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)

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 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)

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)

Early normative studies of human behavior revealed a gap between the norms of practical rationality (what humans ought to do) and the actual human behavior (what they do). It has been suggested that, to close the gap between the descriptive and the normative, one has to revise norms of practical rationality according to the Quinean, engineering view of normativity. On this view, the norms must be designed such that they effectively account for behavior. I review recent studies of human perception (...) which pursued normative modeling and which found good agreement between the normative prescriptions and the actual behavior. I make the case that the goals and methods of this work have been incompatible with those of the engineering approach. I argue that norms of perception and action are observer-independent properties of biological agents; the norms are discovered using methods of natural sciences rather than the norms are designed to fit the observed behavior. (shrink)

Uncertainty can’t be understood without taking into account both properties of the problem situation and agent’s knowledge about it. The correspondence of knowledge and situation of decision-making is crucial for understanding the onto-epistemological nature of uncertainty. At the same time, this correspondence is the key topic in virtue epistemology, especially in its ‘non-classical’, regulatory, branch, related to works of R. Roberts and W.J. Wood. In this article, genetic consultation is chosen as an example of such a problematic situation since a (...) doctor and a patient explicitly deal with the uncertainty of genetic risks. The problems of communication and joint decision-making in the context of medical-genetic consultation are comprehensively described in bioethics. At the same time, its social dimension is limited to the direct interaction of two individual agents, that allows us to use it as a model for constructing the ethics of uncertainty. In this article, four forms of uncertainty are identified: descriptive, normative and radical uncertainties, and translation uncertainty. Referring to the approaches of virtue epistemology, the author brings each of these forms into conformity with the proposed regulatory principle. The regulations assume that generating or disseminating knowledge under conditions of uncertainty require taking into account the incompleteness of the presented model of reality in its four aspects. A modelled fragment of reality could change in a predictable (descriptive uncertainty) or unexpected (radical uncertainty) way. The goals and values of a model’s user can not be hierarchically ordered, and may also change in the future (normative uncertainty). User’s interpretations of the model may be diverse, and can never be strictly defined by the intentions of the model’s author (indeterminancy of translation, or uncertainty whether success of co-reference is achieved). (shrink)

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)

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)

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.

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...

The main varieties of scientific misconduct are fabrication, falsification, misquoting and plagiarism. Considering the "improvement" of fraudulent skills, scientists, editors, and authorities must jointly combat the misconduct. Also, it is important that whistleblowers must be protected from revenge. The response to scientific misconduct requires national and international bodies to provide leadership and guidelines. Whistleblowers need a safe, confidential place to report misconduct. The quality of research and hidden conflicts of interest should be taken into account deciding which studies are to (...) be included into reviews. Forged publications and speculative theories have been used for promotion of drugs, dietary supplements and treatments without proven effectiveness. Marketing of placebos in the guise of evidence-based medications seems to be on the increase. Patients can be misinformed not only by the advertising but also by publications supposed to be scientific. Furthermore, it has become usual practice to disregard published criticism in spite of personal communications and debates at conferences. Some scientists seem to make use of critical comments without citing them, or just continue publications ignoring the criticism. The same scientists continue working sometimes in cooperation with renowned researchers; and it is possible that some later articles are more reliable than earlier ones. However, it is insufficient to hope that reliable publications would be shortly confirmed while forgeries would fall into oblivion. Fake papers are misleading for research and practice, cost time and money. Wrong concepts are persisting and reappearing, which may result in useless experimentation and application of invasive methods without sufficient indications. An international cooperation of bona fide scientists, editors and authorities is needed to eradicate the scientific misconduct and fraude in medicine. The book contains an overview of misconduct in medical research and practice mainly from the former Soviet Union. Ample documentary evidence is provided as illustrations. (shrink)

We describe our explicit Lorentz-invariant solution of the Einstein and null geodesic equations for the deflection experiment of 2002 September 8 when a massive moving body, Jupiter, passed within 3.7’ of a line-of-sight to a distant quasar. We develop a general relativistic framework which shows that our measurement of the retarded position of a moving light-ray deflecting body (Jupiter) by making use of the gravitational time delay of quasar’s radio wave is equivalent to comparison of the relativistic laws of the (...) Lorentz transformation for gravity and light. Because, according to Einstein, the Lorentz transformation of gravity field variables must depend on a fundamental speed c, its measurement through the retarded position of Jupiter in the gravitational time delay allows us to study the causal nature of gravity and to set an upper limit on the speed of propagation of gravity in the near zone of the solar system as contrasted to the speed of the radio waves. In particular, the v/c term beyond of the standard Einstein’s deflection, which we measured to 20% accuracy, is associated with the aberration of the null direction of the gravity force (“aberration of gravity”) caused by the Lorentz transformation of the Christoffel symbols from the static frame of Jupiter to the moving frame of observer. General relativistic formulation of the experiment identifies the aberration of gravity with the retardation of gravity because the speed of gravitational waves in Einstein’s theory is equal to the speed of propagation of the gravity force. We discuss the misconceptions which have inhibited the acceptance of this interpretation of the experiment. We also comment on other interpretations of this experiment by Asada, Will, Samuel, Pascual–Sánchez, and Carlip and show that their “speed of light” interpretations confuse the Lorentz transformation for gravity with that for light, and the fundamental speed of gravity with the physical speed of light from the quasar. For this reason, the “speed of light” interpretations are not entirely consistent with a retarded Liénard–Wiechert solution of the Einstein equations, and do not properly incorporate how the phase of the radio waves from the quasar is perturbed by the retarded gravitational field of Jupiter. Although all of the formulations predict the same deflection to the order of v/c, our formulation shows that the underlying cause of this deflection term is associated with the aberration of gravity and not of light, and that the interpretations predict different deflections at higher orders of v/c beyond the Shapiro delay, thus, making their measurement highly desirable for deeper testing of general relativity in future astrometric experiments like Gaia, SIM, and SKA. (shrink)

