Key Formulas & Frameworks
Question → Hypothesis → Counterexample → Refined Understanding
Elenchus: exposing contradictions in beliefs through systematic questioning
Major premise: All humans are mortal.
Minor premise: Socrates is human.
Conclusion: Therefore, Socrates is mortal.
Deductive reasoning: if premises are true, conclusion must be true
Doubt everything → Find indubitable foundation → Rebuild knowledge
Cogito ergo sum: "I think, therefore I am"
Foundationalism: knowledge built on certain foundations
Formula 1 (Universal Law): "Act only according to that maxim which you can at the same time will to become a universal law."
Formula 2 (Humanity): "Treat humanity never merely as a means, but always also as an end."
Deontological ethics: duty-based, not consequence-based
Greatest Happiness Principle: "The greatest good for the greatest number"
Hedonic Calculus: Intensity + Durationity + Certainty + Propinquity + Fecundity + Purity + Extent
Consequentialist ethics: outcomes determine moral worth
Eudaimonia (flourishing) = Virtuous activity + reason
Golden Mean: Virtue lies between excess and deficiency
Courage = mean between cowardice (deficiency) and recklessness (excess)
The visible world (shadows) vs. The intelligible world (Forms/Ideas)
Allegory of the Cave: prisoners see only shadows, not reality
Thesis → Antithesis → Synthesis
Historical progress through conflict and resolution
Design just society without knowing your position in it
Difference Principle: Inequality only justified if it benefits the least advantaged
Justice as fairness — thought experiment for distributive justice
Modus Ponens: If P → Q, P ∴ Q
Modus Tollens: If P → Q, ¬Q ∴ ¬P
Hypothetical Syllogism: If P → Q, If Q → R ∴ If P → R
Core Concepts
Epistemology (Theory of Knowledge)
The study of knowledge: What is knowledge? How do we acquire it? What are its limits? Plato defined knowledge as "justified true belief" (though Gettier cases challenge this). Major positions: Rationalism (Descartes — knowledge from reason), Empiricism (Locke, Hume — knowledge from experience), Kant's synthesis (knowledge requires both sensory experience and rational categories).
Metaphysics (Study of Reality)
The branch of philosophy examining the fundamental nature of reality. Key questions: What exists? What is the nature of time? Do we have free will? Major positions: Materialism (only physical matter exists — Marx, Hobbes), Idealism (reality is mental or spiritual — Berkeley, Hegel), Dualism (both mind and matter exist — Descartes). Substance, causation, identity, and possibility are central topics.
Ethics (Moral Philosophy)
The study of right and wrong, good and evil. Three major frameworks: Consequentialism (judge actions by outcomes — utilitarianism), Deontology (judge actions by rules/duties — Kant), Virtue Ethics (judge actions by character — Aristotle). Applied ethics addresses specific issues: bioethics, business ethics, environmental ethics, AI ethics.
Existentialism
Philosophy emphasizing individual freedom, choice, and meaning-making. Key thinkers: Kierkegaard ("leap of faith"), Nietzsche ("God is dead," will to power), Sartre ("existence precedes essence," "condemned to be free"), Camus (absurd, rebellion). Core idea: There is no pre-given human nature — we create ourselves through our choices, bearing full responsibility.
Logic and Critical Thinking
The study of valid argumentation and reasoning. Deductive logic: if premises are true, conclusion must be true (validity). Inductive logic: premises support but don't guarantee conclusion (strength). Common fallacies: ad hominem (attacking person, not argument), straw man (misrepresenting opponent), false dilemma (only two options), slippery slope, appeal to authority, circular reasoning, hasty generalization.
Philosophy of Mind
The study of consciousness, mental states, and their relation to the physical body. Key problems: Mind-Body Problem — how do mental states relate to physical states? Other Minds — how do I know others have minds? Personal Identity — what makes me the same person over time? Positions: dualism (Descartes), behaviorism, identity theory (mind = brain), functionalism (mind = software), eliminative materialism (folk psychology is wrong).
Political Philosophy
The study of government, justice, rights, and liberty. Key texts: Plato's Republic (philosopher kings), Hobbes' Leviathan (social contract, absolute sovereignty), Locke's Second Treatise (natural rights, consent, right to revolution), Rousseau's Social Contract (general will), Rawls' Theory of Justice (veil of ignorance), Nozick's Anarchy, State and Utopia (minimal state). Debates: liberty vs. equality, individual rights vs. common good, distributive justice.
Worked Examples & Case Studies
Example 1: Applying Kant's Categorical Imperative
Scenario: Is it morally permissible to lie to protect someone from harm?
Kant's Analysis: Universalize the maxim: "I will lie when it protects someone." If everyone lied when convenient, trust in communication would collapse — the very act of lying presupposes trust. Thus, the maxim is self-contradictory when universalized. Kant concludes: Lying is always morally wrong, even to protect someone. The duty to tell the truth is absolute (deontological ethics).
Contrast (Utilitarianism): Weigh consequences. If lying saves a life, the happiness produced outweighs the harm. Lying is morally required in this case. Shows the fundamental difference between duty-based and outcome-based ethics.
Example 2: Plato's Allegory of the Cave
Allegory: Prisoners chained in a cave, facing a wall. Behind them, a fire casts shadows of puppets on the wall. Prisoners mistake shadows for reality. One prisoner escapes, sees the sun (Form of the Good), returns to free others but is killed.
