A partir de Sylvan [1990] y Urbas [1996] demostramos la heterodoxia de las lógicas de da Costa. Probamos que estas lógicas no satisfacen el teorema de sustitución. Más aún, probamos que no existen extensiones más débiles que la lógica clásica y más fuerte que las lógicas de da Costa las cuales satisfagan el teorema de sustitución.

We study the informational underpinnings of thermodynamics and statistical mechanics, using an abstract framework, general probabilistic theories, capable of describing arbitrary physical theories. This allows one to abstract the informational content of a theory from the concrete details of its formalism. In this framework, we extend the treatment of microcanonical thermodynamics, namely the thermodynamics of systems with a well-defined energy, beyond the known cases of classical and quantum theory, formulating two necessary requirements for a well-defined thermodynamics. We adopt the recent approach of resource theories, where one studies the transitions between states that can be accomplished with a restricted set of physical operations. We formulate three different resource theories, differing in the choice of the restricted set of physical operations. To bridge the gap between the objective dynamics of particles and the subjective world of probabilities, one of the core issues in the foundations of statistical mechanics, we propose four information-theoretic axioms.

A description of the environment cognition process by intelligent systems with a fixed set of system goals is suggested. Such a system is represented by the set of its goals only without any models of the system elements or the environment. The set has a lattice structure and a monoid structure; thus, the structure of linear logic is defined on the set. The cognition process of some environment by the system is described on this basis. The environment is represented as a configuration space of possible system positions which are estimated by an information amount (by corresponding sets). This information is supplied to the system by the environment. Thus, it is possible to define the category of Conway games with a payoff on the configuration space and to choose an optimal system’s play (i.e., a trajectory).

According to epistemic structural realism (EER) scientific theories provide us only with knowledge about the structure of the unobservable world, but not about its nature. The most significant objection that this position has faced is the so-called Newman’s problem. In this paper I offer an alternative objection to EER. I argue that its formulation leads to undesirable skeptical positions in two fields close to scientific realism: the debates on modality and laws of nature. I also show that there is an interesting sense in which my objection is stronger than the one offered by Newman.

Of course, assessing the long-term consequences of Trump’s foreign policy now is like predicting the final score in the middle of a game. Stanford historian Niall Ferguson has argued that “the key to Trump’s presidency is that it is probably the last opportunity America has to stop or at least slow China’s ascendency. And while it may not be intellectually very satisfying, Trump’s approach to the problem, which is to assert US power in unpredictable and disruptive ways, may in fact be the only viable option left.”

An attempt to give a basic outline of the objective role of thinkingmatter in the system of universal interaction (A Philosophical-PoeticPhantasmagoria based on the principles of dialectical materialism).

In this survey, written for the proceedings of the summer school K-theory 2018, Buenos Aires, Argentina (satellite event of the ICM 2018), we give a rigorous overview of the noncommutative counterparts of some celebrated conjectures of Grothendieck, Voevodsky, Beilinson, Weil, Tate, Parshin, Kimura, Schur, and others.

Mathematical conception of infinite quantities forms a cornerstone of many disciplines of modern mathematics — from differential calculus to set theory. In fact, it could be argued that the most significant revolutions in mathematics in the modern period were always triggered by a development in our understanding of infinity. From the pedagogical point of view, the students’ comprehension of the concept of infinity is a competence of interdisciplinary value, helping them to grasp the reasons why and how individual disciplines of modern mathematics were built up. In this paper we present a number of illustrations, examples, and allegories that illuminate and clarify different aspects of infinity. The author has been using and gradually developing these metaphors for infinity in his undergraduate and graduate courses and popular lectures on mathematical logic, set theory, calculus, and nonstandard analysis during the last decade. The aim of this paper is to share the accumulated didactic know-how.

Erik C. Banks Wright State University Abstract Grete Hermann’s essay “Die naturphilosophischen Grundlagen der Quantenmechanik” (1935) has received much deserved scholarly attention in recent years. In this paper, I follow the lead of Elise Crull (2017) who sees in Hermann’s work the general outlines of a neo-Kantian interpretation of quantum theory. In full support of this […]

We formulate a property P on a class of relations on the natural numbers, and formulate a general theorem on P, from which we get as corollaries the insolvability of Hilbert’s tenth problem, Gödel’s incompleteness theorem, and Turing’s halting problem. By slightly strengthening the property P, we get Tarski’s definability theorem, namely that truth is not first order definable. The property Ptogether with a “Cantor’s diagonalization” process emphasizes that all the above theorems are a variation on a theme, that of self reference and diagonalization combined. We relate our results to self referential paradoxes, including a formalisation of the Liar paradox, and fixed point theorems. We also discuss the property P for arbitrary rings. We give a survey on Hilbert’s tenth problem for quadratic rings and for the rationals pointing the way to ongoing research in main stream mathematics involving recursion theory, definability in model theory, algebraic geometry and number theory.