AP):
(AP) “What is said must be intuitively accessible to the conversational participants” (2004: 20).
According to contextualists, (AP) is enough to refute minimalism. The explanation that Recanati gives of (4) in (2004: 8-9) is that what the standard hearer immediately 2 In (2004), chapter 6, Recanati distinguishes five positions from strict literalism to radical contextualism, his own. For the sake of clarity, we will organize them into two groups, since in fact there is a feature that marl a clear division: the acknowledgment of genuine non articulated components. 3 The example is due to Kent Bach (1994:134) and commented by Recanati in Recanati (2004: 8-9). 4 Recanati (1993), (2002), (2004), Carston (2004) understands in the context at issue, i.e. that the child is not going to die because of the cut, is what is literally said, and the level of the Gricean minimal proposition, i.e. that the child is not going to die, is unavailable to the participants in the communicative act. The Gricean minimal proposition does not possess, according to contextualism, either psychological or logical relevance for the determination of what is said and of what is implicated. The main argument that contextualists use is the argument of semantic under-determination: out of a context, a sentence is a scheme without semantic properties. And the argument rest on the analysis of a bunch of examples such as the following (4), (5) and (6),
(4) I’ve had breakfast
(5) I’ve been to China
(6) John has three children.
The standard way in which (4) is understood is as saying that the speaker has had breakfast the day of the utterance, whereas in (5) what is commonly understood is that the speaker has been in China at least once in his life. In (6) what is usually understood is that John has exactly three children. Contextualists consider that what is commonly understood is what is literally said and that the enrichment that is produced from the literal meanings of the words used is prompted by the context in the form of conceptual components not connected to linguistic items.
On the other hand, minimalists too make room for components pragmatically triggered by the context of utterance, but either these components are mandated by the linguistic structure of the sentence or they have to be placed at the level of implicatures. The difference lies in that, whereas minimalist defend that context is only relevant for solving saturation and disambiguation processes, and the rest of contextual contributions gives rise to implicatures, contextualists defend that there is no level of content that is not essentially affected by bottom up and top down pragmatic processes. What is said is what a normal speaker intuitively recovers from an utterance in a particular occasion of use, which in the case of (4) is that the child is not going to die from the cut. The thesis that distinguishes contextualism from the diverse kinds of minimalism is that the determination of what is said essentially requires the participation of context. In what is literally said by an utterance in a context there always are conceptual components triggered by the context and not related to any word in the uttered sentence. And this happens over and above the processes of saturation and disambiguation. The components pragmatically triggered do not fill a slot in the linguistic logical form, but are, as Recanati (2002) following Perry (1993) calls them, genuine “unarticulated constituents”.
The application of this debate to the problem of truth is that no contemporary theorist, either minimalist or contextualist, places truth conditions in sentences. The entities that possess truth conditions are propositions, what is said by sentences in context. Sentences are semantically inert entities that fall short of determining an entity capable of bear logical or semantic properties. The difference between the two views is not relevant for our purposes, since minimalists consider that narrow context is essential to fill the slots represented by context-dependent expressions and to eliminate lexical and structural ambiguity and contextualists consider that wide context is essential to the determination of truth conditions, which are always affected by contextual factors. If sentences out of context don’t possess truth conditions, a fortiori they cannot be the bearers of truth.
Besides this debate, there is another comprehensive view on semantics that is fighting to find its place in the contemporary landscape. The view is known as inferentialism and its latest defender is Brandom (1994). Inferentialism draws the frontier of the debate differently. This time minimalism and contextualism lie on the same side as representational positions and inferentialism opposes them as a non- representational explanation of content acquision. Minimalists and contextualists coincide in that the main job of declarative utterances is representing states of affairs and that representation is the source of content. The content of thoughts and utterances is given through their truth conditions, and the only difference between contextualists and minimalists is the role they concede to the context in the determination of them. A radical contextualist as Recanati considers his proposal not only as a development of Grice’s positions but also an improvement of Austin’s semantics, which is a paradigm of representationalism and of truth conditional semantics. Inferentialism, on the other hand, considers that the property that defines what it is to be a concept is for this entity to be able to stand in inferential relations with other concepts; to possess a concept is for an agent to be able to place the concept in a web of inferential relations. In inferentialism, truth is defined on inference and not the other way around. The content of an utterance is the inference that goes from its application conditions to the consequences of its application and application conditions and consequences are defined in terms of an agent’s entitlements and commitments. Inferentialism stresses that inference is a more basic notion than that of truth and also that inferences are relation between content and not between sentences. The general background behind inferentialism, not only behind Brandom’s but also behind Ramsey’s brand, is pragmatism and pragmatism focus on rational actions and not in sentences detached from their actual uses. The lesson for the issue of truth bearers is clear, the bearers of content are complete speech acts, contents are the components of inferences and truth is what is preserved in a good inference.
