The course will provide a historical introduction to the mechanization of human reasoning by highlighting some philosophical discussions about it.

The course will focus on the following topics:

The analysis of reasoning in Antiquity and in the Middle Ages;

From Lull to Leibniz;

Leibniz and the mechanization of reasoning;

From Leibniz to Boole: the algebrization of logic;

The developments of mathematical logic in 20th Century and the mechanization of reasoning;

Mathematical Logic and Computability Theory;

Mechanized Deduction Systems;

Gödelian arguments.

There are no strict pre-requisites for this course, but a basic introduction to Logic might provide a useful background.

Knowledge and understanding

After the course students should be able to understand and explain texts by history of logic, discuss some of the classical problems in mechanization of reasoning and philosophy of computing, use the bibliographical tools and repertories available in this field.

 Applying knowledge and understanding

After the course students should be able to discuss and evaluate various claims and arguments both in the specialistic debate and in the general contemporary cultural debate.

 Making judgements

After the course students should be able to make autonomous and original judgements about the arguments in the debate. To this end discussions in the classroom will be encouraged. Originality and autonomous judgement will be part of the final evalution of the student's performance

 Communication skills

After the course students should be able to explain and discuss the relevant topics with conceptual and linguistic exactness, and to offer efficacious  and synthetic accounts of the subject matter. To this end, verbal interaction in the classroom and a careful reading and analysis of the relevant texts will be encouraged

 Learning skills

After the course students should be acquainted with the subject matter and the method of research enough to be able to proceed on their own  in gathering further knowledge from the literature in the field and in contiguous fields. To this end they should also improve their ability to read English texts in the field.

The teaching material prepared by the lecturer in addition to recommended textbooks (such as for instance slides, lecture notes, exercises, bibliography) and communications from the lecturer specific to the course can be found inside the Moodle platform › blended.uniurb.it

Lectures: Lectiones Commandinianae

Teaching

Classroom lectures offering general frameworks, analyses of particular topics and exercises, comments to the relevant literature. Before, during and after the lecture questions, comments and discussions by the students are encouraged. Of course personal study at home will be equally important

Attendance

Students should attend classes regularly and actively, since the very beginning. Because of the analytic and often abstract character of the subject matter, active participation in classroom discussion will be very useful. In order to do that, and in general to follow the lectures successfully, it is strongly advised to do every day the homework suggested as preparation for the following lecture.

Course books

Richard L. Epstein and Walter A Carnielli "Computability: Computable Functions, Logic, and the Foundations of Mathematics", Advanced Reasoning Forum, 2008.

Witold Marciszewski and Roman Murawski "Mechanization of Reasoning in a Historical Perspective", Rodopi, 1995.

Assessment

Oral and written examination.

Disability and Specific Learning Disorders (SLD)

Students who have registered their disability certification or SLD certification with the Inclusion and Right to Study Office can request to use conceptual maps (for keywords) during exams.

To this end, it is necessary to send the maps, two weeks before the exam date, to the course instructor, who will verify their compliance with the university guidelines and may request modifications.

Teaching

They will study on their own (individually or with others) according to the directions of this vademecum and if possible with the help which can be given by the teacher during office hours or through e-mail, Skype, etc. 

Attendance

In order to make up for the impossibility of attending classes, a hard and careful study is required. One should already possess good skills of autonomous learning and some capacity to read and understand logic and philosophical texts, at least at a basic level. Whenever possible, it is advisable to work with other students. 

Course books

Richard L. Epstein and Walter A Carnielli "Computability: Computable Functions, Logic, and the Foundations of Mathematics", Advanced Reasoning Forum, 2008.

Witold Marciszewski and Roman Murawski "Mechanization of Reasoning in a Historical Perspective", Rodopi, 1995.

Assessment

Oral and written examination.

Disability and Specific Learning Disorders (SLD)

Students who have registered their disability certification or SLD certification with the Inclusion and Right to Study Office can request to use conceptual maps (for keywords) during exams.

To this end, it is necessary to send the maps, two weeks before the exam date, to the course instructor, who will verify their compliance with the university guidelines and may request modifications.

Foreign students will be allowed to use English for questions and comments during the class, for all the required readings, and for the final examination.