This course is a concise presentation of modern formal logic. At the end of the course, students will have a solid knowledge of propositional logic and some knowledge of predicate logic. They will be able to carry out simple proofs using the method of natural deduction. Students will also have acquired key notions of contemporary logic such as the notion of formal validity, predicate, quantifiers, logical connectors, consistency, tautology, and contradiction.
Propositional Logic:
Chapters I – VII (Volume I) of Paul Teller’s book: “A Modern Formal Logic Primer”.
Logic as the science of argument. Sentences and connectives. Truth functions. Compounding compound sentences. Rules of formation and rules of valuation. Transcription versus translation. Adequacy of transcriptions. Logical equivalence. Substitution of logical equivalents and some more laws. Logical truth and contradictions. Disjunctive normal form and the Sheffer Stroke. Validity. Invalidity and counterexamples. Soundness. The conditional. The biconditional. The idea of natural deduction. Subderivations. The complete rules of inference. Constructing correct derivations. Recognizing the main connective. Derivations: overview, definitions, and points to watch out for. Derived rules. Argument by cases. Further derived rules. Derivations without premises.
Predicate Logic:
Chapters I – IV (Volume II) of Paul Teller’s book: “A Modern Formal Logic Primer”.
Syntax. The need for more logical form. Quantifiers and variables. Predicate logic sentences. Semantics and validity. Interpretations. Truth in an interpretation. Validity in predicate logic. More about quantifiers. Multiple quantification. Quantifier scope, bound variables, and free variables. Substitution instance and truth in an interpretation. Some logical equivalences. Restricted quantifiers. Transcribing from English to logic. Transcriptions strategies.