Still another alternative theory on meaning and content is offered by Relevance Theory (RT), to which contemporary linguistics owes part of its features. (RT) was put forward by Sperber and Wilson in 1986 and its area of influence has extended from linguistics to the philosophy of language. (RT) represents an alternative to the way in which Grice explained the difference between what is said and what is implicated. Instead of assuming a Cooperative Principle with four maxims and a bunch of submaxims, Dan Sperber and Deirdre Wilson proposed only a general principle that does the whole job. This single principle, dubbed the “Principle of Relevance”, states that any utterance conveys its own relevance. What this means is that in order to interpret an utterance the hearer has to assume that the agent has uttered it in a way in which it reaches its communicative goal in the best possible way. (RT) is meant to be a proposal in communicative theory in which the principle of relevance is a cognitive principle about how the agent’s brain interprets acts. To our purposes, it is important to stress that (RT) is a pragmatist proposal and the Principle of Relevance is a pragmatic principle. Relevance is a maximally content-dependent notion and in this setting sentences as linguistic items do not play any role.
These theoretical proposals practically exhaust the contemporary repertoire of theories of meaning and content. The thesis of classical analytic philosophy that sentences are the primary bearers of truth has been substituted by the claim that what is true or false are the products of some speech acts: propositions, what is said, explicatures, or whatnot. This survey should be enough to conclude that the topic of the paradox deserves a new assessment (and for sure a peaceful rest). But a generalized trait of the different versions of the paradox should leave no doubt about the incorrectness of the treatment given to it: all liar sentences include indexicals and, in general, context-dependent expressions. If one is not yet convinced by the latest trends of the philosophy of language, it will suffice to remember any proposal about how indexicals works. Nor even the most conservative positions would reject that sentences with indexicals essentially require a context to determine the reference of referential terms and thus the utterance’s truth condition.
That sentences are not truth bearers is, from the point of view of the contemporary theories of language, an uncontestable claim. What is really paradoxical is that nobody defends today that sentences themselves are entities capable of truth and falsity while at the same time a vast majority of philosophers still consider the liar paradox damaging, if not directly fatal, to the enterprise of semantics. Nevertheless, truth and falsity apply to contents, to propositions, to what is said; if sentences are not primary truth bearers, there is no way of deriving the paradox. Contemporary linguistics and the philosophy of language have dissolved the paradox in their way of identifying the bearers of content. It is now time to definitively eliminate it from the repertoire of living philosophical puzzles.
4. TARSKI’S ACCOUNT
Because of the effects of his view on the matter, Tarski deserves a close look. Our concern is neither textual analysis nor historical accuracy, although the picture we offer of Tarski will be, we hope, fair. Tarski aimed to offer an analysis of the concept of truth in formalized languages, or so he declared. If this were the whole story, the rest of this section would be unnecessary. Formal languages are artificial systems designed with a particular purpose. As theoretical models of some aspect of language, as artificial code systems, they have the properties that their proponents have wanted them to have. One of the more visible characteristics of formalized languages of the kind concerned here is that they represent in their syntax the conceptual structure responsible for the inferential relations among their formulae5. Another is that their formulae are schemas. The formal brand of truth applicable to formulae in an artificial system is thus a theoretical notion
5 This feature of formal languages has been stressed by Etchemendy (1983). belonging of a particular theory. If it is satisfaction by all sequences of a certain kind, satisfaction in a formal model, representation of a state-of-affairs or whatever the theory makes it to be is something that contributes to the theory’s general import. Nothing to object as far as one keeps in mind that theoretical decisions related to artificial languages are not, or do not need to be, automatically exportable to the analysis of natural languages.
