This is a textbook for beginning mathematics students. Knowledge of school mathematics is not presumed: it starts with the basics of counting. The underlying idea is that the best way to learn mathematics is by doing mathematics. For beginning students it is sometimes a problem to assume when looking for proof. For the exercises in this textbook, this situation does not occur: except for the in…
Both Heyting and Gentzen approached questions of meaning in relation to whatit is to prove something, but as seen from the above, their approaches were stillvery different. Gentzen was concerned with what justifies inferences and therebywith what makes something a valid form of reasoning. These concerns were absentfrom Heyting’s explanations of mathematical propositions and assertions. The co…
Logic is often perceived as having little to do with the rest of philosophy, and even less to do with real life. In this lively and accessible introduction, Graham Priest shows how wrong this conception is. He explores the philosophical roots of the subject, explaining how modern formal logic deals with issues ranging from the existence of God and the reality of time to paradoxes of probability…
In logic, we study properties of sentences, such as truth, falsity, necessity, and contin-gency, relations between sentences, such as entailment and consistency, and practicesinvolving sentences, such as argumentation. However, bysentences, we normallyonly mean sentences of a certain particular kind: declarative sentences—statements,and their counterparts in formal languages.There are princip…