South 고등학교 3학년 Logic
Chapters: 5
1. Analysing arguments
Inference and argument · Finding conclusions and premises · Deductive vs inductive
- Logic: How Good Arguments Work – Logic studies good reasoning. An argument has premises (reasons) and a conclusion; inference is the step between them. In a deductive argument, if the premises are true the conclusion must be true; such an argument is valid, and it is sound if the premises really are true. One counterexample shows an argument form is invalid. Inductive arguments move from observed cases to a general or likely conclusion; they are strong or weak, never certain. Categorical propositions (A, E, I, O) and simple predicate logic (∀, ∃) help us write arguments precisely and spot fallacies.
2. Deductive arguments
Validity and soundness · Propositional argument forms · Testing validity · Counterexamples · Categorical syllogisms
- Logic: How Good Arguments Work – Logic studies good reasoning. An argument has premises (reasons) and a conclusion; inference is the step between them. In a deductive argument, if the premises are true the conclusion must be true; such an argument is valid, and it is sound if the premises really are true. One counterexample shows an argument form is invalid. Inductive arguments move from observed cases to a general or likely conclusion; they are strong or weak, never certain. Categorical propositions (A, E, I, O) and simple predicate logic (∀, ∃) help us write arguments precisely and spot fallacies.
- Propositional Logic: From Statements to Valid Arguments – Propositional logic studies statements that are either true or false and the words that join them: not (¬), and (∧), or (∨), if…then (→) and if and only if (↔). A truth table lists every possible combination of truth values. An argument is valid when no row makes all premises true and the conclusion false. Valid forms such as modus ponens and modus tollens become inference rules for natural deduction.
3. Inductive arguments
Strength of inductive arguments · Generalisation from observation · Statistical syllogisms
- Logic: How Good Arguments Work – Logic studies good reasoning. An argument has premises (reasons) and a conclusion; inference is the step between them. In a deductive argument, if the premises are true the conclusion must be true; such an argument is valid, and it is sound if the premises really are true. One counterexample shows an argument form is invalid. Inductive arguments move from observed cases to a general or likely conclusion; they are strong or weak, never certain. Categorical propositions (A, E, I, O) and simple predicate logic (∀, ∃) help us write arguments precisely and spot fallacies.
4. Fallacies
Fallacies as bad arguments · Formal vs informal · Formal fallacies · Informal fallacies · Seemingly good arguments
- Logical Fallacies: How Good-Looking Arguments Go Wrong – A fallacy is an error in reasoning that makes an argument weak or invalid, even though it may look convincing. Formal fallacies are mistakes in the form (structure) of a deductive argument, such as affirming the consequent. Informal fallacies are mistakes in content, language or relevance, such as ad hominem, straw man, false dilemma, slippery slope, appeal to popularity or false authority, hasty generalisation, post hoc and circular reasoning. Spotting them helps us discuss fairly.
5. Using arguments
Evaluating claims · Reconstructing arguments · Complex arguments · Arguments in debate · Logic in reading and problem solving
- Debate Skills: How to Argue Clearly, Fairly and Well – A debate is a timed, rule-based contest of ideas on a motion. One side argues for it, the other against it, and a chair keeps order. A good argument has a claim, a reason, evidence and a link to the motion. Research makes evidence strong: reliable, recent and relevant. Rebuttal answers the other side's weakest points; cross-examination uses short questions to expose them. Good debaters attack arguments, not people, and listen as carefully as they speak.