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1. Kripke prefers to treatneither not as a third truth valuebut 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 beblocked. See Section 4, below.

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

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

5. Permanently declaring nonsentences to be nontrue is an inessentialfeature of the RTT. We could allow the revision rule only to specifythe value of sentences, allowing nonsentences to be in or out of theextension of \(\boldsymbol{T}\), willy-nilly. One complication withthis is that the rule would not determine the new hypothesis given theold, since it would not determine the new hypothesis’s verdictsconcerning nonsentences.

6. According to the definition, a sentence \(A\) isvalid in\(M\)by \(\boldsymbol{T}^*\) iff \(A\) iscategoricallytrue in \(M\).

7. See Section 2 for the notion of a concept’s orpredicate’ssignification.

8. This ‘fixed-point’ theorem holds if our scheme forevaluating the truth of composite sentences has a certain niceproperty ofmonotonicity, which we will not define here.

9. There are common interpretations of the three-valued semanticsaccording to which one of the many ‘acceptable’interpretations of \(\boldsymbol{T}\) can be picked out asthe correct interpretation. This would restore thesupervenience of semantics in the Kripkean context. M. Kremer 1988argues that these interpretations violate thefixed-pointconception of truth, according to which the concept of truth isexhausted by the following: truth can be asserted of a sentence iffthat sentence can be asserted, and denied of a sentence iff thatsentence can be denied. In correspondence with the author, Kripke hasendorsed M. Kremer’s understanding of the three-valuedsemantics.

10. And not even that: we need to make certain decisions at the limitordinal stages.

11. The definitions we give are not theirs, but are equivalent totheirs.