Iterated reflection principles over full disquotational truth

Iterated reflection principles have been employed extensively to unfold epistemic commitments that are incurred by accepting a mathematical theory. Recently this has been applied to theories of truth. The idea is to start with a collection of Tarski-biconditionals and arrive by finitely iterated reflection at strong compositional truth theories. In the context of classical logic it is incoherent to adopt an initial truth theory in which A and 'A is true' are inter-derivable. In this article we show how in the context of a weaker logic, which we call Basic De Morgan Logic, we can coherently start with such a fully disquotational truth theory and arrive at a strong compositional truth theory by applying a natural uniform reflection principle a finite number of times

The fate of non-trivial entanglement under gravitational collapse

We analyse the evolution of the entanglement of a non-trivial initial quantum field state (which, for simplicity, has been taken to be a bipartite state made out of vacuum and the first excited state) when it undergoes a gravitational collapse. We carry out this analysis by generalising the tools developed to study entanglement behaviour in stationary scenarios and making them suitable to deal with dynamical spacetimes. We also discuss what kind of problems can be tackled using the formalism spelled out here as well as single out future avenues of research.Comment: 9 pages, 2 figures. v2: Added Journal reference and small changes to match published versio

Hypatia's silence. Truth, justification, and entitlement.

Hartry Field distinguished two concepts of type-free truth: scientific truth and disquotational truth. We argue that scientific type-free truth cannot do justificatory work in the foundations of mathematics. We also present an argument, based on Crispin Wright's theory of cognitive projects and entitlement, that disquotational truth can do justificatory work in the foundations of mathematics. The price to pay for this is that the concept of disquotational truth requires non-classical logical treatment

Towards a Hamilton-Jacobi Theory for Nonholonomic Mechanical Systems

In this paper we obtain a Hamilton-Jacobi theory for nonholonomic mechanical systems. The results are applied to a large class of nonholonomic mechanical systems, the so-called \v{C}aplygin systems.Comment: 13 pages, added references, fixed typos, comparison with previous approaches and some explanations added. To appear in J. Phys.