Philosophy cheat sheet

Gettier cases: justified true belief fails as knowledge when justification is true by luck; standard responses are no-false-lemmas, causal, reliabilist, and virtue accounts.

JTB analysis: S knows that p iff p is true, S believes p, and S is justified in believing p; each condition is necessary, jointly contested as sufficient.

A priori vs a posteriori: a priori justification does not depend on experience beyond concept possession; a posteriori depends on sensory or introspective evidence.

Analytic vs synthetic: a sentence is analytic if its truth follows from meaning alone (bachelors are unmarried); synthetic if its truth depends on how the world is.

Kant's Copernican turn: necessary truths can be synthetic a priori (arithmetic, causality) because the mind imposes forms of intuition and categories on experience.

Internalism vs externalism about justification: internalism requires accessible reasons; externalism (reliabilism) requires a truth-conducive belief-forming process.

Realism vs anti-realism: realism holds truth is mind-independent; anti-realism (idealism, verificationism, constructivism) ties truth to mind, evidence, or practice.

Identity theory and functionalism in mind: type identity equates mental states with brain states; functionalism individuates mental states by causal role, allowing multiple realizability.

Personal identity criteria: psychological continuity (Locke, Parfit) vs bodily/brain continuity; fission cases pressure any criterion to be non-arbitrary and transitive.

Kant's categorical imperative, formula of universal law: act only on maxims you could will as universal law; formula of humanity: treat persons as ends, never merely as means.

Act vs rule utilitarianism: act evaluates each action by expected utility; rule evaluates actions by rules whose general acceptance maximizes utility.

Mill's harm principle: coercion is justified only to prevent harm to others; self-regarding conduct is protected, though competence and indirect harms complicate the line.

Doctrine of double effect: an unintended bad effect may be permitted if the act is good or neutral, the bad effect is not the means, and proportionality holds.

Trolley vs footbridge: the footbridge case adds using a person as a means, which most deontological accounts forbid while consequentialist accounts may permit.

Rawls's difference principle: social and economic inequalities are just only if they benefit the least advantaged position, constrained by fair equality of opportunity.

Aristotelian virtue ethics: virtue is a stable disposition to feel and act according to the mean relative to us, determined by practical wisdom (phronesis).

Moral realism vs anti-realism: realism holds mind-independent moral facts; expressivism and error theory deny that moral judgments report such facts.

Weakness of will (akrasia): action against one's better judgment; explained by divided motivation, temporal discounting, or failure of practical reasoning.

Validity: an argument is valid iff no possible world makes all premises true and the conclusion false; soundness adds that all premises are actually true.

Modus ponens: from P and P→Q infer Q. Modus tollens: from ¬Q and P→Q infer ¬P. Affirming the consequent and denying the antecedent are invalid.

Truth tables: n distinct sentence letters yield 2^n rows; a tautology is true on every row, a contradiction false on every row, a contingency varies.

Quantifier negation: ¬∀xPx ≡ ∃x¬Px and ¬∃xPx ≡ ∀x¬Px; scope errors produce fallacies such as illicit conversion of A-propositions.

Inductive strength is graded, not binary: a strong inductive argument makes the conclusion probable given true premises; it can still have a false conclusion.

Informal fallacies: ad hominem, straw man, false dilemma, begging the question, equivocation, hasty generalization, post hoc, and appeal to ignorance.

Correlation is not causation: ruling out reverse causation and confounders requires controlled comparison, randomization, or natural experiments.

Bayes's theorem: P(H|E) = P(E|H)P(H) / P(E); base-rate neglect arises when P(H) is ignored in favor of P(E|H).

Necessary vs sufficient conditions: A is sufficient for B if A guarantees B; A is necessary for B if no B occurs without A; confusing them yields converse errors.

Plato's Forms: changeless, non-sensible objects of knowledge; particulars 'participate' in them; the divided line ranks images, sensible things, mathematical objects, and Forms.

Aristotle's four causes: material, efficient, formal, and final; the final cause is the end or function (telos) that explains a natural process.

Aristotle's substance and hylomorphism: primary substances are concrete composites of matter and form; essence is stated in the definition of the species.

Socratic method (elenchus): cross-examination exposes inconsistency in an interlocutor's beliefs, producing aporia rather than a positive doctrine.

Stoic ethics: virtue is the only good and consists in living according to nature and reason; preferred indifferents (health, wealth) are not goods.

Epicurean ethics: pleasure is the highest good, understood as absence of pain (katastematic) rather than active indulgence; ataraxia is tranquility.

Augustine on evil and will: evil is privation of good, not a substance; sin originates in a disordered will, and grace is required for right willing.

Aquinas's five ways: motion, efficient causation, contingency, gradation, and teleology; each argues from an observed feature to a first cause or necessary being.

Medieval universals debate: realism (universals exist independently), conceptualism (they exist only in the mind), and nominalism (only particulars exist).

Descartes's method of doubt: suspend assent to anything dubitable; the cogito ('I think, therefore I am') survives hyperbolic doubt as an indubitable starting point.

Hume's fork: relations of ideas (a priori, analytic) vs matters of fact (a posteriori); causal necessity is not observed but projected by custom and habit.

Hume's is-ought gap: descriptive premises alone do not entail a normative conclusion; deriving 'ought' from 'is' requires an additional normative premise.

