I sort axiomatic theories of truth into two large families, namely into typed and type-free theories of truth. Roughly speaking, typed theories prohibit a truth predicate's application to sentences with occurrences of that predicate, while type-free theories do not. I will not consider syntactically restricted theories, that is, theories in which the truth predicate cannot be combined with any term to form a sentence, but typed theories either impose no restriction on the truth of sentences with the truth predicate or they prove that all sentences with the truth predicate are not true. At any rate, in typed theories one cannot prove the truth of any sentence containing T. Type-free theories of truth are often also described as theories of self-applicable truth.

Making this distinction precise is not entirely straightforward, however, and I will postpone the discussion of the distinction until Chapter 10, as only then will I have some examples of the theories to hand.

Of course, axiomatic theories of truth can be classified in other ways as well. For instance, one can distinguish between compositional and non-compositional theories, or between disquotational and non-disquotational theories. By and large, I find it easier to treat typed theories together in one part as typed theories have more in common technically, than, for instance, compositional theories do. Similarly all disquotational theories, that is, theories based merely on disquotation sentences as their axioms, may initially look much alike, but as I will show, their formal properties vary wildly.

Arguments from analogy are to be distrusted: at best they can serve as heuristics. In this chapter I am using them for exactly this purpose. By comparing the theory of truth with set theory (and theories of property instantiation, type theory, and further theories), I do not expect to arrive at any conclusive findings, but the comparison might help one to arrive at new perspectives on the theory of truth and on the question of how closely truth- and set-theoretic paradoxes are related.

The theory of sets and set-theoretic membership on the one hand and the theory of truth and satisfaction on the other hand exhibit many similarities: both are paradox-ridden, allow circularities, and invite the application of hierarchical approaches. Russell's paradox and the liar paradox are arguably the most extensively discussed paradoxes in the philosophical literature, and they seem so intractable because they are founded on very basic and clear intuitions about sets and truth.

Moreover, certain remedies against the set-theoretic and the semantic paradoxes have been given the same labels; for example, ‘typing’: both kinds of paradoxes can be resolved by introducing type restrictions. While set theory was liberated much earlier from type restrictions, interest in type-free theories of truth only developed more recently.

Throughout this book Peano arithmetic has been used as the base theory. Like many other philosophers, I see the theory of truth for the language of arithmetic as the starting point for developing a theory of truth for other, usually more comprehensive languages as base languages and perhaps eventually for natural languages.

When applying the axiomatic theories of truth discussed in this book to base theories other than Peano arithmetic, one is confronted with at least two kinds of problems: first one needs to settle on a sort of truth theory – choosing between one based on the disquotation sentences, or the compositional axioms, a typed or untyped theory, and so on – such that the chosen sort of theory is both suitable for the base theory in question and consonant with its underlying philosophical motivation; and second, once a kind of truth theory has been chosen, the formulation of this kind of truth theory with the new base theory may not be straightforward: there may be different ways of applying the chosen axiomatic conception of truth to a base theory; moreover, as I will show, some ways have unwanted consequences and may even lead to inconsistencies.

Both kinds of problems are beyond the scope of this book. But in this chapter I will show how some of the formal results about axiomatic theories of truth obtained in this book or closely related results can shed at least some light on the problems.

Philosophers have been very optimistic about the prospects of defining truth. The explicit definability of truth is presupposed in many accounts of truth: only whether truth is to be defined in terms of correspondence, utility, coherence, consensus, or still something else remains controversial, not whether truth is definable or not. The advocated definitions usually take the form of an explicit definition. Hence, if one of these proposed definitions is correct, truth can be fully eliminated as explicit definitions allow for a complete elimination of the defined notion (at least in extensional contexts). It is a quirk in the history of philosophy that many of these definitional theories, according to which truth is eliminable by an explicit definition, have come to be known as substantial theories as opposed to deflationary theories of truth, although most proponents of deflationist accounts of truth reject explicit definitions of truth and in most cases also the eliminability of truth.

A common complaint against traditional definitional theories of truth is that it is far from clear that the definiens is not more in need of clarification than the definiendum, that is, the notion of truth. In the case of the correspondence theory one will not only invoke a predicate for correspondence, but one will also use facts or states of affairs as relata to which the objects that are or can be true are supposed to correspond; in the case of states of affairs one will then also have to distinguish between states of affairs that obtain and those that do not.

