The Prosentential Theory of Truth

PHIL 600 Term Paper, Vered Arnon

The prosentential theory of truth attempts to explain the phrase ‘is true’ as a prosentence. A prosentence, while appearing on the surface structure of a sentence to be predicate, is in fact an anaphor for an antecedent. According to Grover, Camp, and Belnap, in Kirkham’s account, the anaphoric nature of ‘is true’ is not reflected in the surface structure of grammar because it is nonatomic and thus easier to use, enabling the tense to be modified and also enabling negation.(1) In other words, ascriptions of truth work like pronouns, and to say that something is true is to reaffirm it. This theory of truth is an attempt to analyse truth in terms other than correspondence or satisfaction or reference. The prosentential theory falls in the realm of the deep-structure project within the assertion project within the speech-act project, according to Kirkham’s categorisation of theories of truth.(2)

This theory has some problems, however. Kirkham claims that the most serious objection to the theory is the fact that if ‘true’ is vacuous then there would be no need for the use of the phrase to have developed, and the prosentential theory fails the meaning of the word ‘true’.(3) I do not find this objection as serious as Kirkham makes it out to be. My objection to his objection is as follows: if saying that something is true is merely restating or reaffirming it, then use of the phrase ‘is true’ can be explained as a perlocutionary act, rather than an illocutionary act. However, analysis of truth in this way would not be interesting or enriching for philosophers. My objection would be discounted as an avoidance of the issue rather than an addressing of the problem. The study of truth could not advance anywhere based on a perlocutionary theory of truth.

Kirkham raises another objection to the prosentential theory. Other predicates are genuine predicates without some hidden deep structure, and the prosentential theory implies an extreme difference between things that seem to be quite parallel. Proponents of the prosentential theory argue that other genuine predicates ‘are not applicable to propositions, or statements, or sentences. They are applicable to acts of stating.’(4) Kirkham does not find this answer plausible because, among other reasons, not all genuine predicates can make sense when predicating acts rather than propositions or statements.

Where I think the prosentential theory of truth runs into the biggest problems is with the postulation that ‘is false’ is also a prosentence with the deep structure ‘it-is-false-that that is true’. According to Kirkham, the use of hyphens by the postulators of the theory imply that they treat these phrases as single-word operators. If ‘is true’ is a repetition or reassertion, to claim that it is vacuous can make sense. But if ‘is false’ is also a prosentence like ‘is true’, essentially mapping out the deepest structure results in equivocation between ‘is true’ and ‘is false’.(5) This is a very serious objection. I believe that this problem can be solved, however, if ‘is false’ is analysed not as another vacuous prosentence but an assertion of disagreement. If saying that something is true is to repeat it, or reaffirm it, then to say that something is false is to deaffirm it, or negate it. Negation is not vacuous, so ‘is false’ as an operator in a sentence cannot be treated the same way as ‘is true’. I propose that the deep structure of ‘x is false’ is ‘not x’ or ‘it is not the case that x’. This seems to me to further justify the prosentential theory of truth, because in symbolic logic there is a negation symbol, but no affirmation symbol. To say that a premise is true, in a logical argument, one merely states the premise. To say that it is false, one uses a symbol to indicate that.

Whatever objections are raised and however proponents of the theory respond to them, the best examination of the functionality of this theory is to apply it, so in the rest of this paper I will attempt to see how the prosentential theory of truth handles the ‘liar paradox’. There are two variations of this paradox, one self-referential, the other not. The self-referential one is the sentence ‘This sentence is false.’ The non-self-referential one is the sentence pair ‘The next sentence is false. The previous sentence is true.’

According to the prosentential theory, with my own modified treatment of the phrase ‘is false’, the deep structure of the sentence ‘this sentence is false’ is ‘not this sentence’ or ‘it is not the case that this sentence’. On this analysis, its deep structure reveals that it is nonsensical, meaningless. ‘This sentence is false’ is neither true nor false, because it is not a functional sentence with intelligible content.

The non-self-referential variation of the ‘liar paradox’ is considerably more complicated. In the following map, 1 and 2 are the statements of the paradox, and the following 3 and 4 are a prosentential interpretation of 1 and 2 respectively.

The next sentence is false.
The previous sentence is true.
Not 2.
Statements 3 and 4 still obviously contradict each other. But the prosentential theory does not provide any explanation or solution. Both sentences do have intelligible content. In the case of the self-referential statement, the deep structure showed that the referent was not actually anything with content and meaning. In the case where there are two sentences, however, applying the prosentential theory only serves to clarify the contradition and fails to provide any solution to the problem at all.

It appears that the prosentential theory does not work due to treating ‘is true’ as vacuous while ‘is false’ cannot be treated as vacuous. As already explained, ‘is false’ would mean the same as ‘is true’ if both were treated the same, but giving one meaning and treating the other one as vacuous fails to solve problems concerning contradiction. My conclusion is that the prosentential theory of truth simply is not appropriate to logical paradoxes, and thus not extremely useful in this branch of philosophical analysis. Perhaps the prosentential theory of truth is only functional when the phrase ‘is true’ is treated as a perlocutionary act, and for someone who is not a philosopher, that is acceptable, but for philosophers, that is an undeniably significant objection to the theory.


Kirkham, Richard L. Theories of Truth. MIT Press, 1995
1 Richard L Kirkham, Theories of Truth, p327

2 Ibid, chapter 1, sections 7 – 10

3 Ibid, p328

4 Ibid, p328 – 329

5 Ibid, p328

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