Locke's empiricism: the mind is a tabula rasa; all ideas derive from sensation and reflection, and primary qualities resemble real features while secondary qualities do not.

Kant's synthetic a priori and the transcendental deduction: categories are conditions of possible experience, so empirical knowledge presupposes them.

Hegel's dialectic: contradiction drives development through thesis, antithesis, and synthesis; Spirit (Geist) realizes freedom through historical institutions.

Nietzsche: master and slave moralities; slave morality inverts strength into 'evil'; the will to power and eternal recurrence are central thought experiments.

Logical positivism: the verification principle holds that meaningful statements are analytic or empirically verifiable; it is self-undermining on its own criterion.

Phenomenology (Husserl, Heidegger): bracket the natural attitude to describe lived experience; Heidegger's Being-in-the-world replaces the subject-object model.

Hobbes's state of nature: rough equality of power yields competition, diffidence, and glory; the social contract authorizes a sovereign to escape the war of all against all.

Locke's social contract: natural rights to life, liberty, and property precede government; legitimate government rests on consent and may be resisted when it violates trust.

Rousseau's general will: legitimate authority expresses the general will aimed at the common good; citizens who dissent can be 'forced to be free'.

Mill's harm principle and free speech: restricting expression is justified only to prevent harm; false opinions tested in the 'marketplace' strengthen true belief.

Rawls's original position: behind a veil of ignorance, parties choose principles of justice; the two principles are equal basic liberties and fair equality of opportunity plus the difference principle.

Nozick's entitlement theory: holdings are just if acquired justly, transferred justly, or rectified; patterned distributive principles violate liberty and self-ownership.

Berlin's two concepts of liberty: negative liberty is non-interference; positive liberty is self-mastery, which can license paternalist coercion in the name of a 'true self'.

Marx: historical materialism explains institutions by productive forces and relations of production; alienation under capitalism separates workers from product and species-being.

Civil disobedience (Rawls, King): public, nonviolent, conscientious breach of law aimed at injustice, addressed to the majority's sense of justice and accepting punishment.

Kant's aesthetic judgment: judgments of taste are subjective (grounded in feeling) yet claim universal assent and are disinterested, without concepts or purposes.

Hume's standard of taste: aesthetic judgments are sentiments, but a standard emerges from the joint verdict of true judges with delicacy of taste and freedom from prejudice.

The intentional fallacy (Wimsatt and Beardsley): the artist's intentions are not the standard for interpreting a work; the work's meaning derives from public textual features.

The problem of consciousness: the hard problem (Chalmers) is why physical processes give rise to subjective experience; easy problems concern functional capacities.

Qualia: intrinsic, subjective experiential properties (the felt redness of red); inverted-spectrum and zombie cases pressure physicalist accounts.

Chalmers's conceivability argument: if philosophical zombies are conceivable and conceivability entails possibility, then consciousness is not entailed by the physical.

Functionalism and multiple realizability: mental states are causal roles realizable in many substrates, so mental kinds are not identical to specific brain kinds.

Searle's Chinese Room: symbol manipulation by rule does not produce semantic understanding, so syntax alone is insufficient for semantics or genuine intentionality.

The extended mind (Clark and Chalmers): cognitive processes can extend into the environment when external resources are reliably available, accessible, and endorsed.

Gettier cases: justified true belief fails as knowledge when justification is true by luck; standard responses are no-false-lemmas, causal, reliabilist, and virtue accounts.

JTB analysis: S knows that p iff p is true, S believes p, and S is justified in believing p; each condition is necessary, jointly contested as sufficient.

A priori vs a posteriori: a priori justification does not depend on experience beyond concept possession; a posteriori depends on sensory or introspective evidence.

Analytic vs synthetic: a sentence is analytic if its truth follows from meaning alone (bachelors are unmarried); synthetic if its truth depends on how the world is.

Kant's Copernican turn: necessary truths can be synthetic a priori (arithmetic, causality) because the mind imposes forms of intuition and categories on experience.

Internalism vs externalism about justification: internalism requires accessible reasons; externalism (reliabilism) requires a truth-conducive belief-forming process.

Realism vs anti-realism: realism holds truth is mind-independent; anti-realism (idealism, verificationism, constructivism) ties truth to mind, evidence, or practice.

Identity theory and functionalism in mind: type identity equates mental states with brain states; functionalism individuates mental states by causal role, allowing multiple realizability.

Personal identity criteria: psychological continuity (Locke, Parfit) vs bodily/brain continuity; fission cases pressure any criterion to be non-arbitrary and transitive.

Kant's categorical imperative, formula of universal law: act only on maxims you could will as universal law; formula of humanity: treat persons as ends, never merely as means.

Act vs rule utilitarianism: act evaluates each action by expected utility; rule evaluates actions by rules whose general acceptance maximizes utility.

Mill's harm principle: coercion is justified only to prevent harm to others; self-regarding conduct is protected, though competence and indirect harms complicate the line.

Doctrine of double effect: an unintended bad effect may be permitted if the act is good or neutral, the bad effect is not the means, and proportionality holds.

Trolley vs footbridge: the footbridge case adds using a person as a means, which most deontological accounts forbid while consequentialist accounts may permit.

Rawls's difference principle: social and economic inequalities are just only if they benefit the least advantaged position, constrained by fair equality of opportunity.

