Abstract
This is Part I of a two-part essay introducing case-intensional first-order logic (CIFOL), an easy-to-use, uniform, powerful, and useful combination of first order logic with modal logic resulting from philosophical and technical modifications of Bressan’s General interpreted modal calculus (Yale University Press 1972). CIFOL starts with a set of cases; each expression has an extension in each case and an intension, which is the function from the cases to the respective case-relative extensions. Predication is intensional; identity is extensional. Definite descriptions are context-independent terms, and lambda-predicates and -operators can be introduced without constraints. These logical resources allow one to define, within CIFOL, important properties of properties, viz., extensionality (whether the property applies, depends only on an extension in one case) and absoluteness, Bressan’s chief innovation that allows tracing an individual across cases without recourse to any notion of “rigid designation” or “trans-world identity.” Thereby CIFOL abstains from incorporating any metaphysical principles into the quantificational machinery, unlike extant frameworks of quantified modal logic. We claim that this neutrality makes CIFOL a useful tool for discussing both metaphysical and scientific arguments involving modality and quantification, and we illustrate by discussing in diagrammatic detail a number of such arguments involving the extensional identification of individuals via absolute (substance) properties, essential properties, de re vs. de dicto, and the results of possible tests.
Highlights
This is Part I of a two-part essay
We present case-intensional first order logic (CIFOL), an (1) easy-to-use, (2) uniform, (3) powerful, and (4) useful combination of first-order logic with modal logic resulting from philosophical and technical modifications of Bressan’s monograph [6]
A major challenge is to explain how certain terms (e.g., “Daisy”) allow one to trace an individual through the various cases and sustain the ascription of essential properties, while other terms (e.g., “the occupant of the paddock”) are unfit for these purposes. If they can handle the example at all, fail to illuminate the notion of tracing. (We essay to meet the challenge in Section 5.) For a second example, consider that only Bressan touches on the problem of literally “possible measurements,” most of which never get made but which must always give the same results if there is to be a stable concept of what is measured. (See Section 5.5.) We don’t know of another case in which a quantified modal logic has been applied to generating rigorous scientific arguments
Summary
We present CIFOL, an (1) easy-to-use, (2) uniform, (3) powerful, and (4) useful combination of first-order logic with modal logic resulting from philosophical and technical modifications of Bressan’s monograph [6]. 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.. There Bressan, a theoretical physicist, presents the system MLν , which in turn is a profound deepening of the “method of extension and intension” of [10] His purpose was to devise a quantified modal logic not in the interests of either metaphysics or the philosophy of language, but rather to help with understanding some aspects of scientific theory. It is a scandal that Bressan’s brilliant work has been almost universally ignored for forty years
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