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When somebody makes a claim, it is often accompanied by evidence for the claim. The philosophy of intuitionism (or constructivism) takes the notion of evidence to be central to logic: a valid inference must provide a recipe for constructing its evidence. This requirement leads to the rejection of the law of excluded middle, e.g. `either there is extraterrestrial life or there is not.’, because it may not come with evidence for one of the possibilities. Constructive reasoning therefore motivates a non-classical notion of logic, different from the one of classical logic as given by truth tables.
This course offers an introduction to intuitionistic logic, which formalizes constructive reasoning and has a wide range of applications in philosophy, mathematics and computer science. The contents to be covered include philosophical backgrounds for intuitionism, both proof systems and semantics for intuitionistic logic, and some fundamental theoretical results. There will be a focus on comparisons with classical logic, which will illustrate the difference between the two world views.
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Literature:
Hiroakira Ono (2019), Proof Theory and Algebra in Logic. Springer.
Dirk van Dalen (2013), Logic and Structure. 5th edition. Springer.