Review of the basic topics covered in Bachelor, Master and PhD programs in Logic.
For more information, contact radek.honzik at ff.cuni.cz. For PhD students check out our page.
Modern logic emerged at the turn of the 19th and 20th century as an attempt to formalize mathematical constructions in analysis, algebra and in other fields. Its motivations were both mathematical and philosophical: mathematical motivations were applied to mathematics and other exact sciences, and philosophical motivations were applied to natural language and its expressions and philosophical questions in general. The goal was always to clarify the given problem by making it more precise and well defined.
Important mathematical discoveries were soon made, mostly notably the celebrated result of Kurt Gödel on incompleteness from 1930s who showed that there is a sharp distinction between “true statements” and “provable theorems”: in arithmetics (and stronger theories), there will always be statements which are true, but we can never verify their truth by arithmetical methods: some famous open problems, such as Goldbach’s conjecture or P versus NP, may be among them. This distinction between “truth” and “deduction” has had profound effect not only on mathematics, but also on philosophy. In mathematics, new fields were developed which not only deal with Gödel’s result, but also with the more general question of foundations of mathematics (set theory, topology, abstract algebra, category theory etc.). In logic itself, the focus ranged from classical to non-classical forms of reasoning answering questions related for instance to the meaning of the implication and negation, and have rich connections with complexity theory studying the hardness of computational problems. In philosophy, primarily analytic philosophy and philosophical logic, the underlying question has been the concept of truth and meaning and their analysis in mathematics and natural languages (for instance, what does “true statement” mean if we do not have a finite verification method to check it?).
The study of Logic will guide committed students through the concepts described above and let them see and appreciate the complexity and beauty of these constructions.
The Bachelor program in logic provides an overall setting for the results stated above: It contains classes with introduction to mathematics (algebra, analysis, etc.), set theory (constructions of mathematical objects such as real numbers, measuring infinite sizes, Axiom of Choice, Continuum Hypothesis) and mathematical aspects of classical and non-classical logics (rich enough to show and prove Gödel’s incompleteness theorem). These mathematical results are supported by solid philosophical foundations in analytic philosophy and philosophy of mathematics.
In the Master program students can build on their previous studies — not only in logic program, but in other programs as well — and obtain deeper understanding of the problems which lead to the modern results at the edge of the related fields. In the master program, after students pass a general core of classes, they can focus on the field in logic they prefer: set theory and foundations of mathematics, classical or non-classical logics, or philosophy of mathematics and set theory.
Students with master’s degree from a recognized university can start their PhD studies at the Department of Logic. PhD program focuses on independent research work and new and original results. Department of Logic has acquired many important scientific grants and offers an excellent support for gifted students: both in terms of scientific background and international cooperation, and in terms of finances (stipends and travel expenses).
In case of questions regarding any of the programs in Logic, do not hesitate to contact the department.