The scope of Tarski’s proposal is nevertheless unclear. The title of his first paper on truth seems to exclude the run-of-the-mill notion: “Der Wahrheitbegriff in den formalisierten Spragen”6, whereas in his paper of 1944, “The Semantic Conception of Truth and the Foundations of Semantics”, he declares that his aim is not to denote with a familiar word, “truth”, a new notion but to capture the meaning of the old notion of truth”7. Be it as it may, what is undeniable is that he proposed his hierarchy of languages and his semantic conception of truth as a result of his diagnostic of natural languages as inconsistent, and that most philosophers have followed him in this point.
It is interesting to compare Tarski’s analysis with the one given by Ramsey only three years before. Tarski declares that
“[a] thorough analysis of the meaning current in everyday life of the term ‘true’ is not intended here. Every reader possesses in greater or less degree an intuitive knowledge of the concept of truth and he can find detailed discussions on it in works on the theory of knowledge.” (1930/1983:153) Ramsey, in his posthumously published essay “The Nature of Truth”, says:
“What is the meaning of truth? It seems to me that the answer is really perfectly obvious, that anyone can see what it is and that difficulty only arise when we try to say what it is, because it is something which ordinary language is rather ill-adapted to express” (1927/1991: 9). Tarski’s preliminary analysis is (7),
(7) A true sentence is one which says that the state of affairs is so and so, and the state of affairs is indeed so and so (1930/1983:155).
And Ramsey’s proposed analysis is (8), 6 On the second page of this paper, Tarski says: “A thorough analysis of the meaning current in everyday life of the term ‘true’ is not intended here.” (1933/1983: 153) 7“The desired definition does not aim to specify the meaning of a familiar word used to denote a novel notion; on the contrary, it aims to catch hold of the actual meaning of an old notion. We must then characterize this notion precisely enough to enable anyone to determine whether the definition actually fulfils its task.” (1944:§ 1) (8) We can say that a belief is true if it is a belief that p, and p. (ibid.)
The similarities are striking. Besides, both authors vindicate their attainment to the Aristotelian definition, “To say of what it is that it is not, or of what is not, that it is, is false, while to say of what is that it is, and of what is not that it is not, is true” (Metaphysics, Gamma, 6 1011b25)8. But in spite of the many points of agreement their treatments cannot be more disparate. Tarski continues his analysis with (9),
(9) x is a true sentence if, and only if, p (ibid.), where (9) is a schema that gives rise to particular definitions when p is substituted by a sentence and x for a name of this sentence. If one compares what is said in (7) ─ and also in (8), Ramsey’s proposal ─ with what is said in (9) we see that an essential feature of the characterization has changed: the truth bearer. In (7) and (8) what is characterized as true is a content, what is said by a sentence in (7) and the content of a mental act in (8). In (9) the topic has shifted from contents to sentences.
Tarski explicitly defends sentences as truth bearers, the same option that Ramsey considered “not a serious rival” for judgments and propositions, and in doing it the hopes of an appropriate treatment of the paradox vanish. Propositional contents, the contents of our acts of assertion and of our mental acts, such as beliefs and doubts, conjectures and wishes, are the entities put forward as true. Sentences are, at most, appropriate vehicles for expressing them. The substitution of propositions by sentences in the analysis of truth is in no way innocent. It represents a distortion in perspective that impedes a clear assessment of the meaning of the notion and generates a big deal of scholastic muddle. Even if one accepts that the bearers of truth and falsity are not sentences, the risk of resting faithful to sentences is not yet correctly evaluated. Consider what Barwise and Perry declared on the topic of truth bearers:
“Truth, as we ordinarily understand the notion, is a property of things like claims, testimony, assertions, beliefs, statements, or propositions. It is not a property of sentences. But the decision to use sentences as the bearers of truth has proven to be a useful fiction, a good way of getting a certain amount of logic done without bogging down in extralogical questions about the nature of the bearers of truth. But the fiction is harmless only in cases where we can unambiguously associate a claim about the world with each sentence, or where the slippage between different claims made by different uses of a sentence is negligible for the purposes at hand” (Barwise and Etchemendy 1987: 10).
