Reasoning is a central human activity. We reason every day, about everything that is or seems important to us. In science and in philosophy reasoning is everywhere. Philosophers do not only reason in order to support their positions, they also scrutinize philosophical arguments, ask for the premises on which these are based, and investigate whether positions are consistent. Often it turns out that premises were hidden and/or unacceptable and it may also come to light that a some philosophical position under investigation is inconsistent (i.e. contradicts itself).
Logic concerns itself with questions relating to this. Which arguments are valid? When does someone contradict himself? These questions are generally answered with the help of the concept of truth in possible situations. An argument is valid in this approach if in any possible situation in which its premises are true its conclusion must also be true and a set of statements is inconsistent if there is no possible situation in which these statements are simultaneously true. The centrality of the idea of truth in a possible situation makes it the case that modern logic can be interpreted as a simplified model of the relation between language and reality. Philosophical questions regarding these notions arise immediately: What is truth? What are possible situations? What structure should we ascribe to those possible situations and what are therefore our ontological commitments when we make use of these notions?
We thus see that logic interacts strongly with philosophical questions about reasoning, language, thought, and meaning. Aristotle, who created the subject virtually ab ovo about 2350 years ago, already realised that this was the case. Aristotle was a genius and his logical work has withstood the times until the nineteenth century when Gottlob Frege revolutionised the subject and gave us a radical generalization of Aristotelian logic. Nowadays logic is an interdisciplinary subject. It plays not only a central critical role in philosophy, but is also of fundamental importance in mathematics, computer science and linguistics.
There are now many logics, but one of them is generally agreed to take a central place. This is predicate logic, the theory that will be the subject of this course. We will also treat propositional logic, a theory that can be viewed as part of predicate logic and that will serve as a first step towards the full theory.
Type of instructions14x2 hours lectures; 14x2 hours practicals
Type of examsmidterm and final
- W. Hodges, Logic, 2nd edition, Penguin, 2001, ISBN 0141003146.
- Apostolos Doxiades, Christos Papadimitriou, Alecos Papadatos & Annie di Donna, Logicomix, Bloomsbury, 2009. Editions in many languages other than English are available. See http://en.wikipedia.org/wiki/Logicomix.