We tentatively propose two guiding principles for the construction of theories of physics, which should be satisfied by a possible future theory of quantum gravity. These principles are inspired by those that led Einstein to his theory of general relativity, viz. his principle of general covariance and his equivalence principle, as well as by the two mysterious dogmas of Bohr’s interpretation o...

In this paper we study a model of intuitionistic higher-order logic which we call the Muchnik topos. The Muchnik topos may be defined briefly as the category of sheaves of sets over the topological space consisting of the Turing degrees, where the Turing cones form a base for the topology. We note that our Muchnik topos interpretation of intuitionistic mathematics is an extension of the well kn...

We investigate the adjunction between the category of tran-sition systems (with not nec. bounded morphisms) and the topos of treesS from the perspective of the basic modal logic K on transition systems.More specifically, we show how the modal logic K over an object of Sseen as a transition system can be lifted back as a subobject of S . Thisrelies on the usual mutually trans...

The notion of an internal category in a left exact cosimplicial category is introduced. For any topos over sets a certain left exact cosimplicial category is constructed functorially and the category of internal categories in it is investigated. The notion of a fundamental group is defined for toposes admitting the notion of “a discrete category.” Introduction Our primary interest in this paper...

Having survived the «death of rhetoric» (R. BARTHES 1985: 115), metaphor has become the centre of intensive research by philosophers of language and linguists in the twentieth century. Nowadays it is widely accepted that metaphor is not reducible to «a sort of happy extra trick with words» (I. A. RICHARDS [1936] 1964: 90), but is rather said to be a fundamental principle of linguistic creativit...