Realization of constructive set theory into explicit mathematics: a lower bound for impredicative Mahlo universe.Sergei Tupailo -2003 -Annals of Pure and Applied Logic 120 (1-3):165-196.detailsWe define a realizability interpretation of Aczel's Constructive Set Theory CZF into Explicit Mathematics. The final results are that CZF extended by Mahlo principles is realizable in corresponding extensions of T 0 , thus providing relative lower bounds for the proof-theoretic strength of the latter.
Agamben and Politics: A Critical Introduction.Sergei Prozorov -2014 - Edinburgh: Edinburgh University Press.detailsTracing 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.
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Recalling the Past.N. F.Ovchinnikov -2000 -Russian Studies in Philosophy 39 (2):35-69.detailsMy young friends advise me to write my memoirs. For me this is comforting. The future is unpredictable. The present is dark—it is "without repentance or hope" and only the past is remembered. The reawakening of interest in events long ago is a sign that a new view of things is forming: history—the knowledge of the past—forms us, for it lives in our actions. People of the past are our contemporaries: the results of their labors are part of our everyday (...) life. Their insights and mistakes live with us and in us. Contemporary life is only the surface layer of human existence. Faith in the intellectual intuition of the young generation gives hope that the pallid lines of the past I remember might clarify a little the problems of the present time. (shrink)
The Role of Exceptionalism in the Evolution of Bioethical Regulation.Sergei Shevchenko &Alexey Zhavoronkov -2024 -Cambridge Quarterly of Healthcare Ethics 33 (2):185-197.detailsThe paper aims to present a critical analysis of the phenomenon and notion of exceptionalism in bioethics. The authors demonstrate that exceptionalism pertains to phenomena that are not (yet) entirely familiar to us and could potentially bear risks regarding their regulation. After an overview of the state of the art, we briefly describe the origins and evolution of the concept, compared to exception and exclusion. In the second step, they look at the overall development debates on genetic exceptionalism, compared to (...) other bioethical debates on exceptionalism, before presenting a detailed analysis of a specific case of early regulation of genetic screening. In the last part, the authors explain the historical background behind the connection between exceptionalism and exclusion in these debates. Their main conclusion is that while the initial stage of the discussion is shaped by the concept of exceptionalism and awareness of risks of exclusion, the later development centers around exceptions that are needed in detailed regulatory procedures. (shrink)
Byzantine Perspectives on Neoplatonism.MarievSergei (ed.) -2017 - Berlin/Boston: De Gruyter.detailsByzantine intellectuals not only had direct access to Neoplatonic sources in the original language but also, at times, showed a particular interest in them. During the Early Byzantine period Platonism significantly contributed to the development of Christian doctrines and, paradoxically, remained a rival world view that was perceived by many Christian thinkers as a serious threat to their own intellectual identity. This problematic relationship was to become even more complex during the following centuries. Byzantine authors made numerous attempts to harmonize (...) Neoplatonic doctrines with Christianity as well as to criticize, refute and even condemn them. The papers assembled in this volume discuss a number of specific questions and concerns that drew the interest of Byzantine scholars in different periods towards Neoplatonic sources in an attempt to identify and explore the central issues in the reception of Neoplatonic texts during the Byzantine era. This is the first volume of the sub-series "Byzantinisches Archiv - Series Philosophica", which will be dedicated to the rapidly growing field of research in Byzantine philosophical texts. (shrink)
The logic of justification.Sergei Artemov -2008 -Review of Symbolic Logic 1 (4):477-513.detailsWe 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)
Routley Star and Hyperintensionality.Sergei Odintsov &Heinrich Wansing -2020 -Journal of Philosophical Logic 50 (1):33-56.detailsWe 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)
Explicit provability and constructive semantics.Sergei N. Artemov -2001 -Bulletin of Symbolic Logic 7 (1):1-36.detailsIn 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)
