Christian Apologetics: Module 1 â Foundations
Introduction to Apologetics: Logic
Logic Philosophy • Love of wisdom or knowledge • Attempt to think rationally and critically about life’s most important questions • A discipline dealing in logic, aesthetics, ethics, metaphysics (ontology and cosmology), and epistemology
Logic • Study of the rules of reasoning • Orderly, rational way of comprehending
Logical Arguments Argument • A set of introductory statements (premises) leading to a final statement (conclusion)… a syllogism • This is not a disagreement between individuals
Valid Argument • Formally valid - follows the rules of logic • Informally valid – avoids fallacies
Sound Argument • Logically valid, both formally and informally • True premises • Premises are more plausible than their contradictories (their negations)
Types of Reasoning Deductive reasoning • Universal rules (premises) lead to the truth of specific cases (conclusion) • If the argument is sound, the conclusion is guaranteed
Inductive reasoning • • • •
Specific cases (premises) are extrapolated to form a general rule (conclusion) Argument may be valid; however, the truth of premises is not certain Probability of premises lead to the probability of the conclusion The more likely the premises, the more likely the conclusion
Logic Symbology Statements are represented by variables: P, Q, R, … Symbols: ∧ and (both) ∨ or (one or the other) → implies (necessarily leads to) ∴ therefore (conclusion is) ¬ not (negation of)
Example: Men (P) are humans (Q) Humans (Q) are mammals (R) Therefore men (P) are a mammals (Q) or 𝑃→𝑄 𝑄→𝑅 ∴𝑃→𝑅
Fundamental Laws of Thought • The Law of Noncontradiction • Something is not equal to its negation • 𝑃 ≠ ¬𝑃
• The Law of Identity • Something is equal to itself • 𝑃=𝑃
• The Law of Excluded Middle • Something either is or is not • 𝑃 ∨ ¬𝑃, ¬(𝑃 ∧ ¬𝑃)
Formal Rules of Logic modus ponens 𝑃→𝑄 𝑃 ∴𝑄 modus tollens 𝑃→𝑄 ¬𝑄 ∴ ¬𝑃
Hypothetical Syllogism 𝑃→𝑄 𝑄→𝑅 ∴𝑃→𝑅 Conjunction 𝑃 𝑄 ∴𝑃∧𝑄
Formal Rules of Logic (cont.) Simplification 𝑃∧𝑄 ∴𝑃 𝑃∧𝑄 ∴𝑄
Absorption 𝑃→𝑄 ∴𝑃 → 𝑃∧𝑄 Addition 𝑃 ∴𝑃∨𝑄
Formal Rules of Logic (cont.) Disjunctive Syllogism 𝑃∨𝑄 ¬𝑃 ∴𝑄 𝑃∨𝑄 ¬𝑄 ∴𝑃
Constructive Dilemma 𝑃 → 𝑄 ∧ (𝑅 → 𝑆) 𝑃∨𝑅 ∴𝑄∨𝑆
Logical Equivalencies • 𝑃 = ¬¬𝑃 • 𝑃∨𝑃 =P • 𝑃 → 𝑄 = ¬𝑃 ∨ 𝑄 • 𝑃 → 𝑄 = ¬𝑄 → ¬𝑃
Informal Fallacies petitio principia • Circular reasoning or begging the question
Genetic Fallacy • Argument against a claim based on how it originated
Argument from ignorance • Arguing against a claim due to lack of evidence
Equivocation • Using a word in such a way as to have two meanings
Amphiboly • Formulating premises with ambiguous meanings
Composition • Inferring that the whole has a property because all of its parts have that property
Inductive Reasoning: Inference to the Best Explanation Explanatory Scope • Explains a wider range of data
Explanatory Power • Makes observable data more probable
Plausibility • Implied by a greater variety of accepted truths
Less ad hoc • Fewer new assumptions are required
Accord with accepted beliefs • Implies fewer falsehoods
Comparative Superiority • Meets the previous criteria far more than rival hypotheses
