Introduction to Logic

Study Notes

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

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

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

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"

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

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

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.

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.

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.

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.