Abstract

This paper articulates a formal theory of belief incorporating three key theses: (1) belief is a dyadic relation between an agent and a property; (2) this property is not the belief's truth condition (i.e., the intuitively self-ascribed property which the agent must exemplify for the belief to be true) but is instead a certain abstract property (a "thought-content") which contains a way of thinking of that truth condition; (3) for an agent a to have a belief "about" such-and-such items it is necessary that a possesses a language of thought, $M_{a}$ , and that a (is disposed as one who) inwardly affirms a sentence of $M_{a}$ in which there are terms that denote those objects. Employing an extended version of E. Zalta's system ILAO, the proffered theory locates thought-contents within a typed hierarchy of "senses" and their "modes of presentation", the provisional definitions of which (suppressing complications added later to accommodate the contents of beliefs about beliefs) are as follows. A mode of presentation of e is a ternary relation of the sort [λxyz z is a name in $M_{y}$ that denotes x, and $D_{e}yz$ ] in which $D_{e}$ is an e-determiner - a relation between agents and their mental expressions imposing a syntactico-semantic condition sufficient for such an expression to denote e therein. A sense of an entity e is an abstract property that "contains" a mode of presentation $R_{e}$ of e by dint of encoding its property-reduct [λx(∃y)(∃z) $R_{e}xyz$ ]. In particular, a thought-content is a sense T of an ordinary first-order property P containing a mode of presentation whose P-determiner $D_{P}$ is such that, for any y and z, $D_{P}yz$ entails that z is a λ-abstract [λv S] of $M_{y}$ in which S is a sentence whose non-logical parts stand in appropriate semantic relations to the constituents of T's (some of which may themselves be senses). Where $I_{a}$ is agent a's dedicated self-demonstrative and |T| is the mode of presentation contained in a thought-content T, the belief relation itself is then characterized as obtaining between a and T iff a( is disposed as one who) inwardly affirms the substitution instance $S(I_{a}/v)$ of a sentence S in $M_{a}$ such that |T|(P, a, [λv S]). The aforementioned "constituents" and "appropriate semantic relations" are formally characterized so as to permit a system of canonical descriptions for thought-contents of arbitrary complexity. These canonical descriptions are then employed to chart the nature and interrelations of belief de re, de dicto and de se and to identify the source of opacity in belief ascription