South 고등학교 2학년 Logic and Thinking
Chapters: 4
1. Thinking and logic
Logical thinking · Fallacies · Critical and rational attitude
- 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 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.
2. Language and logic
Deduction and induction · Analysing deductive arguments · Building good arguments
- 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.
3. Symbols and logic
Symbolising propositions · Testing validity with symbols · Natural deduction · Logic and coding
- 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.
- Programming Basics: Sequence, Selection, Loops and Functions – A program is a set of exact instructions a computer follows. Every program is built from three structures: sequence (steps in order), selection (if/else choices) and iteration (loops). Variables store values. Functions group code into reusable, named blocks, which makes programs modular and easier to test, debug and maintain.
4. Science and logic
Kinds of induction · Hypothesis and evidence · Evidence-based thinking · Induction in machine learning
- 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.
- The Scientific Method – The scientific method is the careful way scientists find out how the world works. Observe something, ask a testable question, make a hypothesis (a clear, testable guess), test it with a fair experiment (change one variable, measure one, keep the rest the same), repeat and record data, analyse it, draw a conclusion and share it so others can check. Results that fail the test are useful too: they send you back to a new hypothesis.
- Nature of Science: How Scientific Knowledge Is Built and Changed – Science is a way of knowing that rests on evidence anyone can check. Scientists observe, infer, test ideas that could be proved wrong, and let other experts check their work. Laws describe what happens; theories explain why. Scientific knowledge is reliable but always open to change, and sometimes a whole way of seeing (a paradigm) is replaced.
- Machine Learning – Machine learning (ML) is a way for computers to learn a rule from examples instead of being told the rule. We give data made of features (inputs) and, in supervised learning, labels (answers). The machine fits a model: regression predicts a number, a decision tree asks yes/no questions to pick a class, and k-means clustering groups unlabelled data. We train on most of the data, test on data it never saw, and measure accuracy or error. A model that only memorises (overfits) fails on new data.