The article analyzes the interpretation of Fr. Alexander Men of Buddhism as teaching of the “Axial Age”. It is based on his seven-volume work “History of Religion: In Search of the Way, Truth and Life”. First defines the methodology used by Fr. Alexander, which is comparative and hermeneutic in nature. At the same time, he proceeds from a theistic-Christian value position, which, nevertheless, allows him respectfully treats other religious-philosophical traditions. The originality of the author’s interpretation of Buddhism is determined, both (...) its adequate features and one-sided, set by the value orientation. The concepts of transcendence and transcendent are differentiated, which allows conducting a comparative analysis of Buddhism and Christianity, assessments given by Fr. Alexander. The denial of the transcendent in Buddhism does not mean the absence of transcendence, especially in understanding the status of nirvana, which is defined purely apophatically. In the Indian worldview, he finds five essential principles that make Buddhism and Christianity related, despite all the difference in their positions: apophaticism, denial of the highest value of earthly goods, recognition of the high dignity of personal asceticism in spiritual life, the concept of “karma” as retribution, the idea of salvation-liberation as the main goal of religion. These principles, in his opinion, “constitute a strong bridge connecting Eastern religious experience with the Gospel”. The work of A. Men contributes to the expansion of the cultural horizon, liberation from both nationalist and Eurocentric points of view, contributes to the development of a dialogue that is so necessary right now. It is noted that the “Axial Age” concept by K. Jaspers as a whole allows avoiding one-sided assessments, revealing the common source of all axial teachings, which can be defined as “a breakthrough to the transcendent”. (shrink)

An instance of Stratified Comprehension ∀x₁ … ∀x n ∃y∀x (x ∈ y ↔ φ(x, x₁, …, x n )) is called strictly impredicative iff, under minimal stratification, the type of x is 0. Using the technology of forcing, we prove that the fragment of NF based on strictly impredicative Stratified Comprehension is consistent. A crucial part in this proof, namely showing genericity of a certain symmetric filter, is due to Robert Solovay. As a bonus, our interpretation also satisfies some (...) instances of Stratified Comprehension which are not strictly impredicative. For example, it verifies existence of Frege natural numbers. Apparently, this is a new subsystem of NF shown to be consistent. The consistency question for the whole theory NF remains open (since 1937). (shrink)

Книга адресована психоаналитикам, психологам, психотерапевтам, философам, педагогам, студентам и всем работникам "помогающих" профессий.

In this paper, we provide a semantic analysis of the well-known knowability paradox stemming from the Church–Fitch observation that the meaningful knowability principle /all truths are knowable/, when expressed as a bi-modal principle F --> K♢F, yields an unacceptable omniscience property /all truths are known/. We offer an alternative semantic proof of this fact independent of the Church–Fitch argument. This shows that the knowability paradox is not intrinsically related to the Church–Fitch proof, nor to the Moore sentence upon which it (...) relies, but rather to the knowability principle itself. Further, we show that, from a verifiability perspective, the knowability principle fails in the classical logic setting because it is missing the explicit incorporation of a hidden assumption of /stability/: ‘the proposition in question does not change from true to false in the process of discovery.’ Once stability is taken into account, the resulting /stable knowability principle/ and its nuanced versions more accurately represent verification-based knowability and do not yield omniscience. (shrink)

Justification Logic provides an axiomatic description of justifications and delegates the question of their nature to semantics. In this note, we address the conceptual issue of the logical type of justifications: we argue that justifications in the logical setting are naturally interpreted as sets of formulas which leads to a class of epistemic models that we call modular models . We show that Fitting models for Justification Logic naturally encode modular models and can be regarded as convenient pre-models of the (...) former. (shrink)

This 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.

The 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 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)

This paper sheds light on the relationship between the logic of generalized truth values and the logic of bilattices. It suggests a definite solution to the problem of axiomatizing the truth and falsity consequence relations, \ and \ , considered in a language without implication and determined via the truth and falsity orderings on the trilattice SIXTEEN 3 . The solution is based on the fact that a certain algebra isomorphic to SIXTEEN 3 generates the variety of commutative and distributive (...) bilattices with conflation. (shrink)

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)

N4-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)

We 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.

Despite its increasing prominence in critical political and IR theory, the significance of the Foucauldian problematic of biopolitics remains underestimated. The frequent conflation of paradigmatically distinct sovereign and biopolitical forms of power, inspired by influential readings of Agamben and Hardt and Negri, results in increasingly incoherent applications of the concept of biopolitics. This is particularly evident in the attempts to theorise resistance to bio-power, which remains cast in conventional 'emancipatory' terms of resisting transcendent and exterior power. Critically engaging with Hardt (...) and NegriÕs attempt to theorise resistance to biopolitics in terms of the liberation of the domain of biopolitical production, this article offers an alternative pathway of resistance that consists of the refusal of biopolitical 'care of the living' and the creation of autonomous forms of life outside the terrain of biopolitical governmentality. The example of such resistance is offered by the social practices of the late-Soviet period, whereby the alienation from and subversion of the socialist biopolitics and the concomitant experimentation with alternative forms of life in the 'shadow society' reduced Soviet power to its pure form of sovereignty. The article concludes with outlining the implications of this mode of resistance in the contemporary context of the global neoliberal Empire. (shrink)