We give a straightforward computable-model-theoretic definition of a property of \Delta^0_2 sets called order-computability. We then prove various results about these sets which suggest that, simple though the definition is, the property defies any easy characterization in pure computability theory. The most striking example is the construction of two computably isomorphic c.e. sets, one of which is order-computable and the other not.

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.

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)

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)

'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.

This work treats the problem of axiomatizing the truth and falsity consequence relations, $ \vDash _t $ and $ \vDash _f $, determined via truth and falsity orderings on the trilattice SIXTEEN₃. The approach is based on a representation of SIXTEEN₃ as a twist-structure over the two-element Boolean algebra.

Prozorov reinterprets the familiar principles of community, equality and freedom in ontological terms as attributes of pure being, subtracted from all positive determinations, and presents them as axioms of universalist politics valid in any world whatsoever.

The article takes Giorgio Agamben’s declaration of his optimism with regard to the possibilities of global political transformation as a point of departure for the inquiry into the affirmative aspects of Agamben’s political thought, frequently overshadowed by his more famous critical claims. We reconstitute three principles grounding Agamben’s optimism that pertain respectively to the total crisis of the contemporary biopolitical apparatuses, the possibility of a radically different form-of-life on the basis of their residue and the minimalist character of this transformation (...) that consists entirely in the subtraction of existence from these apparatuses. While the first two principles are unproblematic in the wider context of Agamben’s work, the third principle introduces the problematic of will that remains highly ambiguous in his philosophy. In the remainder of the article we address this ambiguity in an analysis of Agamben’s reading of Melville’s ‘Bartleby the Scrivener’ and conclude that Agamben’s optimism ultimately consists in the affirmation of absolute contingency, beyond both will and necessity. (shrink)

This paper introduces a theory of ownership that is rooted in Israel Kirzner’s theory of entrepreneurship – The Entrepreneurial Theory of Ownership. Its central idea is that natural resources are not available to us automatically as other approaches to justice implicitly assume. Before we can use a resource, we need to do preparatory work in the form of making an entrepreneurial judgement on it. This fact, as I argue, makes it possible to put private ownership as a natural right on (...) a firm normative ground and answer many traditional challenges to private property. (shrink)

Historical entitlement theories of property rights, which claim that individuals can acquire moral property rights over natural resources by appropriating them, traditionally face a strong objection: it is widely implausible that a single individual can unilaterally impose duties on everyone around him and yet, apparently, this is exactly what such theories allow. In this essay, I argue that the same problem appears in all other theories of distributive justice and if this problem was a reason to reject historical entitlement theories, (...) it would also be a reason to reject all rival theories. Which means that as long, as one is committed to any theory of distributive justice at all, she, at the risk of inconsistency, cannot rely on the aforementioned objection to criticize historical entitlement theories. (shrink)

This article examines a still contentious question: how conservative and liberal elements are combined in Boris N. Chicherin’s worldview and political doctrine. It considers several points of view...

Why does the theory of law have such a significant role in Russian liberalism, and how is this related to the state of the legal system in Russia and to the public’s legal consciousness? This intro...

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)

Poses of the World develops a theory of the pluralistic coexistence of politics with aesthetic, scientific, ethical and economic procedures that have sought to influence, dominate or even replace politics. We are accustomed to saying that everything is political. It is true that politics has throughout history ventured into the domains that used to be non-political, be they art, science or economy. However, rather than being totally dominated by politics, our societies are marked by the coexistence of diverse procedures, whose (...) logics are distinct but nonetheless remain in contact, ranging from frontal conflict to lasting syntheses. This book develops a theory of this pluralistic coexistence. It builds upon the findings of the first two volumes of Void Universalism to outline an account of pluralism that affirms the incommensurable character of the procedures that regulate the manners of our being and acting in the world. Neither reducible to nor insulated from each other, politics, ethics, art, economy, science and numerous other procedures persist in errancy without ever cohering into any overarching unity. The book demonstrates how the abandonment of the aspiration for such coherence opens up new perspectives on the key sociopolitical debates of our time, from the critique of neoliberalism to concerns over cancel culture. Systematic and accessible, this volume will be of interest to students and scholars of political science, philosophy, sociology, anthropology and cultural studies as well a wider readership beyond academia. (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)

A theory of the emergence of the subject of world politics.

In this paper the philosophical ideology of eclecticism of Modern times is considered, especially as it has been formulated byJ. Ch.Sturm, and assessment of its contribution to development of philosophical and scientific thought is given. The need of differentiation of eclecticism, syncretism and conciliatorics is proved. Eclecticism is characterized as a progressive for its time current. The decisive impact eclecticism on formation of new scientific outlook is emphasized.

t. 1. Filosofii︠a︡ khozi︠a︡ĭstva ; Tragedii︠a︡ filosofii -- t. 2. Izbrannye stat ́i.