Logic Ethics and Major Philosophical Schools Cheat Sheet

A printable reference covering arguments, validity, truth tables, ethical theories, and major philosophical schools for grades 11-12.

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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.