8Tarski in § 2 of his (1944), and Ramsey in (1927/1991) The fiction is not harmless, and not only has not “proven to be a good way of getting a certain amount of logic done” but, on the contrary, it has proven to be the origin of a confusing way of looking at truth that has converted the Liar Paradox in the more pressing difficulty of the topic. Considering sentences as the truth bearers would be harmless if the content of sentences were context-independent and it were possible to establish a one-to-one matching between sentences and the propositions expressed by them. And even so, we would need to be careful not to apply to sentences characteristics of contents and the other way around. Sentences are the bearers of linguistic meaning and they have syntactic properties such as well-formedness, always in connection with particular linguistic systems. The complexes of sentences plus their linguistic meanings might be thought to be the bearers of properties such as synonymy, and are one of the arguments, together with context, of the process that yield propositions as values, although if we assume the central thesis of Contextualism, sentences-plus-linguistic- meanings ─ the Gricean minimal proposition ─ don’t possess any psychological reality nor suppose any theoretical step in the determination of what is said. And finally contents, or propositions, are the bearers of logical properties and relations and the bearers of truth.
Barwise and Perry’s “useful fiction” would be harmless, we have said, if propositional content were context-independent. Contemporary theories of language have shown that it is not. But it is not necessary to go so far to see that neither sentences can bear truth nor the fiction is harmless. The distinction between sentences and their contents ─ which is not the distinction between sentences and their meanings ─ is inescapable as soon as demonstrative and indexicals enter the game. Sentences such as (10)-(14),
(10) He is a good friend of my sister
(11) This is real fun!
(12) I am too tired today
(13) Place the book on the table!
(14) What she said was unacceptable, cannot be assessed for truth or falsehood, simply because they don’t say anything in spite of being perfectly well-formed English sentences. This fact alone should be enough to remove sentences of the set of candidates to be primary truth bearers. Nevertheless, it cannot be said that we don’t understand anything in sentences (10)-(14); it is even possible to imagine type speech acts in which their utterance would be appropriate. What we understand in them is their linguistic meaning, which is always schematic and incomplete. But in the sense of “understand” needed here, the sense in which we can agree or disagree with a content, they cannot be said to be understood. In fact, they cannot be said to be understandable, since the object of understanding is the propositional content and these sentences, out of a context, do not provide one.
To see whether (10)-(14) say something true or false, we should be able to determine who the speakers are, the time of the utterances and the references of indexicals, pronouns and demonstratives. In (12), if we have to believe contemporary contextualism, we would have to recover from context the unarticulated constituent that represents the import of the scalar term “tired” modified by “too” ─ too tired for what?. In (13) “the book” and “the table” are referential terms, they refer to particular objects salient in context. The case of (14) is different, (14) includes the referential term “she”, the verb is in the past tense, what forces to interpret it as a parameter of the time of the utterance, but also includes a description. It is the function of context to supply the entity that satisfies the description. Even if all this is uncontroversial, when the topic is truth and the Liar Paradox the background knowledge that linguists and philosophers wouldn’t dare to challenge without having a serious theoretic alternative at hand seems to evaporate.
Let us take stock. Linguists and philosophers of language reject sentences as entities capable of truth or falsity. This is even so for sentences that don’t include context-dependent elements. Sentences and the contents that can be transmitted by means of them are distinct kinds of entity and possess different properties and features. If one doesn’t feel comfortable with the latest brands of pragmatics and prefers keeping faithful to more conservative positions, it is still possible to acknowledge that context is only indispensable to determine the content of sentences with demonstratives, indexicals, and the rest of referential terms. Radical or conservative, nobody denies that sentences with referential expressions are incomplete until the referents of referential terms are provided. And this can only be done by an appropriate context of use. Then, for sentences with referential terms the distinction between the level of linguistic meaning, whose bearer is the sentence itself, and the level of what is said by means of it in an appropriate context, is inescapable.
