Truth, dependence and supervaluation: Living with the ghost

In J Philos Logic 34:155–192, 2005, Leitgeb provides a theory of
truth which is based on a theory of semantic dependence. We argue here
that the conceptual thrust of this approach provides us with the best way of
dealing with semantic paradoxes in a manner that is acceptable to a classical
logician. However, in investigating a problem that was raised at the end of
J Philos Logic 34:155–192, 2005, we discover that something is missing from
Leitgeb’s original definition. Moreover, we show that once the appropriate
repairs have been made, the resultant definition is equivalent to a version
of the supervaluation definition suggested in J Philos 72:690–716, 1975 and
discussed in detail in J Symb Log 51(3):663–681, 1986. The upshot of this is
a philosophical justification for the simple supervaluation approach and fresh
insight into its workings.