Related papers: Almost all classical theorems are intuitionistic

Isomorphism between formulae is defined with respect to categories formalizing equality of deductions in classical propositional logic and in the multiplicative fragment of classical linear propositional logic caught by proof nets. This…

Based on an analysis of the inference rules used, we provide a characterization of the situations in which classical provability entails intuitionistic provability. We then examine the relationship of these derivability notions to uniform…

We describe a natural deduction formalization of intuitionistic and classical propositional logic in the Isabelle/Pure framework. In contrast to earlier work, where we explored the pedagogical benefits of using a deep embedding approach to…

Using a simple probabilistic model, we illustrate that a small part of a strongly correlated many-body classical system can show a paradoxical behavior, namely asymptotic stochastic independence. We consider a triangular array such that…

Classical logic (the logic of non-constructive mathematics) is stronger than intuitionistic logic (the logic of constructive mathematics). Despite this, there are copies of classical logic in intuitionistic logic. All copies usually found…

We show that an arbitrary probability distribution can be represented in exponential form. In physical contexts, this implies that the equilibrium distribution of any classical or quantum dynamical system is expressible in grand canonical…

As it is well known, classical mechanics consists of several basic features like determinism, reductionism, completeness of knowledge and mechanicism. In this article the basic assumptions are discussed which underlie those features. It is…

The usual canonical Hamiltonian or Lagrangian formalism of classical mechanics applied to macroscopic systems describes energy conserving adiabatic motion. If irreversible diabatic processes are to be included, then the law of increasing…

We show that intuitionistic propositional logic is \emph{Carnap categorical}: the only interpretation of the connectives consistent with the intuitionistic consequence relation is the standard interpretation. This holds relative to the most…

This paper presents a soundness and completeness proof for propositional intuitionistic calculus with respect to the semantics of computability logic. The latter interprets formulas as interactive computational problems, formalized as games…

We revisit the notion of intuitionistic equivalence and formal proof representations by adopting the view of formulas as exponential polynomials. After observing that most of the invertible proof rules of intuitionistic (minimal)…

When compared to quantum mechanics, classical mechanics is often depicted in a specific metaphysical flavour: spatio-temporal realism or a Newtonian "background" is presented as an intrinsic fundamental classical presumption. However, the…

For the classical mind, quantum mechanics is boggling enough; nevertheless more bizarre behavior could be imagined, thereby concentrating on propositional structures (empirical logics) that transcend the quantum domain. One can also…

An explicit Lorentz covariant formulation of the canonical theory for classical fields is established on a space-like hypersurface. Hamilton's equations and a Poisson bracket are defined on the space-like hypersurface. The Poisson bracket…

In this paper of "The Epistemology of Contemporary Physics" series we investigate the epistemological significance and sensibility (and hence interpretability and interpretation) of classical mechanics in its Newtonian and non-Newtonian…

There are good reasons to believe that we are classical algorithms run on (effectively) classical machines. However, the fact that a physical state of a system in a universe described by a classical deterministic model doesn't contain any…

For formulas of the Implicational Propositional Calculus (IPC) that are theorems of the classical Propositional Calculus (PC) we show that PC proofs yield IPC proofs. As a consequence, completeness of PC yields completeness of IPC.

We present a geometric and dynamical approach to the micro-canonical ensemble of classical Hamiltonian systems. We generalize the arguments in \cite{Rugh} and show that the energy-derivative of a micro-canonical average is itself…

We survey some results that provide different versions of classical results through different summability methods. Specifically, in order to adapt such classical results, we analyze which properties should satisfy the summability methods.…

The aim of this work is to show how Einstein's quantum hypothesis leads immediately and necessarily to a departure from classical mechanics. First we note that the classical description and predictions are in terms of idealized measurements…