Niccolò Rossi

If one believes that 2+2=4, then one also believes that either 2+2=4 or 971 is a cousin prime number. This follows from doxastic logics based on standard Kripke relational semantics, which validate disjunction introduction for belief. However, this principle does not hold in topic-sensitive semantics. An agent who lacks the concept of a ‘cousin prime number’ may be unable to entertain, and thus unable to believe, any proposition involving that concept. I argue that while disjunction introduction may fail for belief—and for other epistemic states that presuppose belief—it does hold for certain states that do not require belief. In this paper, I focus on the notion of commitment to the truth. Drawing on the concept of logical grounding, I propose formal semantics that preserve the requirement of topic-grasping, but weaken it in a way that allows for a more standard treatment of disjunction.

Standard epistemic logic, assuming logical omniscience, models agents with highly idealized cognitive capacities. This dissertation explores and proposes different frameworks to model agents whose cognitive capacities are less idealized, and thus more similar to our own. Chapter 1 examines a non-normal epistemic logic developed by Sven Rosenkranz. I analyze the formal semantics he proposes and show how it successfully invalidates certain undesirable principles for knowledge and being in a position to know. While the neighborhood semantics he employs reduces some of the most extreme idealizations, it remains too coarse-grained, treating sentences with the same intension—i.e., those true in the same set of possible worlds—as expressing the same proposition. The rest of the dissertation adopts hyperintensional semantics, which allows for finer distinctions. Chapter 2 develops a hyperintensional account of epistemic possibility and applies it to Stalnaker’s conception of belief as the epistemic possibility of knowledge. This mirrors Rosenkranz’s treatment of epistemic justification as the epistemic possibility of being in a position to know. The approach is flexible and compatible with various hyperintensional frameworks, with a particular focus on awareness-based and topic-sensitive semantics. Chapter 3, inspired by work on logical grounding, proposes a refinement of topic-sensitive semantics and introduces a hyperintensional notion of epistemic justification. Finally, Chapter 4 raises a challenge for topic-sensitive semantics, arguing that it misrepresents certain scenarios by making knowledge more easily attainable than it actually is. This critique highlights potential limitations of the framework and suggests directions for further refinement.

In recent years the study of topic or subject matter has found application in the analysis of epistemic attitudes such as knowledge and belief. To know or believe $$\varphi,$$ one needs to grasp $$\varphi $$’s topic, i.e. what $$\varphi $$ is about. This yields a hyperintensional treatment of epistemic attitudes: if two necessary equivalent sentences differ in subject matter, they cannot be substituted _salva veritate_ in the context of those attitudes. In this paper, I aim to extend this approach to propositional justification. I argue that, in contrast to epistemic attitudes, having propositional justification for $$\varphi $$ does not require grasping the totality of $$\varphi $$’s topic, but only part of it. This is the case because one may possess evidence for $$\varphi $$ even without grasping the totality of $$\varphi $$’s topic. I define what it means to be evidence for a proposition, borrowing some notions from the logical grounding literature. Building on extant frameworks modelling evidential support and subject matter, I then put forward a modal clause for propositional justification. Finally, I prove—together with the failure of some undesired principles—a ground-theoretic closure principle for the justification operator and show how it entails closure under Strong Kleene logic.

It is natural to assume that knowledge, like belief, creates a hyperintensional context, that is, that knowledge ascriptions do not allow for substitution of necessarily equivalent prejacents salva veritate. There exist a variety of different proposals for modelling the phenomenon. In the last years, the topic-sensitive approach to the hyperintensionality of knowledge has gained considerable traction. It promises to provide a natural account of why knowledge fails to be closed under necessary equivalence in terms of differences in subject matter. Here, we argue that the topic-sensitive approach, as recently put forward by Franz Berto, Peter Hawke, Aybüke Özgün, and others, faces formidable problems. The root of these problems lies in the approach’s prediction that a mere grasp of subject matter may help to provide insights into necessary implications that it would seem to require more substantive epistemic work to gain.

If Andrea knows that Biden won the last presidential election, then they also know that either Biden won the last presidential election, or Biden is a reptilian. This is the response that epistemic logics based on standard Kripke relational semantics provide, which is consistent with the fact that minimally rational agents can perform disjunction introduction. This is not the case in topic-sensitive semantics though. An agent might not grasp the concept of what a reptilian is, and therefore not be able to know any proposition dealing with reptilians. By employing the concept of logical grounding, I propose a semantics that keeps the requirement of topic-grasping but weakens it, re-establishing a more standard treatment of disjunction, in line with the capacities of minimally rational agents. The paper is structured as follows. In Section 2 I introduce topic-sensitive semantics. In Section 3 I introduce the concept of logical grounding – focusing on the grounds of disjunction – and motivate some desiderata. The concept of minimal topic, the core of my proposal, is detailed in Section 4 and exploited in Section 5 to propose a new topic-sensitive semantic clause for knowledge. I conclude in Section 6.

The received view says that possibility is the dual of necessity: a proposition is (metaphysically, logically, epistemically etc.) possible iff it is not the case that its negation is (metaphysically, logically, epistemically etc., respectively) necessary. This reading is usually taken for granted by modal logicians and indeed seems plausible when dealing with logical or metaphysical possibility. But what about epistemic possibility? We argue that the dual definition of epistemic possibility in terms of epistemic necessity generates tension when reasoning about non-idealized agents and is a problem of concern for most hyperintensional epistemic logics that alleviate the problem of logical omniscience. The tension is particularly evident when knowledge is taken as a primitive to define other epistemic concepts, such as justification and belief, as done in the knowledge-first tradition. We propose a non-dual interpretation of epistemic possibility, employing a hyperintensionality filter similar to the one that makes the corresponding epistemic necessity operator hyperintensional. We employ the proposed semantics to model Stalnaker's belief as epistemic possibility of knowledge and provide a sound and complete axiomatization for a hyperintensional version of his bimodal logic of knowledge and belief.

The aim of this paper is to show how the invention of imaginary logic by Nikolaj A. Vasil’ev, forerunner of various logical and metaphysical theories appeared in the 20th century, is grounded on a revaluation of Aristotelian ontology. I shall introduce the reason why Aristotle believes that the study of the principle of contradiction is part of ontology (§ 2); I shall explain why Vasil’ev considers the law of contradiction an empirical law, and not a logical one (§ 3.1). I will show his conception of contradiction (§ 3.2) and I will discuss how he believes that it’s possible to renounce this law; (§ 3.3). I shall then explain the fundamental features of imaginary logic (§ 4.1 and § 4.2); and, finally I shall claim how, in spite of a convergence from the logical point of view (§ 5.1), the incompatibility of the two authors takes place on an ontological level (§ 5.2). In order to do so, I shall implement the analysis of the Aristotelian syllogistic conducted by the Polish logician and philosopher Jan Łukasiewicz, together with a crucial distinction between two concepts: the one of ‘law’ and the one of ‘principle’.

Rosenkranz (2021) devised two bimodal epistemic logics: an idealized one and a realistic one. The former is shown to be sound with respect to a class of neighborhood frames called i-frames. Rosenkranz designed a specific i-frame able to invalidate a series of undesired formulas, proving that these are not theorems of the idealized logic. Nonetheless, an unwanted formula and an unwanted rule of inference are not invalidated. Invalidating the former guarantees the distinction between the two modal operators characteristic of the logic, while invalidating the latter is crucial in order to deal with the problem of logical omniscience. In this paper, I present an i-frame able to invalidate all the undesired formulas already invalidated by Rosenkranz, together with the missing formula and rule of inference.