Even the subtlest experts

from Kripke, “Outline of a Theory of Truth”:

The versions of the Liar paradox which use empirical predicates already point up one major aspect of the problem: many, probably most, of our ordinary assertions about truth and falsity are liable, if the empirical facts are extremely unfavorable, to exhibit paradoxical features. Consider the ordinary statement, made by Jones:

(1) Most (i.e., a majority) of Nixon’s assertions about Watergate are false.

Clearly, nothing is intrinsically wrong with (1), nor is it ill-formed. Ordinarily the truth value of (1) will be ascertainable through an enumeration of Nixon’s Watergate-related assertions, and an assessment of each for truth or falsity. Suppose, however, that Nixon’s assertions about Watergate are evenly balanced between the true and the false, except for one problematic case,

(2) Everything Jones says about Watergate is true.

Suppose, in addition, that (1) is Jones’s sole assertion about Watergate, or alternatively, that all his Watergate-related assertions except perhaps (1) are true. Then it requires little expertise to show that (1) and (2) are both paradoxical: they are true if and only if they are false.

The example of (1) points up an important lesson: it would be fruitless to look for an intrinsic criterion that will enable us to sieve out—as meaningless, or ill-formed—those sentences which lead to paradox. (1) is, indeed, the paradigm of an ordinary assertion involving the notion of falsity; just such assertions were characteristic of our recent political debate. Yet no syntactic or semantic feature of (1) guarantees that it is unparadoxical. Under the assumptions of the previous paragraph, (1) leads to paradox. Whether such assumptions hold depends on the empirical facts about Nixon’s (and other) utterances, not on anything intrinsic to the syntax and semantics of (1). (Even the subtlest experts may not be able to avoid utterances leading to paradox. It is said that Russell once asked Moore whether he always told the truth, and that he regarded Moore’s negative reply as the sole falsehood Moore had ever produced. Surely no one had a keener nose for paradox than Russell. Yet he apparently failed to realize that if, as he thought, all Moore’s other utterances were true, Moore’s negative reply was not simply false but paradoxical.) The moral: an adequate theory must allow our statements involving the notion of truth to be risky: they risk being paradoxical if the empirical facts are extremely (and unexpectedly) unfavorable. There can be no syntactic or semantic “sieve” that will winnow out the “bad” cases while preserving the “good” ones.