This cheat sheet covers the core tools students need to analyze philosophical arguments, evaluate ethical claims, and compare major philosophical schools. It helps students distinguish good reasoning from weak reasoning and connect abstract ideas to real decisions. Students in grades 11-12 can use it to review logic symbols, argument structure, ethical frameworks, and key traditions before discussions, essays, or exams.
The most important logic concepts include validity, soundness, conditional statements, truth tables, and common inference rules such as modus ponens and modus tollens. Ethics focuses on how actions, duties, consequences, virtues, and rights guide moral judgment. Major philosophical schools such as empiricism, rationalism, existentialism, utilitarianism, deontology, and virtue ethics offer different answers to questions about knowledge, reality, freedom, and value.
Key Facts
- An argument is valid when its conclusion must be true if all of its premises are true.
- An argument is sound when it is valid and all of its premises are actually true.
- Modus ponens has the form: If P then Q; P; therefore Q.
- Modus tollens has the form: If P then Q; not Q; therefore not P.
- A conditional statement P -> Q is false only when P is true and Q is false.
- A conjunction P and Q is true only when both P and Q are true.
- Utilitarianism judges an action by the rule: choose the action that produces the greatest overall happiness or well-being.
- Deontology judges an action by whether it follows a moral duty or rule, not only by its consequences.
Vocabulary
- Validity
- Validity is the logical property of an argument whose conclusion follows necessarily from its premises.
- Soundness
- Soundness is the property of an argument that is both valid and based on true premises.
- Premise
- A premise is a statement offered as a reason to support a conclusion.
- Consequentialism
- Consequentialism is the view that the morality of an action depends on its outcomes.
- Deontology
- Deontology is the view that morality is based on duties, rules, or obligations.
- Empiricism
- Empiricism is the view that knowledge comes mainly from sense experience and observation.
Common Mistakes to Avoid
- Confusing validity with truth is wrong because validity describes the structure of an argument, while truth describes individual statements.
- Assuming a sound conclusion from a valid argument is wrong if one or more premises are false, because soundness requires both validity and true premises.
- Treating If P then Q as identical to If Q then P is wrong because reversing a conditional creates the converse, which does not always follow.
- Judging every ethical theory only by outcomes is wrong because deontology and virtue ethics also consider duties, character, intentions, and moral rules.
- Mixing up empiricism and rationalism is wrong because empiricism emphasizes observation, while rationalism emphasizes reason as a major source of knowledge.
Practice Questions
- 1 Create a truth table for P -> Q with all 4 possible truth-value combinations, and identify the one row where the conditional is false.
- 2 How many rows are needed in a truth table with 3 variables P, Q, and R, and why?
- 3 Determine whether this argument uses modus ponens or modus tollens: If the law is just, it protects basic rights. The law does not protect basic rights. Therefore, the law is not just.
- 4 A doctor can save five patients by harming one healthy person. Compare how utilitarianism and deontology might evaluate this action, and explain the key difference in reasoning.
Understanding Logic Ethics and Major Philosophical Schools
Logical form matters because everyday language can hide the real structure of a claim. Words such as only, unless, either, and because often cause mistakes. For example, saying that studying is sufficient for passing does not mean passing proves that someone studied.
A student may pass for another reason. This is called affirming the consequent, and it is a common invalid pattern. Deductive reasoning aims for certainty when the starting claims hold.
Inductive reasoning works differently. It uses observations to make a likely conclusion, such as predicting rain from dark clouds and weather data. A strong inductive argument needs enough relevant evidence, not just a few memorable examples.
Truth tables are useful because they force every possible combination of truth values into view. They can show whether a statement is always true, always false, or true only in certain cases. This helps when an argument sounds convincing but depends on an unclear connection between its premises.
In a written argument, students should separate the claims from the reasons offered for them. Then they should ask whether each reason supports the conclusion and whether the reason is trustworthy. A valid structure cannot rescue a false premise.
Likewise, true premises do not guarantee a good argument if the conclusion does not follow from them. Counterexamples are especially powerful. One clear case that breaks a general claim can show that the claim needs revision.
Ethical theories often disagree because they focus attention on different parts of a decision. Consequences matter when an action affects many people, but totals can hide unfair burdens placed on a smaller group. Duties protect important limits, such as keeping promises or refusing to treat people merely as tools.
Yet strict rules can conflict when duties point in different directions. Virtue ethics asks what a wise, honest, courageous person would do over time. It pays attention to character, habits, and relationships.
Students should notice the difference between describing what people believe and defending what they ought to do. Popular opinion is evidence about a belief, not proof that the belief is morally right.
Philosophical schools provide different standards for deciding what counts as knowledge or a meaningful life. Empiricism gives special weight to observation and experience. Rationalism gives reason a central role, especially where sense experience may be incomplete or misleading.
Existentialist thinkers stress personal choice, responsibility, and the challenge of creating meaning without relying on a fixed script. These views appear outside class in debates about science, religion, free will, law, medical choices, and artificial intelligence. When comparing schools, avoid treating them as simple labels.
Identify the question being asked, the kind of evidence accepted, and the values being protected. A strong essay explains why a view is persuasive before presenting its limits. This makes criticism fairer and more precise.