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We consider the generalized Calogero–Moser–Sutherland quantum Hamiltonian H associated with a configuration of vectors AG2 on the plane which is a union of A2 and G2 root systems. The Hamiltonian H depends on one parameter. We find an intertwining operator between H and the Calogero–Moser–Sutherland Hamiltonian for the root system G2. This gives a quantum integral for H of order 6 in an explicit form, thus establishing integrability of H.

Submitted essay is an inquiry into J. G. Fichte's early philosophy focused particularly on Foundation of the Entire Wissenschaftslehre as a central work of his early period. Interpretation is based on assumption that its principal aim consists in manifestation of the way leading to emergence of our commonsense and ordinary understanding with reference to both world and ourselves. This approach carries Fichte's affilation with tendency inherent to transcendental philosophy of his era not only in its search for the origin of empirical knowledge, but for the origin of aprioristic structures of our experience especially. His transcendentally laden search manifests itself as so called "pragmatic history of the human mind", the principal object of our inquiry. Here we can find an attempt to reconstruct just transcendental, but not "real", temporally sequential, genesis of our mind from original state of feeling to our common representation both about independently existing things and ourselves as free cognizing subjects. Application of this philosophical method allows him to genetically derive and justify basic forms of our experience and its aprioristic components like space, time, substantiality or causality. The first part of essay introduces fundamental principles of Fichte's philosophical system and...

In this dissertation we propose to study the identification of the productive imagination with reason within Schelling's aesthetic idealism, an identification which leads us to propose, in what follows, an "inverted" philosophical reading of the power of aesthetic judgement of the Critique of the power of judgement (1790) of Kant, based on the monist- immanent metaphysics of Schelling's System of Identity (1801-1804). This approach to Kant's third Critique also demonstrates the originality of this dissertation, since the traditional reading of the Critique of the power of judgement with German idealism has underlined, from Hegel to Lukacs or Hartmann, the centrality of the teleological part of the work of 1790. The authors of German idealism and romanticism mainly saw teleological judgment as a factor of unity between the theoretical and practical domains. This point of the Kantian argument can be seen as a link between Spinoza and Hegel regarding the concepts of organism, totality and reciprocal action, which Hegel mainly brings into play in his conception of a system. In this dissertation, we will travel a more winding and heterodox path, less explored, which focuses on the objective potential of the aesthetic phenomenon, as well as on its scope and limits, in the reverse transition that we...

The aim of this diploma thesis is to offer a comprehensive commentary of Patočka's unpublished lectures on Hegel's Phenomenology of Spirit, which he gave at the Charles University during the summer semester of 1949. These lectures remain unfinished and the exposition of the Phenomenology of Spirit ends before the chapter on morality. Patočka is influenced, to a considerable degree, by the unorthodox reading of Hegel that Kojéve presents in his Inroduction à la lecture de Hegel (1947) and also by a somewhat more conservative commentary by Jean Hyppolite, published in 1946 under the title Genese et structure de la Phénoménologie de l'esprit de Hegel. This thesis follows their influence on Patočka's commentary, in an attempt to discover Patočka's own interpretative stance. Patočka places the Phenomenology of Spirit into a wide context and tries to illustrate its genesis. Following Kojéve, Patočka's interpretation remains nested within an anthropological perspective, considering the master-slave dialectic to be the centerpiece of Hegel's philosophy.