 Now these sentences should be, on the gappy theorist’s non-bivalent approach, either true, or false, or neither. But, for instance, if (3) is true, then things are as it claims they are; therefore, (3) is not true (either false or truth-valueless). If (3) is false, or neither true nor false, in both cases it is not true; but this is precisely what it claims to be; therefore, it is true. We seem to have to conclude that (3) is both true and not true, contrary to the LNC. A similar line of reasoning goes for (4).