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How did Hume distinguish relations of ideas from matters of fact?

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Marble bust of Aristotle with a beard and draped robe, showing detailed facial features and wavy hair, set against a dark background. — metaphysics Detail of a Roman copy (2nd century bce) of a Greek alabaster portrait bust of Aristotle (c. 325 bce); in the collection of the Museo Nazionale Romano, Rome.

David Hume distinguished between two types of propositions, which he categorized as "relations of ideas" and "matters of fact," to define the limits of human knowledge.12

Relations of Ideas

Propositions concerning relations of ideas are discoverable by the pure intellect through rational inspection. These truths are necessary, meaning their negation would result in a logical contradiction. They are essentially analytic, as they simply make explicit what is already contained within the definitions of the terms involved. Examples include the propositions of arithmetic, algebra, and geometry, as well as logical truths such as the internal angles of a triangle.213

Matters of Fact

In contrast, matters of fact are known only through experience and sense perception. These propositions are contingent; their contradictories are always conceivable, and they do not possess the logical necessity found in relations of ideas. Matters of fact, such as "fire causes heat" or "lead is heavy," are logically independent and reveal no inherent logical connections. Hume argued that because these facts are "logically barren," there can be no demonstrative science of them, and our understanding of their connections—particularly causality—relies on habitual association rather than pure reason.123