Aristotelian virtue ethics: virtue is a stable disposition to feel and act according to the mean relative to us, determined by practical wisdom (phronesis).

Moral realism vs anti-realism: realism holds mind-independent moral facts; expressivism and error theory deny that moral judgments report such facts.

Weakness of will (akrasia): action against one's better judgment; explained by divided motivation, temporal discounting, or failure of practical reasoning.

Validity: an argument is valid iff no possible world makes all premises true and the conclusion false; soundness adds that all premises are actually true.

Modus ponens: from P and P→Q infer Q. Modus tollens: from ¬Q and P→Q infer ¬P. Affirming the consequent and denying the antecedent are invalid.

Truth tables: n distinct sentence letters yield 2^n rows; a tautology is true on every row, a contradiction false on every row, a contingency varies.

Quantifier negation: ¬∀xPx ≡ ∃x¬Px and ¬∃xPx ≡ ∀x¬Px; scope errors produce fallacies such as illicit conversion of A-propositions.

Inductive strength is graded, not binary: a strong inductive argument makes the conclusion probable given true premises; it can still have a false conclusion.

Informal fallacies: ad hominem, straw man, false dilemma, begging the question, equivocation, hasty generalization, post hoc, and appeal to ignorance.

Correlation is not causation: ruling out reverse causation and confounders requires controlled comparison, randomization, or natural experiments.

Bayes's theorem: P(H|E) = P(E|H)P(H) / P(E); base-rate neglect arises when P(H) is ignored in favor of P(E|H).

Necessary vs sufficient conditions: A is sufficient for B if A guarantees B; A is necessary for B if no B occurs without A; confusing them yields converse errors.

Plato's Forms: changeless, non-sensible objects of knowledge; particulars 'participate' in them; the divided line ranks images, sensible things, mathematical objects, and Forms.

Aristotle's four causes: material, efficient, formal, and final; the final cause is the end or function (telos) that explains a natural process.

Aristotle's substance and hylomorphism: primary substances are concrete composites of matter and form; essence is stated in the definition of the species.

Socratic method (elenchus): cross-examination exposes inconsistency in an interlocutor's beliefs, producing aporia rather than a positive doctrine.

Stoic ethics: virtue is the only good and consists in living according to nature and reason; preferred indifferents (health, wealth) are not goods.

Epicurean ethics: pleasure is the highest good, understood as absence of pain (katastematic) rather than active indulgence; ataraxia is tranquility.

Augustine on evil and will: evil is privation of good, not a substance; sin originates in a disordered will, and grace is required for right willing.

Aquinas's five ways: motion, efficient causation, contingency, gradation, and teleology; each argues from an observed feature to a first cause or necessary being.

Medieval universals debate: realism (universals exist independently), conceptualism (they exist only in the mind), and nominalism (only particulars exist).

Descartes's method of doubt: suspend assent to anything dubitable; the cogito ('I think, therefore I am') survives hyperbolic doubt as an indubitable starting point.

Hume's fork: relations of ideas (a priori, analytic) vs matters of fact (a posteriori); causal necessity is not observed but projected by custom and habit.

Hume's is-ought gap: descriptive premises alone do not entail a normative conclusion; deriving 'ought' from 'is' requires an additional normative premise.

Locke's empiricism: the mind is a tabula rasa; all ideas derive from sensation and reflection, and primary qualities resemble real features while secondary qualities do not.

Kant's synthetic a priori and the transcendental deduction: categories are conditions of possible experience, so empirical knowledge presupposes them.

Hegel's dialectic: contradiction drives development through thesis, antithesis, and synthesis; Spirit (Geist) realizes freedom through historical institutions.

Nietzsche: master and slave moralities; slave morality inverts strength into 'evil'; the will to power and eternal recurrence are central thought experiments.

Logical positivism: the verification principle holds that meaningful statements are analytic or empirically verifiable; it is self-undermining on its own criterion.

Phenomenology (Husserl, Heidegger): bracket the natural attitude to describe lived experience; Heidegger's Being-in-the-world replaces the subject-object model.

Hobbes's state of nature: rough equality of power yields competition, diffidence, and glory; the social contract authorizes a sovereign to escape the war of all against all.

Locke's social contract: natural rights to life, liberty, and property precede government; legitimate government rests on consent and may be resisted when it violates trust.

Rousseau's general will: legitimate authority expresses the general will aimed at the common good; citizens who dissent can be 'forced to be free'.

Mill's harm principle and free speech: restricting expression is justified only to prevent harm; false opinions tested in the 'marketplace' strengthen true belief.

Rawls's original position: behind a veil of ignorance, parties choose principles of justice; the two principles are equal basic liberties and fair equality of opportunity plus the difference principle.

Nozick's entitlement theory: holdings are just if acquired justly, transferred justly, or rectified; patterned distributive principles violate liberty and self-ownership.

Berlin's two concepts of liberty: negative liberty is non-interference; positive liberty is self-mastery, which can license paternalist coercion in the name of a 'true self'.

Marx: historical materialism explains institutions by productive forces and relations of production; alienation under capitalism separates workers from product and species-being.

Civil disobedience (Rawls, King): public, nonviolent, conscientious breach of law aimed at injustice, addressed to the majority's sense of justice and accepting punishment.

Kant's aesthetic judgment: judgments of taste are subjective (grounded in feeling) yet claim universal assent and are disinterested, without concepts or purposes.

