This paper argues that unusual coincidences, particularly those involving historical events, can be viewed as design patterns, suggesting an intelligent influence over the course of events. A compelling case examined in detail using probability theory concerns the presidencies of Abraham Lincoln (1809–1865) and John F. Kennedy (1917–1963). This and other coincidences involving historical figures disfavor the materialistic perspective and point to the presence of an intelligent agent acting on a global scale, beyond the arrow of time, influencing human lives and (...) the course of history. (shrink)

The principle motivation of this work is to display the sense in which the epistemic reading of a Kripke model tacitly requires common knowledge of the model, CKM. This requirement significantly restricts the amount of epistemic situations we are able to consider. We explore possible worlds epistemic models in a general setting without CKM assumptions and show that such models can be identified with observable substructures of Kripke models. We argue that such observable models offer a new level of generality (...) and conceptual clarity in epistemic modeling. Similar analysis applies to intuitionistic models. (shrink)

We describe a general logical framework, Justification Logic, for reasoning about epistemic justification. Justification Logic is based on classical propositional logic augmented by justification assertions t: F that read t is a justification for F. Justification Logic absorbs basic principles originating from both mainstream epistemology and the mathematical theory of proofs. It contributes to the studies of the well-known Justified True Belief vs. Knowledge problem. We state a general Correspondence Theorem showing that behind each epistemic modal logic, there is a (...) robust system of justifications. This renders a new, evidence-based foundation for epistemic logic. As a case study, we offer a resolution of the GoldmanRed Barns in Justification Logic. Furthermore, we formalize the well-known Gettier example and reveal hidden assumptions and redundancies in Gettier’s reasoning. (shrink)

'Ontological Semantics' introduces a comprehensive approach to the treatment of text meaning by computer, arguing that being able to use meaning is crucial to the success of natural language processing applications.

Saul Aaron Kripke, the most influential philosopher and logician of his generation, died on September 15, 2022, at the age of 81.

In 1933 Godel introduced a calculus of provability (also known as modal logic S4) and left open the question of its exact intended semantics. In this paper we give a solution to this problem. We find the logic LP of propositions and proofs and show that Godel's provability calculus is nothing but the forgetful projection of LP. This also achieves Godel's objective of defining intuitionistic propositional logic Int via classical proofs and provides a Brouwer-Heyting-Kolmogorov style provability semantics for Int which (...) resisted formalization since the early 1930s. LP may be regarded as a unified underlying structure for intuitionistic, modal logics, typed combinatory logic and λ-calculus. (shrink)

Let ???? be a computable structure and let R be a new relation on its domain. We establish a necessary and sufficient condition for the existence of a copy ℬ of ???? in which the image of R (¬R, resp.) is simple (immune, resp.) relative to ℬ. We also establish, under certain effectiveness conditions on ???? and R, a necessary and sufficient condition for the existence of a computable copy ℬ of ???? in which the image of R (¬R, resp.) (...) is simple (immune, resp.). (shrink)

Veritism is the thesis that the truth is the fundamental epistemic good. According to Duncan Pritchard, the most pressing objections to veritism are the trivial truths objection and the trivial inquiry problem. The former states that veritism entails that trivial truths are as important as deep and important truths. The latter is a problem that a veritist must prefer trivial inquiry that generates many trivial truths to the serious inquiry with the hope but no guarantee to discover some deep and (...) important truth. Both objections arise from the inability of veritism prima facie to properly rate the different types of truths. Pritchard's solution is to approach the truth from the perspective of the intellectually virtuous inquirer who would prefer weighty truth over trivial truth. In my commentary, I criticise the proposed solution as circular reasoning. The necessary virtue for an intellectually virtuous inquirer is that they would prefer the weighty truth over the trivial one and at the same time, the weighty truth is superior because it is the goal for intellectually virtuous inquirer. I suggest another path to substantiate veritism in the face of the two sibling objections. I argue that truth is the fundamental epistemic good as it makes the epistemic realm practically valuable more than any other epistemic good. The weighty truths are preferable to the trivial ones because the practical value of the deep and important truths is usually higher. The suggested path goes away from the attempts to prove the epistemic value of truth only within the epistemic realm, yet I argue it does not compel the intellectually virtuous inquirer to seek the truth only for the sake of practical reasons. (shrink)

The article aims at reconstructing some fundamental aspects of Pletho's aesthetical views by investigating the ontological foundations of the plethonian concept of beauty. In a first step, the analysis concentrates on one extant fragment from the Laws, in which Pletho provides his definition of the concept of beauty. Here its definition in terms of an ,,ontological comparative" is combined with the platonic notions of the limit and the limitless . In the next step, the article shows the position of peras (...) and apeiron in the plethonian ontology: the pair appears as Hera and Poseidon at the very top of the plethonian pantheon. After a brief analysis of the several ways in which Pletho explains their union, in the last step, the article shows that Poseidon is brought explicitly in connection with the notion of beauty in a variety of extant texts. Thus the union of Poseidon and Hera is shown to be both effective at the root of the plethonian universe and to be central for the Plethonian concept of beauty. Beauty thus becomes a constitutive trait of the plethonian universe. (shrink)