Some proponents of deflationism with respect to truth contrast deflationism with various definitional theories of truth – such as definitions of truth in terms of correspondence or coherence – and claim that there is no hope of attaining an explicit definition of truth (see, for instance, Horwich 1990). The axiomatic approach to truth seems to be a hallmark of deflationism, although some deflationists flinch from the word axiomatization and prefer to call their axiomatization of truth an implicit definition. Presumably not all philosophers who reject (non-trivial) explicit definitions of truth qualify as deflationist; Donald Davidson's axiomatic account of truth, for instance, is usually not classified as deflationist. But since an axiomatization of truth seems to be a component of many deflationary conceptions of truth, the discussion of deflationism and the work on axiomatic theories of truth are closely related. So far the more formal contributions to the discussion about deflationism are based on typed axiomatic systems of truth. This applies, for instance, to the extensive debate about deflationism and conservativity. The concentration on typed systems of truth in this context seems to be borne out of the desire to avoid the intricacies of type-free systems and settle for a putatively widely accepted solution of the liar paradox. As I will argue, the focus on typed theories is misleading because in the context of type-free systems general claims about disquotational and therefore deflationist accounts of truth are no longer tenable.

Some words are powerful. ‘War,’ ‘peace,’ ‘death,’ ‘terrorist,’ and ‘security’ are but a few of the innumerable terms that we read or hear every day, and these words clearly lead us to draw a judgment, or feel uncomfortable with, or be attracted by a certain situation. When we encounter words of this kind, we do not simply interpret the message. We do not simply acquire new information. We do not simply modify our systems of belief. We feel an emotion toward what the word is depicting. We fear a war. We are afraid of terrorists. We desire peace. We love children. These words are emotive because they trigger our emotions. They influence the way we regard the reality they represent. They affect our decisions concerning their referents. The emotive power of these words can make them extremely effective instruments to direct and encourage certain attitudes and choices. But at the same time, the very emotions that they evoke make them subtle tools to manipulate the other’s decisions and feelings. Names can be used to conceal reality instead of representing it, to distort the facts instead of describing them, and to omit qualities and particulars instead of depicting them. Names have meanings that can be changed and modified, so that they can be used to classify what they otherwise could not mean. Their definitions can be altered and the emotions they carry directed toward new objects. For these reasons, ever since the ancient studies on rhetoric, emotive words have been regarded as crucial instruments for persuasion and manipulation. The first step to understand what lies beneath them is to analyze how they are used and the effects they can cause.

Words are often used to describe reality, to refer to objects, and to communicate feelings, desires, and emotions. Words can be powerful. They can move us, they can frighten us, and they can lead us to action. Words have been described as tools and weapons, as signs and masks. Words have been described as instruments having the force of creating and changing reality. They have been investigated with regard to their semantic structures, their co-occurrences, and their syntactic combinations. Even so, we rarely realize that words can be arguments. In this book we show how they can be moves that guide us toward judgment or action and function as speech acts that allow certain replies and prevent others. In everyday communications we hardly consider that complex forms of reasoning lie under their uses, and that these forms of reasoning are interwoven with meaning presumptions and dialogical games. In our words we can conceal an implicit change of our interlocutor’s knowledge or a silent alteration of his system of values. These are powerful effects, but they typically go unnoticed.

When Chesterton claimed in one of his famous paradoxical quotes that “Impartiality is a pompous name for indifference, which is an elegant name for ignorance” (Chesterton, The Speaker, 15 December 1900), he did much more than simply describe impartiality. He condensed an attack on a commonly accepted and widely praised implication in a definition, an argument reversing the shared hierarchy of values. When politicians refuse to define ‘terrorism’ or ‘torture,’ or when they use words like ‘peace’ and ‘hostilities’ with new definitions, they cannot be accused of distorting reality or telling lies. They are simply performing a much more powerful action – changing the rules of the game of discourse. When science and knowledge are used “to provide long words to cover the errors of the rich” (Chesterton, Heretics, 88), they are employed to provide instruments for forcing the hearer to accept actions, thereby allowing the speaker to avoid commitment or justification of a kind that might normally be required. Words employed in this way are clever dialectical moves, implicit arguments that not only escape the normal burden to provide reasons for a conclusion, but at the same time lead the hearer to a value judgment or a decision and implicitly modify his possible reactions.

The act of naming is based on a factual premise and a definition, or classificatory principle. Like all conclusions in arguments, the classification depends on the strength of the acceptability of the premises supporting it. The interlocutor can rationally explain that he cannot accept the conclusion because he does not agree with one of the premises supporting it. Emotive words can be used as dialectical instruments of manipulation. They can hide reality or conceal the controversial nature of a definition. In both cases, the interlocutor is prevented from judging a classification and challenging it. Dialectical strategies of hiding facts or meaning can explain the force and the danger of arguments from classification, and help in analyzing the pragmatic dimension of definitions.

