Epistemic Logics of Structured Intensional Groups

Epistemic logics of intensional groups lift the assumption that membership in a group of agents is common knowledge. Instead of being represented directly as a set of agents, intensional groups are represented by a property that may change its extension from world to world. Several authors have considered versions of the intensional group framework where group-specifying properties are articulated using structured terms of a language, such as the language of Boolean algebras or of description logic. In this paper we formulate a general semantic framework for epistemic logics of structured intensional groups, develop the basic theory leading to completeness-via-canonicity results, and show that several frameworks presented in the literature correspond to special cases of the general framework.Comment: In Proceedings TARK 2023, arXiv:2307.0400

Hyperintensional semantics: a Fregean approach

In this paper, we present a new semantic framework designed to capture a distinctly cognitive or epistemic notion of meaning akin to Fregean senses. Traditional Carnapian intensions are too coarse-grained for this purpose: they fail to draw semantic distinctions between sentences that, from a Fregean perspective, differ in meaning. This has led some philosophers to introduce more fine-grained hyperintensions that allow us to draw semantic distinctions among co-intensional sentences. But the hyperintensional strategy has a flip-side: it risks drawing semantic distinctions between sentences that, from a Fregean perspective, do not differ in meaning. This is what we call the ‘new problem’ of hyperintensionality to distinguish it from the ‘old problem’ that faced the intensional theory. We show that our semantic framework offers a joint solution to both these problems by virtue of satisfying a version of Frege’s so-called ‘equipollence principle’ for sense individuation. Frege’s principle, we argue, not only captures the semantic intuitions that give rise to the old and the new problem of hyperintensionality, but also points the way to an independently motivated solution to both problems

In Defence of Extensional Evidence

Intensional evidence is any reason to accept a proposition that is not the truth values of the proposition accepted or, if it is a complex proposition, is not the truth values of its propositional contents. Extensional evidence is non-intensional evidence. Someone can accept a complex proposition, but deny its logical consequences when her acceptance is based on intensional evidence, while the logical consequences of the proposition presuppose the acceptance of extensional evidence, e.g., she can refuse the logical consequence of a proposition she accepts because she doesn’t know what are the truth-values of its propositional contents. This tension motivates counterexamples to the negation of conditionals, the propositional analysis of conditionals, hypothetical syllogism, contraposition and or-to-if. It is argued that these counterexamples are non-starters because they rely on a mix of intensionally based premises and extensionally based conclusions. Instead, a genuine counterexample to classical argumentative forms should present circumstances where an intuitively true and extensionally based premise leads to an intuitively false conclusion that is also extensionally based. The other point is that evidentiary concerns about intensionally based beliefs should be constrained by the truth conditions of propositions presented by classical logic, which are nothing more than coherence requirements in distributions of truth value. It is argued that this restriction also dissolves some known puzzles such as conditional stand-offs, Adams pair, the opt-out property, and the burglar’s puzzle

LOGICAL ANALYSIS AND LATER MOHIST LOGIC: SOME COMPARATIVE REFLECTIONS [abstract]

Any philosophical method that treats the analysis of the meaning of a sentence or expression in terms of a decomposition into a set of conceptually basic constituent parts must do some theoretical work to explain the puzzles of intensionality. This is because intensional phenomena appear to violate the principle of compositionality, and the assumption of compositionality is the principal justification for thinking that an analysis will reveal the real semantical import of a sentence or expression through a method of decomposition. Accordingly, a natural strategy for dealing with intensionality is to argue that it is really just an isolable, aberrant class of linguistic phenomena that poses no general threat to the thesis that meaning is basically compositional. On the other hand, the later Mohists give us good reason to reject this view. What we learn from them is that there may be basic limitations in any analytical technique that presupposes that meaning is perspicuously represented only when it has been fully decomposed into its constituent parts. The purpose of this paper is to (a) explain why the Mohists found the issue of intensionality to be so important in their investigations of language, and (b) defend the view that Mohist insights reveal basic limitations in any technique of analysis that is uncritically applied with a decompositional approach in mind, as are those that are often pursued in the West in the context of more general epistemological and metaphysical programs

Topic-Sensitive Epistemic 2D Truthmaker ZFC and Absolute Decidability

This paper aims to contribute to the analysis of the nature of mathematical modality, and to the applications of the latter to unrestricted quantification and absolute decidability. Rather than countenancing the interpretational type of mathematical modality as a primitive, I argue that the interpretational type of mathematical modality is a species of epistemic modality. I argue, then, that the framework of two-dimensional semantics ought to be applied to the mathematical setting. The framework permits of a formally precise account of the priority and relation between epistemic mathematical modality and metaphysical mathematical modality. The discrepancy between the modal systems governing the parameters in the two-dimensional intensional setting provides an explanation of the difference between the metaphysical possibility of absolute decidability and our knowledge thereof. I also advance an epistemic two-dimensional truthmaker semantics, if hyperintenisonal approaches are to be preferred to possible worlds semantics. I examine the relation between epistemic truthmakers and epistemic set theory

How to Hintikkize a Frege

The paper deals with the main contribution of the Finnish logician Jaakko Hintikka: epistemic logic, in particular the 'static' version of the system based on the formal analysis of the concepts of knowledge and belief. I propose to take a different look at this philosophical logic and to consider it from the opposite point of view of the philosophy of logic. At first, two theories of meaning are described and associated with two competing theories of linguistic competence. In a second step, I draw the conclusion that Hintikka's epistemic logic constitutes a sort of internalisation of meaning, by the introduction of epistemic modal operators into an object language. In this respect, to view meaning as the result of a linguistic competence makes epistemic logic nothing less than a logic of unified meaning and understanding