27387 - Methods of Scientific Knowledge

Learning outcomes

Students are guided to focus on and analyze topics and issues emerging from a methodological reflection on logic-mathematical knowledge and scientific investigation.

Course contents

The course aims to introduce participants to various systems of non-classical logic, exploring formal mechanisms but with a primary focus on their philosophical significance. No prior knowledge of formal logic is required.

Module 1

Elements of classical logic, particularly propositional logic, will be reviewed at the beginning of the course. We will then illustrate several systems of modal logic (the logic of necessity and possibility), which extend classical logic but are not incompatible with it. We will then introduce intuitionistic logic, in which principles such as the excluded middle fail. We will then move on to polyvalent logics, in which a truth value is added to true and false. The liar paradox will also be introduced, demonstrating some initially plausible solutions.

Module 2

Elements of the first module will be reviewed at the beginning of the course. We will then focus on "fuzzy" logic, in which the possible truth values are infinite, gradually moving from true to false, and we will illustrate its application to the sorites paradox or vagueness paradox. We will then move on to consider paraconsistent logics, which allow for the possibility of contradictions. Finally, time permitting, we will consider conditional logics and non-monotonic logics.

Readings/Bibliography

It is possible to require an English bibliography. The defaukt reading are

Dario Palladino e Claudia Palladino, Logiche non classiche. Un'Introduzione, Carocci, 2007

Francesco Berto e Lorenzo Bottai, Che cos'è una contraddizione, Carocci editore, 2015

Recommended reading

Franca D'Agostini, I mondi comunque possibili, Bollati Boringhieri, 2012

 

Assessment methods

Written and oral examination.

Marks:

30 cum laude - excellent as to knowledge, philosophical lexicon and critical expression.

30 – Excellent: knowledge is complete, well argued and correctly expressed, with some slight faults.

27-29 – Good: thorough and satisfactory knowledge; essentially correct expression.

24-26 - Fairly good: knowledge broadly acquired, and not always correctly expressed.

21-23 – Sufficient: superficial and partial knowledge; exposure and articulation are incomplete and often not sufficiently appropriate

18-21 - Almost insufficient: superficial and decontextualized knowledge. The exposure of the contents shows important gaps.

Exam failed - Basic skills and knowledge are not sufficiently acquired. Students are requested to show up at a subsequent exam session.

Teaching tools

Power point slides will be used during lectures.

Further materials (papers, slides) will be uploaded in the course website.

Office hours

See the website of Daniele Sgaravatti