Methods of Philosophizing – Comprehensive Lecture Notes

Pre-Test Concepts, Terms, and Correct Answers

• Logic
  • Defined as the science and art of correct thinking.
  • Centered on the analysis and construction of arguments.
  • Serves as a path to freedom from half-truths and deceptions.
  • Distinguishes facts from opinions or personal feelings.
• Fallacy
  • An illogical argument or a defect in reasoning other than having false premises.
• Validity
  • Refers to the manner by which the premises necessarily support the conclusion; the essential attribute of deductive arguments.
• Soundness
  • A valid argument in which all the premises are actually true.
• Deductive Reasoning
  • Premises support the conclusion necessarily; essential attribute is validity.
• Inductive Reasoning
  • Premises support the conclusion probabilistically; essential attribute is probability.
• Key Named Fallacies & Appeals
  • Fallacy of Division – assuming that parts have the characteristics of the whole.
  • Fallacy of False Cause – superstitious beliefs; presumes causal connection without evidence.
  • Argumentum ad Ignorantiam (Appeal to Ignorance) – claiming something is true because it hasn’t been proven false.
  • Argumentum ad Populum (Appeal to the People) – exploiting popularity or crowd approval.
  • Appeal to Pity – exploiting an opponent’s feelings of guilt or sympathy.
  • Appeal to Force – using threat, coercion, or force as justification for a conclusion.

Logic and Critical Thinking: Tools in Reasoning

• Logic (\textit{logike})
  • Greek root meaning “thought,” “reason,” or “discourse.”
  • Science + art: explains how to think correctly and evaluate arguments.
• Critical Thinking
  • Systematically distinguishes fact from opinion or emotion.
  • Requires suspension of judgment until all relevant facts are gathered and considered.
  • Enhances rational decision-making, problem solving, and protects against deception.
• Importance
  • Equips individuals to identify flawed reasoning, avoid manipulation, and build coherent viewpoints.
  • Connects to ethics (responsible belief-forming) and to real-world tasks (legal reasoning, scientific method, civic debate).

Structure of an Argument

• Argument
  • A structured set of statements meant to establish a claim.
  • Contains premises (reasons/evidence) and a conclusion (claim supported).
• Premise
  • Statement assumed true within the argument; provides rational support.
  • Example: “All men are mortal.”
• Conclusion
  • Statement purportedly proven by premises.
  • Example: “Therefore, Socrates is mortal.”
• Typical Notation
  $\text{Premise}<em>1,\; \text{Premise}</em>2,\;\dots \Rightarrow \text{Conclusion}$
• Sample Everyday Arguments
  • “I need a new coat because it’s getting cold and my current one is too small.”
  • “Violent video games should be banned because they promote aggression in children.”

Deductive Reasoning (Top-Down Logic)

• Definition
  • Starts with general premises and derives a specific, certain conclusion.
  • Form: $P\rightarrow Q,\; P \;\Rightarrow\; Q$
• Essential Attribute: Validity
  • If the premises are true, the conclusion must be true.
  • Validity concerns form, not actual truth of premises.
• Syllogism • Classic deductive form with two premises and a conclusion. • Example:
  • Premise 1: All men are mortal.
  • Premise 2: Socrates is a man.
  • Conclusion: Socrates is mortal.
• Soundness • Deductive argument is sound when it is valid and all premises are in fact true. • Example:
  • Premise 1: Cebu is a part of the Philippines.
  • Premise 2: Juan was born in Cebu.
  • Conclusion: Juan was born in the Philippines.
• Invalid Deduction Example
  • Premise 1: All dogs have four legs.
  • Premise 2: All cats have four legs.
  • Conclusion: Therefore, all cats are dogs.
  • Formal structure allows a false conclusion even with true premises ⇒ invalid.

Inductive Reasoning (Bottom-Up Logic)

• Definition
  • Draws generalizations from specific observations; conclusion is probable rather than certain.
  • Symbolically: $\text{Observation}<em>1,\;\dots,\;\text{Observation}</em>n \;\Rightarrow\; \text{Probable Generalization}$
• Essential Attribute: Probability
  • The strength of the inference is assessed in terms of likelihood.
• Examples
  • Political prediction: 63% of registered voters in District X belong to the opposition ⇒ Congressman Gerry will probably lose reelection.
  • Black-swan problem: Every swan observed so far is white ⇒ all swans might be white (yet may fail if a black swan exists).
  • Allergic reaction: Rash follows peanut consumption ⇒ likely allergic to peanuts.

Common Patterns of Inductive Reasoning

1. Statistical Argument
   • Uses numerical data from a sample to infer about a population.
   • Example: Polling 1000 voters and finding $60\%$ support ⇒ approximately $60\%$ of all voters favor Candidate A.
   • Example: Inspecting 50 widgets, 2 defective ⇒ estimate $\frac{2}{50}=4\%$ defect rate.
2. Predictive Argument (Predictive Induction)
   • Infers a future event from consistent past patterns.
   • Examples:
   – High summer temperatures every year ⇒ this summer will likely be hot.
   – Car needs oil change every 3 months ⇒ it will need change again in 3 months.

Evaluating Argument Strength

• Strong Argument
  • Clear, logically structured, evidence-backed, anticipates counterarguments, free from fallacies.
  • Example: “Studies show employees are more productive with better work-life balance ⇒ a shorter workweek could raise output.”
• Weak Argument
  • Premises do not sufficiently support the conclusion; often rely on feelings, speculation, or irrelevant points.
  • Example: “I have a feeling I’m going to win the lottery, so I’m sure I’ll win money tonight.”

Catalog of Logical Fallacies (Selected)

• Fallacy of Division – Attributing whole’s property to each part.
• Fallacy of Composition – (opposite of division) attributing parts’ properties to whole.
• False Cause (Post hoc / Superstitious) – Mistaking correlation for causation.
• Argumentum ad Ignorantiam – Claim of truth because it has not been disproved.
• Argumentum ad Populum (Appeal to the People) – Relying on popularity or crowd emotions.
• Appeal to Pity (\textit{ad misericordiam}) – Seeking agreement through sympathy.
• Appeal to Force (\textit{ad baculum}) – Using threats as premises.
• Equivocation – Using a word with multiple meanings ambiguously.
• Amphiboly – Grammatical ambiguity.
• Accent – Misleading emphasis or tone.

Illustrative Quotes for Practice (Deductive vs. Inductive)

• “Many people believe a dark tan is attractive … but mounting evidence indicates too much sun can lead to health problems.” — Joseph & Michael Morgan
  • Invite inductive evaluation (from mounting evidence to general claim).
• “Every art and every inquiry … is thought to aim at some good; … the good has rightly been declared to be that at which all things aim.” — Aristotle
  • Deductive structure moving from universal premise to defining ‘good.’
• “The stakes in whistleblowing are high. Take the nurse who alleges that physicians enrich themselves through unnecessary surgery.” — Sissela Bok
  • Opens an inductive or abductive ethical analysis based on a case.
• “Learning without thought is labor lost; thought without learning is perilous.” — Confucius
  • Moral/epistemic claim; can be broken into deductive-style conditional premises.

Ethical & Practical Significance

• Rigorous reasoning prevents moral harm (e.g., avoiding false medical accusations, baseless superstitions).
• Supports democratic deliberation by separating emotional manipulation from sound policy debate.
• Underpins scientific inquiry: hypotheses (inductive) tested and connected via deductive structures.

Quick Reference Equations & Symbols

• Validity schema: $\forall x\,(P(x) \rightarrow Q(x)),\; P(a) \;\Rightarrow\; Q(a)$
• Soundness: $\text{Validity} \;\land\; \bigwedge<em>{i=1}^{n} \text{Premise}</em>i\text{ is true}$
• Probability in induction: P(\text{Conclusion}\mid \text{Premises}) \approx 0.5 < p \le 1 (closer to 1 ⇒ stronger)

Study Tips

• When evaluating any argument, ask:
  1. Are the premises true/plausible?
  2. Does the conclusion follow necessarily (deductive) or with high probability (inductive)?
  3. Are there hidden assumptions or fallacies?
  4. How would counterexamples affect the reasoning?
• Practice converting everyday statements into formal premise-conclusion form; highlight validity or probability.
• Use Aristotle’s syllogistic model for quick checks of deductive validity.