Now, all versions of the liar paradox, all liar sentences, include referential terms. A preliminary conclusion to be drawn at this point is that what the liar paradox shows is precisely that making of sentences the truth bearers leads to contradictions. This conclusion only offers a negative knowledge, that sentences are not truth bearers. The positive development is offered by contemporary theories of language that explain why this is so and which are the entities capable of bear semantic properties.
5. THE LIAR SENTENCES
Consider now the following list of standard versions of the paradox:
(15) This sentence is false
(16) I’m lying
(17) The sentence numbered as (17) on p. 17 of this paper is false
(18) A: What B says is true
B: What A says is false
(19) This proposition is false.
The simplest version of the paradox is represented by sentence (15), which seems to say that a sentence referred to by the demonstrative “this sentence” is false. If sentences are not truth bearers, a point that has been established already, the only way of making sense of (15) is interpreting that what is meant is that the proposition expressed by the sentence referred to by the referential expression “this sentence” is true. That is, sentences can be said to be true or false in a derivate sense, if what is said by means of them is true or false in a strict sense. Which content is said to be true in (15)? What is the structure of the proposition that is the content of (15)? To these questions there is no answer unless a proposition, a semantically evaluable entity, is proposed as the entity referred (indirectly, via another sentence) by the referential expression. Truth ascriptions and falsity ascriptions as (15) –(19) are a kind of propositional variable, they are pro-sentences. Variables are the kind of item for which the diversion between meaning and reference, or character and content, is more evident. A truth (falsity) ascription is a well formed sentence that possesses a precise linguistic meaning. Its content nevertheless has to be drawn from the context. By means of a truth ascription a speaker gives his support to a content, to which he characterizes as true.
A truth ascription such as (20),
(20) What Victoria says is true, doesn’t say, in a strict sense, anything. It is compatible with any proposition whatsoever.
If Victoria had said that (21),
(21) The Earth is warming up dangerously, what the utterer of a particular token of (20), contextually linked to (21), would have said would be exactly (21). If Victoria had said that (22),
(22) In Spain, the birth rate is slowly rising, what the utterer of a particular token of (20), contextually linked to (22), would have said would be exactly (22). Truth ascriptions only make sense as second order acts, since truth ascriptions work as propositional variables that acquire their content through their contextual link to the content of a complete act of assertion. Asking about the content of (20) out of a context is as absurd as asking about the content of pronoun “he” out of a content.
So much is clear. Then, let apply these intuitions to the analysis of the Liar. What invariably happens with the liar sentences is that a truth ascription ─ a falsity ascription, in this case ─ is proposed without the previous occurrence of a genuine act of assertion from which the truth ascription can extract its content.
Consider what happens when (15)-(19) are placed in appropriate contexts:
(23) “China is a democratic country”. This sentence is false
(24) When I said that I wasn’t concerned, I was lying (25) The sentence numbered as (17) on p. 17 of this paper is false
(26) B: There is life in Mars
A: What B says is true
B: What A says is false
(27) That truth cannot be defined is a false proposition
With the exception of (25) which is irrecoverable, the rest acquires perfect sense when complemented by some other information. The standard versions of the Liar severe the truth ascriptions from their content source, and make of them content-less variables. If sentence (15) refers to a particular sentence, it inherits its content. To be able to do so, the sentence referred to has to possess a content on its own. This only happens if the sentence has been uttered as part of an assertive speech act, since sentences can only be said to have contents indirectly. In (23), the falsity ascription refers to a sentence, “China is a democratic country”. As this sentence does not have demonstratives or indexicals, a default context is easily provided and the standard proposition most likely to be expressed by its tokens is recovered. But noticed that in spite of the soundness of (23), the claim that sentences don’t express a content remains true. A token of “China is not a democratic country” can be used to say something only indirectly connected with its linguistic meaning; it might be ironic or metaphoric, for instance. The difference between meaning and content is more difficult to see related to so-called “eternal” sentences, i.e. sentences without directly referential terms, since a standard context, a script for them, is easy to provide. The interpretation of (24) is straightforward. (26) does not give rise to the paradox either. Speaker B says that there is life in Mars; speaker A endorses it, and then he also says indirectly that there is life in Mars. B rejects what A has said, that is, that the proposition expressed by the previous contribution of B is true and hence that there is life in Mars. By doing it, B has rejected himself the proposition with which the dialogue began. At the end, B has said and has rejected at the same time that there is life in Mars. B is trapped in a contradiction, but not in one that affects the notion of truth or any other theoretical notion. Sentence (19) is like (15); in (19) the referential term is “this proposition” and in (15) “this sentence”, in both cases a content has to be expressed in order for them to be content-full. The situation is mended in (27). Let’s now say a few words about (17) (and (25)), (17) The sentence numbered as (17) on p. 17 of this paper is false.