The meaning of words can be controversial, vague, or unshared. In these cases, the definition cannot be considered as acceptable by the interlocutor, and becomes the standpoint of a discussion. In the previous chapter we showed how a definition can be evaluated and rejected by showing that it does not fulfill semantic and logical conditions. If ‘true peace’ is defined as ‘waging war against nations breaching civil rights,’ it is possible to attack the definition and show that war cannot in any case be considered as peaceful. There is nothing inherently wrong in redefining a concept, as long as the freedom of altering, choosing, or précising the meaning does not limit the other party’s freedom to accept or challenge it. The thin line between negotiating, discussing, proposing a definition, and imposing it lies in the pragmatic nature of the conversational framework.

When we think about words we only consider what they express, what they are used for “saying.” We often may not realize that words have a silent side. Their use can hide implicit moves and complex arguments based on propositions that are left unsaid. Nobody would be moved by the description of a battlefield as a place of war, or by the claim that missionaries acted in peace. However, these words become emotive when we speak of the war on terror or missions of peace. Something unsaid hides behind them and justifies their use or appears to justify it, leading us to certain conclusions. They do more than express a categorization of reality. They are silent emotional persuaders.

Some words have the power to influence our judgments and our decisions. We approve of an action when brought about for the purpose of ‘peace.’ We are horrified when a nation allows practices such as ‘torture.’ The use of these words can influence our emotions and our evaluation of reality, and at the same time their deceptive use can distort our perceptions of the world and lead an audience toward accepting conclusions that are not supported by evidence-based reality.

In the previous chapter we showed the different types of acts of defining. The most dialectically powerful is the implicit definition. The speaker, instead of stating or advancing a definition, simply takes it for granted, considering it as part of the interlocutors’ common ground. Zarefsky (1998) and Schiappa (2003: 111-112; 130) pointed out the implicit dimension of this act of naming reality, which they call “argument by definition.” Instead of putting forward a classification and supporting it by a definitional reason, the speaker simply names reality, leaving the definition unexpressed. As seen in Chapter 4, the hearer is left with the burden of reconstructing the move, assessing the definition, and rebutting it if it does not correspond to the shared meaning. This complex mechanism, one that can be exploited for rhetorical and dialectical purposes, has been classified previously as an ‘improper’ act of defining, and it may even be seen as a non-act of defining. It is a definitional act, as it alters the dialectical situation restricting the interlocutor’s possibilities of making further moves. It is a stipulation of a kind, as the speaker commits the hearer to a proposition, but he does not take on any responsibility for it. However, at the same it is a non-action, as it is a speech act required by the act of naming actually performed by the speaker. For this reason, pragmatic and semantic ambiguity plays a crucial strategic role in this kind of dialectical tactic. The hearer needs to retrieve the implicit move from a semantic and pragmatic perspective. At the same time, he needs to reconstruct the definition, and the type of speech act the speaker did not perform, in order to ascertain whether to continue the dialogue or attack the possibility of the implicit act.

The previous chapters have given plenty of good reasons to be suspicious about the use of persuasive definitions and emotive language in argumentation, and to often see them, especially when examining discourse from a logical point of view, as suspicious, or even as inherently illegitimate moves. But is it possible that rational persuasion can be shown to be a legitimate aim of argumentation by providing some kind of objective framework in which there are rules for proper persuasion? Is there a procedural setting in which a persuasion attempt could be an appropriate speech act properly employed so that, under the right conditions, it could be a legitimate move in rational argumentation? In this chapter we show how we need to study how definitions and arguments containing loaded terms are put forth as part of a sequence of argumentation in a dialogue exchange. The move made in a dialogue where a party puts forward an argument, or where a party puts forward a definition that she wants the other party to accept, needs to be seen as a kind of speech act that can only be properly understood in a rule-governed dialogue setting, we will argue.

Although there can be different kinds of dialogues, the principal model for evaluating argumentation in cases of the use of emotively loaded language and persuasive definitions is that of the persuasion dialogue, a formal structure with moves and rules, and in which the aim of each participant is rational persuasion based on the values, commitments, and knowledge of the other party. As shown by a thematic example in the chapter, this model enables an analyst to systematically analyze arguments based on persuasive definitions and emotive terms in order to distinguish between cases where such arguments are reasonable and in cases where they are used as fallacious tactics to try to get the best of a speech partner unfairly.

