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The semantic theory of truth does not single out the correspondence theory as the sole true one. It has been argued that it does not rule out a pragmatist theory either, and moreover, that also the redundancy theory could still hold. According to this theory of truth true and false can be eliminated from all contexts 'without semantic loss' or 'without loss of logical content'. There would be no need for a distinction between object- and metalanguage (or between propositional levels) because it is true that p would not be about the sentence p, but about what p refers to. (It is true that water is transparent would be about transparent water, not about water is transparent.) There are several specific problems which the redundancy theory faces, and redundancy theorists have not managed to eliminate true or implicit notions of truth from all discourse. Attempts to solve the problems of the redundancy theory have merely led to the introduction of new concepts (like that of a 'prosentence') and new words (like thatt) which can only be grasped if one is already familiar with the meaning and/or use of true itself. The foreknowledge which such approaches require make the problem nonexistent and the solutions superfluous.

It is not hard to develop a kind of elimination theory of truth which is both materially adequate and formally correct (in that it acknowledges different language levels) and which is applicable to common ('natural'), that is, nontechnical languages as well. In one such theory truth is treated as a condition of knowing, and truth is eliminated by introducing the notion of 'meaning'. The problem is that it is logically possible that p is true, whereas <p> is true in language M is false. This difficulty is tackled by taking <p> means in language M that p. This seems plausible, for is it not correct that water is transparent means that water is transparent? But one is then immediately struck by the remarkable similarity with <water is transparent> is true iff water is transparent. What happens is that in the accompanying analysis of knowledge the concept of truth is first replaced by that of meaning, and the concept of meaning then included in that of knowing. When the first part of this procedure may not seem acceptable, it is replied that the study of meaning in common language 'holds promise of offering a satisfactory analysis of the concept'. This may be true, but no guarantee is given whatsoever that the analyses of meaning concerned do not make any use of, or in any way refer to, truth or correspondence (for example, with the same fact) or coherence. Truth is thus explained in terms of the much more problematic, intensional notion of meaning. As it is purported to be 'perfectly clear' that everyone knows that p means that p if they know that p, truth can be easily eliminated in the formulation of the truth condition of knowledge. But unfortunately, if your neighbor has found out that you are a human, it does not yet follow that 'e has found out that you are an unfeathered biped means in language M that you are a human. (And if human and unfeathered biped are not accepted as synonyms, other such synonymies within or between languages can certainly be thought of.)

A specific problem of redundancy- or elimination-theories of truth is second-order quantification. Quantification is the operation of binding variables by means of a quantifier such as there is at least one or some (the 'existential quantifier') and such as all or every (the 'universal quantifier'). First-order quantification is, then, the binding of individual variables like in there is at least one x which is F (say, there is at least one human being which is unfeathered ) and like in all x-es are F (all human beings are unfeathered). The objectual interpretation of quantification appeals to the values of the variables which range over objects (like human beings). The substitutional interpretation does not appeal to the values but to the expressions which can be substituted for the variables (like the expression human being for x in all x-es are F). Second-order quantification is, now, the binding of predicate variables themselves, that is, predicate letters like F of which sentence letters are a limiting case (a 0-place predicate letter). When it is said that there is at least one p such that p is true (p being a sentential variable), this is precisely a case of second-order quantification. This device is indispensable where what is said to be true is not explicitly given but only obliquely referred to. A well-formed formula is also there is a p such that S means that p and (such that) p is true, but elimination theorists want us to believe that there is a p such that S means that p and p would be a well-formed formula too. This formula, however, has been rightly criticized for its last p which is a stray variable or name with not any predicate expression to attach to it. To introduce a new rule into the metalanguage in order to turn the problematic formula instantly into a 'well-formed' one --as done by elimination theorists-- is an ad hoc solution which is hardly convincing, if at all.