Disentangling FDE -Based Paraconsistent Modal Logics.Sergei P. Odintsov &Heinrich Wansing -2017 -Studia Logica 105 (6):1221-1254.detailsThe 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)
A thousand healths: Jean-Luc Nancy and the possibility of democratic biopolitics.Sergei Prozorov -2018 -Philosophy and Social Criticism 44 (10):1090-1109.detailsThis article addresses the relationship between ontology and politics in Jean-Luc Nancy’s theory of democracy by probing the implications of his latest ontological innovation, the concept of struction. We argue that Nancy’s democracy is a mode of politics that makes the radical pluralism of struction legitimate, opening and guarding a political space for the coexistence of the incommensurable. From this perspective, and despite Nancy’s own skepticism about the concept of biopolitics, the notion of struction opens a pathway for theorizing democracy (...) in a biopolitical key as the regime of coexistence of radically incommensurable forms of life in the absence of any coordinating principle. We nonetheless take issue with Nancy’s prescription for democracy to remain devoid of any political affirmation of its own. Instead, we suggest that the prescriptive content of democracy consists in the affirmation of the contingency of all the forms of life that coexist in it, which implies their freedom, equality, and comm... (shrink)
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Democratic Biopolitics: Popular Sovereignty and the Power of Life.Sergei Prozorov -2019 - Edinburgh University Press.detailsSergei Prozorov challenges the assumption that the biopolitical governance means the end of democracy, arguing for a positive synthesis of biopolitics and democracy. He develops a vision of democratic biopolitics where diverse forms of life can coexist on the basis of their reciprocal recognition as free, equal and in common.
Boris N. Chicherin and the Problem of the Political Identification of His Legacy.Sergei L. Chizhkov -2021 -Russian Studies in Philosophy 59 (1):1-12.detailsThis 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...
On Some Features of Russian Liberalism.Sergei L. Chizhkov -2022 -Russian Studies in Philosophy 60 (2):89-95.detailsWhy 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...
Fraternity of old‐timers: How ubiquitin regulates miRNA functions.Sergei Ryazansky &Natalia Akulenko -2023 -Bioessays 45 (7):2200220.detailsAbstractmiRNA‐mediated gene repression and ubiquitin‐dependent processes are among the oldest and most versatile mechanisms that control multiple molecular pathways, rather than just protein turnover. These systems were discovered decades ago and have become among the most studied. All systems within cells are interconnected, and these two are no exception: the plethora of studies have demonstrated that the activity of the miRNAs system depends on players of the ubiquitin‐centered universe of processes, and vice versa. This review focuses on recent progress that (...) highlights that very similar mechanisms of regulation of miRNAs by ubiquitin‐related processes are likely to be found in distantly related species, including animals, plants, and viruses. Most of them occur through the ubiquitination of Argonaute proteins, but some of the other miRNA system factors are also regulated. This suggests that their regulatory relationships are either ancient evolutionary acquisitions or have arisen independently in different kingdoms. (shrink)
Watching and feeling ballet: neuroscience and semiotics of bodily movement.Sergei Kruk -2022 -Semiotica 2022 (248):351-374.detailsNeuroscience has established several brain pathways that process visual information. Distinct neural circuits analyze body appearance and movement providing information about the person’s cognitive and emotional states. The activity of the pathways depends on the salience of visual stimuli for the organism in the given circumstances. Since ballet performances are not among the crucial events for the viewer’s organism, not all viewers perceive and interpret bodily signs that express the mental state of the dancer. Treatment of the dancer as close (...) other activates the neural circuits that elaborate emotions, this enables the viewer to feel the internal state of the dancer and enrich the interpretation of the scenic action. (shrink)
