Basic Concepts of Logic

An Overview of Introduction to Logic

Yingrui Yang9-2-05

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