Some non-inerrantists hold the self-defeating theory of meaning called conventionalism. Franke, for example, argues that “since language is a social construct…our words and linguistic conventions do not have timeless and fixed meanings…” (Franke, 194). There are serious problem with this view which Franke and other contemporary non-inerrantists have adopted.
Without going into philosophical detail, the most telling way to see the flaws of this view is to reflect on its self-defeating nature. That is, it cannot deny the objectivity of meaning without making an objectively meaningful statement. To claim that all language is purely conventional and subjective is to make a statement which is not purely conventional and subjective.
In like manner, when Franke claims that truth is perspectival (Franke, 267), he seems to be unaware that he is making a non-perspectival truth claim. This problem is discussed more extensively elsewhere (see Geisler, Systematic Theology, chap. 6). We would only point out here that one cannot consistently be an inerrantist and a conventionalist. For if all meaning is subjective, then so is all truth (since all true statements must be meaningful). But inerrancy claims that the Bible makes objectively true statements. Hence, an inerrantist cannot be a conventionalist, at least not consistently.