Classical second-order intensional logic with maximal propositions

Two Notions of Truth

“…[6] For further discussion of this point, see [10], section O. For issues related to ontological commitment to modalities and expression of this commitment by bindable modal variables, see [7], paragraph 2.…”

Maximal propositions and the coherence theory of truth

“…Our aim in this paper is to point out that within a system with maximal propositions which was developed in [3], a notion of truth and of coherence may be defined. We shall prove a theorem to show that our notion of truth may plausibly be called a coherence notion of truth.…”

“…The unary truth operator to be defined below is likewise similar to the binary operator Tap in [12], p. 90. 3 We are aware that given CMFC2, some philosophers might object to saying that = expresses genuine prepositional identity. This is because in CMFC2, (A = B) amounts to ((A <-> B) = T) and if h(A <-> B), h(A = B).…”

“…In [3], a system of logirwith maximal propositions, called CMFC2, was investigated formally. During the first part of this paper, CMFC2 will be the background logical system.…”

“…Axldi. (Vv,)... (Vv n )(A = B)-»(C<-»C), where n>oandC'isjust like C save that C has B in exactly one place that C has A, provided that if u is a variable free in (Vvj) ... (Vv n )(A = B), then the occurrence of A in C replaced by B in C is not in a subformula of C of the form (Vu)D (see [3] A number of elementary results about the system CMFC2 are recorded in [3]. We mention two in the lemma below.…”