“Inconsistency Theories of Semantic Paradox” Douglas Patterson
Philosophy and Phenomenological Research, forthcoming.
Main authors discussed: Alfred Tarski, Kirk Ludwig, Matti Eklund
Douglas Patterson argues that the best way to respond to the semantic paradoxes that arise in natural language is to take natural language semantics to be (explosively) inconsistent. According to Patterson, to understand a natural language is to share with others cognition of a false semantic theory. Patterson’s main argument runs as follows. English is expressively rich. So, the first sentence occurring in this review could be:
S: The first sentence occurring in this review is not true.
But plausibly truth-conditions and hence meaning are given by T-sentences. That is, a sentence is true iff what it says is the case. S says that it isn’t true. So, S is true iff S is not true. So, the T-sentence for S is inconsistent. If indeed the truth-conditions for English sentences are given by the T-sentences for the English sentences, then the truth-conditions for English sentences are inconsistent. So, if S means what it appears to mean, then English is inconsistent. Everything follows from everything in English. English sentences are true under every condition.
Patterson considers various standard ways around this apparent problem: First, one could insist that English is (classically) consistent and hence deny that S is an English sentence. English then is not expressively rich: it cannot describe its own syntax and semantics. This, however, does not seem right. English appears to be expressively rich. Second, one can revise the logic. For example, we might accept that S is both true and false and deny ex falso (as done by Priest and others). This route holds some promise but requires what some would consider an unintuitive rejection of classical logic. Third, one can insist that S is expressible in English but that it is abnormal or pathological. This is what Patterson calls ‘the orthodox approach.’ On the orthodox approach, it is thought that speakers will assent to the claim that some of their sentences are pathological and have no determinate truth conditions, whereas others have determinate truth conditions. This is supposed to ensure expressive richness and logical non-triviality. However, Patterson argues, if this approach really does ensure expressive richness, then ‘pathological’ must be allowed in the object language. But that then gives rise to new paradoxes, witness ‘This sentence is either not true or is pathological.’ This is the ‘revenge problem.’
Patterson then looks closer at the inconsistency theories offered by Kirk Ludwig and Matti Eklund. Ludwig holds that an adequate meaning theory is one that implies all and only true M-sentences, i.e., sentences of the form ‘s in L means that p.’ The connection between the M-sentences and the T-sentences of a given language are given by the bridge principle: If s in L means that p, and s is semantically complete and coherent, then s in L is true iff p. So, even if the T-theory for L is inconsistent and trivial, the M-theory for L may well be consistent and non-trivial. Given this view, we can accept that S means that the first sentence in this review is not true, but we need not accept that S is true iff S is not true. Patterson, however, argues that Ludwig’s approach ultimately requires supplementation by the orthodox approach because Ludwig assumes that some but not all interpretive axioms are true.
On Eklund’s inconsistency theory, there are expressions in languages like English that can be understood only if one accepts untrue claims about them. So, speakers will accept ‘inconsistent verdicts’ about pathological sentences and yet treat other sentences as normal. The problem that now arises for Eklund is explaining why speakers do not treat all sentences as pathological if they are disposed to treat some as pathological and are also disposed to accept ex falso. Eklund proposes a kind of supervaluationist approach to this problem where speakers implicitly assign the truth-value ‘true’ to sentences of the language if they are super-true (that is, if the truth-value assignment is such as to make speaker judgments maximally correct). But, according to Patterson, this approach too ultimately requires supplementation by the orthodox approach.
Patterson himself defends a version of inconsistency theory which does not attempt to draw a line between pathological and non-pathological T-sentences. If English is expressively rich, then it resists coherent assignments of truth conditions to its sentences. According to Patterson, English seems to its speakers to be both expressively rich and logically non-trivial, but the seeming is a mere seeming – an illusion. According to him, there is no need to think that meaning theories must be true as long as speakers implicitly treat them as such. What is required for communication is that speakers share their opinions about the conditions under which the sentences of a language are true. These opinions, of course, need not be doxastic in nature. According to Patterson, they are pre-doxastic seeming or cognition states. For the speakers, it seems pre-doxastically that there is a true semantics for English. Moreover, ‘acceptance’ is not closed under classical consequence. So, while speakers are in general prepared to accept T-sentences such as ‘ “snow is white” is true iff snow is white,’ they are not prepared to accept that ‘snow is white’ is true iff q, for any arbitrary choice of q, even though the latter is a consequence of semantic theory.
The upshot of Patterson’s view then is this: Because semantic paradoxes occur in English, the semantics for English is false and logically trivial. However, this does not present an obstacle to semantic competence. Cognizing or understanding English requires merely that it seems to its speakers that certain T-sentences are true (but not false).
Owing to length limitations I can offer only one minor criticism here. According to Patterson, the semantics for English is inconsistent and logically trivial. So, every T-sentence obtains according to the semantics for English. But speakers understand English by having a quasi-perceptual impression that a non-trivial set of sentences constitutes the T-theory for English. This set of sentences, however, is not the T-theory for English though it could be the T-theory for a different language. So, competent speakers then understand English by grasping a semantic theory that is a semantic theory for a different language. I think that this is the least attractive feature of Patterson’s otherwise elegant proposal.
Reviewed by Berit Brogaard
University of Missouri, St. Louis
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