This paper describes an attempt to develop a pedagogy for teaching philosophy in science rather than a philosophy of science to be taught in the Bulgarian educational system.

Rather than attempting to combine the two meta-methodological programmes for justifying the epistemological study of science, which is the case of Laudan's normative naturalism, this paper aims at presenting a third alternative to the controversy between the traditional normativism and the reductionistic naturalism. The paper is a preliminary move in developing a theory of the autopoietic cognitive organization of science. The underlying assumption of this project calls that science is a self-constructing, self-specifying and homeostatic system. The scrutinizing of these three (...) predicates leads to the view that the epistemological propositions about science cognitive organization are neither normative, nor descriptive, but transcendental ones. The final discussion shows the connection between this project and the theory of group rationality. (shrink)

Hilbert arithmetic in a wide sense, including Hilbert arithmetic in a narrow sense consisting by two dual and anti-isometric Peano arithmetics, on the one hand, and the qubit Hilbert space (originating for the standard separable complex Hilbert space of quantum mechanics), on the other hand, allows for an arithmetic version of Gentzen’s cut elimination and quantum measurement to be described uniformy as two processes occurring accordingly in those two branches. A philosophical reflection also justifying that unity by quantum neo-Pythagoreanism links (...) it to the opposition of propositional logic, to which Gentzen’s cut rule refers immediately, on the one hand, and the linguistic and mathematical theory of metaphor therefore sharing the same structure borrowed from Hilbert arithmetic in a wide sense. An example by hermeneutical circle modeled as a dual pair of a syllogism (accomplishable also by a Turing machine) and a relevant metaphor (being a formal and logical mistake and thus fundamentally inaccessible to any Turing machine) visualizes human understanding corresponding also to Gentzen’s cut elimination and the Gödel dichotomy about the relation of arithmetic to set theory: either incompleteness or contradiction. The metaphor as the complementing “half” of any understanding of hermeneutical circle is what allows for that Gödel-like incompleteness to be overcome in human thought. (shrink)