Formal fallacy

A formal fallacy is an invalid argument whose logical structure fails to make its conclusion follow from its premises, regardless of their truth.

Logical form: The abstract structure of a statement or argument, apart from the particular meanings of its terms. Formal fallacies arise from patterns that remain visible when an argument’s subject matter changes.
Affirming the consequent: The invalid pattern: if P then Q; Q; therefore P. It treats a consequence of a condition as proof that the condition held.
Informal fallacy: A reasoning error whose diagnosis depends on content, language, context, or conversational practice rather than logical form alone. Unlike a formal fallacy, an informal fallacy cannot be identified from argument structure alone.
Modus ponens: The valid inference: if P then Q; P; therefore Q. It is the valid conditional pattern commonly confused with affirming the consequent.
Aristotle: An ancient Greek philosopher whose writings established foundational approaches to logic and natural science. His syllogistic analysis supplied early systematic accounts of invalid argument forms.
Deductive reasoning: Reasoning in which premises are intended to entail a conclusion. Formal fallacies are failures within arguments that aim at deductive entailment.
Denying the antecedent: The invalid pattern: if P then Q; not P; therefore not Q. It wrongly assumes that a conditional excludes other ways for its consequent to be true.
Sound argument: A deductive argument that is valid and has true premises. Soundness is the successful counterpart to the invalidity at the center of a formal fallacy.
Modus tollens: The valid inference: if P then Q; not Q; therefore not P. It is valid while denying the antecedent is not, despite their superficially similar forms.
Prior Analytics: Aristotle’s treatise on syllogistic reasoning and demonstrative inference. It presents the formal study of valid and invalid categorical argument patterns.

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Constructive dilemmaCompared with: Comparing valid dilemma patterns with invalid forms helps identify structural errors in arguments.