Their syntactic similarity to negation suggests that, like negation, the truth values of ⌈□φ⌉ and ⌈◇φ⌉, insofar as they are determinable at all, must be determined by the truth value of φ.
A truth function defines the truth value of a proposition composed by connectives (conjunction, disjunction, negation) in terms of the truth values of its components.
That context is not a factive context, because it is not the case that it, as well as its internal negation, presuppose the truth of the corresponding sentence.
Finally, if a complex sentence containing an embedded 'that'-clause reports an intentional phenomenon, then neither it nor its negation entail the truth of the proposition expressed by the embedded 'that'-clause.
The existence of a negation operation ensures the truth of B1.
The ultimate truth has no positive content in the Geluk tradition; it is simply the lack of essence in any phenomena: "The ultimate truth is posited as solely the negation of truth [that is, inherent existence] upon a subject that is a basis of negation…" (Tsongkhapa, 396).
It is not a simple task to understand the propositional treatment of such sentences, e.g. to give criteria for forming their negation, or understanding the truth conditions of implications.
One consequence of this view is that the negation of a simple truth is always inconsistent, even if it is not explicitly contradictory.
for example, is truth-valueless when t is nondenoting (assuming an ordinary neutral semantics that makes the negation of a truth-valueless formula truth-valueless).
These findings show that the ordinary systems of elementary logic comprise the correct formulation, provided that the actual choice of the truth functions (say negation and disjunction), of the quantifiers, and of equality as the "logical constants" is assumed to be the correct one.
