95669 - Logic (2) (Lm)

Learning outcomes

At the end of the course, students are supposed to become acquainted with the semantics and the proof theory for classical logic or some extensions, such as modal logic, or alternative systems such as intuitionistic logic or other non classical logics.

Course contents

THOUGHT AS CALCULATION IN GEORGE BOOLE


The utopia of handling reasoning as calculations dates back at least to Thomas Hobbes (1588-1679), for whom reasoning meant calculating. Far beyond such Hobbesian slogan, significant progress in this direction was made by Gottfried Wilhelm von Leibniz (1646-1716), but it was George Boole (1815, 1864) that provided the first systematic exposition of an algebraic treatment of reasoning, starting from Aristotelian syllogistic. This project culminated in "An Investigation of the Laws of Thought" (1854), a work far from being rigorous, but rich in great insights. The reworking of some of Boole's key ideas (including the foundation of a binary algebra) led to the so-called Boolean Algebra and its applications in computer science. The development of this rigorous theory, however, led to the obscuring of Boole's original theory (Boole's Algebra), which still stands as a highly interesting formal system from a historical, mathematical, and philosophical perspective. This has not deterred authors such as Hassler Whitney and Stanley Burris from proposing modifications to Boole's original system that were more faithful to his true conceptions.


In the course, we will analyze Boole's original presentation of his logical system, addressing its linguistic, logical, mathematical, and philosophical aspects, and compare the subsequent developments of Boolean Algebra with the original conceptions of its ideal founder.

 

The treatment of the topics will be homogeneously distributed during the course.

Readings/Bibliography

George Boole, An Investigation of the Laws of Thought, any English or Italian edition, chapters I-VII, XXII.

Handouts of the Teacher available on line.

Non-attending students must also study the chapter X of "La Logica e la sua Storia" by Robert Blanché.

Teaching methods

Lessons in classroom with the aid of a video projector and electronic blackboard. Lessons will be recorded and uploaded on line.

Lessons in classroom with electronic blackboard. Lessons will be recorded and uploaded on line. Classes will generally be recorded and uploaded online, but the teacher reserves the right to suspend recordings based on class attendance monitoring.

Assessment methods

The exam will consist of an oral test in which students will be asked to demonstrate their understanding of the concepts covered in class through oral presentation but also through the written treatment of the definitions of the basic concepts and of the formal proofs analyzed during the lessons.

 

To take the exam, students can register for the regular sessions scheduled by the Teacher or arrange individual sessions. Regular exam sessions will take place approximately every two months starting in June 2026 (July, September, November, January, March), and the dates will be set approximately one month before the exam.

Assessment criteria and thresholds of evaluation:

30 cum laude: Excellent as to knowledge, terminology and critical expression.

30: Excellent, knowledge is complete, well articulated and mostly correctly expressed, although with some slight faults.

27-29: Good, knowledge comprehensive and satisfactory, essentially correct expression.

24-26: Fairly good, knowledge present in significant points, but not complete and not always expressed with correctness.

21-23: Sufficient, knowledge is sometimes superficial, but the guiding general thread is included. Expression and articulation incomplete and often not appropriate

18-21:.Almost sufficient, but knowledge present only on the surface. The guiding principle is not included with continuity. The expression and articulation of the speech show important gaps.

<18: Not sufficient, knowledge absent or very incomplete, lack of guidance in discipline, expression seriously deficient. Exam failed.

Teaching tools

Electronic whiteboard.

Video projector.

Lessons recording.

Office hours

See the website of Guido Gherardi