Hume's standard of taste: aesthetic judgments are sentiments, but a standard emerges from the joint verdict of true judges with delicacy of taste and freedom from prejudice.

The intentional fallacy (Wimsatt and Beardsley): the artist's intentions are not the standard for interpreting a work; the work's meaning derives from public textual features.

The problem of consciousness: the hard problem (Chalmers) is why physical processes give rise to subjective experience; easy problems concern functional capacities.

Qualia: intrinsic, subjective experiential properties (the felt redness of red); inverted-spectrum and zombie cases pressure physicalist accounts.

Chalmers's conceivability argument: if philosophical zombies are conceivable and conceivability entails possibility, then consciousness is not entailed by the physical.

Functionalism and multiple realizability: mental states are causal roles realizable in many substrates, so mental kinds are not identical to specific brain kinds.

Searle's Chinese Room: symbol manipulation by rule does not produce semantic understanding, so syntax alone is insufficient for semantics or genuine intentionality.

The extended mind (Clark and Chalmers): cognitive processes can extend into the environment when external resources are reliably available, accessible, and endorsed.

Gettier cases: justified true belief fails as knowledge when justification is true by luck; standard responses are no-false-lemmas, causal, reliabilist, and virtue accounts.

JTB analysis: S knows that p iff p is true, S believes p, and S is justified in believing p; each condition is necessary, jointly contested as sufficient.

A priori vs a posteriori: a priori justification does not depend on experience beyond concept possession; a posteriori depends on sensory or introspective evidence.

Analytic vs synthetic: a sentence is analytic if its truth follows from meaning alone (bachelors are unmarried); synthetic if its truth depends on how the world is.

Kant's Copernican turn: necessary truths can be synthetic a priori (arithmetic, causality) because the mind imposes forms of intuition and categories on experience.

Internalism vs externalism about justification: internalism requires accessible reasons; externalism (reliabilism) requires a truth-conducive belief-forming process.

Realism vs anti-realism: realism holds truth is mind-independent; anti-realism (idealism, verificationism, constructivism) ties truth to mind, evidence, or practice.

Identity theory and functionalism in mind: type identity equates mental states with brain states; functionalism individuates mental states by causal role, allowing multiple realizability.

Personal identity criteria: psychological continuity (Locke, Parfit) vs bodily/brain continuity; fission cases pressure any criterion to be non-arbitrary and transitive.

Kant's categorical imperative, formula of universal law: act only on maxims you could will as universal law; formula of humanity: treat persons as ends, never merely as means.

Act vs rule utilitarianism: act evaluates each action by expected utility; rule evaluates actions by rules whose general acceptance maximizes utility.

Mill's harm principle: coercion is justified only to prevent harm to others; self-regarding conduct is protected, though competence and indirect harms complicate the line.

Doctrine of double effect: an unintended bad effect may be permitted if the act is good or neutral, the bad effect is not the means, and proportionality holds.

Trolley vs footbridge: the footbridge case adds using a person as a means, which most deontological accounts forbid while consequentialist accounts may permit.

Rawls's difference principle: social and economic inequalities are just only if they benefit the least advantaged position, constrained by fair equality of opportunity.

Aristotelian virtue ethics: virtue is a stable disposition to feel and act according to the mean relative to us, determined by practical wisdom (phronesis).

Moral realism vs anti-realism: realism holds mind-independent moral facts; expressivism and error theory deny that moral judgments report such facts.

Weakness of will (akrasia): action against one's better judgment; explained by divided motivation, temporal discounting, or failure of practical reasoning.

Validity: an argument is valid iff no possible world makes all premises true and the conclusion false; soundness adds that all premises are actually true.

Modus ponens: from P and P→Q infer Q. Modus tollens: from ¬Q and P→Q infer ¬P. Affirming the consequent and denying the antecedent are invalid.

Truth tables: n distinct sentence letters yield 2^n rows; a tautology is true on every row, a contradiction false on every row, a contingency varies.

Quantifier negation: ¬∀xPx ≡ ∃x¬Px and ¬∃xPx ≡ ∀x¬Px; scope errors produce fallacies such as illicit conversion of A-propositions.

Inductive strength is graded, not binary: a strong inductive argument makes the conclusion probable given true premises; it can still have a false conclusion.

Informal fallacies: ad hominem, straw man, false dilemma, begging the question, equivocation, hasty generalization, post hoc, and appeal to ignorance.

Correlation is not causation: ruling out reverse causation and confounders requires controlled comparison, randomization, or natural experiments.

Bayes's theorem: P(H|E) = P(E|H)P(H) / P(E); base-rate neglect arises when P(H) is ignored in favor of P(E|H).

Necessary vs sufficient conditions: A is sufficient for B if A guarantees B; A is necessary for B if no B occurs without A; confusing them yields converse errors.

Plato's Forms: changeless, non-sensible objects of knowledge; particulars 'participate' in them; the divided line ranks images, sensible things, mathematical objects, and Forms.

Aristotle's four causes: material, efficient, formal, and final; the final cause is the end or function (telos) that explains a natural process.

Aristotle's substance and hylomorphism: primary substances are concrete composites of matter and form; essence is stated in the definition of the species.

Socratic method (elenchus): cross-examination exposes inconsistency in an interlocutor's beliefs, producing aporia rather than a positive doctrine.

