Online research in philosophy

The aim of this paper is to provide a logic-based conceptual analysis of the twin paradox (TwP) theorem within a first-order logic framework. A geometrical characterization of TwP and its variants is given. It is shown that TwP is not logically equivalent to the assumption of the slowing down of moving clocks, and the lack of TwP is not logically equivalent to the Newtonian assumption of absolute time. The logical connection between TwP and a symmetry axiom of special relativity is (...) also studied. (shrink)

We present a streamlined axiom system of special relativity in firs-order logic. From this axiom system we ``derive'' an axiom system of general relativity in two natural steps. We will also see how the axioms of special relativity transform into those of general relativity. This way we hope to make general relativity more accessible for the non-specialist.

A part of relativistic dynamics is axiomatized by simple and purely geometrical axioms formulated within first-order logic. A geometrical proof of the formula connecting relativistic and rest masses of bodies is presented, leading up to a geometric explanation of Einstein’s famous E = mc 2. The connection of our geometrical axioms and the usual axioms on the conservation of mass, momentum and four-momentum is also investigated.

In natural sciences, the most interesting and relevant questions are the so-called why-questions. There are several different approaches to why-questions and explanations in the literature, however, most of the literature deals with why-questions about particular events, such as ``Why did Adam eat the apple?''. Even the best known theory of explanation, Hempel's covering law model, is designed for explaining particular events. Here we only deal with purely theoretical why-questions about general phenomena of physics, for instance ``Why can no observer move (...) faster than light?'' or ``Why are Kepler's laws valid?''. Here we are not going to develop a whole new theory of why-questions in physics. We will just touch upon some ideas and examples relevant to our subject. (shrink)

Motivation and perspective for an exciting new research direction interconnecting logic, spacetime theory, relativity--including such revolutionary areas as black hole physics, relativistic computers, new cosmology--are presented in this paper. We would like to invite the logician reader to take part in this grand enterprise of the new century. Besides general perspective and motivation, we present initial results in this direction.