When did biopolitics begin? Actuality and potentiality in historical events.Sergei Prozorov -2022 -European Journal of Social Theory 25 (4):539-558.detailsThe article addresses the ongoing debate about the origins of biopolitics. While Foucault’s analysis of biopolitics approached it as a modern rationality of government, Agamben’s Homo Sacer series presented biopolitics as having a longer provenance, dating back to the antiquity. These polar positions are not mutually exclusive but coexist in these and other theories of biopolitics, which approach its object as both modern and ancient, having its chronological origin in the eighteenth to nineteenth centuries yet also possessing a prehistory of (...) precursors. The article interprets this dual origin in terms of Paolo Virno’s theory of historical temporality, which distinguishes between the chronological past of historical events and their potential past, which accompanies and is negated in them. Coexisting with its own unrealized potential, every historical event remains incomplete and extends itself both backwards and forwards, positing its precursors and prefiguring its future outcomes. While modern in the chronological sense, biopolitics is retrospectively inscribed in a longer historical lineage, its antecedents easily identifiable in the history of political thought. Finally, we apply this approach to Virno’s own account of the history of biopolitics, questioning his identification of past potential with labour-power. (shrink)
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Unusual coincidences, statistics and an intelligent influence.Sergei Chekanov -manuscriptdetailsThis 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 Class of Extensions of Nelson's Paraconsistent Logic.Sergei P. Odintsov -2005 -Studia Logica 80 (2-3):291-320.detailsThe article is devoted to the systematic study of the lattice εN4⊥ consisting of logics extending N4⊥. The logic N4⊥ is obtained from paraconsistent Nelson logic N4 by adding the new constant ⊥ and axioms ⊥ → p, p → ∼ ⊥. We study interrelations between εN4⊥ and the lattice of superintuitionistic logics. Distinguish in εN4⊥ basic subclasses of explosive logics, normal logics, logics of general form and study how they are relate.
On Axiomatizing Shramko-Wansing’s Logic.Sergei P. Odintsov -2009 -Studia Logica 91 (3):407-428.detailsThis work treats the problem of axiomatizing the truth and falsity consequence relations, ⊨ t and ⊨ f, determined via truth and falsity orderings on the trilattice SIXTEEN 3 (Shramko and Wansing, 2005). The approach is based on a representation of SIXTEEN 3 as a twist-structure over the two-element Boolean algebra.
On Definability of Connectives and Modal Logics over FDE.Sergei P. Odintsov,Daniel Skurt &Heinrich Wansing -2019 -Logic and Logical Philosophy 28 (4):631-659.detailsThe present paper studies two approaches to the expressiveness of propositional modal logics based on first-degree entailment logic, FDE. We first consider the basic FDE-based modal logic BK and certain systems in its vicinity, and then turn to some FDE-based modal logics in a richer vocabulary, including modal bilattice logic, MBL. On the one hand, model-theoretic proofs of the definability of connectives along the lines of [McCullough, “Logical connectives for intuitionistic propositional logic”, Journal of Symbolic Logic 36, 1 (1971): 15–20. (...) DOI: 10.2307/2271511] and [[17] Wansing, “Logical connectives for constructive modal logic”, Synthese 150, 3 (2006): 459–482. DOI: 10.1007/s11229-005-5518-5] are given for various FDE-based modal logics. On the other hand, building on [Odintsov and Wansing, “Disentangling FDE-based paraconsistent modal logics, Studia Logica 105, 6 (2017): 1221–1254. DOI: 10.1007/s11225-017-9753-9], expressibility is considered in terms of mutual faithful embeddability of one logic into another logic. A distinction is drawn between definitional equivalence, which is defined with respect to a pair of structural translations between two languages, and weak definitional equivalence, which is defined with respect to a weaker notion of translations. Moreover, the definitional equivalence of some FDE-based modal logics is proven, especially the definitional equivalence of MBL and a conservative extension of the logic BK□×BK□, which underlines the central role played by BK among FDE-based modal logics. (shrink)