Philosophical Meaning: (1) The visible world = shadows (appearances, opinions), (2) The intelligible world = Forms (true reality, knowledge), (3) The sun = Form of the Good (source of truth and being), (4) The philosopher = escaped prisoner who sees truth, (5) Education = turning the soul toward truth, not filling it with facts. Influenced Western philosophy's distinction between appearance and reality.
Example 3: Rawls' Veil of Ignorance — Designing a Just Society
Thought Experiment: Design society's basic structure without knowing your future position (class, race, gender, talents, religion). This ensures impartiality.
Rawls' Two Principles of Justice:
1. Equal basic liberties for all (freedom of speech, conscience, voting)
2. Social and economic inequalities must satisfy: (a) Fair equality of opportunity, (b) Difference Principle — inequalities only justified if they benefit the least advantaged members of society.
Application: A progressive tax system is just because it benefits the worst-off. Meritocracy alone is unfair because talents are morally arbitrary (no one deserves their genetic lottery). The veil of ignorance strips away self-interest, revealing principles any rational person would accept.
Case Study: The Trolley Problem — Ethics in Action
Scenario: A runaway trolley will kill 5 people. You can pull a lever diverting it to a side track where it will kill 1 person. Most people say pull the lever.
Variant: Same scenario, but you must push a large person off a bridge to stop the trolley. Most people say don't push.
Philosophical Analysis: (1) Utilitarianism: Both cases — save 5, kill 1 → pull/push. (2) Deontology: Pushing uses person as means — forbidden. Pulling lever is redirecting existing threat — permissible. (3) Doctrine of Double Effect: Intending death vs. foreseeing death matters. (4) Reveals tension between consequentialist and deontological intuitions. (5) Real-world applications: autonomous weapons, self-driving car algorithms, medical triage.
Case Study: Descartes' Cogito — Foundations of Knowledge
Method: Descartes doubted everything that could possibly be doubted: senses (can deceive), mathematics (evil demon could deceive), the external world (dream argument).
Discovery: Even if deceived, the act of thinking proves existence: "Cogito, ergo sum" (I think, therefore I am). The very act of doubting confirms a doubter exists.
Philosophical Significance: (1) Foundationalism — builds knowledge from indubitable foundation, (2) Rationalism — reason is primary source of knowledge, (3) Mind-body dualism — thinking substance (res cogitans) distinct from extended substance (res extensa), (4) Influenced modern philosophy's turn to subjectivity and epistemology.
Practice Problems
Problem 1: Identify the logical fallacy: "Everyone knows that students today are lazier than previous generations."
Answer: Appeal to popularity (argumentum ad populum) — assuming something is true because many believe it. Also hasty generalization — no evidence provided.
Problem 2: What is the difference between utilitarianism and deontological ethics? Give an example where they conflict.
Answer: Utilitarianism judges actions by outcomes (greatest good for greatest number). Deontology judges actions by rules/duties (never lie, regardless of consequences). Conflict: Lying to save a life — utilitarianism says lie (saves life), deontology says don't lie (duty to truth).
Problem 3: State Modus Ponens and Modus Tollens. Give an example of each.
Answer: Modus Ponens: If P then Q. P. Therefore Q. Example: If it rains, streets are wet. It is raining. Therefore streets are wet. Modus Tollens: If P then Q. Not Q. Therefore not P. Example: If it rains, streets are wet. Streets are not wet. Therefore it is not raining.
Problem 4: What is the mind-body problem? Name two philosophical positions on it.
Answer: The mind-body problem asks how mental states (thoughts, feelings) relate to physical states (brain processes). Positions: (1) Dualism (Descartes) — mind and body are distinct substances that interact. (2) Physicalism/Materialism — mental states are identical to brain states.
Problem 5: Explain Aristotle's Golden Mean with three examples.
Answer: Virtue lies between excess and deficiency. Courage = mean between cowardice (deficiency) and recklessness (excess). Generosity = mean between stinginess (deficiency) and wastefulness (excess). Confidence = mean between self-deprecation (deficiency) and arrogance (excess).
Problem 6: What does "existence precedes essence" mean (Sartre)?
Answer: Sartre's existentialist principle: Humans have no pre-defined nature or purpose. We are "thrown into existence" first, then define ourselves through choices. We are "condemned to be free" — fully responsible for who we become. We cannot blame God, nature, or circumstances for our choices.
Problem 7: Apply Rawls' Veil of Ignorance to: Should university admission be based on merit or affirmative action?
Answer: Behind the veil (not knowing your race/class), you'd choose: Merit system seems fair but ignores systemic disadvantages. Affirmative action corrects historical injustices. Rawls would likely support affirmative action — the difference principle allows inequalities only if they benefit the least advantaged. Fair equality of opportunity requires leveling the playing field.
Problem 8: What is the Gettier Problem? Why does it challenge the definition of knowledge?
Answer: Gettier (1963) showed that justified true belief is not sufficient for knowledge. Example: Smith is justified in believing Jones will get the job (evidence: Jones has 10 coins). Smith believes "man who will get the job has 10 coins." Smith himself gets the job and has 10 coins. His belief is true and justified, but by luck, not knowledge. Led to theories: defeasible justification, reliabilism, virtue epistemology.