The article highlights certain aspects of the obscured structure of the number, which occur irregularly in the teaching of numeracy in Preschool Education. Its absence, as an effect, leads to the child's misunderstanding of the concept of number. In the presymbolic stage, the number is taught through the word. Structural particularities are found in the semantics and phonetics of the number word and are substantial in the processes of speech and listening. The objectives are to make known the obscured structure (...) of the number and its elements and to analyze the nature of the name of the number. It is justified that the basis of the word "ONE" are the first sound manifestations of the infant. It states that there is the same and equal relationship between the acquisition of knowledge of language and speech with the acquisition of knowledge of number through the development of tonal auditory balance. Methodology: the theoretical analysis of the structural parts (semantics and phonosemantics) of the number and the identification of reciprocal correlation between the constructions of the knowledge of spoken numeral word in Preschool Education through the implemented technology. Contribution: the development of the method for learning the concept of number. (shrink)

The spiritual geography of Russian cosmism. General characteristics ; Recent definitions of cosmism -- Forerunners of Russian cosmism. Vasily Nazarovich Karazin (1773-1842) ; Alexander Nikolaevich Radishchev (1749-1802) ; Poets: Mikhail Vasilyevich Lomonosov, (1711-1765) and Gavriila Romanovich Derzhavin (1743-1816) ; Prince Vladimir Fedorovich Odoevsky (1803-1869) ; Aleksander Vasilyevich Sukhovo-Kobylin (1817-1903) -- The Russian philosophical context. Philosophy as a passion ; The destiny of Russia ; Thought as a call for action ; The totalitarian cast of mind -- The religious and spiritual (...) context. The kingdom of god on earth ; Hesychasm: two great Russian saints ; The Third Rome ; Pre-Christian antecedents -- The Russian esoteric context. Early searches for "deep wisdom" ; Popular magic ; Higher magic in the time of Peter the Great ; Esotericism after Peter the Great ; Theosophy and anthroposophy -- Nikolai Fedorovich Fedorov (1829-1903), the philosopher of the common task ; The one idea ; The unacknowledged prince ; The village teacher ; First disciple: Dostoevsky and Tolstoy ; The Moscow librarian ; Last years: Askhabad: the only portrait -- The "common task" ; Esoteric dimensions of the "common task" ; Fedorov's legacy: projectivism, delo, regulation -- The religious cosmists. Vladimir Sergeevich Solovyov (1853-1900) ; Sergei Nikolaevich Bulgakov (1871-1944) ; Pavel Aleksandrovich Florensky (1882-1937) ; Nikolai Aleksandrovich Berdyaev (1874-1948) -- The scientific cosmists. Konstantin Edouardovich Tsiolkovsky (1857-1935) ; Vladimir Ivanovich Vernadsky (1863-1945) ; Alexander Leonidovich Chizhevsky (1897-1964) ; Vasily Feofilovich Kuprevich (1897-1969) -- Promethean theurgy. Life-creation ; Cultural immortalism ; God-building ; Re-aiming the arrows of Eros ; Technological utopianism ; Occultism -- Fedorov's twentieth century followers. Nikolai Pavlovich Peterson (1844-1919) and Vladimir Aleksandrovich Kozhevnikov (1852-1917) ; Svyatogor and the biocosmists ; New wine and the universal task ; Alexander Konstantinovich Gorsky (1886-1943) and Nikolai Alexandrovich Setnitsky (1888-1937) ; Valerian Nikolaevich Muravyov (1885-1932) ; Vasily Nikolaevich Chekrygin (1897-1922) -- Cosmism and its offshoots today. The N.F. Fedorov museum-library ; The Tsiolkovsky museum and Chizhevsky center ; ISRICA - Institute for Scientific Research in Cosmic Anthropoecology ; Lev Nikolaevich Gumilev (1912-1992) and neo-eurasianism ; The hyperboreans ; Scientific immortalism: Igor Vishev, Danila Medvedev ; Conclusions about the Russian cosmists. (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.

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 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.

