What are the bearers of truth? There are three main positions with regard to this philosophical question. Firstly, there is the view that truth is a property, and the question is then what is it a property of?. The diverse answers which may be given are:

• declarative sentences or sentence types (which have a grammatical structure, and which are not interrogative or imperative, for instance)
• declarative sentence tokens (which are physical objects, notably series of visual marks or sound waves) --for example, the sentence token water is transparent and the sentence token water is transparent are different inscriptions of the same sentence (type)
• statements (that is, what is said when a declarative sentence is uttered or inscribed)
• utterances (as speech acts) --compare the 'performative theory of truth' in which truth is predicated to a sentence not by uttering a statement but by performing an action
• propositions or meanings of sentences (that is, what is common to synonymous declarative sentences or sentence types)

Secondly, there is the view that truth is no property. In the redundancy theory of truth and later variants of it, like the 'simple' theory of truth, the question itself is considered to be senseless. Closely related to this question is whether propositions are objects, or whether one does ontologically commit oneself by quantifying over propositions or sentences. So long as one sticks to pure substitution this question of objective entities can easily be evaded, but not when one gives oneself up to all kinds of quantification without providing a plausible alternative for the standard interpretations thereof. (Then the result is something which is neither quantification nor pure substitution.) If propositions are 'things', and if they are true or not, this implies almost automatically that they do have or do not have the property of truth, even tho they would only be imaginary things, and even tho truth would merely be an imaginary property.

On a third view, the right question to ask is what is the relationship between formal and informal arguments with respect to validity and truth?. In this case, the issue of the appropriate constraints on instances of sentence letters --what can be put for p?-- does still arise, also for those denying that truth is a property.

We have called the primary bearers of truth "propositions" and have assumed that they are the language-independent meanings of sentences. It is not important from our point of view whether the primary bearers of truth are actually something else, like sentence tokens or speech acts. It is not important either whether these truth-bearers are 'really' things or not. This is a metaphysical pseudoproblem, for if they are 'things', they are propositional things, and trivially, these things are entirely different from the things of nonpropositional reality we have discussed in the first two chapters of this book. Similarly, if truth is an attribute, it is a propositional attribute not at all comparable with the catenated and noncatenated attributes we have discussed before in the same chapters. In short: if propositions are included in the category of 'things', it is the meaning of thing itself which changes, and if truth is included in the category of 'properties' or 'attributes', it is the meaning of property or attribute itself which changes.

More important than the question whether propositions (in the impartial sense of primary truth-bearers) are 'real' things or not, is the recognition of a hierarchy of (orders of) propositions and propositional functions. Such a hierarchy very much resembles the hierarchy of languages in the semantic theory of truth, and is needed to solve the problem of semantic paradoxes. Semantic paradoxes are contradictions derivable in semantics by apparently valid reasoning with apparently obvious principles about truth --they are 'beyond belief', so to say. A classical semantic paradox is the sentence S reading "this sentence is false". If S is true, then it is false; and if S is false, then it is true. Another type of paradoxes are the set-theoretical ones, which involve sets which are members of themselves (in a purely set-theoretical fashion). The probably best-known example of such a paradox concerns the set of sets which are not members of themselves: 'the set of all sets which are not members of themselves is a member of itself iff it is not a member of itself'.

It has been argued that both semantic and set-theoretical paradoxes are due to one and the same fallacy, namely the violation of the so-called 'vicious circle principle'. According to this principle whatever involves all of a collection must not be one of that collection. As a formal solution to paradoxes resulting from violation of the vicious circle principle a theory of types has been developed. It is in the so-called 'ramified theory' that a hierarchy of propositions, and in the so-called 'simple theory of types' that a hierarchy of (sets of) individuals were proposed for the first time. The former hierarchy starts in our ontology with the level of nonpropositional reality, while the latter hierarchy is present in every separate domain of the nonpropositional world.

Those who do not accept the vicious circle principle have come with proposals which closely resemble this principle nevertheless. A more serious objection is it to claim that a hierarchy like that of the semantic theory of truth is no solution, because paradox might still arise with respect to any truth ascription if the facts would turn out badly. The point made is then that even 'ordinary' ascriptions of truth and falsity could not even implicitly be assigned levels in a hierarchy of languages, for example, when A says that all of B's utterances about S are false, while B says that all of A's utterances about S are false. The objection is itself erroneous, however, because it equates utterances about S with utterances about utterances about S . If A says "all of B's utterances about S are false", this is an utterance about utterances about S. And if B says "all of A's utterances about S are false", this does not involve all of B's utterances about S are false since that is no utterance by A about S, but about utterances about S.

The idea that all well-formed sentences must be either true or false has also been rejected: some of them would just have no truth-value at all. Those stressing this have been using a concept of groundedness. A sentence is, then, said to be 'grounded' if it will eventually get a truth-value in a process in which one starts with a sentence which one is 'entitled to assert' (like water is transparent) and to which one may add .. is true (<water is transparent> is true). On such a construction a sentence like this sentence is true will remain ungrounded, and in this way paradox can be avoided. But --as has already been pointed out-- this concept of groundedness still has strong affinities with the idea that what is wrong with paradoxical sentences is a sort of vicious self-dependence.

A serious objection against the whole intuitive idea of groundedness is that it puts the cart before the horse. That is because it makes use of a normative concept, namely the concept of entitlement. (Intuitive ideas somehow always seem to implicitly appeal to normative notions and the evaluative meanings of words.) If someone is 'entitled' to assert that water is transparent, this is, firstly, because it is true that water is transparent, and secondly, because one may tell something which is true and ought not to tell something which is false. Therefore, it follows from the truth of both water is transparent and a principle of truth or truthfulness that one may say, that is, that one is entitled to say that water is transparent. The advocate of groundedness, however, suggests that it would be the other way around, that the truth of a proposition or utterance would follow from a person's entitlement to assert that proposition or utterance. This fallacy is the same as that in the entitlement theory of property in which it is claimed that something would be someone's property because 'e is entitled to it. Also this is a hysteron proteron: it is when something is one's property (in a moral sense) that one is (morally) entitled to it, not the other way around. Even if in the relationships between entitlement and truth, and between entitlement and property, neither term comes before the other, entitlement alone can never do the groundwork.