Substance and first-order quantification over individual-concepts

Abstract

An individual-concept, hereinafter “individuation”, is a function from possible worlds to individuals. Constant individuations I will call “subsistents” (the notion will presently be generalized). A “substance”, after Thomason [35], is a subsistent whose value exists for the world at hand. In the systems of quantified modal logic developed over the past twenty years, the tendency has been to restrict the range of quantifiers to substances (often represented technically by the simple individuals that would be the values of the constant individuations), while allowing constant terms (particularly descriptions) to express arbitrary individuations. One result is to invalidate unrestricted universal instantiation (and existential generalization), rather as in free logic. Such systems approximate some features of ordinary usage rather nicely, e.g. the behavior of quantifiers and definite descriptions in tensed discourse. Stalnaker and Thomason's Q3r [34], based on the latter's Q3 [35], [36], is exemplary of this approach.The suggestion has repeatedly been considered to quantify over individuations in general (Kanger [14], Kaplan [17], Hughes and Cresswell [12, p. 196], Thomason [35, p. 136], Pollock [30]).

CIFOL: Case-Intensional First Order Logic

“…For more detailed information on many systems of quantified modal logic, see, e.g., [13,15,19]. It is striking that no mainstream discussion of quantified modal logic with the exception of [1,18,27] takes substantial notice of Bressan's ideas; and as we will make clear, even the latter two systems fall short of answering to our purposes. 7 As an extra-logical matter, CIFOL describes "most" predicates as extensional, while avoiding extensionalism by leaving room for non-extensional predication.…”

“…MTT prides itself on two features orthogonal to the concerns of CIFOL: (1) It is what we may call "hyperintensional" in that it is suitable for epistemic and doxastic modalities as well as possibility and necessity. (2) It admits of formulation as a cut free tableau calculus.…”

“…Bacon [1], building on [31], aims at a first-order version of Bressan's framework, although in our judgment he misses the mark. Terms (including variables) have intensions, and an extension in each case.…”

“…On the other hand, invoking a set, , of cases to help with modal thinking in CIFOL brings along with it certain interconnected idealizing presuppositions that go beyond the everyday meaning of "case." (1) In any application, is to be the set of all possible cases; there are no others. (2) Accordingly, each case γ ∈ is elementary, which is to say, there are no subcases.…”

“…Such an intensional first-order logic, or quantified modal logic, must be able to represent facts about the identity and distinctness of things in different possible circumstances or, as we will say, possible cases. 1 One way or the other, this may bring with it a distinction between the extension of an expression in a case, and its intension as the pattern of extensions across cases. 2 The crucial question is how this distinction can be made productive.…”