Demonstration

A demonstration is an argument in which premises necessitate its conclusion. Its force depends on the logical relation between premises and conclusion, rather than on persuasion alone.

Premise: A proposition offered as support for a conclusion in an argument. A demonstration begins from premises that jointly necessitate its conclusion.
Syllogism: A deductive argument consisting of two premises and a conclusion linked through shared terms. Aristotelian demonstrations commonly use syllogisms to derive conclusions.
Aristotle: An ancient Greek philosopher whose works shaped logic, metaphysics, ethics, and natural philosophy. His Posterior Analytics gives the foundational account of demonstration as scientific explanation.
Inductive reasoning: Reasoning that supports conclusions as probable from observations or particular cases. Unlike demonstration, induction does not make its conclusion necessary given its premises.
Conclusion: A proposition an argument aims to establish from its premises. This is the claim a demonstration must make follow from its starting propositions.
Inference rule: A rule specifying which conclusions may be derived from given statements. Demonstrations proceed by applying rules that preserve necessary consequence.
Posterior Analytics: An Aristotelian treatise on scientific knowledge, explanation, and demonstrative reasoning. It specifies the premises and explanatory structure Aristotle requires for demonstrations.
Abductive reasoning: Inference to the hypothesis that would best explain observed evidence. An explanatory hypothesis may be compelling without following necessarily from its evidence.
Logical consequence: A relation in which one proposition must be true whenever specified propositions are true. It captures the necessity connecting a demonstration’s premises to its conclusion.
Axiom: A proposition accepted as a starting point within a formal system or theory. Axioms can serve as the initial premises from which demonstrations derive results.

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