I argue that St. Augustine of Hippo was the first in the history of Christian spirituality who expressed a key tendency of Christian mysticism, which implies a gradual intellectual ascent of the human soul to God, consisting of the three main stages: external, internal, and supernal. In this ascent a Christian mystic proceeds from the knowledge of external beings to self-knowledge, and from his inner self to direct mystical contemplation of God. Similar doctrines may be found in the writings of (...) the Greek Fathers. Although there are many similarities in the overall doctrine and in particular details between them, it does not imply the direct impact of Augustine’s theological thought on the Greek Fathers but rather the influence of the Neoplatonic philosophy on both Western and Eastern Christianity, in particular, of Plotinus’ theory of intellectual cognition. (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)

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)

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 article critically engages with Giorgio Agamben’s reading of Rousseau in order to explore the affinities between the two authors’ subtractive approach to political subjectivation. In The Kingdom and the Glory. Agamben argues that Rousseau’s Social Contract reproduces, in a secularized manner, the providential paradigm of government, whose origins Agamben finds in early Christianity. This paradigm establishes a fictitious articulation between transcendent sovereignty and immanent government, presenting particular acts of government as emanating from general divine laws. We shall demonstrate that (...) Rousseau was neither unaware of the problematic character of this paradigm nor did he venture to conceal its problems, but, on the contrary, he highlighted them throughout the Social Contract, whose key motif was the danger of the contamination of general will by particular acts, identities or interests. The same wariness of particularism characterizes Rousseau’s Reveries of the Solitary Walker, often read as entirely heterogeneous to the political project of the Social Contract. By reading these two works together as the affirmation of generic existence against all forms of particularism, we bring Rousseau’s analysis closer to Agamben’s own attempts to rethink politics as subtracted from all identity predicates and contained in the affirmation of ‘whatever being’. The elucidation of affinities between Rousseau and Agamben will permit us to identify the limits of this subtractive approach to politics and outline an alternative to it. (shrink)

In this paper individual proofs are integrated into provability logic. Systems of axioms for a logic with operators “A is provable” and “p is a proof of A” are introduced, provided with Kripke semantics and decision procedure. Completeness theorems with respect to the arithmetical interpretation are proved.

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)

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)

We consider VC-minimal theories admitting unpackable generating families, and show that in such theories, forking of formulae over a model M is equivalent to containment in global types definable over M, generalizing a result of Dolich on o-minimal theories in [4].

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)

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)

Il s’agit dans cet article de dégager une certaine disposition de la philosophie russe envers la traduction comme opération fondamentale de la pensée. On considérera les cas précis des trois penseurs jouissant d’un prestige européen – Léon Chestov, Mikhaïl Bakhtine et Valery Podoroga. Cette disposition, considérée dans le geste des philosophes face à l’intraduisible, se manifesterait tout simplement par la violence, faite à l’original, de la non-hospitalité culturelle. Cette dernière est masquée parfois par l’idée reçue de l’omniréceptivité de la culture (...) russe, exprimée naguère par Dostoïevski dans son hommage à Pouchkine. (shrink)

The questions of « why » and « how to » translate Deleuze are examined by way of considerations concerning the recent penetration of Deleuze in Russian philosophical culture and the effect this has had on the manner in which one translates philosophy today in Russia. Under the sway of a strange misinterpretation, Deleuze’s thought has been diffused as a sort of introduction to Capitalist life, by which philosophy can be « de-marxised » and Russian thought freed from the burden (...) of Marxism or, rather, pseudo-Marxism. At the same time, the translation of Deleuze has become a site of conflict between traditionalists who reduce Deleuze’s language to that of classical philosophy and proponents of new practices who defend the singularity of Deleuze’s language and style. (shrink)

Some biblical texts suggest that man consists of two parts—body and soul—whereas others seem to indicate instead three parts—body, soul, and spirit. This paper examines how the Church Fathers dealt with this apparent contradiction. It finds that although they generally favor the body-soul dichotomy, they did not see it as contradicting a trichotomous view, for “spirit” can be interpreted in a number of ways: as another term for the soul, or as the lowest imaginative part of the soul, or as (...) its highest rational part, or as the grace of the Holy Spirit. Different approaches can be found in different patristic authors depending on their theological interests and the biblical passages at issue. (shrink)

