- Inter-faculty Studies in Bioinformatics and Systems Biology
- Bachelor's degree, first cycle programme, Computer Science
- Bachelor's degree, first cycle programme, Mathematics
- Master's degree, second cycle programme, Bioinformatics and Systems Biology
- Master's degree, second cycle programme, Computer Science
- Master's degree, second cycle programme, Mathematics
Logic and Metaphysics B 3501-WISIP-LMB-OG
The course will consist of a lecture part (30 h) and tutorial part (30 h). The lecture will focus on the more philosophical-metaphysical aspects of the issues covered, presenting both their historical origins, the basic intuitions behind them and their relationships to problems in other domains (epistemology, philosophy of mind, philosophy of science). The tutorial part will be more technical; its goal will be to introduce the students to the metaphysically relevant aspects of modern formal logic.
Issues to be covered in the lecture part:
(1) Space and time, their nature and structure
(2) Causality and causation
(3) Determinism-indeterminism debate
(4) Modal concepts and modal properties (necessity, possibility, contingency)
(5) Realism vs. antirealism with respect to modality
(6) The status of mathematical and other abstract objects
Topics of the tutorial part:
Below is presented and optimistic version of the programme. It is possible that important details, proofs of theorems or even whole items from the list below will be skipped in the classes.
1. Propositional intuitionistic logic, first-order intuitionistic logic. Kripke semantics for the intuitionistic logic. (2-3 classes).
2. Coding of syntax in arithmetic. Coding of finite sets, definition of provability. Basic properties of the provability predicate. Self-reference in arithmetic: Diagonal Lemma. (2-3 classes).
3. Goedel's Incompleteness Theorems, Tarski's Theorem on undefinability of truth. Rosser's theorem (3 classes).
4. Provability logic, Solovay's Theorem (2 classes).
5. Turing machines, undecidability of the halting problem. Connections with the First Goedel's Theorem. Church's Thesis. (3 classes)
Type of course
Mode
Prerequisites (description)
Learning outcomes
Knowledge: The student is acquainted with topics in contemporary metaphysics and with the principal debates therein. The student has a general orientation in some advanced topics and methods in formal logic and understands their applicability to problems in metaphysics.
Skills: The student is able to give an independent formulation to problems in contemporary metaphysic, and understands how to approach them with logical methods. The student is well prepared for further education and research in the fields of contemporary metaphysics and the applications of logic therein.
Social competence: The student is able to discuss highly abstract philosophical problems in a group, is sensitive to views and arguments of others, understands the importance of clear and disciplined discourse.
Assessment criteria
Attendance, active participation, tests and final exam.
Bibliography
1. James W. Garson, "Modal Logic for Philosophers", Cambridge University Press 2013
2. Rod Girle, "Modal Logic and Philosophy", Routledge 2009
3. Johan van Benthem, "Modal Logic for Open Minds", Center for the Study of Language and Information 2010
4. Paweł Urzyczyn, Morte Heine B. Sorensen (1998), "Lectures on the Curry-Howard Isomorphism", Elsevier Science Publishers
Additional information
Information on level of this course, year of study and semester when the course unit is delivered, types and amount of class hours - can be found in course structure diagrams of apropriate study programmes. This course is related to the following study programmes:
- Inter-faculty Studies in Bioinformatics and Systems Biology
- Bachelor's degree, first cycle programme, Computer Science
- Bachelor's degree, first cycle programme, Mathematics
- Master's degree, second cycle programme, Bioinformatics and Systems Biology
- Master's degree, second cycle programme, Computer Science
- Master's degree, second cycle programme, Mathematics
Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system: