Introduction to Logic Johns Hopkins University Center for Talented Youth Antilles School, St. Thomas, Virgin Islands Summer 2015 William McGeehan, Instructor Jenné Bougouneau, Teaching Assistant Note: As in all CTY courses, the instructor may make some changes to daily activities and assignments as the session progresses. Texts: Student will use a photocopied reader with material from many sources, but deeply indebted to two texts in particular, Introduction to Logic, by Irving Copi, and Understanding Symbolic Logic, by Virginia Klenk. Students will also read three of Plato’s dialogues, Euthryphro, Crito and Apology. Part One ‐ Informal Logic Skills learned in informal logic: 1) How to diagram the inferential structure of complex arguments taken from newspapers, journals, and classic texts. 2) How to recognize, construct and defend a proper definition. 3) How to spot mistaken but psychologically persuasive patterns of reasoning (fallacies). 4) How to construct, appraise, and refute arguments by analogy. 5) How to employ and attack basic deductive argument forms. All these skills are reinforced by means of the debate tournament. After each debate, students critique each other’s arguments, noting flawed arguments, faulty definitions, and fallacious patterns of reasoning. Monday – Week 1 Morning: Definition of Logic. Evaluating arguments in terms of soundness and validity. Necessary vs. sufficient conditions. Deductive vs. inductive arguments. Make it valid: practice in finding implicit premises. Introduction to diagramming arguments. Afternoon: Group work on diagramming arguments. Homework: Practice diagramming arguments. Tuesday – Week 1 Morning: Begin unit on definitions. Using definitions in arguments: ‘loading the deck’ (non‐lexical definitions), verbal vs. genuine disputes, persuasive use of definition. Extension vs. intension. Rules for definition by genus and species. Afternoon: Practice with rules of definition using real life examples. Discussion on virtue and vice. Begin an essay on a virtue or vice of your choice, using the five rules of definition by genus and species. Homework: Complete essay. Wednesday – Week 1 Morning: Share essays, students critique each other’s essays using the five rules. Introduction to the life and times of Socrates. Shared reading: Plato’s Euthyphro. Afternoon: Discussion of Plato’s Euthyphro. Introduction to the fallacies. Homework: Practice on recognizing and explaining fallacies. Thursday – Week 1 Morning: Continue fallacies. Afternoon: Continue fallacies. Homework: Using the fallacies: worksheets on attack and counterattack patterns using the fallacies. Friday – Week 1 Morning: Inductive arguments. Making and evaluating arguments by analogy. Refutation by analogy. Justifying and attacking claims about causal relations. Afternoon: The debater’s toolkit: Using and refuting basic argument forms: reductio ad absurdam, dilemma, modus ponens, modus tollens, disjunctive and hypothetical syllogism. Options for framing a thesis, strengths and weaknesses of each option. Accusations using fallacy forms, counteraccusations. Random selection of topics and opponents for next morning’s debates. Homework: Prepare debate positions. Monday – Week 2 Morning: Begin debate tournament. Afternoon: Debate tournament. Homework: Prepare debate positions. Tuesday – Week 2 Morning: Debate tournament. Afternoon: Debate tournament. Begin unit on symbolic, propositional logic. Translating natural language into symbolic notation. Homework: Translation practice. Part Two: Deductive Logic Skills learned in deductive logic: 1) How to translate arguments from natural language into a symbolic one in which their inferential structure is revealed. 2) How to use inference and equivalence rules to construct proofs in sentential logic. 3) How to use the method of truth trees as an algorithm for determining the validity of arguments in sentential logic. 4) How to construct and evaluate syllogistic arguments using Aristotelian predicate logic. Wednesday – Week 2 Morning: The five truth functional operators. Computing truth values of compound formulas. Begin work on truth tables. Model theoretic definition of validity and invalidity. Tautologies, contradictions, contingencies. Concepts of logical implication, logical equivalence. Afternoon: What is a proof? Substitution instances. Introduction to inference rules. Deciding when a rule has been used or misused. Homework: Work on proofs. Thursday – Week 2 Morning: Introduction to replacement rules. Proofs using replacement rules. Afternoon: Rule of conditional proof. Prooflets: using the completeness theorem to see proof possibilities. Homework: Work on proofs. Friday – Week 2 Independence Day Holiday – no class Monday ‐ Week 3 Morning: Introduction to truth trees (a more efficient validity test than truth tables). Using trees, translations and proofs to analyze and evaluate real‐world arguments. Afternoon: Begin reading Plato’s Apology. Homework: Complete Plato’s Apology. Tuesday – Week 3 Morning: Discussion of Plato’s Apology. Afternoon: Introduction to Aristotelian Categorical (Predicate) Logic. Four basic statements, (A,E,I,O), how to show them in Venn diagrams. Evaluating categorical syllogisms using Venn diagrams. Models for predicate logic. Invalidity and countermodels for categorical syllogisms. Homework: Syllogism practice. Wednesday – Week 3 Morning: Quality, quantity, distribution. Mood and figure. Syllogistic fallacies. Afternoon: Translating natural language arguments into syllogistic form. Enthymemes. Homework: Syllogisms in natural language. Thursday – Week 3 Morning: Sorites (syllogistic proofs). Afternoon: Frege, Boole and the birth of modern logic. Proofs in symbolic predicate logic. Homework: Read Plato’s Crito. Friday – Week 3 Morning: Discuss Plato’s Crito. Culminating activity: evaluating real world arguments using the whole logical toolkit. Afternoon: Overall class review and wrap up. .