Basic Concepts of Logic An Overview of Introduction to Logic Yingrui Yang

Argument Deduction: Step by step from premises to a conclusion, taken the face value of the premises given. Induction: From hypotheses jump to a conclusion Abduction: Allowing revision of beliefs

Deductive Inference All the beads are wooden or metal. The wooden beads are red. The metal beads are green. The square beads are not red. Are the square beads green? Empirical evidence (YB&O, 1998)

Another Type Only one of the following statements is true: Some of the plastic beads are not red, or None of the plastic beads are red. Is it possible that none of the red beads are plastic? Empirical evidence (Y&J-L 2000)

“What follows?” and “To argue for” Two senses of “what follows” (“To argue for”) The syntax/semantics distinction Argument forms and inference rules The logical meanings and truth values

Do Contents matter? Not Logically! Formalize how it matters Natural language and formal language Mathematics and psychology e.g., “The”: All horses with four legs run faster than airplanes”. Formal systems and mental representations Standard logic and logical standard

Kinds of Logical analyses Syntactic: Proofs – “to infer”, deferent logical systems: Axiomatic, natural deduction, Trees Semantic: Validity, soundness, Satisfiable, Contingent (possibly true or false), “imply” Semantic possibilities: Truth tables, Mental models, Truth connectives Contradiction: syntactic, semantic

Levels of Logical Analyses Propositional. Truth connectives (and, or, not, if-then, if and only if) are truth functional First-order: Predicate-argument structure, quantifiers (Universal and existential), value-assignment semantics Modalities: Possible, necessary, ought- to, tense, etc. Possible world semantics

Standards of modern logic Think it through the semester Meta-properties: Consistency and completeness Logic is man-made, logic is a science in development New logic: Logicians and journals of logic

How people Reason? How untrained people reason: Mental logic and/or mental models Empirical evidence Cognitive routines and logical training Education: learning theory and ranking of cognitive capacities Formal science and empirical science Trained and well-trained