Logical validity

An argument is logically valid when no possible interpretation makes all its premises true and its conclusion false. Validity concerns the argument’s form, not whether its premises or conclusion are actually true.

Counterexample: A case that shows a claim or inference is false by satisfying its conditions while violating its conclusion. A single case with true premises and a false conclusion disproves validity.
Premise: A statement offered as support for a conclusion in an argument. Validity asks what follows when every premise is assumed true.
Inductive reasoning: Reasoning in which premises make a conclusion probable without guaranteeing it. An inductive argument can be strong even when its conclusion could be false with true premises.
Modus ponens: The inference rule that derives Q from the premises P and if P then Q. This canonical valid form preserves truth from premises to conclusion.
Aristotle: An ancient Greek philosopher whose works shaped logic, metaphysics, ethics, and natural philosophy. His syllogistic theory offered an early systematic account of valid argument forms.
Truth table: A table listing the truth values of a logical expression under every assignment of truth values to its variables. Truth tables test whether any assignment makes the premises true and conclusion false.
Conclusion (argumentation): The statement an argument presents as following from its premises. The conclusion is the statement that must remain true whenever all premises are true.
Argument strength: The degree to which an argument’s premises support its conclusion, often assessed probabilistically. Strength admits degrees of support, unlike deductive validity’s all-or-nothing standard.
Modus tollens: The inference rule that derives not-P from if P then Q and not-Q. Its validity can be checked by ruling out a true-premise, false-conclusion case.
Prior Analytics: Aristotle’s treatise that presents the theory of syllogistic deduction and demonstration. It is the earliest surviving systematic treatment of deductive validity.

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