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. (shrink)

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. (shrink)

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’. -/- . (shrink)

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. (shrink)