Mathematics

Mathematical objects are intelligible Forms grasped by reason alone, not abstracted from sense experience.

Mathematical objects are not separate Forms but properties abstracted from physical things by the mind.

Geometry proceeds from definitions, postulates, and common notions to rigorous demonstration, establishing the paradigm of deductive science.

Mathematics abstracts quantity from sensible matter, yielding certainty because its objects are stable and determinately known.

Mathematics is the model for all knowledge, grounded in clear and distinct ideas and deductive chains of reasoning.

Mathematics is computation with names: adding, subtracting, and reckoning consequences from definitions.

Mathematical knowledge is certain because it concerns the agreement and disagreement of our own ideas of number and figure.

Mathematical judgments are synthetic a priori: they extend knowledge beyond concepts, yet hold with universal necessity.

Mathematics is limited to external, quantitative relations and cannot reach the dialectical concept that philosophy requires.