Stoic ethics: virtue is the only good and consists in living according to nature and reason; preferred indifferents (health, wealth) are not goods.

Epicurean ethics: pleasure is the highest good, understood as absence of pain (katastematic) rather than active indulgence; ataraxia is tranquility.

Augustine on evil and will: evil is privation of good, not a substance; sin originates in a disordered will, and grace is required for right willing.

Aquinas's five ways: motion, efficient causation, contingency, gradation, and teleology; each argues from an observed feature to a first cause or necessary being.

Medieval universals debate: realism (universals exist independently), conceptualism (they exist only in the mind), and nominalism (only particulars exist).

Descartes's method of doubt: suspend assent to anything dubitable; the cogito ('I think, therefore I am') survives hyperbolic doubt as an indubitable starting point.

Hume's fork: relations of ideas (a priori, analytic) vs matters of fact (a posteriori); causal necessity is not observed but projected by custom and habit.

Hume's is-ought gap: descriptive premises alone do not entail a normative conclusion; deriving 'ought' from 'is' requires an additional normative premise.

Locke's empiricism: the mind is a tabula rasa; all ideas derive from sensation and reflection, and primary qualities resemble real features while secondary qualities do not.

Kant's synthetic a priori and the transcendental deduction: categories are conditions of possible experience, so empirical knowledge presupposes them.

Hegel's dialectic: contradiction drives development through thesis, antithesis, and synthesis; Spirit (Geist) realizes freedom through historical institutions.

Nietzsche: master and slave moralities; slave morality inverts strength into 'evil'; the will to power and eternal recurrence are central thought experiments.

Logical positivism: the verification principle holds that meaningful statements are analytic or empirically verifiable; it is self-undermining on its own criterion.

Phenomenology (Husserl, Heidegger): bracket the natural attitude to describe lived experience; Heidegger's Being-in-the-world replaces the subject-object model.

Hobbes's state of nature: rough equality of power yields competition, diffidence, and glory; the social contract authorizes a sovereign to escape the war of all against all.

Locke's social contract: natural rights to life, liberty, and property precede government; legitimate government rests on consent and may be resisted when it violates trust.

Rousseau's general will: legitimate authority expresses the general will aimed at the common good; citizens who dissent can be 'forced to be free'.

Mill's harm principle and free speech: restricting expression is justified only to prevent harm; false opinions tested in the 'marketplace' strengthen true belief.

Rawls's original position: behind a veil of ignorance, parties choose principles of justice; the two principles are equal basic liberties and fair equality of opportunity plus the difference principle.

Nozick's entitlement theory: holdings are just if acquired justly, transferred justly, or rectified; patterned distributive principles violate liberty and self-ownership.

Berlin's two concepts of liberty: negative liberty is non-interference; positive liberty is self-mastery, which can license paternalist coercion in the name of a 'true self'.

Marx: historical materialism explains institutions by productive forces and relations of production; alienation under capitalism separates workers from product and species-being.

Civil disobedience (Rawls, King): public, nonviolent, conscientious breach of law aimed at injustice, addressed to the majority's sense of justice and accepting punishment.

Kant's aesthetic judgment: judgments of taste are subjective (grounded in feeling) yet claim universal assent and are disinterested, without concepts or purposes.

Hume's standard of taste: aesthetic judgments are sentiments, but a standard emerges from the joint verdict of true judges with delicacy of taste and freedom from prejudice.

The intentional fallacy (Wimsatt and Beardsley): the artist's intentions are not the standard for interpreting a work; the work's meaning derives from public textual features.

The problem of consciousness: the hard problem (Chalmers) is why physical processes give rise to subjective experience; easy problems concern functional capacities.

Qualia: intrinsic, subjective experiential properties (the felt redness of red); inverted-spectrum and zombie cases pressure physicalist accounts.

Chalmers's conceivability argument: if philosophical zombies are conceivable and conceivability entails possibility, then consciousness is not entailed by the physical.

Functionalism and multiple realizability: mental states are causal roles realizable in many substrates, so mental kinds are not identical to specific brain kinds.

Searle's Chinese Room: symbol manipulation by rule does not produce semantic understanding, so syntax alone is insufficient for semantics or genuine intentionality.

The extended mind (Clark and Chalmers): cognitive processes can extend into the environment when external resources are reliably available, accessible, and endorsed.

Gettier cases: justified true belief fails as knowledge when justification is true by luck; standard responses are no-false-lemmas, causal, reliabilist, and virtue accounts.

JTB analysis: S knows that p iff p is true, S believes p, and S is justified in believing p; each condition is necessary, jointly contested as sufficient.

A priori vs a posteriori: a priori justification does not depend on experience beyond concept possession; a posteriori depends on sensory or introspective evidence.

Analytic vs synthetic: a sentence is analytic if its truth follows from meaning alone (bachelors are unmarried); synthetic if its truth depends on how the world is.

Kant's Copernican turn: necessary truths can be synthetic a priori (arithmetic, causality) because the mind imposes forms of intuition and categories on experience.

Internalism vs externalism about justification: internalism requires accessible reasons; externalism (reliabilism) requires a truth-conducive belief-forming process.

Realism vs anti-realism: realism holds truth is mind-independent; anti-realism (idealism, verificationism, constructivism) ties truth to mind, evidence, or practice.

Identity theory and functionalism in mind: type identity equates mental states with brain states; functionalism individuates mental states by causal role, allowing multiple realizability.

