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Why did rationalists compare metaphysical reasoning to mathematics?

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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.

Rationalists compared metaphysical reasoning to mathematics because they sought to employ the formal structure and rigorous methods of the latter as a model for philosophy. This approach, known as mathematicism, was pioneered in the 17th century by René Descartes, who aimed to establish philosophical certainty through systematic inquiry.1

By organizing knowledge into definitions, axioms, and deduced theorems—modeled after Euclid’s geometry—philosophers could ensure consistency of meaning and correctness of inference. This method allowed them to:1

Accept only indubitable, self-evident propositions.1
Divide complex problems into manageable parts.1
Work systematically from simple to complex concepts.1
Ensure complete and general enumerations.1

Rationalists believed the world was a rationally ordered whole, intelligible through logic and a priori insight. By applying mathematical rigor to metaphysics, they aimed to reveal the necessary connections between facts, treating the universe as a coherent system that could be understood through the same intellectual faculties used in mathematical proof.213