Romania Clasa a IX-a Logic
Chapters: 5
1. Logic and argumentation: introduction
Language, logic and argument
- 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. Formal deductive logic: propositional logic
Propositional logic
- 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. Advanced formal logic: predicate logic and its applications
Monadic predicate logic · Terms · Categorical propositions · Deductive inferences with categorical propositions
- 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.
- Logical Reasoning – Logical reasoning means getting from facts (premises) to a conclusion in a way we can check. A statement is either true or false. Statements are joined with NOT, AND, OR, IF…THEN and IF AND ONLY IF, and truth tables show when the result is true. In deduction, if the premises are true and the form is valid, the conclusion must be true (modus ponens, modus tollens, syllogisms). Venn diagrams test syllogisms with 'all', 'no' and 'some'. Induction and analogy go from examples to a general idea: the conclusion is only probable. A direct proof goes step by step from what is known; an indirect proof assumes the opposite and reaches a contradiction. Fallacies are tempting but faulty arguments.
4. Inductive logic: non-deductive reasoning
Induction and analogy
- Logical Reasoning – Logical reasoning means getting from facts (premises) to a conclusion in a way we can check. A statement is either true or false. Statements are joined with NOT, AND, OR, IF…THEN and IF AND ONLY IF, and truth tables show when the result is true. In deduction, if the premises are true and the form is valid, the conclusion must be true (modus ponens, modus tollens, syllogisms). Venn diagrams test syllogisms with 'all', 'no' and 'some'. Induction and analogy go from examples to a general idea: the conclusion is only probable. A direct proof goes step by step from what is known; an indirect proof assumes the opposite and reaches a contradiction. Fallacies are tempting but faulty arguments.
5. Applied logic: argumentation and critical thinking
Evaluating arguments and fallacies · Arguments, counter-arguments, persuasion
- 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.