It was shown in the previous work of the author that one can avoid the paradox of minimal logic { ϕ , ¬ ϕ } ¬ ψ defining the negation operator via reduction not a constant of absurdity, but to a unary operator of absurdity. In the present article we study in details what does it mean that negation in a logical system can be represented via an absurdity or contradiction operator. We distinguish different sorts of such presentations. Finally, we (...) consider the possibility to represent the negation via absurdity and contradiction operators in such well known systems of paraconsistent logic as D.Batens's logic CLuN and Sette's logic P 1. (shrink)

We define a novel interpretation R of second order arithmetic into Explicit Mathematics. As a difference from standard D-interpretation, which was used before and was shown to interpret only subsystems proof-theoretically weaker than T 0 , our interpretation can reach the full strength of T 0 . The R-interpretation is an adaptation of Kleene's recursive realizability, and is applicable only to intuitionistic theories.

We compare the logic HYPE recently suggested by H. Leitgeb as a basic propositional logic to deal with hyperintensional contexts and Heyting-Ockham logic introduced in the course of studying logical aspects of the well-founded semantics for logic programs with negation. The semantics of Heyting-Ockham logic makes use of the so-called Routley star negation. It is shown how the Routley star negation can be obtained from Dimiter Vakarelov’s theory of negation and that propositional HYPE coincides with the logic characterized by the (...) class of all involutive Routley star information frames. This result provides a much simplified semantics for HYPE and also a simplified axiomatization, which shows that HYPE is identical with the modal symmetric propositional calculus introduced by G. Moisil in 1942. Moreover, it is shown that HYPE can be faithfully embedded into a normal bi-modal logic based on classical logic. Against this background, we discuss the notion of hyperintensionality. (shrink)

Here is an account of recent investigations into the two main concepts of negation developed in the constructive logic: the negation as reduction to absurdity, and the strong negation. These concepts are studied in the setting of paraconsistent logic.

The relationships between various modal logics based on Belnap and Dunn’s paraconsistent four-valued logic FDE are investigated. It is shown that the paraconsistent modal logic \, which lacks a primitive possibility operator \, is definitionally equivalent with the logic \, which has both \ and \ as primitive modalities. Next, a tableau calculus for the paraconsistent modal logic KN4 introduced by L. Goble is defined and used to show that KN4 is definitionally equivalent with \ without the absurdity constant. Moreover, (...) a tableau calculus is defined for the modal bilattice logic MBL introduced and investigated by A. Jung, U. Rivieccio, and R. Jansana. MBL is a generalization of BK that in its Kripke semantics makes use of a four-valued accessibility relation. It is shown that MBL can be faithfully embedded into the bimodal logic \ over the non-modal vocabulary of MBL. On the way from \ to MBL, the Fischer Servi-style modal logic \ is defined as the set of all modal formulas valid under a modified standard translation into first-order FDE, and \ is shown to be characterized by the class of all models for \. Moreover, \ is axiomatized and this axiom system is proved to be strongly sound and complete with respect to the class of models for \. Moreover, the notion of definitional equivalence is suitably weakened, so as to show that \ and \ are weakly definitionally equivalent. (shrink)

Tracing how the logic of inoperativity works in the domains of language, law, history and humanity, 'Agamben and Politics' systematically introduces the fundamental concepts of Agamben's political thought and a critically interprets his insights in the wider context of contemporary philosophy.

Two traditions have had a great impact on the theoretical and experimental research of perception. One tradition is statistical, stretching from Fechner's enunciation of psychophysics in 1860 to the modern view of perception as statistical decision making. The other tradition is phenomenological, from Brentano's “empirical standpoint” of 1874 to the Gestalt movement and the modern work on perceptual organization. Each tradition has at its core a distinctive assumption about the indivisible constituents of perception: the just-noticeable differences of sensation in the (...) tradition of Fechner vs. the phenomenological Gestalts in the tradition of Brentano. But some key results from the two traditions can be explained and connected using an approach that is neither statistical nor phenomenological. This approach rests on a basic property of any information exchange: a principle of measurement formulated in 1946 by Gabor as a part of his quantal theory of information. Here the indivisible components are units (quanta) of information that remain invariant under changes of precision of measurement. This approach helped to understand how sensory measurements are implemented by single neural cells. But recent analyses suggest that this approach has the power to explain larger-scale characteristics of sensory systems. (shrink)