Introduction to Logic

Definition of Logic

• Logic is the systematic study of the principles of valid inference and reasoning
• It involves the use of language, symbols, and rules to construct arguments and arrive at conclusions

Types of Logic

• Propositional Logic: deals with statements that can be either true or false, and how they can be combined using logical operators
• Predicate Logic: deals with statements that contain variables and predicates, and how they can be quantified and related
• Modal Logic: deals with statements that involve notions of possibility, necessity, and obligation
• Informal Logic: deals with the study of reasoning and argumentation in everyday life, focusing on the process of critical thinking and argument evaluation

Logical Operators

• NOT (negation): negates a statement, making it false if it was true and true if it was false
• AND (conjunction): combines two statements, making the resulting statement true only if both original statements are true
• OR (disjunction): combines two statements, making the resulting statement true if at least one of the original statements is true
• IF-THEN (implication): states that if one statement is true, then another statement must also be true
• IFF (equivalence): states that two statements are equivalent, meaning they are either both true or both false

Argument Forms

• Modus Ponens: a valid argument form that states "if p, then q; p; therefore, q"
• Modus Tollens: a valid argument form that states "if p, then q; not q; therefore, not p"
• Hypothetical Syllogism: a valid argument form that states "if p, then q; if q, then r; therefore, if p, then r"

Fallacies

• Ad Hominem: attacking the person making an argument rather than addressing the argument itself
• Strawman: misrepresenting an opponent's argument to make it easier to attack
• False Dilemma: presenting only two options as if they are the only possibilities when there may be other options
• Slippery Slope: arguing that a particular action will inevitably lead to a series of negative consequences without evidence

Definition of Logic

• Logic is the systematic study of principles of valid inference and reasoning, involving language, symbols, and rules to construct arguments and arrive at conclusions.

Types of Logic

• Propositional Logic: deals with true or false statements and their combinations using logical operators.
• Predicate Logic: deals with statements containing variables and predicates, and their quantification and relation.
• Modal Logic: deals with statements involving possibility, necessity, and obligation.
• Informal Logic: deals with reasoning and argumentation in everyday life, focusing on critical thinking and argument evaluation.

Logical Operators

• NOT: negates a statement, making it false if it was true and true if it was false.
• AND: combines two statements, making the resulting statement true only if both original statements are true.
• OR: combines two statements, making the resulting statement true if at least one of the original statements is true.
• IF-THEN: states that if one statement is true, then another statement must also be true.
• IFF: states that two statements are equivalent, meaning they are either both true or both false.

Argument Forms

• Modus Ponens: "if p, then q; p; therefore, q" is a valid argument form.
• Modus Tollens: "if p, then q; not q; therefore, not p" is a valid argument form.
• Hypothetical Syllogism: "if p, then q; if q, then r; therefore, if p, then r" is a valid argument form.

Fallacies

• Ad Hominem: attacking the person making an argument rather than addressing the argument itself.
• Strawman: misrepresenting an opponent's argument to make it easier to attack.
• False Dilemma: presenting only two options as if they are the only possibilities when there may be other options.
• Slippery Slope: arguing that a particular action will inevitably lead to a series of negative consequences without evidence.