Introduction to Logic

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• Reasoning, guessing, and persuading ~20 min
• Statements and claims ~20 min
• Arguments, premises, and conclusions ~25 min
• Indicator words ~25 min
• Arguments, explanations, opinions, and descriptions ~25 min

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• Finding the main conclusion ~25 min
• Standard form and paraphrase ~30 min
• Missing premises and conclusions ~30 min
• Intermediate conclusions ~25 min
• Diagrams, independent and joint premises ~30 min
• Diagramming longer arguments ~35 min

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• Deductive and inductive arguments ~20 min
• Validity ~25 min
• Truth and validity come apart ~25 min
• Soundness ~20 min
• Strength and cogency ~20 min
• Proving invalidity with counterexamples ~25 min
• Three questions for any argument ~25 min

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• Form and substitution instances ~20 min
• Modus ponens and modus tollens ~25 min
• Affirming the consequent and denying the antecedent ~25 min
• Hypothetical and disjunctive syllogism ~30 min
• Conjunction, simplification, and addition ~20 min
• Constructive and destructive dilemma ~25 min
• Recognizing forms in the wild ~30 min

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• What makes a fallacy ~30 min
• Ad hominem and tu quoque ~35 min
• Straw man and red herring ~35 min
• Appeals to popularity, emotion, and force ~40 min
• Appeal to authority and the genetic fallacy ~35 min
• Appeal to ignorance ~35 min

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• Begging the question and circular reasoning ~30 min
• False dilemma, loaded and complex questions ~35 min
• Hasty and sweeping generalization and accident ~35 min
• Telling presumption fallacies apart ~30 min

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• Post hoc and false cause ~25 min
• Correlation is not causation ~30 min
• Oversimplified cause and slippery slope ~25 min
• Equivocation and amphiboly ~25 min
• Composition and division ~25 min
• Repairing fallacious arguments ~30 min

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• Classes and the four statement types ~25 min
• Putting statements in standard form ~30 min
• Venn diagrams for single statements ~25 min
• The square of opposition and existential import ~30 min
• Conversion, obversion, and contraposition ~30 min
• Syllogisms, mood, figure, and distribution ~40 min
• Testing syllogisms with Venn diagrams ~35 min

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• Why symbols ~15 min
• Sentence letters and compound sentences ~20 min
• Negation and conjunction ~25 min
• Disjunction ~20 min
• The conditional ~25 min
• The biconditional ~20 min
• Other notations you will see ~20 min

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• Building a symbolization key ~25 min
• Not, but, and both ~25 min
• Or, either … or, and neither … nor ~25 min
• If versus only if ~30 min
• Necessary and sufficient conditions ~25 min
• Unless ~25 min
• If and only if, and longer sentences ~35 min
• What symbols cannot capture ~25 min

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• Well-formed formulas ~20 min
• Scope and parentheses ~25 min
• Finding the main connective ~25 min
• How parentheses change meaning ~25 min
• Scope ambiguity in English ~25 min

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• Truth values and valuations ~25 min
• The five characteristic tables ~30 min
• Why the conditional table looks strange ~25 min
• Computing the value of a compound ~30 min
• Building complete truth tables ~35 min
• Truth table shortcuts ~25 min

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• Tautologies, contradictions, and contingencies ~30 min
• Classifying with truth tables ~35 min
• Predict, then check with partial truth tables ~35 min
• Consistency: can sentences be true together? ~30 min

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• What equivalence means ~20 min
• Checking equivalence with truth tables ~25 min
• Double negation and De Morgan's laws ~30 min
• Commutative, associative, and distributive laws ~25 min
• Idempotence, identity, domination, and negation laws ~25 min
• Conditional and biconditional equivalences ~30 min
• Chains of equivalences ~30 min
• Normal forms ~30 min

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• Symbolizing whole arguments ~25 min
• The truth table test ~30 min
• Counterexamples and countermodels ~25 min
• The short method ~30 min
• Odd cases ~20 min
• Checking the named forms ~30 min

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• Why proofs ~25 min
• Proof format: lines, premises, and citations ~25 min
• The and rules ~25 min
• Conditional elimination and reiteration ~30 min
• Subproofs and conditional introduction ~35 min
• The or rules ~35 min
• The biconditional rules ~30 min

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• Contradiction and the negation rules ~30 min
• Indirect proof ~30 min
• Proof strategy ~35 min
• Derived rules: MT, DS, DNE, and De Morgan ~35 min
• Hypothetical syllogism and dilemmas as derived rules ~30 min
• Theorems: proofs with no premises ~30 min
• Longer proofs ~40 min

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• From English to verdict ~35 min
• Choosing a method ~30 min
• Knights and knaves ~30 min
• Deduction grids and who is lying ~30 min
• Cumulative review ~40 min