On the properties of spectral effect algebras

The aim of this paper is to show that there can be either only one or uncountably many contexts in any spectral effect algebra, answering a question posed in [S. Gudder, Convex and Sequential Effect Algebras, (2018), arXiv:1802.01265]. We also provide some results on the structure of spectral effect algebras and their state spaces and investigate the direct products and direct convex sums of spectral effect algebras. In the case of spectral effect algebras with sharply determining state space, stronger properties can be proved: the spectral decompositions are essentially unique, the algebra is sharply dominating and the set of its sharp elements is an orthomodular lattice. The article also contains a list of open questions that might provide interesting future research directions.

The Difficulty of Being Dead: Aleksandr Veledinskii’s Alive (2006)

The dis/appearances of the characters in Veledinskii’s Alive denotes ruptures in continuity (including the continuity of the gaze). The role of the phantom is to overcome the complete break between the living and the dead as well as to overcome the ruptures in discourse. The persistent revenant is an epitome of the return: they become by coming back and in doing so they create a repetitive experience—teleological aporia, a certain inheritance. The phantom is a trace and also a differance (in Derridean terms) in that their spectral effect is in the ideological tendency and the promise of emancipation. In Alive, the phantom resists the totality of representation and so emerges as a method of paralogy: legitimacy of the subject is determined by a denial of the possibility of legitimation. The spectre as a mediation of discourse which lies in between, and in Alive—not between life and death but between death and death. In Alive political agency is the phantom’s expediency whereby the gaze onto the spectator—the pervasiveness of the ghostly experience problematizes the status of the spectator who—in the presence of the posthumous narrator—emerges as a posthumous spectator.