Dialogue games provide rules to establish the relationship between a move and a possible effect on commitments. However, such games are highly abstract, and the moves are reduced to logical operations between symbols indicating sentences. The type of speech act performed is not considered, nor is the kind of relation between the predicates in the sentence taken into account. However, a statement affects the commitment store differently from an order or a reminder, and a relation of classification leaves to the interlocutor a range of possible rebuttals different from an analogical relation. In order to apply such games to actual dialogues, we need to go a step further and analyze the nature of the moves and the structure of the sentences. In this chapter we will apply dialogue games to a particular type of move, the act of defining or redefining. As seen in Chapters 3, 4, and 5, definitions can be distinguished according to their pragmatic nature and their propositional structure. In our dialectical approach, definitions can be thought of as moves in a dialogue game, which open different possibilities of continuation of the dialogue and refutation according to the definitional act performed and the type of definitional sentence. For this reason, we will examine the dialectical structures of the different types of definitional sentences and combine them with the commitment effects of the different acts of defining.

Words are instruments for modifying our beliefs and affect our decisions. Stevenson (1944) underscored that words have a tendency to alter our knowledge, which he named “descriptive meaning.” Words describe, and at the same time hide, reality (Schiappa 2003). They frame a certain state of affairs by pointing out specific features and leaving out others. This twofold dimension of names, their nature as instruments for providing and excluding information, is crucial for understanding the strategies of meaning listed in the first chapter. Selecting information always results in hiding some characteristics of a situation. Amplifying, or rather emphasizing some features of a complex state of affairs inevitably results in leaving out other characteristics. According to the selection of features, certain emotions can be triggered and others prevented. The strategies of selection are grounded on the power of words to represent, describe, and refer to reality. Sometimes words are not simply used to select what is important for the conversation, but to distort reality. Dictatorships are called ‘democracies’ while the word ‘pacification’ conceals massacres and human tragedies. However, sometimes the boundary between selecting the relevant aspects of reality and lying becomes, or is made to become, blurred. The meanings of words are altered, and also what they represent. The meanings of some words are altered, and a powerful ambiguity is introduced. Sometimes the effect is funny or ridiculous, but sometimes it is extremely effective. We can open the newspaper and notice how difficult it is to judge the boundaries of the words, between ‘true freedom’ and ‘slavery,’ ‘treason,’ and ‘true patriotism,’ ‘war-making’ and ‘peace enforcement’ (Doyle & Sambanis 2006: 1).

Some words have a particular force. Terms such as ‘war,’ ‘peace,’ ‘security,’ or ‘terrorism’ trigger emotions. They lead us to appreciate, hate, fear, or reject a state of affairs. These terms are instruments for influencing affections and choices. In this sense, words are emotive. Stevenson (1944) pointed out how this power of words can be considered as a dimension of meaning, the disposition of a word to change a hearer’s attitudes and emotional reactions instead of altering his structure of beliefs. In the first chapter we showed how emotive words can be used to hide and distort reality. However, the crucial issue to be considered in order to explain such a power of words is to understand what emotive meaning is, and how it affects our feelings, attitudes, and decisions. Where is such meaning? Why is it a characteristic of some words only? Do ethical terms trigger the same emotions in any culture, or is the emotive meaning dependent upon context and knowledge? Is emotive meaning rational?

The starting point for our investigation is a quotation from Huxley’s Brave New World. In this fantastic and metaphorical world, children were produced in laboratories, and the notion of family disappeared. Reality had been drastically modified and the laws of nature completely subverted. In this world, however, words acquired new meanings, and in particular new emotive meanings (Huxley 1998: 22–23):

• “And ‘parent’?” questioned the D.H.C.

• There was an uneasy silence. Several of the boys blushed. They had not yet learned to draw the significant but often very fine distinction between smut and pure science. One, at last, had the courage to raise a hand.

• “Human beings used to be … ” he hesitated; the blood rushed to his cheeks. “Well, they used to be viviparous.”

• “Quite right.” The Director nodded approvingly.

• “And when the babies were decanted … ”

• “’Born,’” came the correction.

• “Well, then they were the parents – I mean, not the babies, of course; the other ones.” The poor boy was overwhelmed with confusion.

• “In brief,” the Director summed up, “the parents were the father and the mother.” The smut that was really science fell with a crash into the boys’ eye-avoiding silence. “Mother,” he repeated loudly rubbing in the science; and, leaning back in his chair, “These,” he said gravely, “are unpleasant facts; I know it. But then most historical facts are unpleasant.”