It has been claimed that the correspondence- and coherence-theories either must be rejected or can be reduced to the elimination theory. The claim is based on an equivalence of correspondence and meaning: 'S in L corresponds to the fact that p iff S means that p in L and p'; and, similarly, of coherence and meaning: 'S coheres with other sentences of L iff S means that p in L and p'. But one may as well look at it the other way around. One may then find that it is precisely because of these equations that the elimination theorist's concept of meaning is founded on correspondence with facts or coherence respectively, and that 'er meaning therefore does not eliminate truth. Meaning merely conceals truth and postpones the fundamental philosophical questions. It has also been argued that not only the coherence theory, but that neither the correspondence- nor the coherence-theory would be a genuine theory of truth at all, but merely a theory of epistemic justification. To say that, one must understand verification in the sense of making true, and not in the sense of determining or finding out or justifying the claim to know. It is then that correspondence- and coherence-theories would reduce to an elimination-theory. The argument requires tho that the meaning of meaning be left in complete obscurity.

In another attempt to do away with the apparent predicate expression .. is true, truth is chiefly analyzed in an opaque context, like in what A says is true. The central thesis of this analysis is that, for example, A says that B has feathers and B has feathers is a verifier of what A says is true. The former position is then formulated as for some p, both A says that p and p. The question is again whether this may be accepted as a well-formed formula. Taking the substitutional interpretation of this quantificational formula one would arrive at some substitution instance of <both A says that p and p> is true. Pure substitution will not do either for one would have to read for some sentence, both A says that sentence and sentence or for some B has feathers, both A says that .. both of which are nonsensical for syntactical reasons. (Pure substitution would only demand both A says that p and p without an operator for some p.)

Interpreting for some p, both A says that p and p in the objectual way will land us in a hopeless muddle as well. To show this, we shall take a look at a few examples of existential quantification. Firstly, an example of first-order quantification: for some x, both .. is a friend of x and x is C's sib. For some x is then for some person, for instance, and for the other x's we must fill in an appropriate constant such as the name of a person. Secondly, let us consider an example of second-order quantification with a predicate letter as variable: for some F, both .. is F and C's tunic is F. For some F is now, say, for some color and for the other F's we should now fill in the name of a color. Thirdly, consider a case of second-order quantification with a sentence letter as variable: for some p, both .. holds that p and A holds that p . For some p is then for some sentence, but this means that we should fill in for the other p's the name of a sentence, or for that matter, a proposition. However, if p is the name of a sentence, then A holds that p does not make sense, and it must be changed into A holds p. For some bird or there is at least one bird for which .. is intelligible, for some (particular bird) B is not. Finally, let us look at for some p, both A's statement states that p and p. Now, for some p is again for some sentence, while A's statement reads "p". However, the conjunct p as the name of a sentence without any predicate expression like .. is true renders the conjunction meaningless, that is, as meaningless as the conjunction B has feathers and C or C and B has feathers.

The advocate of the 'simple' theory of truth assumes that that is (always) logically insignificant and eliminable. Only by assuming this does 'e manage to eliminate true, altho 'e may admit that it is indeed plausible to hold that that prefixed to a sentence turns it into a designation of a sentence. From the third and fourth examples given above it should be clear, however, that the function of that is of paramount importance as it changes a sentence into the name of a sentence. (That is, of the same importance as the difference between a color and the name of a color.) If p is the name of a sentence, A holds p is synonymous to A holds that q (and not .. that p; p means that q or <q>). And when a statement reads "p", this does not amount to the same as a statement reading "that p". Altho that may be deleted in such cases in the present language --the weather-person says (")it will rain(") instead of .. that it will rain-- it should be a warning that it is not permitted to just add that where it is absent in similar cases. ('E says that "It will rain" is not correct.) Single or double quotation marks and angle brackets are often deleted in the traditional, common variant of the written language, yet this does not mean that they have no logical significance. Elimination theorists tend to ignore the difference between p and <p> or that p. So they can begin their exposition with for some p, both A says that p and p, where, if quantificational, it should read " for some p, both A says (")p(") and p is true" (or else, if purely substitutional, "both A says that p and p"). A verifier of this is A says (")S(") and S is true or A says that s and it is true that s (or both A says that s and s).

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Model of Neutral-Inclusivity
Book of Instruments
Theories of Truth