Introduction to Logic

Logic

Definition

• The study of reasoning, argumentation, and inference
• Concerned with the principles and methods of distinguishing good arguments from bad ones

Branches of Logic

• Formal Logic: Deals with the study of logical systems, using formal languages and mathematical techniques
• Informal Logic: Focuses on the study of natural language arguments and everyday reasoning
• Philosophical Logic: Examines the philosophical foundations of logic, including the nature of truth, validity, and inference

Key Concepts

• Argument: A set of statements, one of which is the conclusion, and the others are the premises
• Validity: An argument is valid if its conclusion follows logically from its premises
• Soundness: An argument is sound if it is both valid and has true premises
• Inference: The process of drawing a conclusion from one or more premises
• Fallacy: An error in reasoning that makes an argument invalid or unsound

Logical Operators

• Negation (¬): Not, negates a statement
• Conjunction (∧): And, combines two statements
• Disjunction (∨): Or, combines two statements
• Material Implication (→): If-then, implies a conditional relationship
• Biconditional (): If and only if, implies a necessary and sufficient condition

Rules of Inference

• Modus Ponens (MP): From A and A→B, infer B
• Modus Tollens (MT): From A→B and not B, infer not A
• Hypothetical Syllogism (HS): From A→B and B→C, infer A→C

Famous Logicians

• Aristotle: Ancient Greek philosopher who developed the syllogism
• Gottlob Frege: German philosopher and logician who developed modern formal logic
• Bertrand Russell: British philosopher and logician who worked on type theory and propositional logic

Logic

Definition

• The systematic study of reasoning, argumentation, and inference to distinguish good arguments from bad ones

Branches of Logic

• Formal Logic: Studies logical systems using formal languages and mathematical techniques
• Informal Logic: Focuses on natural language arguments and everyday reasoning
• Philosophical Logic: Examines the philosophical foundations of logic, including truth, validity, and inference

Key Concepts

• Argument: A set of statements with one conclusion and one or more premises
• Validity: An argument is valid if its conclusion logically follows from its premises
• Soundness: An argument is sound if it is valid and has true premises
• Inference: The process of drawing a conclusion from one or more premises
• Fallacy: An error in reasoning that makes an argument invalid or unsound

Logical Operators

• Negation (¬): Not, negates a statement
• Conjunction (∧): And, combines two statements
• Disjunction (∨): Or, combines two statements
• Material Implication (→): If-then, implies a conditional relationship
• Biconditional (): If and only if, implies a necessary and sufficient condition

Rules of Inference

• Modus Ponens (MP): From A and A→B, infer B
• Modus Tollens (MT): From A→B and not B, infer not A
• Hypothetical Syllogism (HS): From A→B and B→C, infer A→C

Famous Logicians

• Aristotle: Developed the syllogism
• Gottlob Frege: Developed modern formal logic
• Bertrand Russell: Worked on type theory and propositional logic