ACADEMIC YEAR

The aim of the course is to show philosophy students how mathematics works in physics. Mathematics is a science of structures: Some of these structures correspond beautifully to the structure of the world, and a resonance between these two kinds of structures leads to correct empirical predictions about the behavior of physical systems. The course is divided into two parts. The first-“Mathematics of Relativity”-will present some mathematical structures widely used in the relativity theory, such as: topological spaces, smooth manifolds, metric structure. In the second part-“Mathematics of Quanta”-the student will have an opportunity to learn basic mathematical tools for quantum mechanics, such as Hilbert spaces and relative operators. This program presupposes only secondary school knowledge of mathematics.

The aim of the course is to offer a first introduction to contemporary cosmology, giving to students some initial hints for further philosophical and theological reflection, especially about the anthropic principle. Introduction to Cosmology: relative role of observations and theory: Uniqueness of studying the universe as a single object. Principal observations supporting Big Bang cosmologies (as contrasted with Steady state cosmologies): The Hubble law or the velocity-distance relationship for galaxies and cluster of galaxies; the cosmic abundances of light elements; cosmic background radiation. Problems with Big Bang cosmologies: Singularities, flatness, isotropy. Inflationary Cosmologies; multi-verses; are such theories falsifiable? The age of the universe; various methods for determining age; history of age determinations as a lesson in the scientific method. Quantum cosmologies: Quantum vacuum fluctuations; philosophical and theological considerations; contingency of the universe; creatio ex nihilo. Evolutionary character of the universe at all levels: physical, chemical, biological; the concept of emergence in the evolution of the universe; the future of the universe and Christian eschatology. The God of the cosmologist, the God of the faith: Theological implications of a person friendly universe; the anthropic principle.

The aim is to help in the understanding of the most basic elements of this theory and to stress the most important philosophical consequences, especially at ontological level, that can be drawn from it. The study of this science will lead to a comprehension of the present tendency of physics with a view to overcoming the materialist frame that has characterized modern science in the 16^th–20^th centuries. Classical mechanics was a mechanistic science whose methodology was reductionist in character and whose basic laws were deterministic. The course will show that quantum mechanics hints at a very different philosophy of nature. In particular, the two central concepts of the course will be that of correlation and of interaction. Quantum systems may be interdependent (correlated) even if at huge distances and without any physical bound. Quantum interactions, in which global as well as local aspects are involved, are basic for the determination of the properties of quantum systems. In other words, a quantum system does not have in general properties that are independent from dynamical interactions with other systems.

The aim is the critical acquisition of gnoseology. What is knowledge? What is the relationship between Science and other human activities? Is science a detached contemplative activity or does it have a pragmatic component? Is science the search of truth? Is the absolute truth scientifically attainable? Is science hypothetical? Is there a progress in science? Is there a ‘natural selection’ about scientific theories?

The aim of the course is that of giving to the students a critical introduction to the foundation, principles and method of the physical sciences in general. The following topics will be treated: Galilei. Newton’s laws of motion and theory of gravitation. Experiments on light: is it wave or particle? Concepts of space and time. Action at a distance. Laplace and Lagrange. Atomic theory. Dalton and Lavoisier. Brownian motion. Perrin. Conservation of mass, energy, linear and angular momentum. Noether. Electricity and magnetism: Faraday, Ohm, Ampere, Volta, Maxwell. Kinetic theory of gases. The electron. Radioactivity and Atomic structure. Planck and the quantum. Atomic spectra. Rutherford and the nucleus. Millikan. Einstein’s theories of relativity and gravitation. Lorentz transformation. Quantum mechanics. Hidden variables. Waves and particles. Nuclear reactions. The neutron, the positron, the pion. Fission. Nuclear shell structure. Cosmic rays and elementary particles. Cosmology. Astrophysics. Chaos and symmetry.

The aim is the acquisition of a first historical background by showing the necessary historical contingency and fallibility that characterize theories. First of all, the course deepens the issue of the relationships among Galilei, Copernicanism and the Church, by comparing it with Kepler’s different contribution, between mysticism and science, the origins of modern science, and Descartes’ affirmation of mechanistic philosophy of science. The dispute between Newton and Leibniz is afterwards put in evidence in all its scientific and philosophical complexity also as a presupposition of following foundation of rational mechanics in 18^th Century’s Europe. Some open problems of Classical Physics are pointed out in view of successive scientific revolutions.

The aim is to stimulate a reflection in philosophy of nature with an openness to metaphysical questions. The main idea is to reconsider some issues in natural philosophy in the light of recent results in quantum mechanics, cosmology, and cognitive sciences. Four philosophical-natural categories are the object of the lecture: contingency, information, process, and temporality. The finality is to show that, in several domains of our universe, with different degrees of complexity, the same fundamental principles are implemented, which also represent a bridge to some essential questions in metaphysics and natural theology.

Theology as scientia fidei and the need of justifying it represents the general framework of the course. Different concepts of “science”-Geisteswissenschaften and Naturwissenschaften-are presented. The hermeneutical change in human sciences and the analogue developments in natural sciences will be discussed. Paradigms and models in natural sciences and theology will be analyzed as well as the “scientific community role” in natural sciences and theology developments. Comparing the concept of truth in natural sciences and in theology will be important: the application of analogy, of images and metaphors in different theological and scientific situations.

The aim is the acquisition of the basic forms of inferences and the understanding of their use and limitations: Deduction, abduction, induction. The main subjects will be: The general characters of these forms of reasoning. The problem of laws and regularities and of random variations. The use of these form of reasoning in science and philosophy. The problem of the connection between universals and singular events and systems. The discussion between Einstein, Bohr, and Schrödinger as an application of these forms of reasoning.

ESTIMATED SCHEDULE

FIRST SEMESTER

(October 2006 – January 2007)

FO2412 Tue – Wed – Thu

V-VI hours

from Nov. 11 to Nov. 30

FO2385 Mon – Tue

III-IV hours

from Oct. 16 to Nov. 21

FO2411 Wed

III-IV, V-VI hours

from Oct. 18 to Nov. 29

FS2308 Wed

VII-VIII hours

from Oct. 18 to Jan. 17

SECOND SEMESTER

(February 2007 – May 2007)

FO2424 Tue – Wed

III-IV hours

from Feb. 20 to Mar. 28

FO2017 Mon – Tue – Wed VII-VIII hours

from Mar. 19 to Apr. 26

FO2018 Mon – Tue

I-II hours

from Feb. 19 to Mar. 27

TF2058 Wed – Fry

I-II hours

from Feb. 21 to Mar. 30

FS2013 Mon – Tue

V-VI hours

from Feb. 19 to Mar. 27