Personal identity criteria: psychological continuity (Locke, Parfit) vs bodily/brain continuity; fission cases pressure any criterion to be non-arbitrary and transitive.

Kant's categorical imperative, formula of universal law: act only on maxims you could will as universal law; formula of humanity: treat persons as ends, never merely as means.

Act vs rule utilitarianism: act evaluates each action by expected utility; rule evaluates actions by rules whose general acceptance maximizes utility.

Mill's harm principle: coercion is justified only to prevent harm to others; self-regarding conduct is protected, though competence and indirect harms complicate the line.

Doctrine of double effect: an unintended bad effect may be permitted if the act is good or neutral, the bad effect is not the means, and proportionality holds.

Trolley vs footbridge: the footbridge case adds using a person as a means, which most deontological accounts forbid while consequentialist accounts may permit.

Rawls's difference principle: social and economic inequalities are just only if they benefit the least advantaged position, constrained by fair equality of opportunity.

Aristotelian virtue ethics: virtue is a stable disposition to feel and act according to the mean relative to us, determined by practical wisdom (phronesis).

Moral realism vs anti-realism: realism holds mind-independent moral facts; expressivism and error theory deny that moral judgments report such facts.

Weakness of will (akrasia): action against one's better judgment; explained by divided motivation, temporal discounting, or failure of practical reasoning.

Validity: an argument is valid iff no possible world makes all premises true and the conclusion false; soundness adds that all premises are actually true.

Modus ponens: from P and P→Q infer Q. Modus tollens: from ¬Q and P→Q infer ¬P. Affirming the consequent and denying the antecedent are invalid.

Truth tables: n distinct sentence letters yield 2^n rows; a tautology is true on every row, a contradiction false on every row, a contingency varies.

Quantifier negation: ¬∀xPx ≡ ∃x¬Px and ¬∃xPx ≡ ∀x¬Px; scope errors produce fallacies such as illicit conversion of A-propositions.

Inductive strength is graded, not binary: a strong inductive argument makes the conclusion probable given true premises; it can still have a false conclusion.

Informal fallacies: ad hominem, straw man, false dilemma, begging the question, equivocation, hasty generalization, post hoc, and appeal to ignorance.

Correlation is not causation: ruling out reverse causation and confounders requires controlled comparison, randomization, or natural experiments.

Bayes's theorem: P(H|E) = P(E|H)P(H) / P(E); base-rate neglect arises when P(H) is ignored in favor of P(E|H).

Necessary vs sufficient conditions: A is sufficient for B if A guarantees B; A is necessary for B if no B occurs without A; confusing them yields converse errors.

Plato's Forms: changeless, non-sensible objects of knowledge; particulars 'participate' in them; the divided line ranks images, sensible things, mathematical objects, and Forms.

Aristotle's four causes: material, efficient, formal, and final; the final cause is the end or function (telos) that explains a natural process.

Aristotle's substance and hylomorphism: primary substances are concrete composites of matter and form; essence is stated in the definition of the species.

Socratic method (elenchus): cross-examination exposes inconsistency in an interlocutor's beliefs, producing aporia rather than a positive doctrine.

Stoic ethics: virtue is the only good and consists in living according to nature and reason; preferred indifferents (health, wealth) are not goods.

Epicurean ethics: pleasure is the highest good, understood as absence of pain (katastematic) rather than active indulgence; ataraxia is tranquility.

Augustine on evil and will: evil is privation of good, not a substance; sin originates in a disordered will, and grace is required for right willing.

Aquinas's five ways: motion, efficient causation, contingency, gradation, and teleology; each argues from an observed feature to a first cause or necessary being.

Medieval universals debate: realism (universals exist independently), conceptualism (they exist only in the mind), and nominalism (only particulars exist).

Descartes's method of doubt: suspend assent to anything dubitable; the cogito ('I think, therefore I am') survives hyperbolic doubt as an indubitable starting point.

Hume's fork: relations of ideas (a priori, analytic) vs matters of fact (a posteriori); causal necessity is not observed but projected by custom and habit.

Hume's is-ought gap: descriptive premises alone do not entail a normative conclusion; deriving 'ought' from 'is' requires an additional normative premise.

Locke's empiricism: the mind is a tabula rasa; all ideas derive from sensation and reflection, and primary qualities resemble real features while secondary qualities do not.

Kant's synthetic a priori and the transcendental deduction: categories are conditions of possible experience, so empirical knowledge presupposes them.

Hegel's dialectic: contradiction drives development through thesis, antithesis, and synthesis; Spirit (Geist) realizes freedom through historical institutions.

Nietzsche: master and slave moralities; slave morality inverts strength into 'evil'; the will to power and eternal recurrence are central thought experiments.

Logical positivism: the verification principle holds that meaningful statements are analytic or empirically verifiable; it is self-undermining on its own criterion.

Phenomenology (Husserl, Heidegger): bracket the natural attitude to describe lived experience; Heidegger's Being-in-the-world replaces the subject-object model.

Hobbes's state of nature: rough equality of power yields competition, diffidence, and glory; the social contract authorizes a sovereign to escape the war of all against all.

Locke's social contract: natural rights to life, liberty, and property precede government; legitimate government rests on consent and may be resisted when it violates trust.