Pornography and Profanation in the Political Philosophy of Giorgio Agamben.Sergei Prozorov -2011 -Theory, Culture and Society 28 (4):71-95.detailsThe article addresses the critical strategy of profanation in the philosophy of Giorgio Agamben, focusing on the example of pornography. Agamben’s references to pornography as a site of radical political transformation have recently been criticized as abstruse, vacuous or absurd. Moreover, his own work on the concentration camps in the Homo Sacer series has been disparagingly referred to as ‘pornography of horror’. This article ventures to refute these accusations by interpreting Agamben’s paradigmatic use of pornography in the context of his (...) wider project of profanation, understood as the overcoming of all social separations and the return of objects of social praxis to free use. Read in this context, pornography is grasped as the paradigmatic site of the constitution of the unprofanable, the epitome of the late capitalist ‘society of the spectacle’ and thus the primary target of profanatory criticism. In the remainder of the article we elucidate the logic of Agamben’s profanatory strategy and conclude that, far from being politically irrelevant, profanation constitutes the condition of the actualization of Agamben’s messianic ideal of a generic and non-exclusive community. (shrink)
Foucault and Agamben on Augustine, Paradise and the Politics of Human Nature.Sergei Prozorov -2024 -Theory, Culture and Society 41 (1):23-37.detailsThis article focuses on Foucault’s and Agamben’s readings of Augustine’s account of human nature and original sin. Foucault’s analysis of Augustine’s account of sexual acts in paradise, subordinated to will and devoid of lust, highlights the way it constitutes the model for the married couple, whose sexual acts are only acceptable if diverted by the will away from desire and towards the tasks of procreation. While Agamben rejects Augustine’s doctrine of original sin and reclaims paradise as the original homeland of (...) humanity, his reappropriation of paradise remains conditioned by our turn towards our true nature, from which we have been estranged by sin. Agamben’s politics of reclaiming paradise necessarily involves the demand for obedience to this originary model of human nature. It therefore follows to the letter Augustine’s description of paradisiacal sex, in which the will prevails over desire by applying itself to and curtailing itself. (shrink)
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Constructive Negations and Paraconsistency.Sergei Odintsov -2008 - Dordrecht, Netherland: Springer.detailsHere 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.
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The Basic Intuitionistic Logic of Proofs.Sergei Artemov &Rosalie Iemhoff -2007 -Journal of Symbolic Logic 72 (2):439 - 451.detailsThe language of the basic logic of proofs extends the usual propositional language by forming sentences of the sort x is a proof of F for any sentence F. In this paper a complete axiomatization for the basic logic of proofs in Heyting Arithmetic HA was found.
On the representation of n4-lattices.Sergei P. Odintsov -2004 -Studia Logica 76 (3):385 - 405.detailsN4-lattices provide algebraic semantics for the logic N4, the paraconsistent variant of Nelson's logic with strong negation. We obtain the representation of N4-lattices showing that the structure of an arbitrary N4-lattice is completely determined by a suitable implicative lattice with distinguished filter and ideal. We introduce also special filters on N4-lattices and prove that special filters are exactly kernels of homomorphisms. Criteria of embeddability and to be a homomorphic image are obtained for N4-lattices in terms of the above mentioned representation. (...) Finally, subdirectly irreducible N4-lattices are described. (shrink)
Intuitionistic epistemic logic.Sergei Artemov &Tudor Protopopescu -2016 -Review of Symbolic Logic 9 (2):266-298.detailsWe outline an intuitionistic view of knowledge which maintains the original Brouwer–Heyting–Kolmogorov semantics for intuitionism and is consistent with the well-known approach that intuitionistic knowledge be regarded as the result of verification. We argue that on this view coreflectionA→KAis valid and the factivity of knowledge holds in the formKA→ ¬¬A‘known propositions cannot be false’.We show that the traditional form of factivityKA→Ais a distinctly classical principle which, liketertium non datur A∨ ¬A, does not hold intuitionistically, but, along with the whole of (...) classical epistemic logic, is intuitionistically valid in its double negation form ¬¬(KA¬A).Within the intuitionistic epistemic framework the knowability paradox is resolved in a constructive manner. We argue that this paradox is the result of an unwarranted classical reading of constructive principles and as such does not have the consequences for constructive foundations traditionally attributed it. (shrink)