Sri Lanka Advanced Level Examination Syllabus - Logic

This syllabus for Logic and Scientific Method is designed for G.C.E. Advanced Level students, implemented from 2017. It aims to develop logical thinking and scientific reasoning skills, enabling students to analyze, criticize, and create sound arguments. The curriculum covers both theoretical and practical aspects, including term calculus, proposition calculus, predicate calculus, truth tree method, logic gates, Indian logic, fallacies, and the application of logic to law and evaluative sciences. It also explores the scientific method, emphasizing modern science and its relationship with society, ethics, and the environment.

Aims of the Course

Upon successful completion of this course, students should be able to:

• Enhance intelligent abilities and identify fallacies in logical thinking.
• Make accurate logical judgments and understand natural laws.
• Develop clear and unique thinking to infer unknown information from known facts.
• Understand logical rules and their importance in forming meaningful statements.
• Apply logical approaches to problem-solving and critical thinking.
• Recognize the logical foundations of scientific, technological, legal, and ethical judgments.

Course Content

The syllabus is divided into several competency levels, each covering specific topics:

1. Introduction to Logic: Definitions, history, and its relationship with other disciplines like philosophy, language, mathematics, psychology, and law. Practical applications of logic in daily life and research. 2. Terms and Propositions: Logical connections of terms, laws of thought, different types of propositions (simple, complex, analytic, synthetic, categorical, hypothetical, disjunctive), and their distribution of terms. 3. Traditional Logic: Immediate and mediate inferences, opposition of propositions, syllogisms (pure and mixed), rules of syllogism, enthymeme, sorites, and limitations of syllogistic reasoning. Comparison of Aristotelean and Indian logic. 4. Class Logic and Set Theory: Basic concepts of set theory (universal set, subsets, null set, etc.), Euler's and Venn's diagrams, representation of propositions and arguments using Venn diagrams. 5. Modern Logic and Propositional Calculus: Nature and objectives of modern logic, deductive systems, simple and complex sentences, well-formed formulae, truth table method (direct and indirect), truth tree method, derivational methods, and proving theorems. 6. Predicate Calculus: Symbols, formulae with quantifiers and variables, bound and free variables, substitutions, derivation of arguments, and proof of theorems. Truth tree method in predicate calculus. 7. Logic Gates and Electronic Circuits: Relationship between logic and computer science, Boolean and logical expressions, truth tables for logic gates, constructing circuits for symbolic formulae, and simplification using Karnaugh maps. 8. Logical Fallacies: Formal and non-formal fallacies, fallacies of irrelevance, weak induction, presumption, ambiguity, and grammatical analogy. Distinction between factual and evaluative statements. 9. Logic and Law: Relationship between law and logic, different fields of law, nature of evidence in legal field, deductive and inductive reasoning in law, and case studies of criminal law. 10. Introduction to Science: Definition of science, distinction between science and non-science (Popper's demarcation principle), divisions of science (natural, social, pure, applied, descriptive, evaluative), and their interrelations. 11. Scientific Methodology: Basic features of scientific methodology, different schools of thought (inductive, deductive verification, deductive falsification), relative methodology (Kuhn, Feyerabend), and Lakatos' scientific research programme. 12. Scientific Hypotheses: Formation and development of hypotheses, features of scientific hypotheses, difference between laws and theories, universal and statistical generalizations, scientific explanation, and covering law model. Methods of scientific tests (observation, experiment, control group, case study, crucial test, thought experiment, Mill's methods). 13. Probability: Basic concepts of probability, different approaches (historical, statistical, psychological, mathematical), permutation and combination, laws of probability, conditional probability, and applications in problem-solving. 14. Measurement in Science: Introduction to measurement, instruments and benefits of measurement, different types of scales, and errors of measurement. 15. Statistical Methods: Nature of statistics, descriptive and general statistics, sampling methods, central tendencies (mode, median, mean), dispersion measures (variance, standard deviation), correlation methods, and statistical errors. 16. History of Science: Scientific concepts before and after the Renaissance, contributions of different civilizations, key figures (Copernicus, Galileo, Newton, etc.), and the relationship between science and society throughout history. Modern and contemporary views of science, theories about the universe, origin and evolution of life, atomic models, and key theories in various scientific disciplines. 17. Social Sciences: Nature and subject matter of social science, differences between natural and social sciences, research methods in social sciences (observation, interviews, questionnaires, etc.), and challenges to the substantiality of social sciences. 18. Science, Technology, and Society: Relationship between science, technology, and society, ethical problems arising from scientific and technological advancements, environmental problems, and strategies to address these challenges.