Rousseau's general will: legitimate authority expresses the general will aimed at the common good; citizens who dissent can be 'forced to be free'.

Mill's harm principle and free speech: restricting expression is justified only to prevent harm; false opinions tested in the 'marketplace' strengthen true belief.

Rawls's original position: behind a veil of ignorance, parties choose principles of justice; the two principles are equal basic liberties and fair equality of opportunity plus the difference principle.

Nozick's entitlement theory: holdings are just if acquired justly, transferred justly, or rectified; patterned distributive principles violate liberty and self-ownership.

Berlin's two concepts of liberty: negative liberty is non-interference; positive liberty is self-mastery, which can license paternalist coercion in the name of a 'true self'.

Marx: historical materialism explains institutions by productive forces and relations of production; alienation under capitalism separates workers from product and species-being.

Civil disobedience (Rawls, King): public, nonviolent, conscientious breach of law aimed at injustice, addressed to the majority's sense of justice and accepting punishment.

Kant's aesthetic judgment: judgments of taste are subjective (grounded in feeling) yet claim universal assent and are disinterested, without concepts or purposes.

Hume's standard of taste: aesthetic judgments are sentiments, but a standard emerges from the joint verdict of true judges with delicacy of taste and freedom from prejudice.

The intentional fallacy (Wimsatt and Beardsley): the artist's intentions are not the standard for interpreting a work; the work's meaning derives from public textual features.

The problem of consciousness: the hard problem (Chalmers) is why physical processes give rise to subjective experience; easy problems concern functional capacities.

Qualia: intrinsic, subjective experiential properties (the felt redness of red); inverted-spectrum and zombie cases pressure physicalist accounts.

Chalmers's conceivability argument: if philosophical zombies are conceivable and conceivability entails possibility, then consciousness is not entailed by the physical.

Functionalism and multiple realizability: mental states are causal roles realizable in many substrates, so mental kinds are not identical to specific brain kinds.

Searle's Chinese Room: symbol manipulation by rule does not produce semantic understanding, so syntax alone is insufficient for semantics or genuine intentionality.

The extended mind (Clark and Chalmers): cognitive processes can extend into the environment when external resources are reliably available, accessible, and endorsed.

Gettier cases: justified true belief fails as knowledge when justification is true by luck; standard responses are no-false-lemmas, causal, reliabilist, and virtue accounts.

JTB analysis: S knows that p iff p is true, S believes p, and S is justified in believing p; each condition is necessary, jointly contested as sufficient.

A priori vs a posteriori: a priori justification does not depend on experience beyond concept possession; a posteriori depends on sensory or introspective evidence.

Analytic vs synthetic: a sentence is analytic if its truth follows from meaning alone (bachelors are unmarried); synthetic if its truth depends on how the world is.

Kant's Copernican turn: necessary truths can be synthetic a priori (arithmetic, causality) because the mind imposes forms of intuition and categories on experience.

Internalism vs externalism about justification: internalism requires accessible reasons; externalism (reliabilism) requires a truth-conducive belief-forming process.

Realism vs anti-realism: realism holds truth is mind-independent; anti-realism (idealism, verificationism, constructivism) ties truth to mind, evidence, or practice.

Identity theory and functionalism in mind: type identity equates mental states with brain states; functionalism individuates mental states by causal role, allowing multiple realizability.

Personal identity criteria: psychological continuity (Locke, Parfit) vs bodily/brain continuity; fission cases pressure any criterion to be non-arbitrary and transitive.

Kant's categorical imperative, formula of universal law: act only on maxims you could will as universal law; formula of humanity: treat persons as ends, never merely as means.

Act vs rule utilitarianism: act evaluates each action by expected utility; rule evaluates actions by rules whose general acceptance maximizes utility.

Mill's harm principle: coercion is justified only to prevent harm to others; self-regarding conduct is protected, though competence and indirect harms complicate the line.

Doctrine of double effect: an unintended bad effect may be permitted if the act is good or neutral, the bad effect is not the means, and proportionality holds.

Trolley vs footbridge: the footbridge case adds using a person as a means, which most deontological accounts forbid while consequentialist accounts may permit.

Rawls's difference principle: social and economic inequalities are just only if they benefit the least advantaged position, constrained by fair equality of opportunity.

Aristotelian virtue ethics: virtue is a stable disposition to feel and act according to the mean relative to us, determined by practical wisdom (phronesis).

Moral realism vs anti-realism: realism holds mind-independent moral facts; expressivism and error theory deny that moral judgments report such facts.

Weakness of will (akrasia): action against one's better judgment; explained by divided motivation, temporal discounting, or failure of practical reasoning.

Validity: an argument is valid iff no possible world makes all premises true and the conclusion false; soundness adds that all premises are actually true.

Modus ponens: from P and P→Q infer Q. Modus tollens: from ¬Q and P→Q infer ¬P. Affirming the consequent and denying the antecedent are invalid.

Truth tables: n distinct sentence letters yield 2^n rows; a tautology is true on every row, a contradiction false on every row, a contingency varies.

Quantifier negation: ¬∀xPx ≡ ∃x¬Px and ¬∃xPx ≡ ∀x¬Px; scope errors produce fallacies such as illicit conversion of A-propositions.

Inductive strength is graded, not binary: a strong inductive argument makes the conclusion probable given true premises; it can still have a false conclusion.

