A subspace V of an infinite dimensional fully effective vector space V ∞ is called decidable if V is r.e. and there exists an r.e. W such that $V \oplus W = V_\infty$ . These subspaces of V ∞ are natural analogues of recursive subsets of ω. The set of r.e. subspaces forms a lattice L(V ∞ ) and the set of decidable subspaces forms a lower semilattice S(V ∞ ). We analyse S(V ∞ ) and its relationship with L(V (...) ∞ ). We show: Proposition. Let U, V, W ∈ L(V ∞ ) where U is infinite dimensional and $U \oplus V = W$ . Then there exists a decidable subspace D such that U |oplus D = W. Corollary. Any r.e. subspace can be expressed as the direct sum of two decidable subspaces. These results allow us to show: Proposition. The first order theory of the lower semilattice of decidable subspaces, Th(S(V ∞ )), is undecidable. This contrasts sharply with the result for recursive sets. Finally we examine various generalizations of our results. In particular we analyse S * (V ∞ ), that is, S(V ∞ ) modulo finite dimensional subspaces. We show S * (V ∞ ) is not a lattice. (shrink)

This long and complicated sentence has not been correctly translated nor clearly explained by any of the editors of the Phaedo that I have been able to consult. Bekker, Stallbaum, Wohlrab, Geddes, Wagner, Archer-Hind, Williamson, Burnet, in their notes on the passage say much that is true, but all seem to fall into certain errors. None of them has given an accurate and coherent picture of the passage as a whole. In attempting to supply such a picture I have pointed (...) out what I believe to be the mistakes of these editors, and on certain points of grammar, textual criticism, and interpretation I have some new suggestions to offer. So much emphasis on one sentence is not misplaced, for this is an important sentence, the culminating point of the first section of the dialogue, and containing in brief the essence of the ethics which Plato expounds through the mouth of Socrates. It is the peroration of Socrates' Apologia pro Vita sua, introduced by the impressive words: ⋯ μακ⋯ριε ειμμ^iota;α, a form of address often used by Socrates in passages of ‘pith and moment’. (shrink)

Union with Christ was a key doctrine for second-generation Reformed theologian Girolamo Zanchi. As a Thomist, Zanchi shared similar elements with Thomas Aquinas in his understanding of salvation as participatio, but his understanding of union with Christ differed with regard to the difference between infused and imputed righteousness. Unlike Aquinas’s doctrine of infused righteousness, Zanchi argued for imputed righteousness, which was both the foundation for one’s justification in this life as well as appearing before the divine bar at the final (...) judgment. Zanchi’s doctrine of union with Christ has the utmost significance for personal eschatology and the judgment believers undergo at the great assize, insights that are worth retrieving for a clear understanding of the relationship between justification and the final judgement. (shrink)

The current rise in malpractice litigation has led to concern in the research community as to the prospect of litigation against researchers. Clearly as the responsibility for the day-to-day conduct of the research falls upon the researchers they will be potentially liable should there be negligence in the conduct of the research project itself. But to what extent can the research ethics committee and its members be held liable should harm result to the research subject? How far does the prospect (...) of the threat of litigation equate with the reality of the prospect of liability? Although the NHS research governance framework suggests that primary responsibility for the conduct of the trial is with the researcher this does not mean that REC members will be immune from actions in tort where research subjects suffer harm in the conduct of a research project approved by their NHS REC. This paper focuses upon the prospect for liability in the law of tort of NHS RECs and their members. While in practice the vast majority of such claims are unlikely to be successful members of RECs may incur resultant legal costs as a consequence of involvement in proposed litigation. It is submitted that the scope of indemnity provision provided to RECs and their members should be precisely determined, otherwise there is a real prospect that the risk of malpractice litigation may deter individuals from serving on such committees. (shrink)

The double slit experiment for a massive scalar particle is described using intuitionistic logic with quantum real numbers as the numerical values of the particle's position and momentum. The model assigns physical reality to single quantum particles. Its truth values are given open subsets of state space interpreted as the ontological conditions of a particle. Each condition determines quantum real number values for all the particle's attributes. Questions, unanswerable in the standard theories, concerning the behaviour of single particles in the (...) experiment are answered. (shrink)

The paper discusses the philosophical and historical doctrine of the Russian philosopher and historian George Petrovich Fedotov. The author focuses on the analysis of imperial issues in the works of G.P. Fedotov, especially of his views on the cultural history of the Russian empire and the essence of imperial project in Russia. Fedotov reconsiders the historical experience and revolutionary catastrophe of Russia and searches for the foundations of the social and cultural processes determining the events of Russian history. Fedotov’s works (...) offer a variety of interpretations of the political and cultural phenomenon of empire. This reflects his evolution as a philosopher of history: the focus of his vision shifts from the Medieval Rus to the Empire of Peter the Great, then to the collapsed empire of Nicholas II and finally to the USSR. Fedotov’s concept of Empire evolves into a timeless cultural-philosophical phenomenon but originates from the historical description of the centralization of power in the feudal monarchy of Ivan the Terrible. The evolution of the philosophical and historical views of Fedotov is influenced by the changes of his attitude to the historical conception of Klyuchevsky. In the 1940s Fedotov considers the empire as a universal idea. The concept of empire proposed by Fedotov gives an understanding of the Russian historical development, especially the causes of the decline and fall of the Russian Empire. Fedotov associates the cause of the salvation of Russia with the study of ancient Russian culture, in which he founds a moral and political ideal of the “Republic of Saint Sophia.” The paper shows heuristic potential of Fedotov’s cultural and philosophical ideas on the vocation of spiritual elite and the creative role of personality in the process of nation-building. (shrink)

In the paper, the multilevel concept of methodology of science is reviewed. The author distinguishes five levels in the methodology of science. These levels vary in degree of generality and the nature of the relationship with philosophy. The first, most general level of the methodology of ways of learning of the studies on the application of science to philosophical methods such as dialectical and metaphysical. The doctrine of general scientific ways of knowing is the second, less common level of methodology (...) of science. The essence of scientific methods is studied at this level, given their theoretical rationale. There are heuristic dignity, epistemological possibilities, and the boundaries of applicability are identified. The third level of the methodology of science is the study of the system of general scientific ways of learning applied in any basic science. In addition to knowledge of the essence of these methods for the researcher requires knowledge of the basic problems of this science. The fourth level of the methodology of science is the study of the system of general scientific ways of learning and epistemological problems in any basic science. The fifth level of the methodology of science are the problems of narrower plan. This study questions the use of certain, specific methods of scientific learning. Thus, the methodology of science is complex and has a complicated structure. The two most general level the methodology are philosophical, the next two are common to philosophy and science, the fifth level is of a specifically scientific nature. (shrink)