## Notes to The Revision Theory of Truth

1. Kripke prefers to
treat *neither* not as a third truth value but as the absence
of a truth value.

2. The RTT is also designed to avoid contradictions in these situations, so the last step, to (1) being both true and not true, will be blocked. See Section 4, below.

3. Proving this would, of course, necessitate explicating in detail the various ways of implementing the three-valued approach.

4. For an *n*-ary
predicate *R*, standard presentations of classical model theory
require *I*(*R*) a subset of
*D*^{n}. Clause (2c) is clearly equivalent to
that, but will be slightly easier to generalize to three-valued
logics.

5. Permanently declaring
nonsetences to be nontrue is an inessential feature of the RTT. We
could allow the revision rule only to specify the value of sentences,
allowing nonsentences to be in our out of the extension of
** T**, willy-nilly. One complication with this
is that the rule would not determine the new hypothesis given the old,
since it would not determine the new hypothesis's verdicts concerning
nonsentences.

6. See Section 2 for the
notion of a concept's or predicate's *signification*.

7. This
‘fixed-point’ theorem only holds if our scheme for
evaluating the truth of composite sentences has a certain nice
property of *monotonicity*, which we will not define here.

8. There are common
interpretations of the three-valued semantics according to which one
of the many ‘acceptable’ interpretations of
** T** can be picked out as

*the*correct interpretation. This would restore the supervenience of semantics in the Kripkean context. M. Kremer 1988 argues that these interpretations violate the

*fixed-point conception of truth*, according to which the concept of truth is exhausted by the following: truth can be asserted of a sentence iff that sentence can be asserted, and denied of a sentence iff that sentence can be denied. In correspondence with the author, Kripke has endorsed M. Kremer's understanding of the three-valued semantics.

9. And not even that: we need to make certain decisions at the limit ordinal stages.

10. The definitions we give are not theirs, but are equivalent to theirs.