Logic Philosophy • Love of wisdom or knowledge • Attempt to think rationally and critically about life’s most important questions • A discipline dealing in logic, aesthetics, ethics, metaphysics (ontology and cosmology), and epistemology
Logic • Study of the rules of reasoning • Orderly, rational way of comprehending
Logical Arguments Argument • A set of introductory statements (premises) leading to a final statement (conclusion)… a syllogism • This is not a disagreement between individuals
Valid Argument • Formally valid - follows the rules of logic • Informally valid – avoids fallacies
Sound Argument • Logically valid, both formally and informally • True premises • Premises are more plausible than their contradictories (their negations)
Types of Reasoning Deductive reasoning • Universal rules (premises) lead to the truth of specific cases (conclusion) • If the argument is sound, the conclusion is guaranteed
Inductive reasoning • • • •
Specific cases (premises) are extrapolated to form a general rule (conclusion) Argument may be valid; however, the truth of premises is not certain Probability of premises lead to the probability of the conclusion The more likely the premises, the more likely the conclusion
Logic Symbology Statements are represented by variables: P, Q, R, … Symbols: ∧ and (both) ∨ or (one or the other) → implies (necessarily leads to) ∴ therefore (conclusion is) ¬ not (negation of)
Example: Men (P) are humans (Q) Humans (Q) are mammals (R) Therefore men (P) are a mammals (Q) or 𝑃→𝑄 𝑄→𝑅 ∴𝑃→𝑅
Fundamental Laws of Thought • The Law of Noncontradiction • Something is not equal to its negation • 𝑃 ≠ ¬𝑃
• The Law of Identity • Something is equal to itself • 𝑃=𝑃
• The Law of Excluded Middle • Something either is or is not • 𝑃 ∨ ¬𝑃, ¬(𝑃 ∧ ¬𝑃)
Formal Rules of Logic modus ponens 𝑃→𝑄 𝑃 ∴𝑄 modus tollens 𝑃→𝑄 ¬𝑄 ∴ ¬𝑃
Hypothetical Syllogism 𝑃→𝑄 𝑄→𝑅 ∴𝑃→𝑅 Conjunction 𝑃 𝑄 ∴𝑃∧𝑄
Formal Rules of Logic (cont.) Simplification 𝑃∧𝑄 ∴𝑃 𝑃∧𝑄 ∴𝑄
Absorption 𝑃→𝑄 ∴𝑃 → 𝑃∧𝑄 Addition 𝑃 ∴𝑃∨𝑄
Formal Rules of Logic (cont.) Disjunctive Syllogism 𝑃∨𝑄 ¬𝑃 ∴𝑄 𝑃∨𝑄 ¬𝑄 ∴𝑃
Constructive Dilemma 𝑃 → 𝑄 ∧ (𝑅 → 𝑆) 𝑃∨𝑅 ∴𝑄∨𝑆
Logical Equivalencies • 𝑃 = ¬¬𝑃 • 𝑃∨𝑃 =P • 𝑃 → 𝑄 = ¬𝑃 ∨ 𝑄 • 𝑃 → 𝑄 = ¬𝑄 → ¬𝑃
Informal Fallacies petitio principia • Circular reasoning or begging the question
Genetic Fallacy • Argument against a claim based on how it originated
Argument from ignorance • Arguing against a claim due to lack of evidence
Equivocation • Using a word in such a way as to have two meanings
Amphiboly • Formulating premises with ambiguous meanings
Composition • Inferring that the whole has a property because all of its parts have that property
Inductive Reasoning: Inference to the Best Explanation Explanatory Scope • Explains a wider range of data
Explanatory Power • Makes observable data more probable
Plausibility • Implied by a greater variety of accepted truths
Less ad hoc • Fewer new assumptions are required
Accord with accepted beliefs • Implies fewer falsehoods
Comparative Superiority • Meets the previous criteria far more than rival hypotheses