Consciousness has been and will continue to be one of the central problems of philosophy. In written works the fact that the consciousness can sing is presented as one of the most interesting and enigmatic properties of consciousness. That consciousness can sing, and in fact does so, and to prove that this is the case is relatively easy. It is enough to say that “one is singing within oneself”, not loudly and only one or various simple sounds in a way (...) so that the Phonologic system does not take part at all. The arguments over whether or not the consciousness can sing are based on comparisons of paragraphs 15 to 27 from the first and second editions of Kant’s “Critique of Pure Reason” which were modified in the second edition, where no categorical statement about the similaritybetween reproduced representations and phenomenon is found. The problem between the similarity between the reproduced representations in the consciousness/brain and the consciousness/brain phenomenon were investigated by Kant in his first and second edition, where Kant reached his conclusion about the reproduced representations in the phenomenon. We are in agreement with Kant that there can exist in “the interior” of consciousness/brains of all human beings the state of similarity or difference between the represented and the perceived, but the unity of the consciousness can be found in only one state: the similarity between the represented and the perceived in the “interior”, of the consciousness/brain. In view of the similarity of the reproduced representations and the phenomenon of the consciousness/brain, the consciousness can sing and be united, or, if not, referring to the dissimilarity, the consciousness cannot sing and can be divided. (shrink)

In 1961, at the 22nd Congress of the Communist Party of the Soviet Union, a new program of the C.P.S.U. was adopted. The adoption of the Third Program of the C.P.S.U. was accompanied by a “nationwide discussion”. People expressed their opinions regarding the draft of the new Program at meetings and lectures and in their letters to various institutions. Naturally, not all the women actively demanded changes; for some there was probably no such thing as “women’s communism”. However, the individual (...) and collective letters attest to the complex of expectations that may be analyzed within the conceptual framework of “women’s communism”. The body of letters to various publications illustrate the most popular measures which, according to the letter writers, should have been implemented during the period of the “full-scale construction of communism” and, therefore, were thought of as intrinsic elements of communism. (shrink)

We 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)

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)

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)

The research is devoted to the study of the phenomenon of spiritual culture of Modern times - creationism. Authors analyze the causes of creationist teachings, as well as develop a classification of forms of creationism. As such, the following are distinguished and analyzed: biblical creationism, scientific creationism, theological evolutionism, teleological creationism, alterism, missionary creationism. Biblical creationism is a literal understanding of the texts of the Bible relating to the creation of the Earth and man. Scientific creationism is an attempt by (...) individual scientists to combine scientific knowledge with religious beliefs. It gathers scientific evidence in favor of the biblical narrative, and, at the same time, rational arguments against the scientific theory of evolution. On the contrary, theological evolutionism, especially in the form of concordism, tries to reconcile the scientific and religious view of evolution. This is achieved through the interpretation of Biblical symbols through modern scientific concepts, or by the creation of a new pseudo-religion (for example, Teilhardism). Teleological creationism, in the modern form of Intelligent Design theory, popular in Western Protestantism, using the data of natural sciences, criticizes the foundations of the theory of biological evolution, thus demonstrating the gap of natural causality in order to justify the supernatural purposefulness of the Universe. Alterism asserts that the very nature of the world before original sin was different, therefore, the current knowledge of nature cannot correspond to the original plan of God reflected in the Bible. For the first time, highlighted and explored in this work, missionary creationism seeks to interpret the Bible from the point of view of concepts of modern science in order to bring a person with an already formed scientific picture of the world to faith. It is shown that most of the above forms demonstrate a pseudoscientific or pseudo-religious essence. The authors make an assumption about the origins of creationist teachings rooted in the introduction of elements of Neoplatonic philosophy into Christian teaching. The seeming contradiction between science and religion in understanding the evolution of nature finds its explanation through the disclosure of creationism's claim to understand the world as a "thing in itself". (shrink)

Various features of the interpretation of these schools main positions, the reasons for their appearance and the consequences for the development of Mahayana Buddhism have been the subject of discussion in this research. Attention is drawn to the existence of various ideas of Buddhist authors about the interpretation of fundamental philosophical ideas of these schools. The influence of the peculiarities of translation into other languages for the adequate transmission of the author’s thought is discussed. It is noted that the possibility (...) of different interpretations was already established in the very methodology of the transmission of Buddhist doctrines, formed at the earliest stages of Buddhism. The opinions of a number of Tibetan authors are analyzed. The study presents the derivation of the existence of different interpretations of some categories central to Mahayana Buddhism due to the presence of different philosophical methodologies. A number of features were associated with the interpretation of the correlation of logical-critical knowledge, yogic methods and their priority in choosing ways to achieve an exit from the chain of rebirth. The factor of similarities in the positions of such authors as Nāgārjuna and Vasubandhu (traditionally attributed to different schools) makes it problematic to unambiguously interpret their philosophical positions; Some features of these schools were determined not only by theoretical backgrounds, but also by political struggle for a leading place in the Buddhist hierarchy of a certain country, as well as the desire to affect authorities. (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)

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.

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...