The Pathological Liar: An Exclusionary Approach to SelfReferential Contradictions in Natural Language Shomir J. Wilson, Virginia Polytechnic Institute and State University
The liar’s paradox is a simple yet harrowing problem that has plagued logicians and philosophers who study natural language. It is an uncommon sentence, and perhaps a largely useless one outside of artificially-created circumstances. However, it threatens to undo any naivelyconstructed theory of natural language semantics, if the theory does not take the paradox into account. Indeed, many well-known theories of language semantics have been built specifically to avoid the liar’s paradox or to solve it altogether. For theorists to spend so much effort on a single problem—moreover, a case with virtually no practical use—seems, intuitively, a misdirection of effort. To articulate this, first the structure and significance of the liar’s paradox will be examined, as well as Richard Kirkham’s five criteria for solutions that handle the paradox and preserve the integrity of natural language. Next, the liar’s paradox will be classified as a pathological problem, which will influence the development of a theory of natural language semantics. Then, Kirkham’s five criteria will be reexamined in light of the pathological nature of the liar’s paradox, demonstrating how some of the criteria are unnecessary for its resolution. This will point to conclusions on what a solution to the liar’s paradox can possibly mean, and what forms such a solution might have. The liar’s paradox is a pathological problem, a status that dramatically affects the criteria for any solution. In its simplest form, the liar’s paradox is a single sentence that denies its own truth. For instance, the sentence 1. This sentence is false. is a concise instance of the paradox. To assume that sentence (1) is true is to assert its meaning, that sentence (1) is false. To assume that sentence (1) is false is to assert the negation of its meaning, that sentence (1) is true. In either case, the sentence is simultaneously true and false— not one or the other, but both at the same time. In our standard conception of logic, true and false are mutually exclusive and comprehensive properties for declarative statements. That is, it should be possible to classify any declarative sentence as either true or false, but never both. Because it is effectively both at once, sentence (1) is indeed a paradox. Additionally, the liar’s paradox need not be confined to one sentence. Consider the pair of sentences 2. Sentence (3) is false. 3. Sentence (2) is true. To assume that sentence (2) is true leads us to assert that sentence (3) is false. However, to assert that sentence (3) is false leads us to assert that sentence (2) is false, contrary to our original assumption; and if sentence (2) is false, then sentence (3) is true, contrary to our derivation. To