97920 - Paradoxes of Space Time

Learning outcomes

The course aims to:

• promote in the student interdisciplinary skills that allow him/her to recognize the constitutive foundations of the epistemological structure of the various disciplines, also by means of comparing the different disciplines involved;
• cultivate critical thinking and judgment skills and develop communicative competence.

At the end of the course, the student will have acquired basic knowledge relating to:

• the nature of a paradox, with particular regard to space-time paradoxes;
• the structure and contents of some prominent paradoxes (for example, Zeno's paradoxes, the paradoxes of time travel, the Banach-Tarski paradox);
• the role that space-time paradoxes have played both in the evolution of philosophy, mathematics and physics and in establishing important interdisciplinary relationships.

Course contents

Space-time has been the subject of a series of conceptual puzzles and revolutions the history of ideas: Zeno's paradoxes, time paradoxes (is it possible to travel in time and influence the past?) are connected to the question of the linearity or circularity of time and the existence of past, present and future (Laplace's demon and the question of determinism), mental experiments in relativity (both limited and general) and those in quantum physics (EPR, quantum teleportation).

The course deals with the problems raised by the theme of space-time in relation to philosophy, mathematics and physics. At the center of the course is the question of how space-time has given rise to paradoxes that have opened a discussion on the status of the various disciplines and on the relationship between them.

The topics addressed are:

• the nature of a paradox: what is a paradox? Argumentative structure (logical, epistemological, dialectical and rhetorical) and types of paradoxes in general.
• Space-time: what is special about space-time paradoxes? The reasons for the popularity and controversy of space-time paradoxes.
• Role of space-time paradoxes in the three disciplines of main interest (philosophy, mathematics, physics): what role can the analysis of a paradox play within a discipline and across the different disciplines? The role that the formulation and resolution of paradoxes has played in the construction and evolution of a discipline and how their resolution sometimes determines the modification of the relationship between the disciplines.
• Analysis of space-time paradoxes: What diagnostics and prognosis for space-time paradoxes? The assessments and the strategies adopted for the space-time paradoxes. Characterization of the disciplines on the basis of their critical position with respect to paradoxes.

These are addressed in the three modules that compos the course:

Module 1) Paradoxes as an argumentative challenge

Paradoxes will be first treated, following a philosophical tradition, as an argumentative form aimed at testing the strength of a logical reasoning. Philosophy offers tools to operate this treatment and a characterization of the different types of paradoxes. In particular we will consider the birth of the space-time paradoxes within ancient philosophy and the paradoxes of Zeno up to their contemporary reception.

Module 2) Paradoxes as disciplinary lenses

In this module space-time paradoxes will be analyzed to widen our understanding the nature of a discipline. The analysis of the paradox within the disciplines will be conducted with the tools and forms of reasoning that are characteristic of the discipline in order to bring out some focal points: divisibility, parts-all, movement (prevalent focus on mathematics-philosophy); in-depth study on the relation intuition-axiomatic setting in the geometric field and on the role of paradoxes in making implicit hypotheses explicit (R-line).

Module 3) Paradoxes as a disciplinary test

In this module we will study some space-time paradoxes (the "paradox" of the Einstein train, the twins, the barn and / or the grandfather) to reflect on how disciplines have tried to control the internal coherence of a theory and the rational and empirical hold of their paradigms. We will also discuss how the paradoxes formulated within a disciplinary theory, physics (or mathematics), have played a creative role in generating new hypotheses and new knowledge. We will also study the focal topics, the underlying concept of space and time, as well as the nature of the acceptability of the consequences of resolving a paradox by applying the criteria developed in the first two modules.

Transversely to the discussion of paradoxes, a discussion is carried out on

T1) type of arguments accepted in the disciplines: mental experiments / laboratory experiments, constructive / inductive / nonsensical demonstrations;

T2) "truth value" attributed to the hypotheses of reasoning in the disciplines and the kind of acceptability attributed to the consequences;

T3) formal correctness and level of persuasion of an argument.

START DATE: February 21st  2022

CLASS SCHEDULE: Monday and Friday 16-19

 

Readings/Bibliography

Vincenzo Fano I paradossi di Zenone, Carrocci, 2012.

Kleiner, N. Movshovitz-Hadar, The role of paradoxes in the evolution of mathematics, The American Mathematical Monthly 101, (1994), 963-974.

Agustìn Rayo On the Brink of Paradox, MIT Press 2019.

R.M. Sainsbury, Paradoxes, Cambridge University Press 2009.

Teaching methods

(a) problem solving, argumentation

(b) community of inquiry

Assessment methods

Final exam

The final exam consists of an oral exam divided into two parts.

I part

Presentation, analysis and discussion of a paradox and, agreed with the lecturers, its role within the discussion on space-time starting from one or more reference sources (chapters of textbooks, research articles, popular texts, original memoirs, essays of historical-epistemological criticism, websites, films, applets...) The presentation of the analysis (12 minutes long) should contain a discussion about: i) the criteria for selecting the paradox and the texts/supports; ii) the general criteria and theoretical references used to conduct the analysis; iii) the results of the analysis; iv) an overall assessment of the role of the paradox within the discipline(s).

Part II

"disciplinary" and "didactic" discussion on concepts or themes on space-time paradoxes treated during the course.

In the first part of the exam we will assess the student's ability to:

1) move within the sources and bibliographic material in order to select, in a critical and conscious way, significant materials for the space-time paradoxes;

2) select and elaborate research results on space-time paradoxes in order to construct specific analysis criteria;

3) integrate the different dimensions that intervene in the paradoxes of space-time (disciplinary, cognitive, epistemological, didactic).

In the second part of the exam, the following elements will be assessed:

1) the level of understanding, from a disciplinary point of view (of mathematics, physics or philosophy) of a concept or theme covered in the course;

2) the student's ability to analyze a space-time paradox from an argumentative point of view, knowing how to recognize critical relevant for a proper understanding;

3) the student's ability to place the discussion of this theme or concept in an interdisciplinary perspective.

The final grade will be the average of the evaluations obtained in the first and second part.

Teaching tools

Virtuale (https://virtuale.unibo.it/), Perusall (httpps://perusall.com).

Office hours

See the website of Sebastiano Moruzzi

See the website of Alessia Cattabriga

See the website of Olivia Levrini