Informal fallacies: ad hominem, straw man, false dilemma, begging the question, equivocation, hasty generalization, post hoc, and appeal to ignorance.

Correlation is not causation: ruling out reverse causation and confounders requires controlled comparison, randomization, or natural experiments.

Bayes's theorem: P(H|E) = P(E|H)P(H) / P(E); base-rate neglect arises when P(H) is ignored in favor of P(E|H).

Necessary vs sufficient conditions: A is sufficient for B if A guarantees B; A is necessary for B if no B occurs without A; confusing them yields converse errors.

Plato's Forms: changeless, non-sensible objects of knowledge; particulars 'participate' in them; the divided line ranks images, sensible things, mathematical objects, and Forms.

Aristotle's four causes: material, efficient, formal, and final; the final cause is the end or function (telos) that explains a natural process.

Aristotle's substance and hylomorphism: primary substances are concrete composites of matter and form; essence is stated in the definition of the species.

Socratic method (elenchus): cross-examination exposes inconsistency in an interlocutor's beliefs, producing aporia rather than a positive doctrine.

Stoic ethics: virtue is the only good and consists in living according to nature and reason; preferred indifferents (health, wealth) are not goods.

Epicurean ethics: pleasure is the highest good, understood as absence of pain (katastematic) rather than active indulgence; ataraxia is tranquility.

Augustine on evil and will: evil is privation of good, not a substance; sin originates in a disordered will, and grace is required for right willing.

Aquinas's five ways: motion, efficient causation, contingency, gradation, and teleology; each argues from an observed feature to a first cause or necessary being.

Medieval universals debate: realism (universals exist independently), conceptualism (they exist only in the mind), and nominalism (only particulars exist).

Descartes's method of doubt: suspend assent to anything dubitable; the cogito ('I think, therefore I am') survives hyperbolic doubt as an indubitable starting point.

Hume's fork: relations of ideas (a priori, analytic) vs matters of fact (a posteriori); causal necessity is not observed but projected by custom and habit.

Hume's is-ought gap: descriptive premises alone do not entail a normative conclusion; deriving 'ought' from 'is' requires an additional normative premise.

Locke's empiricism: the mind is a tabula rasa; all ideas derive from sensation and reflection, and primary qualities resemble real features while secondary qualities do not.

Kant's synthetic a priori and the transcendental deduction: categories are conditions of possible experience, so empirical knowledge presupposes them.

Hegel's dialectic: contradiction drives development through thesis, antithesis, and synthesis; Spirit (Geist) realizes freedom through historical institutions.

Nietzsche: master and slave moralities; slave morality inverts strength into 'evil'; the will to power and eternal recurrence are central thought experiments.

Logical positivism: the verification principle holds that meaningful statements are analytic or empirically verifiable; it is self-undermining on its own criterion.

Phenomenology (Husserl, Heidegger): bracket the natural attitude to describe lived experience; Heidegger's Being-in-the-world replaces the subject-object model.

Hobbes's state of nature: rough equality of power yields competition, diffidence, and glory; the social contract authorizes a sovereign to escape the war of all against all.

Locke's social contract: natural rights to life, liberty, and property precede government; legitimate government rests on consent and may be resisted when it violates trust.

Rousseau's general will: legitimate authority expresses the general will aimed at the common good; citizens who dissent can be 'forced to be free'.

Mill's harm principle and free speech: restricting expression is justified only to prevent harm; false opinions tested in the 'marketplace' strengthen true belief.

Rawls's original position: behind a veil of ignorance, parties choose principles of justice; the two principles are equal basic liberties and fair equality of opportunity plus the difference principle.

Nozick's entitlement theory: holdings are just if acquired justly, transferred justly, or rectified; patterned distributive principles violate liberty and self-ownership.

Berlin's two concepts of liberty: negative liberty is non-interference; positive liberty is self-mastery, which can license paternalist coercion in the name of a 'true self'.

Marx: historical materialism explains institutions by productive forces and relations of production; alienation under capitalism separates workers from product and species-being.

Civil disobedience (Rawls, King): public, nonviolent, conscientious breach of law aimed at injustice, addressed to the majority's sense of justice and accepting punishment.

Kant's aesthetic judgment: judgments of taste are subjective (grounded in feeling) yet claim universal assent and are disinterested, without concepts or purposes.

Hume's standard of taste: aesthetic judgments are sentiments, but a standard emerges from the joint verdict of true judges with delicacy of taste and freedom from prejudice.

The intentional fallacy (Wimsatt and Beardsley): the artist's intentions are not the standard for interpreting a work; the work's meaning derives from public textual features.

The problem of consciousness: the hard problem (Chalmers) is why physical processes give rise to subjective experience; easy problems concern functional capacities.

Qualia: intrinsic, subjective experiential properties (the felt redness of red); inverted-spectrum and zombie cases pressure physicalist accounts.

Chalmers's conceivability argument: if philosophical zombies are conceivable and conceivability entails possibility, then consciousness is not entailed by the physical.

Functionalism and multiple realizability: mental states are causal roles realizable in many substrates, so mental kinds are not identical to specific brain kinds.

Searle's Chinese Room: symbol manipulation by rule does not produce semantic understanding, so syntax alone is insufficient for semantics or genuine intentionality.

The extended mind (Clark and Chalmers): cognitive processes can extend into the environment when external resources are reliably available, accessible, and endorsed.