This sentence is self-reflexive. It has been common to blame self-reflexivity for the production of paradoxes, semantic and non-semantic9, but self-reflexivity is not the cause of the difficulties. There is, in principle, nothing wrong with self-reflexivity. Sometimes it produces awkward effects, but by itself it does not yield contradictions. Examples such as (28),
(28) This is an English sentence, are perfectly sound. In (28) a sentential property, “being an English sentence”, is predicated of a sentence, “This is an English sentence”. What happens here is a mixed case of use and mention. If the import of (28) had to be unfolded, it would become (29),
(29) “This is an English sentence” is an English sentence.
The famous Quinean example, “Giorgione was so called because of his side”, illustrates the mixture of use and mention present in (28)10.
Examples such as (26) above show that the paradox also appears without self- reference. Gödel numbering, on the other hand, is often put forward as a poof of the soundness of the self-reference procedure. The difficulty with (17), which is a version of the sentence used by Tarski to draw the paradox, lies in that it neither remits to a context from which the needed proposition can be brought in nor permits such a context to be provided. The rest of the examples give room for a context that make them proper assertions, examples such as (17) are nevertheless sealed tight; they begins a loop that excludes the sentence to be part of a wider situation. Any act in which something like (17) is uttered is ungrounded, since there is no level that allows the act to land and thus to set off a process of provision of content. For this reason, (17) is necessarily content- less.
Cases such as (17) don’t prove the inconsistency of the notion of truth. What they show is the domain inside of which the notion has to be applied. When the notion trespasses the limits of its application domain, it produces cases of nonsense. (17) is a case of nonsense, a categorical mistake, to use Ryle’s well-established term, since
9 Consider for instance Russell’s Principle of Vicious Circle in Russell (1908); in some sense Tarski’s hierarchy is a way to reject circularity. 10 To a complete treatment of the phenomenon of mention, see Recanati (2000). allegedly a property is predicated of an entity that does not belong in its domain. (17) is as much a nonsense as (30) and (31),
(30) Julius Caesar is a prime number,
(31) The Queen of England abounds.
The correct move to take is not to deduce from the paradox that truth is inconsistent, a claim that is refuted by its infinitely many ordinary and scientific uses, and difficult to defend form a theoretical point of view, but to reject some of the assumptions that give rise to it. Behind the many different versions of the paradox there are a handful of suspicious postulates, but only the assumption that sentences are the bearers of truth11 is shared by all of them. Once this assumption is removed, the paradox disappears. Besides, there are independent reasons to reject sentences as semantically evaluable entities, and these reasons come from the contemporary theories of language. Given the state of the sciences of language at the time in which Tarski wrote his work on truth, he cannot be censured for assuming that sentences were the bearers of truth. On the contrary, Tarski was in complete harmony with the science of his time. Nevertheless, linguistics and the philosophy of language have evolved enormously from Tarski’s times and now it is no longer justifiable to maintain his assumptions. Still, if we want to honor his memory, we should rest faithful to his attitude of developing semantics in harmony with the rest of sciences, and not that much to the details of his own particular proposals now outdated. Acknowledging that truth only makes sense when characterizes propositional contents, i.e. to what is said by the use of sentences in successful acts of assertion, not only places the analysis of truth in complete accordance with the current state of science but it also has as a bonus the possibility of get rid of one of the most far-reaching puzzles of the history of philosophy.
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