INNOVATIVE USE OF A TABLET DEVICE TO DELIVER INSTRUCTION IN UNDERGRADUATE CHEMISTRY LECTURES

This report describes a simple, inexpensive and highly effective instructional model based on the use of a tablet device to enable the real-time projection of the instructor's digitally handwritten annotations to teach chemistry in undergraduate courses. The projection of digital handwriting allows the instructor to build, present and adapt the class contents in a dynamic fashion and to save anything that is annotated or displayed on the screen for subsequent sharing with students after each session. This method avoids the loss of continuity and information that often occurs when instructors switch between electronic slides and white/chalk board during lessons. Students acknowledged that this methodology allows them to follow the instructor's cognitive process and the progressive development of contents during lectures as the most valuable aspect of the implemented instructional model.

The mathematics of McTaggart's paradox

Mc Taggart's celebrated proof of the unreality of time is a chain of implications whose final step asserts that the A-series (i.e. the classification of events as past, present or future) is intrinsically contradictory. This is widely believed to be the heart of the argument, and it is where most attempted refutations have been addressed; yet, it is also the only part of the proof which may be generalised to other contexts, since none of the notions involved in it is specifically temporal. In fact, as I show in the first part of the paper, McTaggart's refutation of the A-series can be easily interpreted in mathematical terms; subsequently, in order to strengthen my claim, I apply the same framework by analogy to the cases of space, modality, and personal identity. Therefore, either McTaggart's proof as a whole may be extended to each of these notions, or it must embed some distinctly temporal element in one of the steps leading up to the contradiction of the A-series. I conclude by suggesting where this element might lay, and by hinting at what I believe to be the true logical fallacy of the proof.

HILBERT BETWEEN THE FORMAL AND THE INFORMAL SIDE OF MATHEMATICS

Abstract: In this article we analyze the key concept of Hilbert's axiomatic method, namely that of axiom. We will find two different concepts: the first one from the period of Hilbert's foundation of geometry and the second one at the time of the development of his proof theory. Both conceptions are linked to two different notions of intuition and show how Hilbert's ideas are far from a purely formalist conception of mathematics. The principal thesis of this article is that one of the main problems that Hilbert encountered in his foundational studies consisted in securing a link between formalization and intuition. We will also analyze a related problem, that we will call "Frege's Problem", form the time of the foundation of geometry and investigate the role of the Axiom of Completeness in its solution.