MGF1121 - Introduction to Logic

Topical Outline with Specific Course Objectives

1. Introduction to Basic Concepts of Logic
   1. Recognize an argument
      1. Determine the premises
      2. Determine the conclusion
   2. Recognize deductive arguments
      1. Valid
         1. Sound
         2. Unsound
      2. Invalid (and unsound)
   3. Recognize Inductive Arguments
      1. Strong
         1. Cogent
         2. Uncogent
      2. Weak (and uncogent)
2. Informal Fallacies
   1. Recognize instances of fallacies of relevance including:
      1. Argumentum ad baculum
      2. Argumentum ad hominem
      3. Argumentum ad populum
      4. Argumentum ad misericordiam
      5. Argumentum ad ignorantiam
      6. Argumentum ad verecundiam
      7. Accident
      8. Converse Accident
      9. False Cause
      10. Petitio Principii
      11. Complex Question
      12. False Dichotomy
   2. Recognize instances of fallacies of ambiguity, including:
      1. Equivocation
      2. Amphiboly
      3. Composition
      4. Division
3. Categorical Propositions
   1. Recognize and classify a standard-form categorical proposition as to:
      1. Form
      2. Quantifier
      3. Copula
      4. Subject term
      5. Predicate term
      6. Quantity
      7. Quality
      8. Distribution or non-distribution of terms by the proposition
   2. Use the traditional square of opposition to form valid inferences using the relationships of:
      1. Contrary
      2. Subcontrary
      3. Sub-alternation
      4. Contradictory
   3. Recognize and perform the immediate inference operations
      1. Conversion
      2. Obversion
      3. Contraposition
   4. Use the modern square of opposition
      1. Make inferences using the relationship of contradictory.
      2. Recognize the existential fallacy.
   5. Use 2-class Venn diagrams to:
      1. Visually represent the class relationship expressed in each categorical proposition.
      2. Validate the relationships found in the squares of opposition.
      3. Validate the inferences of conversion, obversion and contraposition.
4. Categorical Syllogisms
   1. Recognize a categorical syllogism and put it in standard form by:
      1. Recognizing the major, minor and middle terms.
      2. Recognizing the major and minor premises, and the conclusion.
   2. Classify a standard-form categorical syllogism as to:
      1. Mood
      2. Figure
      3. Test a given mood-figure form for validity
   3. Test a syllogism for validity by:
   4. 1. Venn diagram method
      2. Method of the syllogistic rules
      3. Numerical or other method
   5. Test the validity of:
   6. 1. Categorical arguments that can be reduced to logically equivalent standard-form syllogisms
      2. Categorical arguments that can be evaluated using diagrams representing four and five categories
      3. Sorites and/or enthymemes
5. Truth-Functional Logic
   1. Symbolize any combination of the five (5) types of compound statements (below) in propositional logic.
      1. Conjunction
      2. Disjunction
      3. Conditional
      4. Bi-conditional
      5. Negation
   2. Apply the definitional truth tables for each of the five (5) truth functional connectives in order to:
      1. Assess the truth-value of a statement based on the given values of its atomic components.
      2. Test the logical equivalence of two statement forms using truth tables.
      3. Classify statement forms as to contingent truths, logical truths or self-contradictions by means of truth tables.
      4. Test argument forms for validity by means of truth tables.
      5. Use indirect (shortcut) truth tables to test validity of argument forms.
      6. Test the consistency of sets of premises by the indirect truth table method.
6. Formal Deductive Proof
   1. Recognize instances of any of the following nine rules of inference:
      1. Modus ponens
      2. Modus tollens
      3. Disjunctive syllogism
      4. Hypothetical syllogism
      5. Constructive dilemma
      6. Simplification
      7. Addition
      8. Conjunction
      9. Absorption
   2. Recognize instances of the use of the rule of replacement with any of the following ten tautologous bi-conditionals:
      1. DeMorgan's theorems
      2. Commutation
      3. Association
      4. Distribution
      5. Double negation
      6. Transposition
      7. Material implication
      8. Material equivalence
      9. Exportation
      10. Tautology
   3. Recognize both the specific form and any non-specific forms of an argument:
      1. Given the argument in verbal form.
      2. Given the argument in symbolic form.
   4. Use the method of deduction and the 19 rules of deduction to formulate:
      1. Direct proofs
      2. Indirect proofs
      3. Conditional proofs
      4. Natural deduction of tautologies
      5. Proofs involving inconsistent premises

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